Corporate Finance 9e 1-7

Introduction to Corporate Finance

Compensation 01 corporate executives in the United Slates continues 10 be a hOI-button

issue. It is widely viewed thai CEO pay has grown to exorbitant levels (at least in some

cases). In response, in Apri l 2007, the U.S. House of Representatives passed the -Say on

Pay" bill. The bill requires corporations to allow a nonbinding shareholder vole on executive

pay. (Note that because the bill applies to corporations. il does not give voters a ~say on pay"

for U.S. Representatives.)

Specifically, the measure allows shareholders to approve or disapprove a company's

executive compensation plan. Because the vote is nonbinding. it does nol permit share­

holders to velo a compensation package and does nol place limits on executive pay. Some

companies had actually already begun iniliatives to allow shareholders a sayan pay before

Congress got involved. On May 5. 2008. Aflac, the insurance company with the well·known

~spokesduck.~ held the first shareholder vote on executive pay in the United States.

Understanding how a corporation sets executive pay, and the role of shareholders in that

process, takes us into issues Involving the corporate form of organization, corporate goals,

and corporate control, all 01 which we cover in this chapter.

1.1 What Is Corporate Finance? Suppose you decide to start a firm to make tennis ba lls. To do this you hire managers to buy mw materials. and you assemble a workforce that will produce and sell finished tennis balls. In the language of finance, you make an investment in assets such as inventory. machinery, land, and labor. The amount of cash you invest in assets must be matched by a n equa l amount of cash mised by fimll1cing. When you begin to sell ten· nis balls. your firm will generate cash. This is the basis of value creation. The purpose of the firm is to create value for you, the owner. The va lue is renected in the framework of the simple balance sheet. model of the firm .

The Balance Sheet Model of the Firm suppose we take a financial snapshot of the firm and its activities at a single point in lime. figure 1.1 sbows a grapbic conceptualization of the balance sheet. and il will help inlroduce you to corporate finance.

The assets o f the rtrm are on the left side of the balance s.beet. These assets can be thought of as current and fixed . Fixed assets are those that will last a long time. such as buildings. Some fixed assets are tangible. such as machinery and equipment. Olher fixcd assets are imangible, sucb as patents and Irademarks. The other category of assets. cllrre", assets. comprises those that have short lives, such as inventory. The

,

Figure 1.1 The Balance Sheet Model or the FIrm

Pari I Ovcrvieo.v

Current assets

T0'I81 Value of Assets

..... ".

Total Value 01 the Firm to InveSlors

(cnnis balls tbat your firm has made, but has not yel sold, are part of its inventory. Unless you have overproduced, they will leave the firm shortly.

Before a com pany can invest in an asset, il must oblnin linanci ng, which means that it must raise the money to pay for the investment. Tbe forms of financing are repre­sen ted o n the right side of the balance sheet. A firm will issue (scll ) pieces of paper called debt (loan agreements) or equity shares (stock cert ificales). Just as assets are classified as long-lived or short-lived. so too are liabilities. A short-term debt is called a curremliabilit),. SborHerm debt represent s loans and olher obligations that must be repaid within one year. Long-term debt is debt that docs not have 10 be repaid within one year. Shareholders' equity represents the difference between the value of the assets and the debt of the finn. In this sense. it is a resid ual claim on the firm 's assets.

From the bal ance sheet model o f the firm. it is easy to see why finance can be thought of as the study of the following three questions:

I. In wbat lo ng-lived assets should the firm invest? This question eOJ1c;ems tbe left side of the balance sheet. Of course the types and proportions of assets the fi rm veeds lend to be set by the nature of the business. We use the term capital budgeting to describe the process of making and managing expenditures on Jong-lived assets.

2. How can the finn raise cash for requ ired capital expenditures? This question con­cems the right side of the balance sheet. The answer to this question involves the firm's capital structure, which represents the proportions of the firm 's linancing from current and long-term debt and equity.

3. How should shorl-term operating cash flows be managed? This question concerns the upper portion of the balance sheet. There is often a mismatch between the timing of cash inflows and cash o utnows during operating activi­ties. Furthermore, the amount and timing of operati ng cash flows are not known with certainty. Financial managers must attempt to manage the gaps in cash n ow. From a bala nce sheet perspective, sbort-term maoagement of cash now is

For currenl lssue'S I lacing CFOs, S&fJ

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Figure 1.2 Hypothetical Organization Chart

Chapter I lnl roctvc\iol'l loCorpora\l: Fin:.m;e

associated with a firm's net working capila!. Net working capital is defined as cur­rent assets minus current liabilities. From a financial perspective, short -term cash now problems come from the mismatching of cash inflows and outflows. This is the suhje<:t of ShOrt -term finance.

The Financial Manager

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In large firms. the finance activity is usua lly associated with a top officer of the firm. suc~ as the vice presideDt a nd chief financia l officer, and some le.sserofficers. Figure I.i depicts a general organizational structure emphasizing the finance activity within Ine firm. Reporti ng to the chief financial officer a re the treasurer and the cont roller. The t~easurer is res~onsible fO.r handling cash flows. managing capital expenditure deci­SIO~S. ~nd makmg finanCIal plans. The controller hand les lhe accounting function. whIch tncludes taxes, cost and financial accounting, and information systems.

Cash Manager

Capital Expenditures

Credit Manager

Financial Planning

Tal( Manager

Financial Accounting Manager

Cost Accounting Manager

Illformation Systems Manager

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1.2

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organization. see tile "Business and Human Resources" section at

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Part J Overview

The Corporate Firm llle firm is a way o f organizing the economic activity o f Illa ny individuals. A basic problem of the firm is how 10 raise cash. The corporate fo rm of busi ness- that i ~ orga­nizing the firm as a corporation- is the standard method fo r solving problems encoun­tered in raising large amounts of cash. However, businesses can take other forms. In Ihis sectio n we consider tbe three basic legal forms of orga nizing fi rms.. and we see how rirms go about the task o f ra ising large amounts of money under each form.

The Sole Proprietorship A sole proprietorship is a business owned by one person. Suppose you decide to sta n a business to produce mousetraps. Going into business is simple: You announce to a ll wbo will listen. ··Today. I am going to build a better mousetrap."

Most la rge cities require that you obtain a business license. Afterwa rd . you ca n begin to hire as many people as you need and borrow whatever money you need. At yea r-end all the profits and the losses wi ll be yours.

Here are some factors that are impon ant in considering <t sole proprieto rship:

I. The sole proprietorship is the cheapest business to form. No fo rmal charter is required, and few gove mment regu latio ns must be satisfied for most industries.

2. A sale proprietorship pays no corporate income taxes. All pro fi ts of the business are taxed as individual income.

3. The sole proprietorship has unlimited liability for business debts and o bligations. No distinction is made bet ween personal and business assets.

4 . The life of the sole proprietorship is limited by the life of the sole proprietor.

S. Because the only money invested in the firm is the proprietor's, the equity money that can be raised by the sale proprietor is limited 10 the propriclOr's personal wealth .

The Partnership Any twO or morc people can get together and for m a partnership. Partnerships fa ll inlo two categories: ( I) general partnerships and (2) limited partnerships.

In a general pUrIIU!Tship all pa rtners agree to provide some fraction of the work a nd cas h and to sha re the profits a nd losses. Each partner is liable for al l of the debt s of the partoership. A partncrship agreement specifies the nature of the arrangemen t. The part nersh ip agreemen t Inay be an o ral agreement or a fo nnal document setting forth the understanding.

Limited partnerships permit the liability of some of the part ners to be limited to the amount of cash each has contributed to th e partnership. Limited p.m nerships usually requi re that (I) at least o ne partner be a general panner and (2) the limited partners do not participate in managing the busi ness. Here are some things that are important when considering a partnership:

I . Partnerships are usually inexpensive and easy to form. Written document s are required in complicated arrangements. Business licenses and fili ng fees may be necessary.

2. General partners have unlimited liability for all debts. The liability of limited partners is usua lly limi ted to tbe con trib ut ion each has made to tbe partnership. If o ne general partner is unable to meet his or her commitment. the shortfall must be made lip by the other general partners.

Chaplet I InlroouC\;on to Corporal\' f inance

3. The general partnership is term inated when a general part ner dies or withdraws (but this is not so for a limited partner). It is difficult for a partnersh ip 10 transfer ownership without dissolving. Usua lly all general partners must agree. However, limi ted partners may sell thei r interest in a business.

4. 11 is difficu lt for <I p<lrtnership to raise large amounts of cash. Eq uity contribu­tio ns are usual ly limited to a part ner's ability and desi re to contribute to the pan­nership. Ma ny companies., such as Apple Compute r, start life as a proprieto rship o r pa rtnership, but at some point they choose to convert to corporate form .

S. 1J1come from a partrlership is taxed as personal income 1O the pa nners.

6. Management control resides with the general partners. Usually a majority vote is required all important matlers., such as the amount of profit to be reta ined in the business.

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It is difficult for large business o rganizations 1O exist as sale proprietorships or pannecships. The ma in advontage to a sale proprietorship or partnership is the cost of getting started. Afterward. the di sadvantages, which may become severe. are ( I ) unlimited liability, (2) limited life of the emerprise. and (3) diOlcul!y of transferring. ownershi p. These three disadvantages lead to (4) difficulty in raising cash .

The Corporation Of the forms of business enterprises. the corporation is by fat the most importa!)!.lt is a distinct legal ent ity. As such, a corporation ca n have i l name a nd enjoy many of the legal powers o f natural persons. For example. corporations cOIn acquire <Jnd e;.;cha nge property. Corporations can enter contracts nnd may sue nnd be sued. For jurisdic­tional purposes the corponnion is .. citizen of its state o f incorporation (it cannot vote, however).

Starting a corpoT<nion is more complicated than sta rting a proprietorship or part­nership. The incorporators must prepa re articles of incorporation and a set of bylaws. The a rticles of i.ncorporat ion must include the following:

I . Name of the corporat ion.

2. Intended life of tbe corporation (it may be forever) .

3. Business purpose.

4 . Nu mber of shares of stock that the corporation is a uthorized to issue, with a statement of limit ations and rights o f diITcrent cla sses of shares.

5. Nature of the rights gran ted to shareholders.

6. Number of members of the initial board o r directors.

The bylaws arc the rules to be used by the corporat ion to regulate its own existence. and they concern its sharebolders. directors. and officers. Bylaws range from the brief­est possible statement of rules fo r the corpo ration's management to hundreds o f pages of tex t.

In its simplest form, the corporat ion comprises three sets of distinct interests: the shareholders (the owners), the directors. and the co rporation officers (the to p man­agement). Trad itionally. the shareholders control the corporation's d irection, poli­cies, and activities. The shareholders elect a boa rd of directors. who in turn select top management. Members of top management serve as corporate officers and manage the operatioos of the corporation in the best interest of the sha reholders. In closely held corporations with few shareholders., there may be a large overl ap among the

, shareho lders. the directors. and the top ma nagement. However. in larger corporations, the shareho lders, directors, and the lo p management are likely to be dislinct groups.

The potential separation of ownership from management gives the corpo ratio n sev­eral advantages over proprietorships and partnerships:

I. Because ownership in a corporal ion is represented by shares of stock. ownership can be readily transferred to new owners. Because the corporation exists indepen ­dent ly of those who own its sha res, there is 0 0 limit to the transferabili ty o f sha res as there is in pannerships.

2. The corporation has unlimi ted life. Because the corporation is separate from its owners, tbe death or withdrawal o f an owner does not affect the corporation's legal exis tence. The corporation can continue on arter the original owners have withdrawn.

3. The shareholders' liability is limited 10 the a mount invested in the ownership shares. For example. ir a shareho lder purchased $ 1.000 in sha res o f a corpora­tion, Ihe pOlential loss would be $ 1.000. In a partnership, a general partner with a $1,000 cont ribut ion could lose the S I ,000 plus any other indebtedness of the partnership.

Limited liability. e<lSC of ownersh ip transfer, and perpetual sllccession are the major advantages o f the corporate form of business organization. These give the corporaTio n an enhanced abili ty to raise cash.

There is. however. o ne great disadvantage to incorporation. The federal government taxes corporate inco me (the states do as well). This tax is in addition to the persona l income tax thai shareholders pay on dividend income they receive. This is double laxa­tion for shareholders when compared to taxation on proprietorships and partnerships. Table 1.1 summarizes our d iscussion of partnerships a nd corporations,

Table 1.1 A Comparison of Partnerships and COI"pOr8tlons

Co,.po,.ation Pa,.tnershlp

Uquidity and marketability

Voting r ights

Taxation

Reinvestmenl and dividend paYOUt

Liability

Shares can be exchanged without te rmination of the corporation. Common stock can be liseed on a stock exchange.

Usually each share of common stock emides the holder to one vote per share on matters requiring a vote and on the election of the directors. Directors determine cop management.

Corporations have double tax.ation: Corporate income is QX.3ble. and dividends to shareholders are also taxable.

Corporations have broad latiwde on dividend payout decisions.

Shareholders are not personally liable (or obligations of the corporation.

Continuity of existence Corpo,.ations may have a perpetual life.

Units are subject to substantial restrictions on transferability. There is usually no established trading market for partnership units.

Some voting rights by limited partners. However. general partners have exclusive control and management of operations.

Partnerships are not taxable. Partners pay personal taxes on partnership profits.

Partnerships are generally prohibited from reinvesting partnership profits. All profits are distributed to partners.

Limited partners are not liable for obligations of partnerships. General partners may have unlimited liability.

Partnerships have limited life.

Chapll'f I Inlroduction 10 Corporale Finance 7

Table 1.2 International Corporations

Bo!yerische Motoren Werke (BMW)AG

Dornier GmBH

RoUs-Royce PlC

Shell UK Ltd.

Unilever NV

Fiat SpA

VolvoAB

Peugeot SA

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1.3

Germany Aktiengesellsdlaft Corpontlon

Germany Gesellschaft mit Limited liability Beschrankter Haftung company

United Kingdom Public limited company Public ltd. Company

United Kingdom limited Corpontion

Netherlands Naamlo"te Vennootschap joint stock company

Italy Societa per Azioni joint stock company

Sweden Aktiebolag joint stock company

France Societe Anonyme joint stock company

Today all 50 slales have enacled laws allowing for the creation or a relatively new foml of business orgaoizalion , the lim iled Iiabil ily company (LLC). The goal of lhis en lilY is to operate a nd be laxed like a pannership but retain lim ited liability for own­ers, so an LLC is essentia lly a hybrid o f partnership a nd corporation. Although states have dinering definilions for LLCs. Ihe morc important scorekeeper is the Internal Revenue Service (fRS). The IRS will consider an LLC a corporat ion, thereby subject­ing it to double taxalion. unless it meets certain specific crileria. In essence, an LLC cannot be too corporation-like. or it will be treated as one by the [RS. LLCs have become common. For example. Goldman. Sachs and Co., one of Wall Street's last remaining partnerships. decided to convert from a private pa nnership to an LLC (it later "went public," becoming a publicly held corporation). Large acco unting finns and law firms by Ihe score have converted to LLCs.

A Corporation by Another Name • .. The corporate rorm of organizat ion has many variations around the world. The exact laws and regulation s differ rrom cou nt ry to country, of course. but the essential fea· tures of public ownership and limited liability remain. These fmns are often called joil1l stuck companies, public limiled companies. or limited liability compollies, depend­in g on the specific oature of the firm and the country of origin .

Table 1.2 gives the names or a few well-known international corporations, theircoun­lries of origin, and a tram;lation of the abbreviation thai follows each company name.

The Importance of Cash Flows The mosl importa nt job of a fi nancial manager is to create value fronl the firm's capital budgeting, financing, and net working capi tal activities. How do IInancia l managers create va lue? The answer is that the finn sho uld:

I. Try to buy assets that generate more cash than Ihey cost.

2. Sell bo nds and stocks and othe r financial instruments that raise mo re cash tban Ihey cost.

In Their Own \'\'ords

SKILLS NEEDED FOR THE CHIEF FINANCIAL OFFICERS OF eFINANCE.COM

Chj~f risk officer: Limiting risk will be even more important as ma rkets become mort global and hedg­ing iostruments become more complex.

Ch;efs'raugi.~': CFOs will need to use real- time finan­cial information to make crucial decisions fast.

Ch;~1 communicator: Gaining the confidence of Wall Street and the media will be essential.

Chief dea/maker: CFOs must beadep! at venture capital, mergers and acquisitions, and strategic pannen;hips.

Figure 1.3 Cash Flows between the Arm and ttle FinancIal Markets

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Thus, the firm must creale more cash now tnan it useS. The cash nows paid to bond­holders and stockholders of the firm shou ld be greater than the casb nows put into the firm by the bondholders and stockholders. To sec how Ihis is done, we can trace Ihe cash nows from the firm to the fi nancial markets and back again.

The interplay of tbe firm 's activities with the financial markets is illustrated in Fig­ure J .3. The arrows in Figure 1.3 trace cash flow from the firm to the fina ncia l markets a nd back again . Suppose we begin with the firm's financing activit ies. To raise money, the fi rm sells debt and equity shares to investors in the financial markets. This results in cash flows from the financial markets to the firm (A). Tbis eash is invested in the investment activities (assets) of the firm (8) by the firm's management. The cash gen­erated by the firm (q is paid to shareholders and bondholders (F) . The shareholders receive cash in the form of d iv idends; the bondholders who lent funds to the tlrm receive interest and , when the initial loan is repaid, principal. Not all of the firm's cash is paid out. Some is retained (E), a nd some is paid to the government as tal(CS (D).

Over time. if the cash paid to shareholders and bondholders (I) is greater than the cash raised in the financial markets (A) , val ue will be created.

Finn invests in assets

(81

Current assets Fixed assets

Tolal Value of Assets Total Value olthe Finn to Investors in

rile Financial Markets

EXAMPLE 1.1

Chapl",r I Introduct ion 10 Corpor..l le Finance ,

Identification of Cash Flows Unforlunately. il is sometimes not easy to o bserve cash flows directly. Much of the information we obta in is in the form of accounting statements, and much of the work of financial analysis is to ex tract cash flow informa­tion from accountiog statemen ts. The following e.xample illustrates how this is done.

Accounting Profit versus Cash Ftows The Midland Company r~fines and trades gold. At the end of the Ye<U'. it sotd 2.S00 ounces of gold for $1 million. The company had acquirN the gold for $900.000 at the beginning of the year. The company paid cam for the gold when it was purthased. Unfortunately it has yet to collect from the customer (0 whom the gold was sold. The following ii a standard accounting of Midl:tnd's financial circumS[ances at year-end:

The Midland Company Accounting View

Income State ment Ye ar Ended De ce mbe r 31

Sales

- COSts

Profit

$1.000.000

- 900.000

$ 100.000

By generally accepted accounting principles (GAAp). the sale Is recorded even though the co.momer has yet to ply. It is lSsumed that the customer wilt pay soon. From the accounting perspective, Mid­land seems co be profitable. However. the perspective of corporate fimll'Ke is different. Ie focuses

on cuh flows:

The Midland Company FinancialView

Income Statement Year Ended December 31

$ o Cash inflow

Cash outflow - 900.000

-$ 900.000

The perspective of c.orporate finance is interested in whether c.ash flows ue being created by the

gold trading operations of Midland. Value creation depends on c.ash flows . For Midland. value c.re­ation depends on whether and when it actually receives $1 million.

TIming of Cash Flows The value of an investment made by a firm depends on the timing of cash flows. One of Ihe mosl imponant principles o f finance is that individu­als prefer to receive cash flows earlier rather thalliater. One dollar received today is worth more than o ne doUar received next year.

10

EXAMPLE 1.2

EXAMPLE 1.3

1.4

Pan I Overview

Cash Flow Timing The Mldlaoo Com~ny is attempting to choose between twO proposals for new products. Both proposals will provide additional cash flows over a fouf'-year period and will

i.,ioally cost $10,000_ Thoe cash nows from the propc$~ls are as follows:

Year New Product A New Product B

I $ 0 S4,OOO

2 0 ' .000 3 0 '.000 • 20,000 ' .000

Total $20,000 $16,000

Al first it appears that new product A would be ben. Howcv!t. the cash flows from proposal B come earlier than those of A. Without more information. we cannot decide which set of cash flows would create the most value (or the bondholden and shareholders. It depends on whether the value of

geulng cash 'rom B up front outweighs the extra total cash from A. Bond and stock prices reflect this preference for earlier cash. and we will see how to use them to decide between A and 8.

Risk of Cash Flows The firm must consider risk. The amount and timing of cash nows are not usua lly known with certainty. Most investors have an aversion to risk .

Risk Th~ Midland Company is considering expanding operations (Wef"seas. It is evaluating Europe

atld J1Pl1"1 15 pouible sites.. Europe is considered to be relatively safe, whereas operating in Jlpa.r1 is seen as very risky. In both cases the company would dose down operations after one year.

After doing <II complete financial analysis. Midland ha..s come up with the foll owing cash flows of the alternative pllns for expansion under three s<:enarioJ---1>essimistk, most likely, and optimistic:

Europe

Japan

Pessimistic Most likely Optimistic

$75.000

o $100,000

150,000

$125,000

200.000

If we ignore the pessimistic scenario, perhaps Japan is the best alterniltlve. When we tilke the pes· simistlc scenario into account. the choice is unclea r. Japan appears to be riskier, but it also offers a higher expected level of cash flow. What is risk and how can it be defined! We must try to answer this important question. Corporate finance cannot ",void coping with risky altem",tives, and much of

our book is devoted to developing methods for ev",Juating risky opportunities.

The Goal of Financial Management Assuming that we restrict our discussion to fo r-profit businesses, the goa l of financial management is to make money o r add va lue fo r the owners. This goal is a little vague.. of course. so we examine some different ways of formulating it to come up with a more

Chllpll'r I Int roUuction 10 Corpor.llc Finane.: 11

precise definition. Such a definition is impo rta nt because it leads to an objective basis for making and evaluating lina ncia l decisions.

Possible Goals If we "''ere to consider possible financial goa ls. \\.-e mighl come up with some ideas Ijke the fo llowing:

Survive.

Avoid -financia l dist ress and bankruplcy.

Beat the competition.

Maximize sales or market share.

Minimize costs.

Maximize profits.

Maintain steady earnings growt h.

These are only a few of the goa ls we could list. Furthermore, each of these possibilities presents problems as a goal for the financial manager.

For example, it's easy to increase market share or unit sales: All we have to do is lower our prices or relax our credit terms. Similarly, we can always cut costs simply by doing away with things such as resea rch and development. We can avoid bankruptcy by never borrowing any money o r never taking a ny risks. and so on. It's not clellr t!ult any of these actions are in the stock holde rs' best interests.

Profit maximization would probably be the most commonly cited goa l, but even this is not a precise objective. Do we Olean profil s this yea r? If so, tben we should no te that actions such as deferring ma intcnam."e, letting inventories run down , and tak· ing other short·rull cost--cutting measures will tend to increase profits now. bUI these activities ilren't necessa rily desintble.

The goal o f maximizing profit s may refer to some sort of " Iong-run" o r "average"" profits, but ir's still unclea r exactly what this mea ns. First , do we mean someth ing like accounting net income or ea rni ngs per share? As we will see in more detail in the nex t chapter, these account ing numbers may have little to do with what is good or bad for the firm. We are actually more interested in cash nowS. Second, what do we mean by the long run'! As a famous economist once remarked, in the long run. we're all dead! More to the pain!, this goa l doesn' t tell liS what the appropriate trade-ofT is between current and future profits.

The goals we've listed here ,Ire a ll different. but they tend 10 fall into \\\'0 classes. The first of these relates to profitability. The goa ls involving sales. market share. and cost control all relate. at least potentia lly, 10 different ways of earning or incrc:asing profits. The goals in the second group, involving bankruptcy avo idance. stabi lity, and safety. relate in some way to co ntrolliug risk. Unfonunalcly, these two types o f goals are somewhat contradictory. The pursuit of profit nonnaJly involves some element of risk. so it isn't really possible to maximize both safety and profi t. What we need. therefore, is a goal that encompasses both factors.

The Goal of Financial Management T he financia l manager in a corporation makes decisions fo r the stockholders o f the firm. So. instead of list in g possible goa ls fo r the financial manager. we really need to answer a more fundament al question: From the stockholders' point of view, what is a good financial management dccision?

12

Business elllies are considered at

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Plrt I Overview

1 r \VC ass lUTIe that stock ho lders buy stock bee .. usc they seck to ga in financi<tlly. then the answer is obvious: Good decisions increa5e the value of the stock. and poor deci­sions decrease the va lue o f the stock.

From ou r observations. it fo llow$ that the financia l ma nager aCls in the sharehold­ers' best interests by making decisions Ihm inc rease the va lue of the stock. The appro­priate goa l fo r the financial manager can thus be stated quite easily:

The {!oal or fioaocia l mansgeml'nI is to m:iXlmize the currtnl v:.lue per !>hart of Ih(' e:l:isling

stock.

The goal o f maximizing the value of the s tock avoids the problems associated wit h the dilTe rent goa ls we listed ea rlier. T here is no a mbiguit y in Ihe c rite rion. and there is no shari-run versus long-run issue. We explicitly mean Ihut our goal is to maximize the curr('/U stock vnlue.

If this goa l seems a little strong or one-diOlcnsional to you. kee p in mind that the stockholders in a firm are residual owners. By th is we mC31l1l1al they are entitled only to what is len aner employees, suppliers, and creditors (and everyone else with legiti­mate cla ims) a re paid their due. If any of these groups go unpaid. the stockholders get nothing. So if the stockholders are winni ng in the sense that Ihe leftover. residual portion is growing, il must be true that e\'eryone else is wi nning also.

Beca use the goal of financial managemenl is to maximize the va lue o f the stock, we oeed to learn how to identify investmen ts and financing arrangements Ihat f,l\'oritbly impact the val ue of the Slock. This is preci sely what we will be study­ing . In the previous section we emphasized the importance of cash flows in va lue crea tion. In fact . we could have deli ned corpor(lfe j'ilUlI/et' as the study of the rela ­tionsh ip between business decisions. cash nows. and the value of the stock in the business.

A More General Goal If our goal is as slated in the preceding secti on (to maximize the: va lue of the stock). an ob\,jous question comes up: What is the appropriate goal when the finn has no traded stock? Corporations are cert~inly not the only type of business: and the stock in many co rporati ons rarely changes hands. so it's d ifficult to say what the value per share is at any particular time.

As long as we are considering fo r-profit businesses. only a slight modifiC'ltion is needed. The total value of the stock in a corporation is sim ply equal 10 the value of the owners' equity. Therefore. a more genera l way of stating our goal is as fo llows: Maximize the value of the existing owners' equ ity .

With Ihis in mind. we don't care whether the business is a proprietorship. a part­nership. or a co rporation. For each of these, good fina ncia l decisions increase the market va lue of the owners' equity, and poor financia l decisions decrease it. In fact, although we choose to focus on corporations in the chapters ahead, the principles we develop apply 10 a ll fo rms of business. Many of them even apply to thc not-for-profit sector.

Finally. our goal does not imply that the financia l manager should take illegal or unethical actions in the hope of increasing the value of the equity in the firm. What we mean is that the financial ma nager besl serves the owners of the busi ness by identify­ing goods and services tbat add value to the firm because they are desired and vd lued in the free marketplace.

Oapoler I Introduction to (orporutc Finll""'\:'

1.5 The Agency Problem and Control of the Corporation

13

We've seen that the linancial manager acts in the best interests of the stockholders by taking actions that increase the V'd lue of the stock. However. in I:nge corpora· tions o\\'Ilership can be spread over a huge number of stockholders.' This disper­sion of ownership arguably means Ihat management effecti vely cont rols the firm . In this case. will managemen t necessarily act in the best interests of the stockholders? Put another way, migh t not mamtgement pursue it s own goa ls at the stock.holders· expense? In the fo llowing puges we briefly consider some o f the arguments relating to this question.

Agency Relationships The relationsh ip between stockholders and management is called an agel/(\' I'(' /(l/ ioll­ship. Such a relationship exists whenever someone (the principa.l) hires another (the agent) to represent his or her interests. For example. yOll might hire someone (an agent) to sell a car that you own while you a re aWdy at school. In all such relationships there is a possibi lity of a eonniet of in tcrest be tween the principal and the agent. Such a connict is ca ned an agency problem.

Suppose you hire someone to sell your car and you agree to pay that person anal fce when he or she sells the car. The agent 's incentive in this case is 10 make the Sl"tle. not necessa rily to get you the best price. If you o ITer a commission of, say. 10 percent of the sales price instead of a flat fec, then this problem migh t not exist. T his cX<l mple illustrates that the way in which an agent is compensaled is one factor thnt affects agency problems..

'This is a bit oJ( an o\,entatcmcnt. Actually. in mO$t countriesOlhcr ,han th~ u.s. and the U.K .. publ icly traded comp>l nies;t~ usually controlled by one or mo~ 1;lll!e shareholders. Morecn-er. in countriC'$ wilh limited sha~holder protection. \\ hen compared 10 countries with strong shareholder protection like the U.S. and the U K .. large shareholdeD rna}' hllve a greater opportunity to impose agcncy CO~f5 on the minority shareholders. 5«. for Clii3lOple. " Investor Protection and Corpontte Valuation:' b) Rafaella Porta. F1orendo Lopel· De-Silancs. Andrei Shldfcr. lind Robo:rt Vi . hn y. Jour,,,,I'-if FillUlrr .. 57 (:!002,. pp. 1147-11 10: and "Cash ]-Ioldings. Di" idend Pol icy. and Corporate GOI'Cman~: A Cross.Country Analysis." by L..ec Pinkowil'!. Rene M. Stulz. and Rohan Williamson. Jour/wi of Applied Cor(KJfflll.' f"II/I/(·I'. VoL 19. No. I (2007). pp. 81- 87. Thc)' show tha! a country's investor proJtection framework is imponan! to unders tanding firm cash holdin! s and dIvidend payout. For t:'I.lImpte. they find thaI shareholders do not highly v-dlue cash holdinls in firms in coumries with low investor protC'Ction when compared to iirms in the U.S. where investor protcction is high.

In Ihe basic corporate gOlernance setup. the shareholders elcct the board o f directors \\ ho in turn appoin t the top corpomte managers. such as the CEO. The CEO is usua lly a member of tbe bwrd or d ircctors. One aspect of corpora te go\'trn30~ we do not t:llk much abou t is Ihe issue of an independent chair of a fi rm's board of din'c tors. Howel'er. in:a large number of U.s. corporat ions. the CEO and the board cha ir arc the same person. In "Us. Corporate GO'I'cmance: Aceomplishmenls and Failings.. A Discussion ",·;tll Michael knsen and Robert Monks"( moderated b} Ralph Walk]ing). JourJla/oj Applit·/I Q)'l'oml(' FilI(lIK't'. Vol. 20. No. I (Winter 200S1.lhe point is made that combining the CEO and board \'hair positions c;an contribute 10 poor corporate govemance. Both Jc:n~n and Monks give an edge to the­U K. in go'.emarKX partially because o,'er 90 percent of U.K. companies an: ehll ircd by outside dircC'lors aoo not the CEO. This is iI content ious issue cODfro ntin! man)' U.S. oorporlltions. For ullmpk. in May :mos. 19 institu tional in\"CSIOr.5. including some of EuonMobirs tllrgnt sharcholden a nd memhC'Ts or the founding Rockddkr fa mily. $upported II rcsolution to spl it the jobs of CEO and bo:Ird chair. Aboul 40 pen:ent of the $harellolders I'oled for the 5ptil.

14 Pari I Overview

Management Goals To see how management a nd stockholder interests might differ. imagine that a firm is considering a new investment. The new investment is e:o;peclcd 10 favorably impact the share value. but it is a lso a relatively risky venture. The owners of the firm will wish to take Ihe investment (because the stock value will rise), bm management may nOI because there is the possibility that things will !Urn out badly and mamlgcmenl jobs will be lost. ff management does not lake the investment. then the stockholders may lose a valuable opportunity. This is o ne example of an ageflcr cost

More generally. the term agency ('ost::; refers to the costs of the conflict of interest between stockholders and management. These costs can be indirect or direct. An indi­rect agency cost is a lost opponunity, such as the one we have just described.

Direct agency costs come in two forms. The li rst type is a corporate expenditure tllll! benefits management but costs the stock holders.. Perhaps the purchase of a lu xu­rious and unneeded corporate jet would fall under this heading. The second Iype of direct agency cost is an expense that arises from the need to monitor management aclions. Paying outside auditors to assess Ihe accuracy of financial statement informa­tion could be o ne example.

II is sometimes argued that, left to themselves. managers would tend to maximize the amount of resources over which they have control or, more generally, corporate power or wealth. Thi s goa l cou ld lead to an overemphasis OJ) corporate size or growth. For example. cases in which management is ae<:used of overpaying to buy up another company just to increase the size of the business or to demonstrate corporate power are not un<.'ommon. Obviously, if overpayment docs take place, such a purchase docs not benefit the stockholders of the purchasing company.

Our discussion indicates that management may tend to overemp hasize orga niza ­lional survival to protect job security. Also, management may dislike outside interfer­ence, so independence and corporate se lf-sufficiency may be important goa ls.

Do Managers Act in the Stockholders' Interests? Whether managers will. in fact, act in the best interests of stockholders depends on two factors. First. how closely are management goals aligned with stockholder goals? This question relates. at least in pan, to the way managers arc compensated . Second, can man­agers be replaced if they do not pursue stockholder goals? Tbis issue relates to contro l of the lirm. As we will discuss. there are a number of re<l sons to think that . even in the larg­est linns. management has a significant incentive to act in the interests of stockholders,

Managerial Compensation Management will frequen tly have a significant eco­nomic incentive to increase share value for two reasons. First. managerial compen­sation. particularly a t the top, is usually tied to financial performance in general and often to share value in particular. For example. managers are frequently given the option to buy stock at a bargain price. The more the stock is worth, the more valuable is this option. In fac t, options arc often used to mo tivate employees of all types. not just top management. According to 711e Wall SIr~('/ Journal, in 2007. Lloyd L Blankfdn. CEO of Goldman Sachs, made $600.000 in sa lary and $67.9 million in bonuses tied to financial performance. As menti oned. many firms also give manag­ers an ownership stake in the company by granting stock o r stock opt ions. In 2007. the total compensation of Nichol as D. Chabraja, CEO of General Dynamics, was reported by The Wall S treet JOllrnalto be $15.1 million . His base salary was $1.3 mil­lion with bonuses of £3.5 millio n, stock option grants of $6.9 million, and restricted

Cha jHu I Int roduction to Corponlle Financ-e 15

stock grants of $3.4 million. Although there are many critics of the high level of CEO compensation, from the stock holders' point of view, sensitivity of compensation to firm performance is usually more importa nt.

The second incentive managers have relates to job prospects. Better performers within the firm will tend to get promoted. More generally. managers who are success­fuJ in pursuing stockholder goals will be in greater demand in the labor market and thus command higher salaries.

In f<lct, managers who are successful in pursuing stockholder goals can reap enor­mous rewards. For example, the best-paid executive in 2008 was L.arry Ellison, the CEO of OrJclc; ac<.'ord ing to Forbe.f magazine. he made about $ 193 million. By way of comparison, J. K. Rowling made $300 million and Oprah Winfrey made about $275 million. Over the period of 2004--2008, Elli son made $429 million.:

Control of the Finn Control of the firm ulti.mately rests with stockholders. They elect the board of directors, who, in turn, hire and fire management.

An important mechanism by which unhappy stockholders can replace exist­ing management is called a proxy fight. A proxy is the authority to vote someone else's stock. A proxy figh t develops when a group solicits proxies in order to replace lhe existing boa rd a nd thereby replace existing management. In 2002, the proposed merger between HP and Compaq triggered one of the most widely followed, bitlerly contested , and expensive proxy fight s in history. with a n estimated price tag of well over S I 00 million.

Another way that management can be replaced is by ta keo ... er. Firms that are poorly managed are more at{raciive as acquisitions than well-managed firms because a greater profit potential exists. Thus. avoiding a takeover by another firm gives management another incenLive to act in the stockholders' interests. Unhappy prominent sharehold­ers can suggest different business strategies to a firm 's top management. This was the case with Carl leahn and Motorola. Carl leahn specializes in takeovers. His stake in Motorola reacbed 7.6 percent ownership in 2008. so he was a particularly imponam and unhappy shareholder. This large sta ke made the threat of a shareholder vote for new board membership and a takeover more credible. His advice was for Motorola to split its poorly performing handset mobile phone unit from its home and networks business and create two publicly traded companies-a strategy the company adopted.

Conclusion The available theory and eviden<.'e are consistent with the view that stockholders control the firm and that stockho lder wealth maximiz.ation is the rel­eva nt goa l of the corporation. Even so. there will undoubtedly be times when manage­ment goa ls afC pursued at the expense of the stock holders, at least temporarily.

Stakeholders Our discussion thus far implies that management and stockholders are the only parties with an interest in the firm's decisions. This is an oversimplification. of course. Employees. cuslomers, suppliers. and \!Ven the govemment al l have a financial interest in the firm.

'This raises the issue of the levet of top m:lIlagcme.u pay and ils relationship to olhtr cmptoye..s.. Ac..:ord· ing. 10 Til,. Nel\" York Time.~ Ihe average CEO compe-ns.alion was greater than tSO times the average employee comptnsalion in 2001 and onty 90 times in 1994. Ilowever. there is no pred~ fom1uta Iha' I!0"ern~ Ihe gap between top mana~menl compenS;l1ion and Ih;1\ of employees..

16 Pan I Overview

Taken toget her. these va rio us groups are called stakeholders in the firm . In gcnenll , a stakeholder i:i someone other than a stockholder or creditor who potentia lly has a claim on the cash flows of the firm . Such groups will also aHem pli O exert contro l over the fi rm. perhaps to the detriment of the owners.

1.6 Regulation Until now, we have talked mostly about the act ions that shareholders and boards of directors can take to reduce the conniets of interest between themselves and manage­ment. We have not talked about regulation. ) Unt; l recently the ma in thrust of fed­era l regulation has been to require that compan ies disclose all relev".:I.nl info rmation 10 investors and potemiai investors. Disclosure o f relevant information by corporat ions is intended to put all investors on a level information playing field and. thereby to reduce connicts of interest. Of course, regulation imposes costs on corporatio ns aDd any a nalysis of regulation must include both benefits and costs.

The Securities Act of 1933 and the Securities Exchange Act of 1934 The Securities Act of 1933 (the 1933 Act) and the Securili~s Exchange Act of 1934 (the 1934 Act) provide the basic regulatory framework in tbe United States for the public tmding of securities.

The 1933 Act focuses on the iss uing of new securities. Basically. (he 1933 Act requires a corporation to file a registration statement with the Securities and Exchange Comnlission (SEC) that must be made available to every buyer of a new security. The intent of the registration statement is to provide potential stockholders with all the necessary informatio n to ma ke a reasonable decision. The 1934 Act extends the disclosure requirements of the 1933 Act to securities trading in markets Clner th ey have been issued. The 1934 Act establishes thc SEC a nd covcrs a large number of issues includ ing corporate reporting. tender offers, and insider trading. The 1934 Act requires corporations to file repons to the SEC on an annua l basis (Fo rm 10K). on a quarterly basis (Form IOQ), and on a mo nthly basis (Form SK).

As mentioned, the 1934 Act deals with the important issue of insider trading. Illegal insider trading occurs when any person who has acquired nonpublic. special informa­lion (i.e .. inside information) buys or sells securi ties based upon that information , One section of the 1934 Act deals with insiders such as directors. officers, and large share­holders. wh ile another ueals wilh any person who has acquireu inside inComation. The intent of these sections of the 1934 Act is to prevent insiders or persons witb inside infor­mation from takiog unfair advantage of tbis information when trading witb outsiders.

To illustrate, suppose you learned that ABC firm was about to publicly a nno unce that it had agreed to be acquired by another finn al a price significantly greater than its current price. This is an example of inside info rmation. The 1934 Act prohibits you from buying ABC stock from shareholders who do not bave this informa.t ion. This

·'At th is stage in our book, we focus on th~ regulation or corporate governancc. We do not ta lk about mom}' other regUlators in fin ancia l marke ts such as the Foocral Reserve Board. In Chapte r 8. we discuss the nationally re<:ognized sta tistical rating organizations (NRSROs) in thc U.S. They aT\: Fitch Ratings, Mowr's, and Standard & Poor's.. Thcir ratings are used by market parl icipanb 10 help value s«uritil"S such as corporate bonds. Many crilics of the rating agmcies bl.ame the 2007-1009 subprimc credit crisis 011 weal; rc&ulatory o\"ersight or these agencies.

Chapter I r ntrouuction to Corpor4to: fin;tnce 17

prohibition wou ld be especially stro ng if you were the CEO of the A BC firm. O ther kinds of a fi.rm's inside information could be knowledge of an initial dividend about to be paid, the discovery of a drug to cure cancer, or the defauh or a debt obligntion,

A recen t example of insider t rading involved Samuel Waksal. the fo under and CEO of TmClone Systems, a biopharmaceutica l company. He was chacged with learning that the U.S. Food and Drug Administ ration was go ing to reject an application fo r ImCione's cancer drug, Erbi trux. What made this an insider trading case was Waksal's allegedly trying to sell shares of ImClonc slock before reJcuse of the Erbit rux informa­ti on, as well as his family and friends also selling the stock, He was arrested in June 2002 and in October 2002 plcadC<l guilty to securities fra ud among other thi ngs. In 2003. Waksal was sentenced to more tha n scven years in prison .

Sarbanes-Oxley In response to corpordte scandals at companies such as Enron, WorldCom, Tyco, a nd Adelphia , Congress enacted the Sarbanes-Oxley Act in 2002. The act , bener known as "Sarbox:' is intended to protect investors fro m corporate abuses. For example, o ne section of Sa rbox prohibits personal loans from a company to its officers, such as the ones that were received by WorldCom CEO Bern ie Ebbers.

One of the key sections of Sarbox took cO'ect on November 15, 2004. Section 404 requires. among other things. thai each company's annua l re'port must have an assess­ment of the company's internal cont rol st ructure and financia l reporting. The auditor must then evaluate and altcst to management's assessmen t of these issues.. Sarbo.'i also creates the Publ ic Com pao ics Accountiog Oversight Board (PCAOB) to establish new audit guidelines and ethical standards. It requires public companies' audit committees of corporate bO<lrds to include only independent, outside directors to oversee the annual audits and disclose if the committees have a financia l expert (and if nOl , why not).

Sarbox contains other key requirements.. Forexample., the officers o f the corporation must review a nd sign the annual reports. They must explicitly declare that the annual report does not contain any false statements or material omissions: that the lina n­ciaT statements fa irly represent the financial resu lts: and that tbey are responsible fo r all interna l controls.. Finally, the annual report must list any deficiencies in internal controls. In essence, Sarbox makes company management responsible for the accurdcy of the company's financial statements.

Of course. as with any law, there are COSts. Sa rbox has increased the expense of cor­porate audits. sometimes dramatically, In 2004, the average compli ance cost for large firms was S4.5 1 million. By 2006. the average compliance cost had fallen to 51.92 mil­lion , so the burden seems to be dropping, but it is st ill not trivial, particularly for a smaller firm. Tbis added expense has led to sevcral unintended results.. For example.. in 2003, 198 firms delisted their shares from exchanges. Of" " went dark:' and abo ut thc same nu mberdelisted in 2004. Bo th numbers were up from 30 dcJistings in 1999. Many of the companies that delisted stated the reason was to avoid lhe cost of compliance with. Sarbox.~

A company that goes dark does not have to file quanerly or annual repons. Annual audits by independent auditors are not required . and executives do not have to certify

' But in "Has New York Becomc Lc:\;!; Competitive in Global Markets? E\'alualing Foreign Lis ting Choices O"er Time"' (N BER Working Paper No. 13029) 2008, Craig Doid~. Andrew Karolyi. and Rene Stutz rind Ihat the decline in delistings is not directly rc1aled to Sarbanes·O:c:ley. They conclude that mO!;t New York deli..§t illS was becausc of mergers and acquisitions. dist ress. and restrUCll.lring.

18

Summary and Conclusions

Concept Questions

Part I Ol'erv;cw

the accurdcy of the financial statements. so the savings can be huge. or course, there are costs. Stock prices Iypically fall when a company announces it is going dark . Fur­ther. such companies will typica lly have limited access 10 capital markets and usually will have a higher interest cost on bank loans.

Sarbox has also probably affected the number of companies choosing to go public in the United Slates. For example, when Peach Holdings, based in Boynto n Beach, Florida, decided to go public in 2006. il shunned the U.S. stock markets. instead choosing the London Stock Exchange's Alternative Investment Market (AIM), To go public in the United States, the firm would have paid a $100,000 fee, plus about $2 million !O comply with Sarbox. Instead. the company spenl on ly $500,000 on its AIM slock offering. Overall. the European exchanges had a record year in 2006, with 65 1 companies going public. while the US. exchanges had a lackluster year, with 224 companies going public.

This chapler introduced you 10 some of the basie ideas in corporate finance:

I. Corporate finance has three main areas of concern: a. Capilallmdgetillg: Whiliiong-term invest ments should the firm take'! b. Capital SlruCflm': Where will the firm get Ihe long-Ierm financing to pay for its invest­

ments? Also. what mixlUre of debt and equi ty should it usc to fund operations'! e. Working capiwl m(l1wgemellf: How should the fi rm roanage il.:) evcryday fimtnc ial

activities?

2. The goal of financial management in a for-profi t business is 10 make decisions tbat increase the value of the stock , or. more gCll crall}~ increase the market value of the eq u i t }~

3. TIle corporate form of organization is superior to other forms when il comes 10 raising money aod tr • .Illsferring ownership interests. but it has the significant disadqllltage of double w.xali on.

4. There is the possibility of connie!s between stockholders and management in a large corporation. We called these connicts (lgcllq prob/elm" and discussed how they might be controlled and reduced.

5. The advantages of the corporale form ilre enhanced by tbc c:.xislence of financial markets.

Of the topics we've discussed thus fin, the most imponant is the goa! of financial manage­ment: maximizing Ihe va lue of the stock. Througiloulthc lext we will be analyzing many different financial decisions. but \.\·C wi ll always ask the same question: How does the deci­sion undcr consjderation atlect the vnlue of tbe stock?

I . Agency Problems Who owns a corporation"? Describe the process whereby the own­ers control the firm's management. What is the main reason thai an agency relat ion­ship exists in the corporate form of orgll11izillion? In this context. what kinds of problems can arise?

2. Not-fur-Profit Firm Goals Suppose you were Ihe financial manager of a not-for­profit business (a fl ot-for-p rofit hospital. perhaps). Wbat kinds of goals do you think would be appropriate"!

S&P Problems

STANDARD & POOR'S

(.'bllptcr I Introduc tion to Corpor.ille Finance 19

3. Goal of the Firm Eval uate the following statement: Managers should not focus 011 the current slock value because doing so wjllicad 10 an ovcremphasis on shon-term profits at Ihe expeose of long-term profits.

~. Ethics and Firm Goals elm the goal of maximizing the va luc of the stock COflnicl with other goals. such as avoiding unelhical or iIleg:11 behavior? In panicular, do you think subj(''Cls like customer and employee safety, the ellvironment . and the gcncml good of society fit in this framework. or arc they cssen tia lly ignored? Think of wme specific scenarios to il lustrate your answer.

5. International Firm Goal Would Ihe goal of maximiziog tbe value of the stock differ for finaIKi:l1 management in a foreign country? Why or why fl a t?

6. Agency Problems Suppose you own slock in a company. The culTCl1t price per share is 525. Another company hasjusl illlllOt11lccd thilt it W·,.lIlIS 10 buy your company and will pay $35 persharc 10 acqu ire all the olHstanding stock. Your comp.lllY·S manage­ment immediately begins fighting off this hostile bid. Is management aCling in the shareholders' best interests? Why or why nOI'!

7. Ag(>l1c~' Problems and Corporate Ownership Corporate ownership varies around the world. HislOrically. individuals have owned thc majority or sh ares in public cor­porations in Ibe Un ited Stales. In Germany and Japan . however. banks, olher large financial inslitulions. and other companies; own most or the siock in public corpora­lioos. Do you think ,Igency problems are likely to be more or less severe in Germany and Japan than in the Uilitcd States?

8. AgcnQ- Problems and Corporate OtHICrship In recent years, large financial institu­tions such as mUluill funds and pension funds have become the dominant owners of stock in the United Slates, and these inSlilUtiofls arc lx"'Coming more aClive in cOT) oratc affairs. What arc the implicat ions of this trend for agency problems and corporate control?

9. Exccutire Compensation Critics have charged that compensation to top managers in the Uni ted States is simply too hi gh and should be cuI back. For e.umple. focusing on large corporations. Larry Ellison of Oracle has been one or the bcst-compensated CEOs in the Un itt.-d Slates. earning <lboll t SI93 million in 2008 alone and $429 mil· lion over Ihe 2004-2008 pcriod. Are such amoun ts excessive? In answering. it might be helpful to recognize that superstar athletes such as Tiger Woods., top entertainers sucb as TOil! Hanks and Oprah Winfrey. ;lIld many others at the top of their respec­tive fields carn at least as much. if not a great deal more.

to. Goal of Fin!lIlcinl Managemcnt Why is the goal of fi nancial management to maxi­mize the current share price of the company's stock? In OI her words. why isn't the goal 10 maximize the fut ure share price?

WW\\·.Il1h.he.eom/cdurnarkctinsight

I. Industry Comparison On the Markel Insight home page. follow the "I ndustry" liflk at the top of the page. You will be on the industry page. You can use the drop-do .... n menu to select diffe rent industries. Answer the following questions ror these indus­tries; airlines. automobilt!" manufacturers. biotech nology. computer hardware. home­buildi ng. marine. restauraots. soft drinks. ,md \\'; re!css Ie.lecommuflieations. a. How many companies are in eaeh induslrv? b. What are the total salcs (or each industry? c. Do the industries with the largest lotal sales hm'C tbe most companies in the

industry"? What does this tell you about competition in Ihe va rious industries?

20

Financial Statements and Cash Flow

A write-off frequently means that the value of the company's assets has declined. For exam·

pie, in the first quarter of 2009, luxury homebuilder Toll Brothers said il was writing down

$157 million in assets, much of which was a reflection of the reduced value of land the

company owned . Of course, Toll Brothers was not the only homebuilder suffering. Hovnanian

Enterprises announced it would lake a $132 million write-oH, and Genlax Corp. announced

a $590 million write·off. At the same lime, O. A. Horton, Inc., the largest homebuilder by

volume, had a much smaller write-off of only $56 million. However, D. R. Horton had already

written off $1.15 billion In the fourth quarter of 2008.

So did stockholders in these homebuilders lose hundreds 01 millions of dollars

(or more) because 01 the write-offs? The answer is probably nol. Understanding why ulti­

mately leads us to the main subject 01 this chapter: that all-important substance known as

cash flow.

2.1 The Balance Sheet

Two excellent scuces tor ~y IINndat

WormatiOn are fi!\i!lC8.ohoo com

"'" II'lODIJ CM&9R'.

The b21aoce shet't is an accou nta nt 's snapshot of a finn's accounting va lue on a partic­ular date. as though the fi rm stood momentarily sti.ll . The balance sheet has two sides: On the left are the assets and on lhe right are the liabilities a nd slock/Jo/ders' I!quity. The balance sheet states what the firm owns and how it is financed . The accounting definition that underlies the balance sheet and describes the balance is:

Assets !!!!! Liabilities + Stockholders' equity

We have put a three-line eq uality in Ihe balance equation to indicate that it must always hold . by definition. In fact. the stockholders' equity is dejiJll'd to be the difference between the assets and the liabilities of the flnl1 . In principle. equity is wha t the stockholders would have rcmaining afler tbe rum discharged its obligations.

Table 2.1 gives the 2010 and 2009 balance shee t for the fictitious U.S. Compos­ite Corporation . The assets in the balance sheet are li sted in order by the length of lime it nonnally would lake an ongoing finn to convert tbem into cash. The asset side depends on the nature of the busi ness and how management chooses to conduct il. Management must make decisions about cash versus marketable securities, credit versus cash saJes, whether to make or buy commodities.. whether 10 lease or pu rchase ilems, the types of business in which 10 engage, and so on. The liabilities and the stock holders' equity are listed in the o rder in which they would typically be paid over time.

Chapll"f 2 Finar.("iul Sta l,'menu ynu Cash Flow 21

Table 2.1 The Ba lanee Sheet 01 the U.S. Compostte Corporaotlon

U .S. COMPOSITE CORPORATION Balance Shee t 20 I 0 and 2009 ($ in millions)

Liabilities (Debt) and Assets 2010 2009 Stockholders' Equity 2010 2009

Current asseu: Current liabilities: C.lSh and equivalenu $ 140 $ 10' Accounts payable $ 2IJ $ 19' Accounu receivable 294 270 Notes payable SO 53 Inventories 26' 280 A<;crued expenses m 205 Other 58 SO Total current liabilities $ 486 $: <I SS

Total current assets $ 76 1 $ 707 Long-term liabilities: F1xed assets; Deferred t.l)(es $ 117 $ 104

Property, plant, and equipment $1.423 $1.274 long-term debt*' 471 458 Less ,,,cumulated depredation SSO 460 Total long-term liabilities $ 588 $ 562 Net property. plant. ind 873 8" Stockholders' eqUity:

equipment

Intangible assets md others 245 221 Preferred stock

Common stock ($1 par value) $39 $ 39

Total fixed assets $1.118 $1 ,035 SS 32

Capiul surplus 347 327 Accumulated retained earnings 390 34'

l ess treasury stock' 26 20 Tau.! equity $ 80S $725

Toul liabilities and Tot<lll iueu $1.879 stockholders' eqUity: $1 ,879 $1 .742

=

"lotlc·COl'Tt'l deb< role by $-411 ..-.ilion - $-4S8 ......", .,. $ 13 miIion. TN, n 11M: ditfeAnce ~ $86 ",;1!Ion new debc M>d $n ~ ... ~ of old deb<.

'TruWl")' I.OCI< role by $6 .... ion. Thd ~ the 'WJMIl'cnue of $6 million of U.s'ComposU'f campa..,. noctc.

'U.S. Composl .. ~ $ -43....nion in.- tqUicy. Thct,~ "wed:U million sNreu •• price 01 $1.11. The ~ value of c ............ !Cock increuM b)' S 13 mil""'" IIOd capouI """l'Iu. -.eel by $20 mllian.

Annual alld Quarterty 1lnanda1 statemt!lfllS lor most pOOIic u.s. corporaliORs can be bJlld In !he EDGAR

oatabase at WWWsec.Q0,

The liabili ties and stockholders' equi ty side reOect s the types and proportions of financing. wbich depend on management 's choice of capital StruCture. as between debt and equity and belween current debt a nd long-term debt.

When analyzing a ba lance sheet. th e financial manager should be aware of Ihree concerns: liquid ity, debt v..e rsus equity. and value versus cost.

Liquidity Liquidity refers to the case and quickness wi th which assets ean be converted to cash (without significant loss in val ue). Current (IsseIS an: Ihe most liquid and include cash a nd assets that w1ll be turned into cash wi thin a ycar from the date of Ihe- ba lance sheet. Accounts rtuil"llble are a mounts not yet collected from customers for goods or services sold 10 them (a ft er adjustment for potential bad debts). 11Il"C'mory is composed of raw materials to be used in production. work in process. and finished goods. Fixed lISSC'ls are the least liq uid kind of assets. Tangible fi .'(ed assets incl ude property, plant,

22

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Pari I O\>( rview

and ~quipment. These assets do nOI convert to cash from normal business activity, and they are nOl usually us_cd 10 pay expenses such as pHyrol1.

Some fixed assets are not tangible. Intangible assets have no physical existence but can be very valuable. Exa mples of imangible assets are the value of a trademark or the vil lue of a patent. The more liquid a lirm's assets. lhe less likely the firm is 10 experience problems meeting short-term obligations. Thus. the probabi lity that a firm \ \ 'i11 avoid financial distress can be linked to the firm 's liquidity. Unfo rlunatcly.liquid assets frequently have lower rales o f relUrn than fixed assets; for example, cash gener­ates no investment income. To the extent a firm invests in liquid assets, it sacrifices an opponunity to invest in more profitable in .... estment vehicles.

Debt versus Equity Liubili,;"s are obligations of the firm that requi re a payout of cash within a stipulated period. Many liabil ities involve contractual obligations to repay a stated amount and interest ovcr a period. Thus., li<lbilities are debts and arc frequently associated with nominally ru.ed cash burdens., ca lled debt servit'e. that put the lirm in default of a contraci if they arc not paid . Stuckholders ' equity is a claim against the firm's assetS that is residual and not filted. In genen!:1 terms. when the firm borrows. it gh'es the bondholders first claim on the firms cash now.1 Bondholders can sue the finn if the firm defaults on its bood cont racts. This may lead the firm to declare itself bankrupt, Stockholders' equity is the residual difference between aS5CtS and liabilities:

Assels - Liabilities - Stockholders' equit y

This is the stock bolders' share in the firm stated in accou nting terms. The accounting value of stockholders' equity increases when retained earnings are added. This occurs when the firm rttilins pan of its earnings instead of paying them out as dividends.

Value versus Cost The accounting value of a firm 's assets is frequently referred to as the carryillg l'ulUI! or the book mlue of the assets. ~ Under generally accepted Ilccounling principles (GAAP), audited financial statemen ts of li rms in the United States carry Ihe assets 81 cos!.J Thus the terms (:arryillg ,·tlille and book w;{lIe are unfortunate. They specifically say "value: ' when in fact the accounting numbers are based on cost. This misleads many readers of fioancial statements to think that Ihe firm's assetS are recorded 31 truc mar· kel values. Markel nt/lie is the price at which willing buyers and sellers would lrade the assets. It would be only a coincidence if accounting value and market va lue were the same. In fact, manilgement 'sjob is to cfCilte value for the firm that exceeds its cosl.

Many people use the balance sheet, but tbe information each may wish to extraci is not the same. A banker may look at a balance sheet for evidence of accounting

'BomJhol.kn lite iO\'eSlo rs in the lirm'$ debl . Thc)' an: ct>:dirors or the linn. 10 Ihis distussion. the lerm b.mdJwhlttr means the same Ihin! as (·" ·Jlt,,,.

lConl"usiQn ol'lel'l arises bocau~ mllny financia l lIIXounting terms haVt the same mClIning. This prCS<.'nts a problem wilh jargon for Ihe ",aller of financial st:lIemcnu. For eX/lmpte. the fol1owin! terms u~ually rdo:r 10 the s:ime thin!: u:m:1S miltus fi<J/Jifi/i"s.. ''''/ " ·or,h. JlodhoJders' rq" it.l: u<mrr.t' "I/l ity. book <',/IIi1y. and (,<{u ily ("i'p,tu /izulilJll.

'G(ner..!. Uy. GAAP ""Iuires asselS 10 be OI.rried al lbe lower of COSI or markct value. In mrn.1 iMtanres. COSI is lower than markcl value. HO\\"~"~r. ill some c-dSCS when a f<lir markel value c<tn be ,,",adil~' de tcr­mincll_ the assc:ts have Ihrir vallie adjustwlO Ihe fair market va lue.

EXAMPLE 2.1

Chilplft" 2 Financi~l StalCm~nlS and Ca$h Flow lJ

liquidity a nd wo rking capital. A supplier may also note the size of accounts payable and lherefore the general promplness of paymenls. Many users of financial stale, ments, including managers and investors. wanl to know the value of Ihe firm. not its cost. This information is not found on the balance shed. In fac\. many of the true resources of tbe firm do not appear on the balance sheet: good management, proprie­lary assets, favorab le economic conditions. and SO o n. Hencefonb. whenever ","-e speak of Ihe value of aD asset or the value of the firm. we will normally mean its markel value. So. for example, when we say the goal of the fioaneial manager is to increase Ihe value of the slock. we usually mean the market value of Ihe stock not the book value.

Market Value versus Book Value The Cooney Cor-pontion hu fixed assets with a book

value o f $700 ilnd an appraised market value of about S I ,000. Net worltillg a.piul i$ $-400 on

the books. but appro>rinucely $600 would be rulized if all the current accounts were liquidated.

Cooney has $500 in long- term debt. both book value and market value. What is the book value 01 the equity~What is the market value/

We can COllstruct two simplified balance Sheil;u.one in aceouming (book value) term~ and one in economic (market YO/Itue) terms:

COONEY CORPORATION Balance Sheets

Milrket VaJue venus Book Value

Assets Liabihties and Shareholders' Equity

Book Market Book Marke t

Net working capital $<00 $ 600 Long-term debt $ SIlO $ SIlO Net fixed iIIueu 700 1.000 Shareholders' equity 600 1.1 00

$1.100 $1,600 $1.100 $ 1.600 = = =

In this example. shareho!de~' equity is iIIcwallyworth almost twice as much as what i, shown on the

books. The distinction between book and market Y.llues is important precisety because book values can be so diffe rent from market values.

2 .2 The Income Statement The income slatemenc measures perfonnance over a specific period-say a yea r. The accounting definition of income is:

Revenue - Eltpenses - Income

If Ihe balance sheet is like 3 snapshot. the income statement is like a video recordinl!: of what the people did between two snapshots. Table 2.2 gives the income statemeni for the U.S. Composite Corporation for 2010.

The income SUltement usua lly includes several sections. The o perations section reports the firm 's revenues and expenses from principa l operations. One number of particulllr imporlance is earnings before interest and taxes (EBIT). which summa rizes earnings before t3ltCS a nd financing cost s. Among ot her things. the nonoperating: sec­tion of the income statement includes aU financing COSts.. such as inlereSt expense.

24

Table 2.2 The Income Statement of the U.S. Composite Corporation

U.S. COMPOSITE CORPORATION Income Statement

2010 ($ in millions)

Total operating revenues

COSt of goods sold

Selling,general. and administrative expenses

Depreciation

Opeli'lting income

Other income

Earnings before interest and taxes (EBIT)

Interest expense

Pretax income

Taxes

Current:: $71

Deferred: I]

Net income

Addition to retained earnings;

Dividends:

$2.262

1.655

327

.0

S '90 29

$ 219 .. $ 170

• 4

$ .,

~ 43

NOTE: ThU'l! ~ .... l'l ""Uion o/Qrt \ O<lnonodl",. E.u-nOn,. pU ,hu. and dM6tndl per ;k.lre un be ulc\l" t~ U fc;IIkM1:

Nee 1nc0/TMl Earni"X, per snan! • Tow lharn ouciiiAd""

'" -" '" $1.97 pu smore

""""", DiYid.""h pet IN .... - Toal shlorM O\I0;:5aM;n&

S., =19 = $1.48 pcr w ...

Usually a second section reports as a separate item the amouni of taxes levied on income. The last item on the income statement is the bottom line. or net income. Net income is frequently expressed per share of common stock- that is. earnings per share. .

When analyzing an income statement. the fina nci<ll manager should keep In mind GAM, noncash items., time, and costs.

Generally Accepted Accounting Principles Revenue is recognized on an income statemen t when the earnings process is virtu­ally completed and an exchange of goods or services has occurred . Therefore, the unrealized appreciation from owning propeny will not be recognized as income. This provides a device for smoothing income by selling appreciated propeny at convenient times. For example, if the firm owns a trcc farm that has doubled in value. then. in a year when its earnings from other businesses are down, it ca n raise overall earnings by sell ing some trees. The matching principle o f GAAP dictates that revenues be matched with expenses. Thus, income is reported when it is earned. or accrued. even though no cash now has necessarily occurred (for exa mple, wheD goods are sold for credit , sales aJ)d profits a re reponed).

ChapleT 2 FinOlnciOlI S';lIcmt U'$ lind ('ash Flow 2S

Noncash Items The economic value o f assets is intimately connected to thei r future incremental cash nowS. However. cash now does nOt appear on an income statement. There are several noncash items Ihal are expenses <Igai nst revenues but do not affect cash flow. The most important of these is depreciatiQII. Depreciation renects the accountant 's estimate of the cost of eq uipment used up in the production process. For example, suppose an asset with a five-year life aod no resale \·a lu.: is purchased tar $1.000. According to accountants, the $LOOO cost must be expensed over Ihe useful life of the assel. If straight-line depreciation is lIsed, there will be fi ve equal installments. and S200 of depredation expense will be incurred each yea r. From a finance perspective. the cost of the llssct is the actua l negative cash flow incurred when the asset is acquired (that is, SI .OOO, 1101 the accountant's smoothed S200-per-year depreciation expense).

Another noncash expense is deferred taXi'S. Deferred taxes result fro m dinerences between accounting income and true tlIx.able income: Notice that the accounting tax shown on the iocorne statement for the US. Composite Corpormion is $84 million . It can be broken down as current III xes and deferred taxes. The current tax portion is actually sem to the tax 3Ulhorities (for example. the Internal Revenue Service). The deferred tax ponion is not. However. the theory is thai if taxable income is less tban accounting income in the currenl year. it will be more than accounting income later on. Consequently. the taxes that are not paid today will have to be paid in tbe future, and they represent a liability of the firm. This shows up on the balance sheet as deferred tax liabilit y. From the cash flow perspective. though. deferred tax is not a cash outnow.

In practice. the dilThence between cash nows and accounting income can be quite dramatic. so i( is imporlan l to understand the diflerencc. For example. in the first quar­ter of 2009, media giant Cablevision. whose holdings incl ude the New York Knicks and New York Rangers. reported a loss of $321 million . SOllnds bad. but Cablevision reported a posilil'e operating cash now of 5498 million! In large part . the difference was due to nonca sh charges associated with Cablcvision's purchase of the /Ilcu's(/ay newspaper the previous year.

Time and Costs It is oflen useful to visualize all o f future time as having two distinct parts.. the shorl rUff and the long rim. The short run is the period in which cenain eq uipmcnt. resources. and commitments of the firm are fixed; but the time is long enough for the fiml to vary it s output by using more labor and raw materials. The short nm is not 3 precise period that will be the same for a ll industries. However. a ll firms making decisions in the short rUIl have some fixed costs- that is. costs that will not change because o f fixed commi t­ments. In real busi ness activity, examples of fixed costs are bond interest, overhead. and property taxes. Costs that are not fixed are variable. Variable costs chaDge as the output of the firm changes: some exa mples are raw materials and wages for laborers on the production line.

In the long run, all costs lire variable. Financial accountants do not distingu ish between variable costs and fixed costs. Instead . accounting costs usually fit into a classification that distinguishes product costs from period costs. Product costs are the total production costs incurred during II period- raw materials., direct labor, and

'{)Il\' $;lUa, ion ;11 which 13.\ablt income- may be lowe.r Ih.:ln accoun!;ng income is when the firm uses !leeel· eraltd depreciation o pense procedures for ,h"' IR S but uses straigh,·!inc procedures allowed by GAAP for rtpor,;ng pUrp<lses.

26

2.3

Table 2.3 Corpora .. Tax Rates

Part I Overy~

ma nufacturing overbead- and are repon ed on the income statement as cost of goods so ld. Both va riable and fixed costs arc included in product cOStS, Period costs are costs Ihat a re allocated \0 a time period : they are called selling. general. aDd " t/muliSIrOlil'e expen.\'('s . One period cost would be the company president 's sn lary.

Taxes Taxes ca n be o ne of the la rgest cash outnows a firm experieoces. In 2007. according to the Department of Commerce. total corporate profit s before taxes in the United Slates were about SJ.6 trillion. and taxes on corporate profits were about $450 billion or about 28 percen t of pretax profits. The size of the firm 's lax bill is determined by the tax code. an often amended set of rules. fn Ibis section. we examine corporate tax rates and how taxes arc calculated .

If the various rules of taxation seem a l.iule biza rre or convolUied to you, keep in mind that the tax code is the resuh of political. 001 economic. forces. As a result. there is no reason why it bas to make economic sense. To put the complexity of corporate taxation into perspective, General Electric's 2006 tax retum requ ired 24,000 pages, far 100 much to print. The electronically filed retu rn ran 237 megabytes.

Corporate Tax Rates Corporate tax rates in effect for 2008 are shown in Table 2.3. A peculiar feat ure of taxa· tion instituted by the Tax Reform Act of 1986 and expanded in the 1993 Omnibus Bud­get Reconciliation Act is that corporate tax rdtcs art nOt strictly iocreasing. As shown. corpomte tax rates rise from 15 percent to 39 percent. butlheydrop back to 34 percent on income over 5335.000. They then rise to 38 percent and subsequently fall to 35 percent.

According to the originators of the current tax rules. there a re only four corporate r.ues: 15 percen t, 25 percenl. 34 percent. and 35 percent. The 38 and 39 percent brack­ets arise beca use of "surcharges" applied on top of the 34 and 35 percent rates. A tax is a tax. however, so there arc really six corporate tax brackets. as we have shown.

Average versus Marginal Tax Rates In making financial decisions, it is freq uently important to distinguish between average and ma rginal tax rates. Your average fax n.te is your tax bill d ivided by yoW" taxable income- in other words., the percentage of you r income that goes to pay taxes. Your marginal tax rate is the lax you wou ld pay (in percent) if you ea rned one more dollar.

Taxable Income Tax Rate

$ 0- 50.000 15% 50.001 - 75.000 lS 7S,OOI- 100.000 H

100.001- 335.000 " 335,001-10,000.000 H 10.000.001 - 15.000,000 3S 15.000.00 1- IB.333.333 38

18,333.33<4 + 3S

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EXAMPLE 2.2

Table 2.4 Corporate Thes and Tall: Rates

Cb-aptH 2 Financial SlatcmenlS and Cash Flow 27

The percentage tax rates shown in Table 2.3 arc a ll ma rginal rates. Put ano ther way, the tax rales apply 10 the part of income ill the indicated range on ly. not a ll income.

The difference between average aod ma rginal tax rates can best be illustrated with a simple example. Suppose our corporation has a taxable income of $200,000. What is the tax bill? Using Table 1.3 ...... eca ll figure our tax bill like this:

. 15($ 50.000) - 5 7.500

.25(5 75.000 - 50.000) - 6.250

.34(5100.000 - 75.000) - 8.500

.39(S200.000 - 100,000) - 39.000 $61.250

Our tota l tax is thus $61.250. In ou r example, what is tbc average tllX ra te? We had a taxable income of $200.000

and a tax bill of S61,250. so Ihe average tax rate is 561.250/200,000;::: 30.625'%. What is the marginal tax rale? If we made one more dollar, the tax on that dollur would be 39-cents. so ou r marginal rate is 39 percent.

Deep in the Heart of Taxes Aigemon. Inc .. has a tuable income of $85,000. Whu is its taX

bi U~ Whu is iu average tax rate11u rT\iIrglrul ux rue~

fromTabfe 1.3,we see that the ux rate ~plied to the first $50.000 Is 15 percen~the note applied 10 the next S25.000 is 25 p4!rcent: and tne nne _w'ied _fter that up (0 $100.000 is 34 percenL So Algernon mu~t pa.y . 15 X $50.000 + .25 X 25.000 + .3<4 X (B5.ooo - 75,000) :: SI7.150. The aver­age (ax rate is thus $1 7.1 SOISS.ooo '" 20.18%. The motrxirul rate Is H percent because Algernon's Dxes would rise by H cents if it had another dollar in ~.u.bIe income.

Table 2.4 summa rizes some different taxable incomes, ma rginalli:lx rates. and aver­age tax rales ror corporations. Notice how the average and marginal tax rales come together at 35 percent.

With aj1il1-rate tax. there is only one tax rate, so the rate is the same ror all income levels. With such a tax. the ma rginal tax rate is always the sumc as the average tax nile. As it sta nds now. corporate taxation in the Uo ited States is based on a modi lied n<u­rate tax. which becomes a true fl at rate fo r Ihe highest incomes.

In looking at Table 1.4. notice that the more a corporation makes. the greater is the percentage of taxable income paid in taxes. Put another way. under current tax law, the

(I) (2) (') (')/(1) Taxable Income MarginalTax Rate Total Tax AverageTax Rate

$ 4S.OOO 15% $ 6,7S0 15.00% 70,000 lS 12.500 17.86 95.000 H 20,550 21.63

250.000 " 80.750 32.30 1,000.000 ,. 340,000 34.00

17.500.000 38 6.100,000 34.B6 50.000.000 3S 17.S00,000 35.00

100,000.000 3S 35.000.000 35.00

28 P3rl I Q\'crview

average lax rate never goes down. even though the marginal lax rdle docs. As illustrated, for corporations.. average tax rates begin at 15 percent and fi se to a maximum of 35 percent.

Normally, the marginal tax rate will be relevant for financia l decision making. The reason is th at any new cash nows wil ] be taxed at Ibat ml.lrginal rate. Beca use fin ancia l decisions usually involve new cash !lows or changes in existing ones. th is rale will teU us the ma rgi nal effect o f a decision on our lall hill.

There is one last thing to notice aboUilhe lax code as it affects corporations. It's easy 10 verify that the corporate tax bi ll is just a l1at 3S percent of la xable income if our tax­able income is morc than S 18.33 million. Also. for the many midsize corporations with taxable incomes in the range of $335,000 to SIO.OOO.OOO. the tax rate is a nat 34 per­cent. Beca use we will usua lly be talking about large corpor<ltions. you can assume that the average and ma rgina l tax rates are 35 percent un less we explicitly say otherwise.

Before mov ing on. we sho uld note that the tax rates we have discussed in this sec­tion relate to federal (a xes only. Overall [ax rates can be higher if Slale. local. and any Ol her taxes are considered .

2.4 Net Working Capital Net working capi ta l is cu rrent assels minus current liabilities. Net work.in g capital is. positive when current assets are grea ter than current liabilities. Th is mea ns the cash that will become ava ilable over the next 12 months wi ll be grcuter than Ihe cas h that must be paid out. The net working capital of the U.S. Composite Corporation is $275 million in 2010 and 5252 million in 2009.

Curreol llSSelS Current liabiliries Net working capital ($ millions) ($ millions) ($ millions)

2010 S76l S4S6 5275 2009 707 455 252

In addition to invest ing in fixed assets (i.e., capital spending). a firm call invest in net working capita l. This is called the change in nel working capital. The change in ne t work iog capilal in 2010 is the difl'crel1ce between the net work ing capital in 2010 and 2009- lbat is. S275 million - $252 million = S23 million. The cha nge in net wo rking capi tal is usually posit ive in a growing firm.

2.5 Financial Cash Flow Perhaps the most important item tha i can be extracted from financi,lI statements is the actual eash flow of the finn. An official accounting statement called the stalemelll of ('{/sh flows helps to explain the change in accounti ng cash and equivalents. which for U.S. Composile is $33 million in 2010. (See Section 2.6.) Notice in TClbie 2.1 tha i cash and equiva lents increase from $ 107 million in 2009 to $1 40 million in 2010. However. we will look at cash Oow from a different perspective: the perspective of fina nce. In finance. the value of the firm is its ability to generate fi na ncial cash flow. (We will talk more about financia l cash now in a later chapter.)

The fir st pojnl we should men ti on is that cash flow is not the sa me as net working capital. For example, increasing il)vcntory requires using cash. Because both invento­r ies and eash are current assets. this does not affect net working: capita l. In this case. an increase in inventory is associa ted wit h decreasi.ng cash flow.

Just as we established thai the va lue of a firm's assets is always equal to the com­bined value o f the liabi lities and the value o f Ihe equity. the cash !lows received fro m

Table 2.5 FinancIal Cash Flow of the U,S. Composite Corporation

Oulp!l'r:2 Fin,lnci'il S!alem(n!s and Cash Flow

U.S. COMPOSITE CORPORATION Financial Cash Flow

Cash flow ofth e firm

Operating cash flow

2010 ($ in millions)

(Earnings before interest and taxes plus depreciation minus taxes) Capital spending

(Acquisitions of fixed assets minus sales of fixed assets) Additions to net working capital

Total

Cash flow to investors in the firm Debt

(Interest ptus retirement of debt minus long·term debt finanCing) EqUity

(Dividends plus repurchase of equity minus new equity financing) Total

$238

- 173

-23

$"

$ 36

6

$ " =

----------------~--~

29

the fi rm:s asse~s (that is, its operating activities), CF(A). must equa l t he cash nows to the firm s cred Itors. eFtS). and equit y inves tors. eF(S):

CFIA) = CF(BI + CF(S)

The t'i~t s tep in determinin~ cash n ows of the firm is to fig ure out the ('(tshjlullIrulI! Up(!mIlOIlS . . As can ~. ~en. III Ta?Je 2.5. operating cash now is the cash now gener­ated by busmess actI VIties, lIlciud mg sales of goods and services. Operating cas h now (e!l~cls tax p<lym en ls, but not financing, capital spending. or changes in net working c<lpllal:

$ in mIllions

E.lrnings before interest and taxes

Depre<:jation $219

90 -71

$238

Current taxes

Operating cash flow

Another importa nt component of cash now involves c/wng{'s ill fixed assl'ls. For e:.:amp;e, ":h::" l!'S, Composite sold its power systems subsidiary in 2010. it gener. ated $_5 mllll~n III cash now. T he ne l change in fixed assets equals the acquisition of fi xed ~ssets mlllUS the sales of fi xed assets. The resu lt is the cash flow used for capital spending:

Acquisition of fixed assets Sales of fixed assets

Capital spending

$198 - 25

$173 ($ I 49 + 24 == Increase in property. plant. and equipment + Increase in intangible aSSets)

PHI l Ove rview

We can also calculate capital spending simp ly as:

Capital spending = Ending net fixed assets - Beginning net fi xed assets + Depreciation

= $ 1, 11 8 - 1,035 + 90 = $173

Cash nows are also used for making investments in net working capital. In U.S. Composite Corporation in 2010, additions fO net working capital are :

Additions to net working capial $23

N ote that this $23 million is the change in net working capital we previously calculated. Total cash flows generdted by the firm 's assets are then equal to :

Operating Glsh now Capital spending

Additions to net working Glpical

Total cash flow of the firm

$21B

- 173

- 23

$ 42

T he total outgoing cash flow of the firm can be separated int? cash no~ paid to creditors and cash now paid to slockholders. Tt.e cash flow paId to. credlt~rs rep­resents a regroupi ng of the data iT) Table 2.5 and an expliCit recordmg of mterest expense. Creditors are paid aD amount general~y r:eferred to. as d~bt serl'ice. Debt ser­vicc is interest payments plus repayments of pnnclpal (that IS, re ti rement of.de.bt).

An important source of cash now is the sale o f new debt. U:S: C~mPOslle s long­term debt increased by $ 13 ilu \1ion (the difference between $86 Imlhon III new.debt and $73 million in retirement of old debt). s Thus. an increase in long-ten:n debt IS the net effect of new borrowing and repayment of maturing obligations plus mterest expense:

Cash Flow Paid to Cr-editol"S ($ in millions)

Interest $ 49

Retirement of debt 73

Debt service 122

Proceeds from long-term debt sates - 86 Total $ 36

Cash flow paid to creditors can also be calculated as:

Cash flow paid to creditors = Interest paid - Net new borrowing = Interest paid - (Ending long-term debt

- Beginning long-term debt) = $49 - (471 - 458) = $36

' New deb! and 11K retirement of old debt nre usuaH~ found in Ihe "notl:s" 10 the balance shec-I.

Chapter 2 Fjn a l\cj~1 SUltemems and Cash FJ.ow " Cash now of the firm also is paid to thestockhoiders. It is the net effect o f paying divi­

dends plus repurchasing outstanding shares of stock and issuing new shares of stock:

Cash Flow to Stockholders ($ in millions)

Dividends

Repurchase of stock

Cash to Stockholders

Proceeds from new stock Issue

Total

In general. cash flow to stockholders can be determined as:

$43

6 4.

- 43

$ 6

Cash flow 10 stockholders = Dividends paid - Net new equity raised = Dividends paid - (Stock sold

- Stock repurchased)

To determine stock sold, fi rst not ice that the common stock and capital surplus accounts went up by a combined S23 + 20 = $43 , which implies tbat the company sold $43 millio n worth o f stock. Second , treasury stock went up by $6, indicating that the company bougbt back $6 million worth of Siock. Net new equity is thus $43 - 6 = $37. Dividends paid were $43 million. so the cash now to stockholders was:

Casb now to siockhoiders = $43 - (43 - 6) = $,6,

which is what we previously calculated . Some important observations can be drawn from ou r discussion of cash now:

[. Several types of cash now are relevant to understanding the financia l situat ion of the firm. OpenniDg cash flow, derUled as earnings before interesl p lus depreciation minus taxes, measures the cash generaled from operations not counting capital spending or working capital requirements. It is usuaJly positive: a firm is in Irouble if operating cash flm\' is negative for a long lime because the firm is not generating enough cash to pay operating costs. Total cash flow of tbe film includes adjust­ments for capital spending and additions to net working capital . It will frequently be negative, When a fi rm is growing at a rapid rate, spending o n inventory and fi xed assets can be higher than operating cash flow.

2. Net income is not cash now. The net income of the U.S. Composite Corporation in 2010 was $86 million,' whereas cash now was 542 million . The two numbers are not usually the same. In determining the economic and financial coodition of a firm, cash flow is more revealing.

A firm 's tot<l l ~sh flow sometimes goes by a different name, free cash flol\'. Of course, there is no such thing as "free" cash (we wish!), In stead, the name refers to cash that the firm is free to distribute to creditors and stockholders because it is not needed for working capital o r fi xed asset investments. We will stick with "tota1 cash now of the firm " as our label for this important concept because, in practice, there is some variation in exactly how free cash flow is computed. Nonetheless., whenever you hear tbe phrase "free cash flow," you should understand that what is being discussed is cash now from assets o r something quite similar.

32 PUt I Ovc:rview

2.6 The Accounting Statement of Cash Flows As previously mentioned. there is an official acco unting statement called the s/aremel1f of clIslljlows. This stalemenl helps explain the change in accounting cash. which for U.S. Composite is $33 million in 2010. It is very useful in underslanding financial cash now,

The fi rst step in determining the change in cash is to ligure out cash now from operating activi ties. This is the cash flow that results from the fi rm's normal activities in producing and selling goods aod services. The second step is to make a n adjustment for cash flow from investing acliviries. The final step is to make an adjustment for cash now from fi nancing activities. Financing activities are the nel payments to creditors and owners (exclud ing interest expense) made during the year.

The three components of the statement o f cash flows are determined next.

Cash Flow from Operating Activities To calculate cash flow from operating activities we start with net income. Nel income ca n be found on the income statement and is equal to $86 million. We now need 10 add back noncash expenses a nd adjust for changes in current assets and liabilities (other than cash and notes payable). The result is casb now from operating activities. Notes payable wi ll be included in the fina ncing activities section.

U.S. COMPOSITE CORPORATION Cash Flow from Operating Activities

2010 ($ in millions)

Net income $ 86

Depreciation 90

Deferred taxes 13 Change in assets and liabilities

Accounts receivable - 24 Inventories

Accounts payable

Accrued expense

Other

" " 18

-8 Cash flow from operating activities $202

Cash Flow from Investing Activities Cash flow from investing activities involves changes in capital assets: acquisition of fixed assets and sales of fixed assets (i.e., net capital expenditures). The result for U. S. Composite is shown here:

U.S. COMPOSITE CORPORATION Cash Flow from Investing Activities

2010 ($ in millions)

Acquisition of fixed assets

Sales of fixed assets

Cash flow from In .... esting acti .... ities

- $198

25 - $ 173

Table 2.6 Statement of Consolidated Cash Flows of the U.S. Compos ite Corporation

Chapter 1 Financial SI:llerncnlS .md Cash Flow

Cash Flow from Financing Activities Cash nows to and from credilOrs a Dd owneTS inc lude changes in eq uity and debt:

U .S. COMPOSITE CORPORATION Cash Flow from FinancingActivities

2010 ($ in millions)

Retirement of long-term debt

Proceeds from long-term debt sales Cha~ in notes payable Dividends

Repurchase of stock Proceeds from new stock issue

Cash now from financing activities

- $73

86 - 3

- 43 - 6 43

$ 4

The statemen t of cash nows is tbe addition of cash flows from operations. cash flows ~rom invest ing activities. and cash nows from financing activities. and is pro­duced In Table 2.6. When we add all the cash flows togetber, we get the change in cash on the balance sheet of $33 million.

U.S. COMPOSITE CORPORATION State m ent of Cash Flows

2010

Operations Net income Depreciation Deferred taxes

($ in millions)

Changes in usets and liabilities Accounts receivable Inventories

Accounts payable Accrued expenses Other

Total cash now (rom operations

Investing actl .... ities Acquisition of fixed assets Sales of fixed a.ssets

Total cash now from investing activities

Financing activities

Retirement of long-term debt Proceeds (rom long-term debt sales Change in notes payable Dividends

Repurchase of stock Proceeds from new stock issue

Total cash flow from financing activities Change in cash (on the balance sheet)

$ 86 90 13

- 24

" 16 18

- 8 $202

- $198

25 - $173

- $ 73

86 - 3

- 43 - 6 43

$ 4 $33

Pan I Overview

There is a close relationship between Ihe offic ial accounting statement called the statement of cash flows aod the totaJ cash now of the firm used in finance. Going back to the previous section, you should note a slight conceptual problem here. Interest paid should really go under financing ac tivities, but unfort unately that is not how the accounting is handled. The reason is tbat inieresl is deductcd as an expense when net income is computed. As a consequence, a primary difference between the accounting cash now and the financial cash flow of the firm (see Table 2.5) is interest expense.

2.7 Cash Flow Management One of the reasons why casb now a nalysis is popular is the difficulty in man ipulating, or spinning, <.:ash flows. GAAP accounting principles allow for significant subjective decisions to be made regarding roany key areas. The use of cash flow as a metric to evaluate a company comes from the idea th at there is less subjectivity involved, and , therefore, il is harder to spin Ihe numbers. BUI severa l Teccnl ex-a mples have shown that companies can still fmd ways to d o il.

For example, in 2007, rental car company Avis' Budget Group was forced to revise its first quarter 2007 operating cash flow by more than 545 million. The company had improperly classified the cash flow as an operating cash flow ra ther than an investing cash flow. This maneuver had the effect of decreasing investing cash fl ows and increas­ing operating cash flows by the same amount. In August 2007, Vail ResoflS faced a similar problem when it was forced to restate cash flows resulting from its real estate investments as investment cash flow ralher than operaling cash flow.

Tyco used several ploys to alter cash flows. For example, the company purchased more than $800 million of customer security alarm accounts from dealers. The cash flo .... 'S

from these transactions were reponed in the financing activity section of the accounl­ing statement of casb flows. When Tyco received paymenJs from customers. the cash inflows were reported as operating cash flO ..... '$. Ano ther method used by T yeo was to have acquired companies prepay operating expenses. In Oloor words, the company acquired by Tyco ,",,'Quid pay vendors for items not yet received . In one case, the paymenJs to taled more than $50 million. When the acquired company was consolidated with Tyco. the prepayments reduced Tyco's cash outflows, thus increasing the operati ng cash flows.

O ynegy. the energy giant, was accused of engagjng in a number of complex " round­trip trades."The round-trip trades essentially involved the sale of nalural resources to a counte rparty, with the repu rchase o f the resources from the same party a t the sa me price. In essence, Oynegy would sell an asset for SIOO, and immediately repurchase it from the buyer for 5100. The problem arose with the treatment or the cash flows from the sale. Dynegy treated the cash from the sale of the asset as an operating cash flow, but classified the repurchase as an invest ing cash outflow. The total cash flows of the contracts traded by Dynegy in these round-trip trades totaled $300 million.

Adelphia Communicatio ns was another company tha t apparently manipulated cash fl ows. ]n Adelphia's case., the company capitalized the labor required to install cable. In other words, the company classified this labor expense as a fi xed asset. While this prac­tice is fairly common in the telecommunications ind ustry. Adelphia capitalized a higher percentage of labor than is common. The effect of this classification was that the labor was treated as an investment cash flow, which increased tbe operating cash flow.

In each of these examples, the companies were trying to boost operating cash fl ows by shifting cash Oows to a different heading. The important thing to notice is Ihat these movements don't a ffect the total cash flow of the firm, which is why we recom· mend focusing 00 this number, not just operating cash flow.

Sununary and Conclusions

Concept Questions

Questions and Problems

connect BASIC (Queillonil - IO)

Chapter 2 Fiuancial SIMrnJ~nIS and Cash Flow

Besidcs introducing you tocorpor.IIC accountin g, Ihe purpose of this chapter has been 10 leach you how to determine cash flow from the accouTHing statemems of ,1 typical company.

t. Cll~h fl ow is gener.ned by the firm and paid to cred itors and shareholders. It ca n be classi fi ed as: n. Cash flow from operations. b. Cash now from changes in fixed assets. c. Cash flow from changes in working capilal.

2. Calculalions of cash flow lire not difficult . but they require ca re and particular attention to dcla.il in properly accounting. for noncash expenses such as depreciation and deferred taxes. It is especially impOI1 :uH that you do not con fuse cash flow wilh changes in net working capital and net income.

I. Liquidity True or false: All assets are liquid at SOllle p(ice. Explain .

2. Accounting and Cash Flows Why mighl the revenue and cost figures shown on a standard income st<\temenl not represent the actual cash inllows and ou tflows that occurred during a period?

3. Accounting Statement of Cash Flows Looking at Ihe accounting statement of cash flows, what docs the bottom line number mean? How useful is this Dumber for ana­lyzing a company?

4. Cash Flows How do lil)ancial cash flows and the accounting statement of cash OOW$ ditTer? Which is more useful for analyz.ing a company?

5. Book Values n,'rsus Market Values Under standard accounling rules. it is possible for a company's liabilities 10 exceed it ~ assets. Whcn this occu rs. Ihe owoers ' equity is negative. Can lhis bappen wilh market values? Why or why not?

6. Cash Flow from Assets Why is it nOI necessarily bad fo r the cash flo w from assets to be ocgativc for a pa rticular period?

7. Operating Ca..'ih Flow Why is it not necessarily bad for tbe operatlllg cash lIo .... to be negat ive for a pa rt icular period?

8. Net Worldng Capital and Capital SI.ending Could a comp..1.IlY's clwnge in net work­iog capilal be nega tive in a given year? (/lillt: Yes.) Explai n how this might come aboul. What aboul net capiw1 spending?

9. Cash Flow to Stockholders and Creditors Could a company's cash flow to stock­holders be negative in a given year? (H im : Yes.) Explain how this might come about. What about cash flow to creditors?

10. Firm Values Referring back to the D. R. Horton example at the beginning oflhechap­ter. nOlc that we sugge~!ed lhat D. R. Horton's stock holders probably didn't suffer as a result of the reported loss. What do you think was the basis for our conclusion?

,

l. Building a Ralance Sheet Culligan. Inc .. has current assets of $5.300. nCI fixed assets of 526,000, current li.abilitie·s of $3.900, and long-term debl of 514,200. What is the vallie of the shareholders' equity account for Ihis firm? 1-1 0\ .... much is net work­ing capital?

2. Building an Income S tatement Ragsdale. Inc .. has sales of S493,000. costs of 5210,000, depreciation expense of $35.000, interest expense of 5 19,000, and a tax mte of 35 percent. What is the net income for the firm? Suppose the company paid out 550.000 in cash dividends. What is the addition to retained earnings?

3. Market Va lues and Book Values Kl ingon Cnliscn,. Inc .. purchased new cloilk ­ing machi nery three years ago for 59.5 million. The machinery can be sold to the Romulans !Od ay for 56.3 million. Klingon's current ba.lance sheet shows net fixed :lSSets of 55 million. current li;Jbiiilics of 52.1 million. and net working capital of $800.000. If all tbe current assets were liquidated today. the eOl1lp;J ny would receive S2.8 million cash. Whlll is the book value of Klingon's assets today? What is the market "alue?

4. Calculating Taxes The Herrer:! Co. had 5246.000 in tax;lblc income. Using the rates from Table 2.3 in Ihechapter. calculate the compilny's income taxes. Whilt is the aver­age tax rate? What is the marginal lax rate?

5. CalcuJaling OCF Ranney. Inc .. has sales of 514.900. cOSts of 55.800. depreciation expense of SI.300. and interest expense of 5780. If the tax rme is40 percent , what is the operating cash now. o r OCF?

6. Calculating Net Ca pital Spending Gordon Driving School's 2009 balance sheet showed net fixed assets of 51.65 million. and the 2010 balance sheet showed net fixed asscls of $ 1.73 mil lion. Thecompany's 2010 income slatement sJlOwed a deprecialion expense of S284.000. \\'ha t was Gordon's net capital spending for 201Q?

7. Ruilding a Balance Sheet The following table presents the long-term liabilities and stockholders' equity of Information Control Corp, one year ago:

8.

9.

Long-term debt

Preferred stock

Common stock ($1 par 'I1lue)

Accumulated fet1.ined urnings

Capital surplus

572.000.000

9.000.000

20.000.000

97.000.000

"').000.000

During the past year. hlformation Control issued 10 million shares of new stock :It a total price of 543 million. and issued SJO million in new long-term dcbt. The company generated 59 million in net income and paid 52 million in d ividends. Con­struct the curren t balance sheet rencr:t1ng the chClnges that occurred al Informalion Control Corp. during the year.

Cash Flow to Creditors Thc 2009 balanceshcet of Aou:t's Tennis Shop. I nc .. showed long-term debt of 51.34 l1)i1lion .• md the 20 10 balance sheet showed long-Ierm debt of S 1.39 million. The 20 I 0 income sl<l!emcnt showed art interest ex.pense of S 118.000. Whll! was the fir m's cash now to credilOrs during 20107

Cllsh Flow 10 Stockholders The 2009 balance sheet of Anna's Tennis Shop. Inc .. showed S430.000 in the common siock account and S2.6 million io the addilional pllid-in surplus account. The 2010 ba lance shcel sbo\\w 5450.000 and 53 .05 million in the same two accounts. respectively. If the company p."1id out S385.000 in cash dividends during 2010, what was Ihe cash now to stockholders for the year?

10. Calculating Cash flows Gh'en the information fo r Anna's Tennis Shop. Inc .. in the prc\'ious IWO problems.. suppose you also know that the firm 's net C'dpital spending ror 20 10 was S875.000 and that the firm reduced it5 net working capilal investment by S69.000. What was the firm's 20 I 0 opera ting cash flow, or OCF?

INTERME01ATE (OuelUonl 11-24)

Chnpll'r 2 Financial Slalcmen($ and Cash Flow 37

II . Cash Flows Ritter Corporation's account;Jots prepared the following Jinanci;d Sl;l!ements for yeaN!nd 20\0:

12.

11 _ Explain the-change in clIsh during 20 10. b. Determine Ihe change in net working capi tal in 2010. e. Determine the cash now generated by the finn's assets during 2010.

RITTER CORPORATION Incom e Sta t ement

2010

Revenue

Expenses

Depreciation

Net income

Dividends

RITTER CORPORATION Balance Sheets De ce m ber 31

2010 Assets

Cuh • SO Other current <lsseu ISS Net fixed assets 3<0

Toul unu $5<f5

liabilities and Equicy

Accounts payab~ , 85

long-term debt I3S Stockholders' equity l2S

Total liabilities and equity ,5<5

.. 00 <OS

90

$105

$15

2009

, JS

'<0 200

5"'65

'" 105 265

$465

Financial Cash Flows The Stanci l Corporation provided the following current information:

Proceeds 'from long-cerm borrowing

Proceeds from the sale of common stock

Purchases of fixed assets Purchases of Inventories

Payment of dividends

$19.000

3.000 15.000

1.500

19.500

Determine the cash flows from the firm and the cash tlows to in\'estors of the finn.

ParI I O"l'rvic\\'

13. Building an Income S tatemenl During the year. the Scnbet Discount Tire Compa ny had gross sales of $1.2 million . The firm's COSt of goods sold and seJliug e .... pcnscs were S450.000 and S225.000. rcs)X."Clh'cly. Scn bct a lso had notes payable o f S900.OOO. These notes carried an interest rate of9 percent. Depredation was $ 110.000. Scnbct's tax n ile was 35 percent. a. What was Scnbc(s net income? b. What was Senbct's openll;ng c;lsh fl ow?

14. CaJculaling Total Casb Flows Schwcrt Corp. shows tbe following info nnation 00 its 2010 income statement: sales :: S I67.000; costs:: 591.000: olherexpenses :: $5.400: depreciation expense :: S8.000: interest e .... pcnsc :: S II.(X)(): taxes = $18.060: divi­dends :: $9.500. In addition. you're lo ld that the firm issued S7.250 in new eq ui ty during 2010 aud redeemed S7.100 in outstanding long-term debt. a. " 'hat is the 2010 oper.ttingcash fl ow? b. What is the 2010 cash flow to credito rs? c. What is the 2010 cash flow to stockholders? d. If net lixcd assets increased by $22.400 during tJle yeur. what was the addition 10

net working capital (NWC)?

IS. Using Income Statements Given the fo llowing info rmation for O' Hara J\'larine Co. , clIJcu latc th t: depreciation expense: suks - $43,000; C(;Ists ... $27.500: addition 10

rctaioed ea rnings:: S5 ,300; dividends paid ., $1.530: interest expense = $1.900; tax rate = 35 pcn.:ent.

16. Prtparing a Balance S heet Prepare a 2010 balance sheet for Jarrow Corp. based on Ihe following information: cash = $183.(X)(): pillelllS and (.:opyright s = S695.000: accounts paya ble = 5465,000; accounts receiv'abk "" S 138,000; tangible net fL>::ed asselS = 53,200.000; inventory:: $297.(X)(): notes payable "" SI45.000: accumulated retained earnings = SI.960.000: long-ternl debt ,. S I.550.000.

17. Residual Oaims Huang. Inc .. is obligated to pay its credjlo rs 59.700 vcry soon. a. What is the market value of the shareholders' equ ity if assets have a ma rket val ue

of SIO.500? b. What if assets equal S6,800'!

18. Margioal n~rsus A"eragc Tax Ra te!l (Refer to Table 2.3.) Corporation Growth has S78.(X)() in ta;table income, and Corporation Income has S7.800.000 in taxable income. a. What is the tax bill for each firm? b. Suppose both fi rms have identified a new projC'Ct th"t will increase taxable income

by $ 10.000. How much in additiona l t3XCS will each firm pay? Why is this amount Ihe same'!

19. Net Incomc and OCF During 2010. R.1i ncs Umbrella Corp. had sales of S740.000. Cost of goods sold, administ rativc and sell ing eltpcnses, and depreciati.on expenses wcre S61O,000. $ 105.000. ,md SI40.000. respect ively. In addit iol.l. the company had an inlcrest cxpense of $70.000 lind i l ta.>:: ra te of 35 percent. (Ignore any tax loss car· ryback or C'.lrryforward provisions.) a. What is Raines 's net income fo r 20107 b. What is its operating cash now? e. Explain your results in (a) and (b).

20. Accounting Values "ersus Cash .' Iows In Problcm 19. suppose Ra ines Umbrella Coq ). pllid out 530.000 in cash dividends. Is this possible? If spending on net fL-..;ed assets ~lI1d net working capital was 7.ero. and if no new stock was issued during Ihe year, \\hat was the change in (he firm 's long-term debt account?

21. Calculating Cash Flows Cusic Industries had the following operating results fo r 2010: saJes = SI5.300: cost of goods sold = $10.900: depreciation expense :: S2. 100; interest expense = S520; di\'idends pa id '" 5500. At the beginn ing of tbe year. net

Chapll'r 2 Financi:1l Stl!.lemi:l1ls and Cash Flow 39

n .

fi xed assets were S I1.800. current assets were $3.400. and current liabilities were 51.900. At the end of the yeOl r. net fixed assets \\-"erC $12.900. curnnt assets were S3.95O. a nd curren t liabili ties were S1.95O. The tax Tate fo r 2010 \\laS 40 percen t. H. What is net income for 20 I O? b. What is the oper'dting cash flow for 20 I O? c. Wha t is thc cash fl ow from assets fo r 20ID? Is Ihis possible? Explain. d. If no new debt WllS issued during tbe year. what is Ihe cash flow to creditors'? What

;s the cash flow to stockholders? Explain and interpret the posilhe and negati\'e signs of your answers io (a) through (d).

Calculating Cash Flows Consider the following abbreviated financial statements for Weston Enterprises:

WESTON ENTERPRISES WESTON ENTERPRISES 2010 Income Statement 2009 and 20 I 0 Partial Balance Sheets

Assets liabilities iU1d Owners' Eq uity Sales $10.320

2009

Cur,..nt assets , 780

Net fixed users 3.480

2010 2009 2010 COSts 4.980 , ... Curnnt li.abllitlM $ 118 • 348 Depreciation 960

' .080 long-term debt 1.800 2. ... Interest paid 259

a. What is owners' eq uity fo r 2009 and 20101 h. What is the change in oct work ing capital fo r 20 I O? c. In 2010. Weston Enterprises purchased S1.800 in new fi.-..;ed asset s. Ho ..... much in

fixed assets d id Weston Enterprises sell'? What is the cash now from assets for the year? (The tax rate is 35 percellt.)

d. During 20 10. Weston Enterprises raised S360 in new long-term debt. How much long-ternl debt must WeSlon EllIerprises have paid all' during the yea r'.' \\'hat is thc cash flow to creditors?

Use the following info rmat ion lor Ingersoll. Inc .. fo r Problems 23 and 24 (assume the tax rate is 34 percent):

2009 2010

S,IK $ 5.223 $ ' .606 Depre<: inion 750 751

COSt of goods sold 1,797 2,040

Other expenses .,. 356

tn terest lSO 402 C..h 2.739 2.802

Accounu receivable 3,626 4.0SS

Short-term noteS p3Y'1b1e 529 '" l ong·term debe: 9. t 73 10.702

Net fn<ed 3SSets 21,970 23.5 IS

Accounts ~Y'1ble 2.Sn 2.790

Inventory 6.+47 6,625

D iVIdends 6J7 701

4\1

CHALLENGE (QuesUons 25-27)

23. Financial Statements Dmw up:tn income statement and txllance sheet for this COIn­

pany for 2009 and 2010.

24. Calcul:lting Cash Flow For 2010. c:tlculate the cash Ilow from assets. C'ash ilow (0

creditors. lind cash flow to stockholders.

25. Cash F1o .... -s You are researching Time Manufacturing and have found the following accounting statement of cash flows for the most n"Ccot year. You also know that the compa ny paid S82 millioo in current taxes and had an interest expense of 543 mil­lion. Use the accounting statemen t of cHsh flows to construct the linancial statement of cash nowS.

26.

Operations

Net Income

Depreciation

Defer'Ted taxel

TIME MANUFACTURING Statement of Cash Flows

($ In millions)

Changes In assets and liabilities

Accounu r«~lvable

Inventories

Accounu payable

Accl'\.led expenses

Other

Total cash flow from operations

Investing activities

Acquisition of fixed assets

Sale of fixt!d ;useu

Total cash flow (rom investing activities

Financing activities

Reti rement of long-term debt

Proceeds from Io.-.g·term debt ules

Change in notes payable

Dividends

Repurchase of stock

Proceeds from new stock issue Total cash now from financing activities

Change In cash (on balance sheet)

$I" 7. "

-IS I. 14

- 7 2

$250 =

- $ 118 ,. -$129 =

-$135

97 , -12 - II

37

-$ 79

$12

Net fixed Assets and Depredation On the balance sheet. the net li;-.;ed assets (N FA) account is equal 10 the gross lixed assets (FA) a\.'Couni . which records the acquisi­tion cost of fi.'(ed assets. minus the accumulated depreciation (AD) account. which records Ihe total depreciation taken by the firm against its lixcd assets.. Using the fac t that NFA = FA - AD. show that the e1tprcssion given in we chapter for net capital spending. NFA....,. - NF.I\ .... + D (where D is the depreciation e.xpcnS( during the year). is equivalent 10 FAted - FAlooi•

S&P Problems

STANDARD & POOR'S

Ch9pl~ 2 Fin:lndal Statcrn<:n\s~md Cash .. 10w

17. Tax Rates Refer to the corpor.tte margina! tax rate intonnalion in Table 2.3. 3. Why do you th.ink the margi nal tu rate jumps up from 34 percent to 39 percent lit

a taxable income of SIOO.OOI. and then fal ls back to a 3-1 percent marginal ratc :It a taxable income of S335.00I?

b. Compute the aver.lge ta.'( rale for a corpor.ltion with exact ly 5335.001 in taxable int"OlIIe. Does Ihis confinn your explanation in part (a)? What is the average tax rate for a corporation with e.'l;actly SI8.333.334? Is the same thing happening here?

c. The 39 percent and 38 percent tax rates both represent what is called a tax ·'bubble:· Suppose the govern ment wanted to 10M-r the upper threshold of lIle 39 percent marginal t:lX bracket from S335.000 to S200.000. What would the ncw 39 percen t bubble rale have to be?

www.mhhe.eom/edum arketinsight

1. Marginal and A\-erage Tas Rates Download the annual income stalements for Sharper Image (SHRP). Loolcing back at Tab!e 2.3. what is the marginal income tn.'!: rate for Sharper 1111:lge? Using the lOW I income tax and the pretax int"Ome numbers. calculate the average tax rate fo r Sharper Image. Is this number greater than 35 per­cent '? Why or why not:

2. Net Working Cllpital Find the annual balance sheets for American Elect ric Power (A EP) ilod HJ Heinz (HNZ). Calculate the net working capital lor each company. Is American Elet:trtc Power"s net working capitlll negative? If so. does Ibis indicate poten tial rtnaocial difficulty for the comp:IllY? What aboul Hcinz?

3. Pcr Share Earn ings und Dh·idcnds Find the annual income statements for Harle)· D:l\'idsoll (HOG). Hawaiian Electric Industries (HE). and Time Warner (TWX). Wbat are the earnings per share (EPS Basic fro m operations) for each of these com· panics? What arc the dividends per share for each compan)~! Why do these campa· nics pay OUI a diffefCn t por.ion of income in the form of divideods?

-f. Cash Flow Identit)' Download the annual balance sheets and incomc statements lor Landf)·s Restauran ts (LNy). Using the most recent year. calculate the cash flov. identit), for Landrys Resta urants.. E1tplain your answer.

CASH FLOWS AT WARF COMPUTERS, INC. \\larf Com pute-rs. Inc .. was founded 15 years ;tgo by Nick Warf. a computer programmer. The small initial invest ment to start the company \\'3S made by Nick and his friends. O\cr the years. this same group has supplied the limited additional investment needed by the company in the form of bpth cquity and short· and long-term debt. Rccently the com· pany has de\'eloped a virtual keyboard (VK). The VK uses sophisticated artilidal intel­ligence 'llgorilhrns th at a(low the user to spc:lk naturally and have the computer input the text. correct spelling and grammatica l errors. and format the document according to preset user guidelincs. The VK even suggests alternative phrasing and sentence struc­ture. and it provides delaiJcd stylist.ie diagnostics. Based 00 a proprietary. ycry ad\-anced softwarelhardware hybrid technology. the :.-ystern is a full generation beyond what is cur­renlly on the market. To introduce the VK. the company will req uire signifICant oUhide investmenl .

Nick has made tbe decision to seek this outside linancing in the form of new equit) investments and bank loans. laturally. new investors and the banks will require a detailed financial analysis. Your employer. Angus Jones & Partners. LLC. has asked you 10 examille

Ihe financial statements provided by Nick. Here lire the balancc shcet for the 1\\"0 mOSI recent years and the mosl recent income statemen1 :

Cur~flt assets

Cuh and equivale(lt:S

Accounts receivable

Inventories

0""' TotAl CUrTti\l assets

Fixed ass-ets

Property. plant, ~nd equipment

Len accumulued depnaciilt ion

Net property, plant, and equipment

Inu"lible useu and Others

Toul fixed useu

Total asseu

WARF COMPUTERS Balance Sheet

($ in thousands)

2010 2009

Curreot liabilltiH

$ 290 $ 251 Accounts ~ble

<S9 428 Notes payable

.11 m Accrued explUlSes

59 '0 Total current

$ 1.219 $1 ,1 S04 llibilities

Long-term llibilitles

$ 2.631 n038 Deferred lUtS

Long.term debt

'59 700 Total lOI\8-lerm liabililiM

$ 1.7n $1 ,339 Stockholders' equity

508 ". Pr.ferred stock

Common stock $ 1.290 $ 1.792

Capital surplus

Accumulated retained eamlngs

Leu treasury stock

Total equity

Total liabilitil$ and $ ) .,,99 $2,9" 6 Iha,..holde!"5' equity

2010 2009

• 262 • 245 71 ..

IS. 257

S 049 1 • '68

$ 212 $ 103 756 736

$ 968 $ 839

• 13 $ 13

" 80

'09 ... I,SS8 1,028

12' " $2.0040 SI,SJ9

$3.0499 S2,9-% = =

Nick has also provided the following information : During tJle year the corupany raised $ 11 8,000 in new long-term debt and retired S98.000 in long-term debt. The company also sold $11.000 in new stock and repurchased S40,000 in stock, The company purchilscd S786,000 in fixed assels and sold $ 139.000 in fixed assels.

Cl1apler 2 Financial Statements nnd C;lsh Flow

5,t,lu

WARF COMPUTERS Income Statement

($ In thousands)

Con of goods w Id

Stlll"l, general. and administrllti"'f expense

Oepre<:iation

Oper.tting i'ltome

Orner income

Eami"&~ before. inlereS( aod tlIxe$ (fBIT) tntereSl expen5e

freta}{ Income

Taxes

CUlTellt: $386

Dt lured: 109

Net income

Addition to retaiMd earnings

Dividends

$".8« 2.858

'" 15. $ 1.2&4

" $ 1,]]2

.5 SI .237

495

$ 7042

S 5]0

$ 2 t2

43

Angus has asked you 10 prepare the financial statement of cash nows and the account­ing statement or cash flows. He has also asked you to answer the foJlo\\'ing questions:

1. How would you describe Warf Computers ' c:lsh nows?

2. Yo'hich cash flow statement more 'H..'curately describes the cash flows :lt the company"?

3, In light or YOllr prc\·ious 'InS\\'crs, comment on Nick's expansion plans.

44

Financia l Statements Ana lysis and Financial Models

The price 01 a share of common stock in Aeroposlale, the trendy clothing retailer. closed at

about $28 on Apri l 2. 2009. At that price. Aeropostale had a price-earnings (PE) ratio of 12.7.

That is, investors were willing to pay $12.7 for every dollar in income earned by AeropostaJe.

At the same time, investors were willing to pay $6.0, $18.2, and $27.2 lor each dollar earned

by Chevron. Coca-Cola, and Google, respectively. At the other extreme was the lumber

company. Weyerhauser, which had negative earnings for the previous year, yet the stock

was priced at about $30 per share. Because il had negative earnings. the PE ratio would

have been negative, so it was not reported. At the same time, the typical stock in the S&P

500 Index of large company stocks was trading at a PE of about 12.4, or about 12.4 times

earnings, as they sayan Wall Street.

Price-to-earnings comparisons are exampl es of the use of financial rat ios. As we will see

in this chapter, there are a wide variety of financial ratios, all designed to summarize spe­

cific aspects of a firm's financial position. In addition to discussing how to analyze financial

statements and compute financial ratios, we will have quite a bit to say about who uses this

information and why.

3.1 Financial Statements Analysis In Chapter 2, we discussed some of the essent ial concepts of financial statements and cash flows. This chapter continues where o ur ea rlier d isc ussion left 01T. Our goal bere is to expand your understanding of the uses (and abuses) of financial statement information.

;\ good working knowledge of financial statement s is desirable simply because such statements, and numbers derived from those statement s. are the primary means of communicating financial information both within the firm and outside the firm. In short., much of the language of business finance is rooted in the ideas we discuss in this chapter.

Clearly, one important goal of the accountant is to report financial information to the user in a form useful fo r decision making. Iro nica lly. the information frequemly docs 001 come to the user in such a fo rm . ]n o the r wo rds., financia l statements don't come with a user's guide. This chapter is a lirst step in filli ng this gap.

Standardizing Statements One obvious thing we might want to do wilh a company's fin <l ncial statements is to compa re them to those of other, similar companies. We would immed iately have a pro blem, however. It 's almost impossible 10 direclly co mpare the finaocial statement s fo r two co mpanies because of differences 10 size.

Table 3.1

(napIer 3 Financial Statements Analysis and Finan~i;l l Models

For example.. Ford and GM a re obvio usly se rio us ri .... als in the auto market , but GM is larger, so it is difficult 10 compa re them directly. For that matler, it's difficult even to compare. financial statements fro m different poi nts in time for the same company if the company's size has changed. The size problem is compounded if we try 10 compa re GM and_say. TOyOia. If TOyOia 's financia l statements are denominated in yen , Iben we have size olld currency differences.

To start making comparisons, one o bvio us thing we might Iry to do is 10 somehow standardize tbe financial s tatements. O ne commo n and useful wa,. of doing this is to \\'ork with percentages instead of lotal do llars. The resulting financial statements a re ca lled common-size statements. We consider these next.

Common-Size Balance Sheets For easy reference, Prufrock Corporation's 2009 and 2010 balance sheets arc provided in Table 3.1. Using these. we construct com mOD-size balance sheets by expressing eaeh item as a percentage of to tal asset s. Prufrock's 2009 and 20[0 common-size balance sheets are shown in Table 3.2.

Notice that some of the tot als don't check exactly because of rounding errors. Also notice that the total change has to be zero because tbe beginning and ending numbers must add up to ]00 percent.

In this form, financial statements are relat ively easy to read and compare. For exam­ple. just looking at the two balance sheets for Prufrock, we see that current assets were 19.7 percent of total assets in 20 10, up fro m 19. 1 percent in 2009. Current liabilities

PRUFROCK CORPORATION BaJance Sheets as of December) I. 2009 and 20 I 0

($ in millions)

"'- 100. 2010

Current ;luets C,., $ .. $ •• Accounts receivable 165 188

Inventory 393 <2, Toul $ 64' S 708

Fixed a$se.u

Net plant and equipment $2.731 $2.880

Total a5seu $Un $3,588

liabilities and Owners' Equity Current liabllities

Accounu ~able $ 312 • 344 Note$ pa)'ilble '31 '"

Total $ 5-4] $ 540

l Ollg-term debt $ 531 $ 457

Owners' equity

Common stock and paid.in surplus $ 500 $ 550

Retained eamings 1,799 UH f Tow 52,299 $2.591

Total liabilities and owners' equity $3.373 5:3.588

46

Table 3.2

Pllrt I Q"crview

PRUFROCK CORPORATION Common·Size Balance Sheers December] I, 1009 and 20 I 0

"'~" 1009 2010 Chan .. CUl"I"entuseu

Cuh 2.5% 2.'" + .n< Accounts receivable ••• 5.2 + .3

1_'"'1 11.7 11.8 + .1

To'" 19. 1 19.7 + .6

fixed assets

Net pbnt Vld equipment 80.' 80.3 - .6

Total ;lSSets 100.0% 100.0% .... Liabilities and Owners' Equity

Current liabilities

Actounu pa~le 9.2% 9.6% + .• %

Notes ~ble 6 .• 5.5 - 1.3

Total 16.0 15. 1 - .. long-term debt 15.7 \2.7 - 3.0

Owners' equity

Common stock al'ld paid-in wrylus 1".8 15.3 + .5

Retained earnings 53.) 56.9 + 3.6

Tou] 681 72.2 + " .1

Totall~bil~ md owners' equity 100.0% '00.0% .... = =

declined from 16.0 percenllO 15. 1 percen t o f tOlal liabili(ies and equity over thal same lime. Simila rly. to tal equity rose from 68.1 percent of total liabilities and equity to 72.2 percent .

Overall , Prufrod (s liquidity. as measured by current assets compared to current liabililics, increased over the year. Simultaneously, Prufrock's indebtedness d iminished as a percentage of total assets. We might be tempted to cooclude thai Ihe balance sheet has grown ·'stronger."'

Common-Size Income Statements Table 3.3 describes some commonly used measures of ea rnings.. A useful way of Stan­dardizing the income statement shown in Table 3.4 is to express eaeh item as a percent­age of total sa les. as iUustrated for Prufrock in Table 3.5.

This income statement tells us what happens to each do lla r in sa les. For Prufrock, interest expense eats up $.06 1 out of every sa les do llar, a nd laxes take another S.08 1. When all is said and dOlle, $.157 of each do llar nows th rough ro the bottom line (net income), and that amount is split into S.105 retained in the business and S.052 paid out in d ividends.

These percentages a re useful in comparisons. Fo r exam ple, a relevant figure is the cost percentage. For Prufrock. $.582 of each $ 1.00 in sales goes to pay for goods sold . I! would be interesting to compute the same percentage for Prufrock's main competi­tors to see bow Prufrock stacks up in terms of cOSt con lrol.

Table 3.3 Measures of Eamlngs

Table 3.4

Qapler.) Fim:Hlcial S(atcrncntJ; Analysis and Financial Mooels 47

Investors and analy5u look closely at the Income natemeflt for clues on how well a comp:any has performed during a ~rticular year. Here are some commonly used measures of earnings (numbers in millions).

N et Income

.PS

' EBIT

The lO-Cailed bottom line, defined as total rew:nue minus total expenses. Net income for Prufrock In the latest period is $363 million. Net income reflew differences in a firm's capital structure and taxes as well as open-ting income. Interest expense and taxes are subtracted from operating income in computing net Income. Shareholders look closely at net. income because dividend payout and retained earnings are closely linked co net income.

Net income divided by the number of shares ouutanding. lt expresses net income o n a per sh:are basis. For Prufrock. the EPS = (Net Income)l{Shares outstanding) - $363/33 = $11.

Earnings before interest expense and taXes. EBIT is usually called " income from operations" on the Income statement and is income before unusual Items, discontinued operating or extraordinary icems. To calculate EBIT. operating expenses are subtracted from total operations revenues. Analysu like EBIT because It abstracu from differences in earnings from a firm 's capital structure (interest expense) and taXes. For Prufrock, EBIT is $691 million.

EBITDA Earnings before interest expense. QXes, depredation, and amortization. E8ITOA "" EBIT + depreciation and amortization. Here amortization refers to a noncash expense simil:ar to depreciation except It applies to an intangible asset (such as a ~tent), rather than a tangible asset (such as a machine).The word :amortization here does not refer to the plyment of debt. There Is no amortization in Prufroc k's income statement. For Prufrock. E8ITOA - $691 + $276 = $967 million. Ana~u like to use EBITOA because it adds back two noncash items (depredation and amortization) to EBIT and thus is a bener measure of before-u.x operating cash flow.

Sometimes these measures of e.arnlnp are preceded by the letters LTM, meaning the lut twelve months. For example, LTM EPS is the last twelve months 0( EPS :and LTM EBlTDA is the last twelve months 0( EBITOA At other times, the letters TTM are used, meaning trailing twelve months. Needless to say, LTM is the same as TIM.

PRUFROCK CORPORATION 20 I 0 Inco m e Statement

Sales 4

COst 0( ioocts sold

Deprec:ation

($ in millions)

Earnings before intereu and taXes

Interest paid

Taxable income

Taxes (3-4X)

Net income

Divi~ $121

Addition to retained earnings 2-42

$2,3 tl

1,]-44

276

$ 691

'41 • SSO

'.7 $ 363 =

Table 3.5

3.2

Go to www revtltl'S com!

flnao""sMcts

al'ld lind the ratios link 10 examine comparative

ratios for a ttuge IlUmber of companies.

Part I Overview

PRUFROCK CORPORATION Common·Size Income Statement 2010

Sales

Cost of goods sold

Depreciation

Earnings berore interest and taXes

Interest ~id

Taxable Income

Taxes (304%)

Net Income

Dividends

Addition to retained earnings

Ratio Analysis

5.2%

10.5

100.0% 58.2 11.9 29.9

6.1

23.8

8.1

15.7%

Another way of avoiding the problems involved in comparing compan ies of differenl siLes is to calculate and compare financial ratios. Such ralrOS a re ways of comparing and investigating the relatioaships between different pieces of financial infonnation. We cover some of the more commOQ ratios oexi (I here a re many o thers we don't dis­

cuss here). One problem wj,h ralios is Ihat different people and d ifferent sources rrequenlly

don't compute them in exactly the same way, and this leads to much con rusion. The specific defin itions we use here mayor may not be the same as o nes you have seen or will see elsewhere. Ir you a re using ratios as tools ror analysis, you should be carerul 10 document how you calculate each one; and, ir you are comparing your numbers 10 Ihose or another source, be sure you know how theiT numbers are computed.

We will derer much or our discussio n of how rati os are used and some problems that come IIp with using them until later in the chapter. For now, fo r cach ratio we discuss, several questions COme to lDind:

1. How is it computed?

2. What is it intended 10 measure, and why might we be interested?

3. What is the unil or measurement?

4 . What might a high or low value be telling us? How might such values be misleading?

5. How could this measure be improved?

Financial raLios are traditionally grouped into the following categories:

1. Sbor(-(enn solvency, or liquidity. rati os.

2. Long-term solvency, or financial leverage, ratios.

3. Asset management, or turnover, ratios.

4. Profitability ratios..

5. Market value ratios.

We \vill consider each or these in turn. In calculating these numbers ror Prufrock, we will use the ending balance sheet (2010) figures unless we explicitly say ot herwise.

EXAMPLE 3.1

Cbaptff J Finr.n<;ial Sllilenl<:rnS Analysis lind Financial Model~ 49

Short-Term Solvency or Liquidity Measures As the name suggests. sho rt-term solvency ratios as a group are intended 10 provide information ahout a firm's liquidity, and these ratios are sometimes ca lled liqllidil), measures. The primary concern is the firm's ability to pay ils bills over the short run wi thout undue stress. Consequently. these ratios focus on current assets and curreat liabilities.

For obvious reasons, liquidity ratios are pa rticula rly interesting to shan -term credi­tors. Beca use financial managers. are constantly work ing with banks and other short ­term lenders, an understanding of these ratios is essential.

One adva ntage of looking al current asseLS and liabi lities is tbat their book values and market values are likely to be simila r. Orten (tho ugh not always) , these assets and liabilities just don't live long enough ror the two to get seriously out of step. On the other hand . like a ny type or near·cash. current assets and liabilities c .. ln and do change fairly rapidly, so tOOay's amounts may not be a reliable guide to the future.

Current Ratio O ne o f the best-known and most widely used ratios is Ihe ClIl'l'e'"

rario. As you might guess, the current ratio is defined as:

C . Current assets urrent rallO = Current liabilities (3. 1)

Fo r Prufrock, the 20lO current ratio is:

. $708 CurreDt ratiO = $540 = 1.3 1 times

Because current assets and liabil ities are. in principle. converted to cash over the followi ng 12 months. the current ratio is a measure or short-term liquidity. The unil of measurement is either dollars or times. So, \ve could say prurrock has $1.3 1 in cur­rent asscts for cvcry S 1 in curreot liabilities.. o r we could say Prufrock has it s curren t liabi li ties covered 1.3 1 times over.

To a creditor. particularly a short-term creditor such as a supplier, the higher the current ratio, the better. To the firm. a high current ratio indicates liquidity, bUI it also !Uay indica te an inefficient use of cash aDd other short-tcrm assets. Absent some ex traordinary circumstances. we would expect to sec a current ratio or at least I; a current ratio or less than I would mean that net working capital (curren t assets less current liabilities) is negative. This would beunusual in a healtby firm, at least for most types or businesses.

The current ratio, like any ratio, is affected by va rious types or transactions. For example. suppose the firm borrows over the long term to rajse money. The short-run effect would be an increase in cash rrom the issue proceeds and an increase in lo ng­term debt. Current liabil iries would not be afTected, so the current ratio would rise.

Current Events Suppose a firm were to pay off some of its suppliers ,lind short-term creditors. What would happen to the current ratio? Suppose a firm buys rome inventory. What happens In this case! What happens if a firm sells some merchandise!

The first case is a trick question. What happens is that the CUrTent ratio moves away from I . If it is greater than I (the usual case). it will get bigger, but if it is leu than I . it will gee smaller.To see (his.suppose the firm has $4 in current assets and $2 in current Ii:!bilities for a current Id.cio of 2. If we use $1 in cash to reduce current liabilities, the new currene ratio is ($4 - 1)/($1 - I) = 3.

(continued)

Part 1 Ovt:rvicw

If we ~ene the original siwation to $2 ill current ,n$ets and $-1 In current liabilities. the (hange will

QUSt. the current rilcio to filii to 1/3 (rom In.

The st.(ood Gilse is IlOt quite iI.S tricky. Nothing happens to the current riltio because cash goes

down while inventory goes up--total currellt ilUeu are umffea:ed. In the third case. the current r.atio would usually rise because inventory is normally shown at

COst and the sale would normally be at somethi"l greater than cost (the difference is the markup).

The Increase ill either cash or receivables is therefore grener than the decrease in inventory. This

incruses cu~( asseu.and the current ratio rises.

FinaJly, note that an apparently low current ralio may oat be a bad sign for a com­pany with a large reserve of untapped borrowing power.

Quick (or Acid-Test) Ratio Inventory is often tbe least liquid current asset. It's also the ooe for which the book values are least reliable as measures of market value because the quality of the inventory isn't considered. Some of the inventory may later tum out to be damaged, obsolete, or losl.

More to the point. relatively large inventories are often a sign of short-term trouble. The lirm may have overestimated sales and overbought or overproduced as a result. In this case, Ihe firm may have a substantial portion of its liquidity tied up in slow­moving inventory.

To further evaluate liquidity, the quick, or acid-lest, Talia is computed just like the current ratio. except inventory is omitted :

. . Current assets - Inventory QUick ratiO = Current liabilities (3.2)

Notice that using cash to buy inventory does not afTC(:t the current ratio, but it reduces Ihe quick ratio. Again, the idea is that inventory is relatively illiquid compared to cash.

For Prufrock, this ratio in 2010 was:

Quick ratio S708 - 422 .

SS40 = .53 times

The quick ratio here teUs a somewhat different story than the cu rrent ratio be<:ause inventory accounts for more than half of Prufrock's current assets. To exaggerate the point, if this inventory consisted of. say, unsold nuclear power plants, then this would be a cause for concern .

To give an example or current versus quick (alios, based on recent financial state­ments, Wal-Mart and Manpower. Inc ., had current ratios of .89 and 1.45, respectively. However, Manpower carries no inventory to spea k of, whereas Wal-Mart 's cu rrent assets are virtua lly all inventory. As a result, Wal-M art's quick ratio was on ly .13, and Ma npower's was 1.37, almost tbe same as its current ratio.

Cash Ratio A very shan-term creditor might be interested in the cash ratio:

. ___ Cash Cash ratio - Current liabilities (3.3)

You cao veri fy tbat this works OUIIO be . 18 times for Prufrock .

The online Women's Business t:ent&r I'Ias

fl)(J(e InIOfmation about lirWIeIaI statements.

tatlos. and small ~e&S topics at

'«'!W.w .goy.

Chapter 3 Financial Sutemellis Analysis ~ nd Finunci~1 Models

" Long-Term Solvency 'Measures Long-lenn solvency ratios are intended to address the firm's long-run ability to meet its obligations or, more generally, its financial leverage. These ratios aIe sometimes caJledfinallcialle\'erage ratios or just lel'l'Tage ratios. We consider tbree commonly used measures a nd some variations.

Total Debt Ratio Tbe lotal debt ratio takes into account all debts of all maturities to all creditors. It can be deftned in several ways. the easiest of which is th is:

T . Total assets - Total cquity Otal debt mtlO - Total assets

$3,588 - 2,591 _ 28 . = S3,588 - . umes

(3.4)

In this case. an analyst might say that Prufrock uses 28 percent debt. ' \\'hether this is high or low or whether it even makes any difference depends on whether capital struc­ture matters. a subject we discuss ill a later chapter.

Prufrock has S.28 in debt for every 51 in assets. Therefore. there is S.72 in equity (=$1 - .28) for every S.28 in debt. With this in mind , we can dcline two useful varia­tions on the tota l debt ratio, the debt-eqllit)' ratio and the eqlliry multiplier:

Debt-equity ratio = Total debtffotal equity = $.28/S.72 = .39 times

Equity multiplier = TOlal asselSlTotal equity = SIIS.72 = 1.39 times

(3.5)

(3.6)

The fact that the equity multiplier is I plus the debl-equit}, ratio is not a coincidence:

Equity muhiptier = Total assetsITotal equity = $ 11$.72 :..: J.J9times = (Total equity + Tota l debtyrotal equity = I + lR=bt-equi IY ratio = 1.39 times

The Ihing to notice here is that given anyone of these three ratios, you can immedi­ately calculate the othe r two, so tbey a ll say exactly the same tbing.

Times Interest Earned Another common measure of long-term solvency is the limes ifllel'es/ l'Ol'lled (TIE) rmio . Once again, Ihere a re several possible (and common) definitions, but we'l] Slick with (he mostlrad itional :

Times inlerest eamed ratio = I ;t~:~t S691 .

=$141 =4.9nmes (3.7)

As the Ilame suggests, tbis ralio measures how well a company has its imerest obliga­tions covered, and it is often called the intereSI cOl'eragl' ratio. For Prufrock. the inter­est bill is covered 4.9 times over.

Cash Coverage A problem with the TIE ralio is that it is based on EBIT, which is not really a measure of cash available to pay illierest. The reason is thai depreciation

'Totat cquily here includes preferred stock. if lhere is ;in)'. An equi\<a1ent numeralor in Ihis ra lio would be (CUl'Knt tiabilities + Long-term debt).

Pur I Overview

and amortization, noncash expenses.. have been deducted out. Because interest is most dcflJlitelya cash outflow (to creditors), one way to define the cash corerage ratio is:

. EBlT + (Depreciation and amortizati on) Cash coverage rauo = Interest (3.8)

$69 1 + 276 5967 . = $1 41 - $141 = 6.9 limes

The numerator here, EBIT plus depreciat ion and amortization, ~ s o~ten ab~reviate.d EBITOA (earnings before interest, taxes. depreciation, and amortl7..atlon) . It IS a busle measure of the firm's ability to generate cash from operations. and it is frequently used as a measure o r cash flow available to meet financial obligations. .

More recently another long-term solvency measure is increasi:ngly seen in 0nancla l statement analysis and in debt covena nts. It uses EBlTOA and mterest beanng debt. Specifically, for Prufrock:

Interest bearing debt EB ITDA

5196 million +. 4.57 rniJlian = .68 limes $967 millton

Here we include nOles payable (most likely nOles payable is bank debt) and 10n:B-ter~ debt in the l1umerdtor and EBITDA in the denominator. Values below 1 on thiS rallO are considered very strong and values below 5 arc considered weak. .. HO\vever a ca~ful comparison with other comparable fir ms is necessary to properly Interpret the rallo.

Asset Management or Turnover Measures . We nex t turn our attention to tbe emciency with wbich Prufrock uses Its assets.. The measures in this section are sometimes called asset managemelll o r utilization ratius. The specific ratios we discuss can all be interpreted as measures of turnov~r. What they are intended to describe is how efficiently, or intensively, ~ firm uses lis assets to generate sales. We first look at two important current asse ts: Inventory and

receivables..

Inventory Turnover and Days' Sales in Inventory During the year, Prufrock had a cost of goods sold of $ 1,344. Inventory at the end or the year was $422. Wit h these numbers. im'entury tUrIlOI'er can be calculated as:

Cost of good s sold Inventory turnover = Inventory

$1,344 32' = $422 = . tImes

(3.9)

In a sense we sold ofT o r turned over, the ent ire inventory 3.2 times during the year. As long a; we are not ~unlling out of stock and thereby fo rgoing sa les, the higher this ratio is, the more eOiciently we are managing inventory.

Ir we know that we turned our inventory over 3.2 times during the year, we can immediately figure oul how long it took us to turn it over on average. The result is the avera ge days' soles ill iJ1\'emory:

365 days Days' sa les in inventory = Inventory turnove r

= ~~i = 114days

(3.10)

EXAMPLE 3.2

Chapter 3 Financial Stlltements Analysis and Financial Models " Tbis tells us that. roughly speaking. inventory sits 114 days on average berore it is sold . Alternatively, assuming we used (he mOst recent inventory and cost figu res, it wilJ take about 114 days to work otT our curren I inventory.

For example, in September 2007. sales of Genera l Motors (GM) pickup trucks could have used a pick.up. At that time., tbe company had a l20-day supply of the G MC Sierra and a 114-day supply of the Chevrolet Silverado. These numbers mean that at the then-current rale of sa les., it would take GM 120 days to deplete the avail­able supply of Sierras whereas a 6O-day supply is considered normal in the industry. Of course, the days in inventory are lower for better-selling models, and. fort unately for GM . its crossover vehicles were a hit. The company had only a 22-day supply or Buick Enclaves and a 32-day supply of GMC Acadias.

Receivables Turnover and Days' Sales in Receivables Our im-enlOry measures give some indication of how fast we can sell products. We now look at how fast we collect o n those sa les. The receivables /Urllover is defined in the same way as invento ry turnover:

Receivables turnover = Aecoun~: I!sceivable _$2,3 11_ 1'3' - $188 - _. times

(3.11)

Loosely spea king. \ve collected our outstanding cred it accouotS and lent the money again 12.3 times during the year.~

This ratio makes more sense if we conven it to days., so the days' ${lIes ill receimbleJ is:

D ' at· . b 365 days ays s es 10 recelVa les = Receivables turnover

= 365 = 30 days 12.3

(3. 12)

Therefore, on average., we collect on our cred it sales in 30 days. For obvious reasons., this ratio is frequently caUed the average collectioll period (ACP). Also note that if we are using the most recent figures. we can also say Ibat we have 30 days' worth of sales currently uncollected.

Payables Turnover Her~ is a variat ion on the receivables collection period. How long. on aver· age, does it take for Prufrock Corporation to pay its bill s ~ To answtr. we need to calculate the a("counts payable turnover rat~ using COst of goods sold. We willl.$$ume th<It Prufrock purchases

~rythlng on credit. The con of goods sold is $1,3+1. and acco unts payable are $344. The tumover is therefore

$1,344/$344 =; 3.9 times. So. payables turned over about every 365/3.9 = 94 days. On average. then. Prufrock takes 94 days to pay. As a potential creditor. we might take note of this faCt.

'He~ we have imJlt icitly assumed that all sales are credit salcs. lf they we~ not. we would simply use total credit salc-s in lhe5e cakul:uions. not total sales.

EXAMPLE 3.3

PII1 I Overview

To tal Asset Turnover Moving away from specific accounts like inventory or receiv­ables, we can co nsider an important "big picture" ratio, the total asset IImuwer rat io. As the name suggests. total asset turnover is:

Total asset turnover z:: Tot~f~e;sets $2,311 64 .

= S3.588 =. times

(3.13)

In other words, fo r e"ery dollar in assels, we geoeratw $.64 in sa les.

More TlImover Suppose you find that a parJcolar (ornp3ny gtncrues $.40 in annual SAles for

wvery donar in total assets. How often does this Compilny tum over itS toa.1 asseu! The total uset turnoyer here is AO times per year. It takes 11.40 = 2.S years to turn usets over

completely,

Profitability Measures The three types of measures we discuss in this section a re probably the best-known and most widely used of all financial ratios. In o ne fonn or another. they are intended 10 measure how efficiently the firm uses it s assets and how efficiently the firm maoages

its operations.

Profit Margin Companies pay a greal deal of aneOlion to their profit murgil1:

. Net income Profit ma rg.m = Sa les

$363 -= $2 .311 = 15,7%

(3.14)

This te ll s us that Prufrock. in a n accounting sense, generates a linle less than 16 cents in net inco me for every do llar in sa les.

EBITOA Margin Another commonly used measure of profit.'\bility is Ibe EBITDA margin . As menlioned, EBITDA is a measure o f before-tax operating cash now. It adds back noncash expenses and does not include laxes or interest expense. As a consequence., EBITDA margin looks more directly at operating cash flows tban does net income and does not include Ibe effect of capital structure or taxes. For Prufrock, EBITDA margin is:

EBITDA S967 million Sales - S2,3 11 million

41.8%

AU other things being equal, a relatively high margin is obviously desirable. This situ· ation corresponds to low expense ratios relative to sa les. However, we hasten to add that 01 her things are often nOI equal.

For example. lowering our sales price will usually increase unit volume but wiU nor­mally cause margins 10 shrink. Tota l profit (or, more importantly. operating cash now) may go up or down, so the fact that margins are smaller isn't necessa rily bad . After all, iso'l it possible that. as the saying goes, "Our prices a re so low Ihat we lose money on everything we sell , but we make it up in volume"?'

INo. i("s 00(.

Cha.pter 3 fio3neiaJ SUteml'fl tS Analysis and Financial Modth 55

Margins are very difTerent for d ifferent industries. Grocery sto res have a nmori­au sty low profit margin , generally around 2 percent. In contrast , the profit margin for the pharmaceutica l industry is about 18 percent. So, for example, it is nol surpris­ing that. recent profit margins fo r Albertson's and Pfizer were about 1.2 percent a nd 15.6 percent. respectively.

Return on Assets Retllrn on assets (ROA) is a measure of profil per doUar of assets. It ca n be defined severa l ways, 4 bUllhe mos t common is;

N . Return o n assets = et Income

To tal assets _ S363_ 0

- $3,588 - IO.12Yn

(3.15)

Return on Equity Return 011 equity (RO E) is a measure of how the stockholders fared during the year. Beca use benefiting shareholders is o ur goal, ROE is. in a n accounting scnse. the true bottom-line measure o f performance. ROE is usually measured as:

Return 0 11 equilY = Net incol:!le To tal eqUIty

_ 5363_ 0 - S2,591 - 14 Yn

(3.16)

Therefo re, for every dollar in equity, Prufrock generated 14 cents in profit ; but, again, this is correct only in accounting terms.

Because ROA and ROE are such commo nly cited numbers, we stress that it is importa nt to remember Ihey are accounting rates of return. For thi s reason , Ihese measures should properly be called relll". on book asscu' and Teturn on bock eqllilY. In addition, ROE is sometimes cal led Tellim on net \fOTlh. Whalever iI's called, il wo uld be inappropriate to compare the result to, for e:a:ample, an interest rate observed in the fina ncial markets.

The fact that RO E exceeds ROA rcOcclS Pnlfrock 's use of financial leverage. We will exa mine the relationship between these two measures in the next section .

Market Value Measures Our final group o f measures is based, in part, on information not necessarily con­tained in financial statcments- the ma rket price per share of the stock , Obviously, Ihese measures can be calculated directly only for publicly lraded companies.

We assume that Prufrock has 33 million sbares outstanding and tbe stock sold fo r S88 per share at the end of Ihe year, If we recall that Prufrock 's oet income was $363 mill ion. then we can ~alculate that its earnings pe r share were :

PS Net income $363 E = Shares o utsta nding - 33 = $11 (3.17)

'For example. we might want a relurn on am l.$ measure thai i5 ne\JlraJ wit h rcspccltocapil31 su ucture (i flte~( expense) and lales. Such a measure for P(urrock ",,-ouid be:

EBIT S691 TOlal a.ssel.$ .. 53,588 .. t9.3Y.

This measure has a very natural interpretation. If 19.3 percenl eJl:c.eeds Prurrock's borrowina rale, Prufrock .... iII earn more money on its investments Ihan il will payout 10 in cn:dhors. The surplus will be a.vailable 10 prurrocks shareholders after adjusting fo r taxe$.

56 Part 1 O\'~niew

Price-Earnings Ratio The first of our markcl value measures, the price-e(lrIlings or PE ralio (or muhiple), is defined as:

. Price per share PE rallO = ",=~. ::::=::":1::'::: Earm ngs per share

SS8 8' = ill = tlmc.s (3.18)

In Ibe vernacul ar. we would say Ihal Prufrock shares sell for eighllimes earoings. or we might say that Prurrock shares have. or "carry,'- a PE multiple of 8.

Because the PE ralio measures how much investors are willing \ 0 pay per dollar of current earnings, higher PEs are oflen taken to mean that Jhc firm has significam prospects for futu re growth. or course. if a finn had no o r almost no earnings. its PE would probably be quite large; so, as always, care is needed in interpreting thi s ralio.

Market-ta-Book Ratio A second commonly quoted measure is the murkeHo-book ratio:

. Market va lue per share Market-to·bool\: rallO = Book value per sha re

$88 $88 . $2,59 1/33 =- $78 .5 = I.! 2 urnes

(3.19)

Notice that book value per share is to tAl equity (not just common stock) divided by the number of shares outstanding.

Book value per sha re is ao accounting number that rcnects historical costs. In a loose sense. the market-to-book ratio therefore compares the market va lue of the firm's invest ments to their cost. A value less than I could mean that the firm has not been successful overall in creating value for its stockholders.

Market Capitalization The market capitalization of a public firm is equal to the firm 's stock market price per share multiplied by the number of shares out standing. For Prufrock, this is:

Price per share x Shares o Ulstanding = $88 x 33 million = S2,904 million

This is a useful number for potential buyers of Prufrock. A prospective buyer of aU of the outstand ing shares of Prurrock (in a merger or acquisition) would need to come up wi th at least S2 ,904 million plus a premium.

Enterprise Value Enterprise value is a measure of firm value that is very closely related to market capitalization. Inslead of focusing on only the market value of out· standing shares of stock, it measures !.he market value of DlllStanding shares of stock plus the market value of outstanding interest bearing debt Jess cash on hand . We know the market capi talization o f Prufrock but we do not know the market va lue of its outstanding interest bearing debt. III this situation, the common practice is 10 use the book va lue of outstandi ng interest bearing debt less cash on hand as an approxima­tion . For Prufrock , enterprise value is (in millions):

EV = Market capitalization + Markel value of in terest bearing debt - cash = $2,904 + ($196 + 457) - $98 = $3.459 million (3.20)

Chapter 3 Finan .. :;"l Sta~ C"ments Analysis and FiTl3nciaJ Models

" The purpose of th~ EV measure is to better estimate how much it would take to buy all Of. the o.utstandlllg stock of a firm and also to payoff the debt. The adjustment for cash IS to recognize t.h~ t if we were a buyer the cilsh could be used immediately to buy back debt or pay a dIVId end.

Ent~rprise V~lue Multiples Financial analysts use valuation multiples based upon a finn s enterpnse value when the goal is to estimate the value of [he firm 's lolal business rather I.han just ,foc~~jng on the va lue of its equity. To form an appropriate multiple, enterpnse value IS diVided by EBJTDA. For Prufrock, the enterprise value multiple is:

EV 53,459 million . EBITDA $967 million = 3.6 hmes

The multiple is especially useful because it allows comparison of one firm with another when .there are dif!"ercl~ces in .capital structure (inlereSt expense), taxes, or ca pita l spend mg. The multiple IS not directly affected by these differences .

. Similar to ~E ratios. we would expect a firm with high growth opportunities to have high EV muluplcs.

This completes our definition of some common ratios. We could tell you about more o f them, b.ut these are enougb for now. We'll leave it here and go onto discuss som~ ways of usmg these ratios instead of j ust how to calculate them. Table 3.6 sum­manzes some of the ralios wc·ve discllssed.

Table 3.6 Common financial Ratios

I, Short· Term Sol..,ency, or Liquidity, Ratios

Current ratio = Current assetS Current liabilities

Q . k . Current assetS - Inventory UIC ratio = Current liabilities

Ch- Cash as ratio'" Current liabilities

II. Long.Tenn Solvency, or Financial Leverage, Ratios

11 I db· Total assetS - Total equity Ota e t ratio '" Total assets

Debt~quity ratio :: Total debtITotal equity

EqUity multiplier = Total assetsITotal equity

Times interest earned ratio = , EBIT nterest

Cash coverage ratio = EBITDA Interest

III, Asset Utilization,orTumover, Ratios

Cost of goods sold Inventory turnover := ==,,='=="'''' nvemory

Days' sales in inventory "" , 365 days nventory turnover

Receivables turnover = At Sales counts receivable

< •

Days' sales in receivables '" R _ 3:15 days

ecelva es turnover

Total asset turnover Total assets

Capital intensity = Total assets

"'" IV, Profitability Ratios

Profit margin = Net income Sales

Return on assets (ROA) = Net income Total assets

Return on equity (ROE) = Net inco~ Total eqUity

ROE = Net income X Sales x Assets Sales AssetS EqUity

V. MaricetValue Ratios

. . _ Prke per share Pnce-earnmgs ratio = ,,;;;c.. ;;;;~O':~" amlngs per share

M ".- bo k . ,M~'~rl<e",,';;~;:;;:'U~'~P~·~'~'ch;:;';:''' a, "",t-to· 0 ratro = Book value per share

EV multiple Emerprise value

EBITDA

58

EXAMPLE 3.4

Part J Overvjcw

Consider the following 2008 data for lowe's Companies and Home Depot (billions except (or price

per share):

Lowe's Companies, Inc. The H om e Depot,lnc.

Sal" $48.3 $77.3

ESrT $ 4.8 $ 7.3 Net income $ 2.8 $ .....

Cuh $ .S $ .5

Depredation $ 1.5 $ 1.9 Interest bearing debt $ 6.7 $13.4

Total usea $]0.9 $-4'1.]

Price per sh,tre $24 $27

Shares outstanding 1.5 1.7

SNreholder equity $ 16.1 $17.7

I. Determine the profit margin. RO E. market Cilplta IUt/O . . I' . n enterprise value, PE multiple. 3nd EY

multiple for both lowe's and Home Depot.

Lowe's C ompanies. Inc. The H ome Depot, Inc.

Equity multiplier

AuK turnover -....... RO' Market opIQliDtion

Enterprise "alue

PE multiple

'BirnA

EV multiple

30.9116. 1

-48.3130.9

1.8148.3

1.8116.1

!.5 X 2<1 -

(1.5 x 24) + &.7 - .s 24/1.87 ..

I.' I.. 5.'" 17.-4%

S36 billion

$11.2 billion

I>. 4.8 + 1.5 $6.3

42.216.3 _ 6.7

..... 3111.7 .. 2.5

77.1' ..... 3 .. 1.7

" .4177.3 .. 5.7% 4:4117.7 24.~

1.7 X 27 $45.9 billion

(1 .7 X 21) + Il." - .s D $58.8 biIIIoI'I

2712.6 .. 10."

7.3 + 1.9 $9.2

58.819.2 - 6.4

How would you describe these twO companill'S (rom a financial point of Y.If:W! These are 2. . . d . I 2008. Home Depot had a higher R.OE (par tially beuuse of simllarfy sltuatll' compiulles. nEVI' I

using more debt ~d higher turnoyer) . but Lowe's had slightly higher PE and . mu tlp es.

Both companies' multiples ~r. somewhat below the gener,' market.nlsing queHions about

future growth prospects.

Chapt ec- J F ina ncial Sta tcmerus AnalySiS and Financial Mode ls

" 3.3 The Du Pont Identity

As we mentio ned in discussing: ROA and ROE, tbe d ifference between these two prof­ilabil ily measures reflects the use o f debt fi nanCing or financia l leverage. We illustrate tb e relationship between Ihese measures in Ihis secl ion by invcSligaling a famous way of decomposing ROE into ils componem pa r ts.

A Closer Look at ROE To begin, leI's recall Ihe definition of ROE:

Return on equity = ~~~:~~ou~;

If we were so incfined , we could mulliply this ra lio by AS5el s/Assels wi lho u{ changing anything:

. Net inco me Net income Assels Relllro on equity == TOlaJ eq uity - Total equi ty x Asset s

= Net income X Assels Assets Tota l cQuily

Noli~ Ihat We have expressed the ROE as the prod uct o f two ol hcr ratios- ROA and Ihe equity mu lt iplier:

ROE = ROA x Equity mult iplier = ROA X ( 1 + Debt-equity ratio)

Looking back at Prufrock. for aample, we see that the debl-equity ratio was .39 and ROA was 10.12 percent . Our work here implies that Prufrock's ROE. as we previously calculated, is:

ROE == 10.12% x 1.39 = 14%

T he difference between RO E aod ROA can be substantial , particularly for certain busi nesses. For example, based on recent financia l statemenl s, U.S. 8ancorp ha s an ROA of only 1.1 1 percent, which is actua lly fairly typica l for a bank . However. banks leod to borrow a lot of money. and , as a result. havc relatively large equity multiplie rs. For U.S. Bancorp, ROE is abou t 11.2 percent, implying a n eq uilY multi­plierof 10. 1.

We can further decompose ROE by mu ltiplying the top ;'lnd bottom by to ta l 5.'llcs:

ROE = Saks x Net income x Assets . 'Sales Assel s Total eqUlly

If we rearrange Ihings a oit, ROE is:

Nel income x ~ X Assets .... Sales Assets , Total equity

ROE -

(3.21) Return on asselS

"" Profi l margin x Total asset turnover x Equit y mult iplier

What we haVe now done is to partition ROA into its two component pa ris, profil mar­gin and tOlal asset tumOVer. The las t expression of the preceding equation is ca lled the Ou Pont identity after the Du POn! Corporation, which popu larized il s use.

.. We can check this relationship for Prufrock by noting that the profit margin was

t S. 7 percent :md the total asset turnove r was .64. ROE should thus be:

ROE = Profi t mare.in x Total aSSCllumover X Equity muhiplie r = 15.7% • x .64 x 1.39 = 14%

Tllis 14 pe rcent ROE is exactly what we had before. The Du Po nt idcnlity tells us that ROE is a ffected by three things:

I. Operating efficiency (as measured by profit margin).

2. Asset useefl'ic iency (as meas ured by 10lal asscllurno\,er).

3. Financial leverage (as measured by Ihe eq uity Illuiliplier).

Weakness in either opera ting or asset use efficiency (or both) will show up in tI dimin· ished return o n assets.. wh ich will translute into a lower RO E.

Considering tbe Du Pont identit y. il appears Ihallbe RO E could be levemged up by increasing the amounl o r debt in the firm. However, notice that increasi ng debt also increases interest expense, which reduces profit margins. which acts to reduce ROE. So. ROE could go up or dowe , depending. More imponant. the use or debt financing has a number of other e lTect 5. a nd , as we discuss a t some length in later chapters. the am ount of leverage a finn uses is governed by ilS capilill structure policy.

T he decomposition of ROE we'vc discussed in this section is a convenient way o r sys­lematically approaching finaocia l statement ana lysis. If ROE is unsatisfactory by some measure, then the Du Pont identity tells you where to start looking for the reasons. j

Ya hoo! a nd Google are among the most importan t Interne t companies in the world . In spring 2008, Yahoo! was being urged by a group of dissiden t investors to sell the comp<my or some port io n to Microso ft in Microsoft's bid to bolster its onl ine services to beller compete with Google.

Yahoo~ and Google may be good cxa mples o r how Du Pont analysis can be useful in helping to ask the right questio ns about a firm 's financia l performllm.:e. The Du Pon t brea kdowns for Yahoo! and Google a rc summarized in Table 3.7.

Table 3,7 The Ou Pont Breakdown for Ylihoo! and Ooogle

Yahoo!

Twe lve Months En ding ROE = Profit Margin x Total Asse tTurnove r x Equity Multiplie r

12107 ..... 9.5% X .570 X 1.28 12106 • . 1 11.7 X .558 X 1.24

12105 10.0 16.04 X .0485 X 1.26

Goagle

Twe lve Months Ending ROE = Profit Margin x Total A sset Turnove r x Equity Multiplie r

12107

12106 12105

18.6% 18.0 17.7 =

25.3% 29.1

23.9

X

X

X

.655

.57"1

.598

X

X

X

1.12

1.08

U4

'PerhaPl' th is is (I time 10 menlion Abrah:un Brilofl: a well-known rimUlaal commentator who f:unoos ly rrol.trked Ihal " fi nancial SI:nnllmlS II rc like fine perfume: to be sniffro bul nOI su· ... tlowed:·

OUlpfrr J Finanei:d Sla l~menl~ Analysii and FinOlncial Model$.

" . As can be seen, in 2007. Yahoo! had a n ROE of 6.9 percent. down from its ROE 10 2~5 of !O.~ percen!. In contrast. in 2007, Google had an ROE o f 18.6 percen t, up from 115 ROE tn 2005 or 17.7 percent. Given this information , how is it possible thai <?oog le's ROE could be so Ollich higher than the ROE o f Yahoo! during this period of tllne, and what accounts for the decl ine in Yahoo!'s ROE?

~n close i ns~tion of t.he Du. Pont .breakdown . .... 'C see that Ya hoo! 's profil margin dechned dramallcally durmg thiS pen od o f time from 16.4 percent to 9.5 pe rcent. Meanwhile Googk's profit margin was 25.3 pen:ent in 1007. about (he same as the 2 y~ars before. Yet Yahoo! and GoogJe have very compa rable asset turnover and fi nall­c~a~ leverag7· What .can. account for Googl~'s advantage over Yahoo! in profit mar. gin. Operatmg effiCienCies CM come from higher volumes, higber prices, and/or lower costs.. It is clear thm the big: difference in ROE between Ihe IWO firms can be attributed 10 the difference in profit margins.

Problems with Financial Statement Analysis w~ cOnlinue. o ur chapter by discussi ng some additional pro blems that Ct1n arise in usmg financial statcment s. In one way or another. the basic problem with !inaneial s.t~tcment analysis is tha t Ihere is no underlying theory to help us identify which quan­tities to look at and to guide us in establishing benchmark s..

As w~ disc~ss in o.ther c~ .. pters. there are many cases in which financ ial theory and eco nomIC loglc' provlde gUidance in making judgmenls about value and risk. Little sitch help exisls wit h financial statemcnts.. This is why we ean't say which ratios matter Ihe mos t and when a high or low va lue might be.

O ne particula rl~ sever~ pro~lem is th at.many firms are conglomerates, owning more or les~ unrelaled lilles 01 bUSiness. GE IS iI well-known example. The consolidated fina ncia l state~ents fo r such tinns do n't really !it any neat industry category. More generally, the killd of peer group analysis we have been dcsnibing is going to work beSl when .the lirms are strictly in the same line o f business. the indust ry is competitive. and there IS only one .... ~dy of operating.

Another problem that is becoming increa singly com mon is that major competit ors and natural ~r.group m~mbers in a n industry may be scanered around the globe. The automobile Industry IS nn obvious example. The problem here is Ihal fi millcial s t:~tcmen lS from Outside the United Slates do not necessarily confo rm to GAAP. The eXIs tence of dilTerent sta ndards and procedures makes it d ifficult 10 compa re financial sta temelllS aCross nat ional borders.

Even compan ies tha ~ are.c.le.arly in tile same line o f business may not be compara­b.le. F~r example. electrtc utIliti es engaged prima rily in power gene ra tion nre a ll clas­Sified In the same group. T his gro up is on en thOUght to be relatively homoeeneo us. Howeve~. most utilit ies 0llCra te as regulated monopolies. so thcy don't ~ompete much wllh e:tch o ther. at least not historica lly, Many have stockholders. and manv are organi~d as cooperati.ves wit h no stockholders. There arc severa l differe nt way~ ~f senemtmE ~?~\'er. ra l1~tng from hydroeJc:ct ric to nuclea r. so the operating activi­ties of these ut lh t l ~s cil n differ qui te a bit. Finally. profi tability is strongly aOecteO by the regulatory enViro nment, so utililies in differcn t locations ca n be simi lOlr but show different profits.

Several o ther general problcms freq uent ly crop up. Fi rst. different firms use di lTer­ent account ing procedures- for inven tory, for example. This makes it di llicu h to Com­pare statements. Second, different firms end thei r fiscal year.; at tlitferent times. For firms in seasona l businesses (such as a reta iler with a large Ch ristmas season). lhis ca n lead to difficulties in comparing ba lance shce ts because of nuctumio ns in aCCOlillts

"

3.4

Pan I O .. ervitw

during the year. FinaJly, for a ny particular fi rm, unusual o r transient events, such as a o ne-rime profit from an asset sale, may atTect financial pe rformance. Such events can

giye misleading signals as we compare fi rms.

Financial Models r r. . I tatemenl<: Most financ ia l F inancial planning is another impon a nt .use 0 .manCla S ~. ."

planning models output pro forma financial s latcm~nls. where pro fo rm a means as a matter of form." In our case, this means tbat financial statements are the form we use \0 summarize the projected furore fina ncial stalUs of a compaoy.

A Simple Financial Planning Model . . , We ca n begin our discussio n of fina ncial piallllil1g models with a relatlvely SImple example. The Computerfield Corporation's I1nancial statements from the most recent

year are shown below. h II Unless otherwise stated. the financ ia.l planners al Computerfie l~1 assum~ t at a

variables are t ied directly to sales and current relationship~ 3.re opt.UTla!. ThJS ~ean.s that all items will grow at exactly the same rate as sales. TillS IS obvlousl), ovcrsllnph· fied ; we use this assumption only to make a point .

COMPUTERFIELD CORPORATION Financial Statements

Income Sn.tement Balance Sheet

Sales $1.000 As.sets $SOO Dob, $250

800 Equity 250 Cons

Net income $ '00 Toul $SOO Total $500 =

Suppose sales increase by 20 percent. rising from $1.000 to $ 1.200. Pla nners would then also forecast a 20 percent increase in costs. from S800 to $800 x 1.2 = $960. The prO forma income statemen t would thus look like this:

Sales

Pro Forma Income Statement

Costs Net;ncome

$1.200

.60 $ ,<0 =

The assumption Ihat all variables will grow by 20 percent lets us easily construct (he

pro forma balance sheet as well:

Aneu

Toul

Pro Forma Balance Sheet

$600(+ 100)

$600 (+ tOO)

Debt

Equity

Toul

$300 (+ 50)

300 (+ 50)

$600 (+ 100)

P\aIlW3re proviDes insight into cash now

lorecastirlg at mm,pIanware om.

Chaplcr 3 Financ;a l Slalcmcnl$ Amdysi; and Financial Modeh

NOlice we have simply increased every item by 20 percent. The numbers in parentheses are the dollar changes for the di fferen t items.

Now we have 10 reconcile these two pro forma statemen ts. How, for example, can net income be equal to $240 and eq uity increase by onJy $50? T he answer is th at Com· puterfield must have paid out the d ifference of $240 - 50 = $ 190. possibly as a cash dividend. In this case dividends are the " plug" variable.

Suppose Computcrfield does not payout the $ 190. In this case, the addition to retained earnings is the fuJI 5240. Compllterficld's eq uity will thus grow to $250 (the starting amount) plus $240 (nct income), or $490. and debt must be retired to keep total assets equal to $600.

With S600 in total assets and $490 in equity. debt will have to be $600 - 490 = $110. Because we sta rted with $250 in debt, CompUlerlieid will have to reti re $250 -110 = $140 in debt. The resulting pro forma balance sheet wou ld look like thi s:

Pro FOm1a Balance Sheet

$600 (+ tOO)

$600 (+ 100)

Deb,

Equity

Total

$ 110(- 140)

190 (+240)

$600 (+ 100)

In this case, debt is the plug va riable used to balance projecled tala I assets and li abilities.

This example shows the interaction between sa les growth and financia.l policy. As sales increase, so do total assets. Th is occurs because the lirm must invest in net work­ing capital and fixed assets to support higher sales level s. Because assets are growing. total liabilities and equity, the right side of the balance sheet , wi\[ grow as well.

The thing to notice from our simple example is thai the way the liabilities and owoers' equity change depends o n the firm 's financing policy and its divideod policy. The growth in assets requires that the lirm decide on how to finance that growth . This is strictly a managerial decision. Note that in our example the firm needed no outside funds. This won 't usually be the case. so we explore a more detai led situation in the neJlt section.

The Percentage of Sales Approach In the previolls section, we described a simple planning model in which every item increased al (he same rate as sales. This may be a reasonable assumption for some elements. For others, such as lo ng-term borrowing. it probably is not : The amount of long· term borrowing is sel by management, and it does nOI necessa rily rdate directly to the level o f sales.

In this sect io n, we descri be an extended version of our simple model. The basic idea is to separate the income stat~mellt and balance sheet accounts into twO groups, those that vary directly with sales and those that do not. Given a sa les forecast , we wililhen be able 10 calculute how much financing the lirm will need to support the predicted sa les level.

The financial planning model we describe next is based on the percentage of sales approa ch. Dur goa l here is to develop a quick and practica l way of generating pro forma statements. We defer discussion of some "bells and wh istles" to a later section .

The Income Statement We sta rt out with the most recent income statement for the Rosengarten Corporation, as shown in Table 3.8. Notice thaI we have sti ll si mplified th ings by includ ing costs. deprecialion. and interest in a single cost figure.

Table 3.8

Table 3.9

f'lI,f1 I Ovcroicw

ROSENGARTEN CORPORATION Income Statement

"' .. Cosu

Taxable income

Taxes (H%)

Net income

Dividends

Addition to reulned earnings

$4<

88

ROSENGARTEN CORPORATION Pro Forma Income St;atement

Sales (projected)

Cosu (80% of sales)

Taxable Income

T;ues (3~%)

Net income

51.250 1.000

5 250 8S

$ 165 =

51 ,000 BOO

$ 200

68 5 132 =

Rosengarten has projected a 25 percent increase in sales fo r the coming ~ear, so we are a nticipating sales of $ 1.000 x 1.25 = $ 1,250. To generate a pro forma mcome statement. we assume that total costs will continue to run at $800/ 1,000 = .80 percent of sa les. With this assumption. Rosenga rten's pro forma income statement IS as shown in Table 3.9. T he effcct here of assumlng Ihat costs are a constant percentage of sales is 10 asswne th at the pro fit margin is constant. To check this., notice thai the pro~t margin was S I321 1.000 == 13.2 percent. In o ur pro forma slatemenl. (he profit margm

is $ 165/1 ,250 = 13.2 percent ; so it is unchanged. • Next, we need to proje<:l the dividend payment. This ~mount is ~p to Roseoga nen s

management. We will assume Rosen garten has a policy of payIng out a consta llt fraction or net income it) the fonn of a cash dividend. For the most recent year, the

dh'idend payoul rntio was:

Dividend payout ratio = Cash dividendsfNet income = $44/1 32 = 33 113%

(3.22)

We can a lso calculate the ratio of the addition to retained cu rnings to net income:

Addit ion to retained earningsfNcl income = $88/J 32 = 66213%

111is ratio is called the retention ratio or plowback ratio. and it is equal to .1 minus the dividend payout ratio beca use everything nol paid OUI is re ~~ined . AS$u~mng that. the

payo ut ratio is constant, the projected dividends and additIon to retained earmngs

will be:

Projected dividends paid to shareholders = $165 x 113 == $ 55 Projectcd addition to retained earnings = 5 165 X 2/3 = JJQ

$165 =

Chapl t r ) Fina.ll<."i~1 SlalemenlS Analysi$ lInd Finandal Models 65

Table 3.10

ROSENGARTEN CORPORATION

Current assets Current liabilities

C"h $ 160 I." Accourlu pil}'ilble $ 300 3<," Accounu receivabte +10 +I Notes payable 100 01. Inventory 600 60 To tal $ <00 01.

Total $1.200 120 Long-term debt $ BOO "" Fixed ilssets Owners' equfty

Net plant and equipment 5 1.800 180 Common stock and paid-in $ BOO 0'.

Total asseu

surplus

Retained earnings 1.000 01. Total $1.800 01.

Total liabilities ilnd owners' equity $3.000 0'. =

The Balance Sheet To generate a pro fo rma balance sheet, we stan with the most recen t Stalement. as shown in Table 3. 10.

On our balance sheet, we assume that some items vary direc tly with sales a nd others do not. For (hose items that vary wi th sales. we express each as a percentage of sa les fo r the year j ust completed. When an item does not vary directly with sales, we write "n/a" fo r "not applicable."

For example, o n Iheasset side. inventory iscqual to60percent of sales (= $600/1 ,oro) for the year JUSt ended. We assume this percentage applies to the comi ng year, so for each $ 1 inere,lse in sa les., inventory will rise by 5 .60. Mo re generally. the ratio of total assets 10 sales for the year just ended is $3.00011 ,000 = 3. or 300 percent.

This ratio o f tOla l assets to salcs is sometimes called the capital intensity ratio. It tells us the amount or assets needed to generate 51 in sa les; the higher the ratio is, the marc capitul intensive is the firm. Notice also thai thi s ratio is juSt Ihe reciproca l of the lotal asset turnover ratio we defined previously.

For Rosenganen. assuming that lhis ratio is constant, it takes $3 in tota l assets to generate $ 1 in s..'lJes (apparently Rosenganen is in a relatively capital-intensive busi­ness). Therefore, if sales are to increase by $ 100, Rosengarten will have to increase total assets by three ti mes t\lis amount , or $300.

On the liabili ty side o f fhe bala nce sheet , we show acco unt s payable varying with sales. The reason is that wrtexpect to pl<Jcc more orders with o ur suppliers as sa les vol­ume increases., so payables will change "spontaneously" wit h sales. Notes payable. o n tlte other hand , represents sho rt -term debt such as bank borrowing. T his will nOt vary unless we take specific actions 10 change the amount , so we mark this item as "n/a.'·

Similarly, we use "n/a" for long-term debt because it won't au to matically change with sa les. The same is true ror common s tock and paid-in surplus. The last item on the right side, retained eamings, will vary with sales. but it won 't be a simple percent­age of sales. Instead. we wiJI explicitly calculate the change in re tained earnings based o n ollr projected net income and dividends.

We can now construct a partial pro fo rma balance sheet for Rosengarten. Wedo [his by using the percentages we have just ca lculated wherever possible to c.1.\culate the projected

66 PlIr1 1 Overview

Table 3.11

ROSENGARTEN CORPORATION

Assets Lill:~ilities and Owners~ Equity --- -

Change Change (rom (rom

Next Current Next Current Year Year Year Year

CUrTeflt assets CUrTeOt liabilities

c..h $ 200 $<0 Accounts ~ble $ m $75 Accounts re<eivable 550 110 Notes payWIe 100 0 Inventory 750 ISO T=I $ 475 $75

Tow $1,500 $300 Long, term debt $ 800 $ 0 fixed assets Owners' equity

Net plam and equipment 52.250 $<SO Common stock and paid. ln $ 800 $ 0

Total assets

surplus

Retained aminp 1.110 110 Tool $1,910 SilO

$3.750 $750 Toalliabilities and owners' equity $),1 85 Sl85 Extemal financing needed S 565 $565

= =

amounts. For example, net fixed assets are 180 percent of sales; so, with a new sales level of $1.250. the net fixed asset amoun t will be 1.80 X $1,250 = $2.250, represeming an io.crease of $2.250 - 1,800 = $450 in plant and equipment. It is importanllo notc that for items that don't vary directly with sales. we initially assume no change and simply write in Iheoriginal amounts.. The result is shown in Table 3.11. Notice thai the change in retained earnings is equal to the $1 10 addition to retained earnings we calculated earlier.

Inspecting our pro forma balance sheet, we notice that assets are projected 10 increase by $750. However, without additional fi nancing, liabil ities and equity will in crease by only $ 185, leaving a shortfall o f $750 - 185 ""- $565. We label this amount eXlI?malfinancing needed (EFN).

Rather Ihan create pro fonna statements, if we were so inclined. we could calculate £FN directly as follows:

Assets Spontaneous li abilities EFN = Sa les x 6.Salcs - Sales x llSales - PM

X Projected sa les X ( I - d) (3.23)

Tn this expression, "~Sa[es" is the projected change in sales (in dollars). In our exam­ple projected sales fo r next year are $ 1.250, an increase of $250 over the previous year, so .1.Sales = S250. By "S ponta neous liabilities:' we mean liabilities that naturally move up and down with sales.. For Rose nga rten, the spontaneous liabilities are the $300 in accou nts payable. Finally, PM and d arc the profit margin and dividend payout ratios, which we previously calculated as 13,2 percent and 33 1/3 percent, respectively, TOlal assets find s<11es are $3,000 and $1,000, respectively, so we have:

EFN= $3,000 X $250 - $300 x S250 - .132 x $1,250 x (1 --31) =$565

1.000 1,000

Table 3.12

Current anets

c"h

Accounts re<efvable

InventOf)'

T=I

FIxed anets

a..pler J Fmancial Statemen ts Ana l ~~i s and Fin:mci,,} Mooels 67

In th is ca lCu J ~t ion, nOTice Ihal there ~re three parts.. The first part is Ihc projected increase in assets, which is calculated usi ng the capital intensity ratio. The second is the spontaneo us increase in liabilities.. The third part is the product of profit margin and projected sales, which is projected net income, multiplied by the retention ratio. Th us, the Ihird part is the projected addition to retained earnings.

A Particular Scena rio Our fi na ncial planni ng model now reminds us of one of those good news-bad news jokes. The good news is we're projecting a 25 percent increase in sales, The bad news is this isn't going to ha ppen unless Rosengarten can somehow raise $565 in Dew financing.

This is a good example of how the pl<mning process can point out problems and potentia l con nicts. If. for example, Rosengarten has a goal of not borrowing any addi­tional funds a nd not selling any new equity, then a 15 percenl increase in sa les is prob­ably nOl feasible.

If we lake the need for $565 in new financing as given, we know (hat Rosengarten has three possible so urces: short-term borrowing, long-term borrowing, and new equity. The choice o f so me combination among these three is up 10 management ; we will illustrate only ooe o f the many possibilities,

Suppose Rosengarten decides to borrow the needed fu nds. 1n thi s case, the firm might choose to bo rrow some over the short term and some over Ihe 10Dg term . For example, current assets increased by S300 whereas current liabilities rose by only $75. Rosengarten could borrow $300 - 75 '=" $225 in shorHcrm notes payable and leave lotal net worki ng capital uncha nged . With S565 needed, the remaining $565 - 225 = S340 wo uld have to co me from long-term debt. Table 3,12 shows the completed pro forma ba la nce sheet for Rosengarten.

ROSENGARTEN CORPORATION

, Current li3bilities

$ 200 $<0 , Accounts payable $ 375 $ 75

SSO 110 • Notes payable 325 225 750 /SO Tota l $ 700 $300

$1,500 $300 Long' term debt $ 1. 110 $3«1 Ownerf equity

Net plant and equipment $2,250 $<450 Common stock and paid-in $ 800 $ 0 surplus

Retained earnings ~ 110 Total $(.910 $110

Total assea $3,750 $750 Total liabilities and owners' equity $),750 $750 =

68 Part I Overview

We bave used a combination of shon- and long-term debt as Ih~ plug here. but we emphasize that this is just one possible strategy; it is not o~nly the ~t one ,by any means. We could (and should) investigate many other scenanos. Th: vanous ra~lOs we discussed earlier come in handy here. For example, with, the scenario we have Ju.st c:\amined . we would surely want to exa mine the current ratio and the total debt ratto to see if we were comfortable with the new projected debt levels.

3.5 External Financing and Growth

Table 3.13

Currentuseu

Net fixed U$eu

Totalusets

External financing oeeded and growth are obviously related. All oth.er things Slaying the same. the higher the rate of growth in sales or assets. the greater w~n be the need for external financing. In the previous section. we look a growth rale as gIven, and then \\:e determined the amount of external financing needed to support Ih.at gro;-'th. In .t~lIS sect ion. we turn things around a bit . We will take the ~rm s ~nancJaI poliCY ~s gl.\ .en and then examine the relationship between that financial policy and the firm s ability

to finance new investments and thereby grow. . ' We emphasize that we are focusing o n growth not becau~ growth IS all appr?~n­

ate goal; instead, for our purposes. growth is si,"?ply a ~o.nvenlent ~eans of cxamml~g the interactions between investment and financmg decIsiOns. 111 eO(,.'Ct, we ~ssuOle that the use of growth as a basis for planning isjus t a rel1ect ion of the very lugh level of

aggregatio~ used in the planning process.

EFN and Growth The first thin g we need to do is establish the relationship between EFN .and growth . To do Ihis, we introduce the simplified income statement and balance sheet tor the HO~I~an Comp;.my in Table 3.13. Notice that we have simplified the balance sheet by combmlOg

HOFFMAN COMPANY Income Statement and Balance Sheet

Sales

Cosu

Taxilble income

Taxes (3-4%)

Net income

Dividends

Income Statement

Additiofl to retained e;!.rnings

Ba lance Sheet

,500 «Xl

$100 ,. ,66 =

Liabilities and Owners Equity

Percentage $ of Sales

$200

300

$500

"'"' 60 100%

Total debt

Owners' equity

TOl3.lliabilities and owners' equity

, $250

2SO $500

Percentage of Sates

0/.

0/.

010

Table 3.14

Currentuseu

Net fiKed usets

Totoll a.sreu

ChaprCf J FinanciHI Stalemems Analys;s..;nd Financi:ll Models

HOFFMAN COMPANY Pro Fonna Income Statement and Balance Sheet

Sales (projected)

Cosu (80% of u let)

Taxable income

Taxes (14%)

Net income

Dividelld$

Income Statement

Addition to retolin-ed earnings

Ba lance Sheet

$26.4

52.8

$600.0 ...... $120.0

<0.8

$ 79.2

Liabilities and Owners' Equity

, $2040.0

360.0

$600.0

Percentage of Sales ..,.

6. 100%

, Total debt $250.0

Owners' equity 302.8

Toulllabilities and $552.8 · owners' equity

External fiNnc;n, needed $ 47.2

"

Percentage ofS ....

N. N. ",. N'

short-tenn and long-term debl into a single lOla! debt figure. Effectively. weare assuming that none of the current liabilities vary spontaneously with sales. This assumption isn'l as restrictive as it sounds. If any currenlliabilities (such as accounts payable) vary with sales, we caD assume that any such accounts have been netted out in current assets... Also. we continue to combine depreciation, interest, and costs on the income statement.

Suppose the Hoffman Company is forecasting next yea r's sales level at $600, a $100 increase. Notice that the percentage increase in sales is $1001500 = 20 percent. Using the percentage of sales approach and the figures in Table 3. 13, we can prepare a pro forma income statement and balance sheet as in Table 3. 14. As Table 3.14 illustrates. at a 20 per­cenl growt h rate. Hoffman needs $100 in new assets. The projected addition to retained earnings is $52.8. so Iheex.temal linancingneeded.E FN.is $ 100 - 52.8 = $47.2.

Notice that the debt--eq~iIY ratio for Hoffman was originally (froID Table 3. 13)cqual to $2501250 = 1.0 . We will assume that Ihe Hoffman Company does not wish to sell new equity. In this case, the $47.2 in EFN will have to be borrowed. What will the nc\ .... debt--equity ratio be? From Table 3.14. we k.now that total o .... mers· equity is projected at 5302.8. The new total debt will be the original $250 plus $47.2 in new borrowing. or $297.2 tOlal. The debt--equity ratio thus falls slightly from 1.0 to $297 .::!/302.8 = .98 .

Table 3. 15 shows EFN for several different growth rates. The projected addition to retained earnings and the projected debt-equity ratio for each scenario are a lso given (you should probably calculate a few of these for practice). In determinin g the debt-equilY ratios. we assumed that any needed funds were b.orrowed, and we also assumed any surplus funds were used to pay 00' debt. Thus. for the zero grow th case the debt fa lls by $44, from $250 to 5206. In Table 3.15, notice that the increase in assets

70

Table 3 .15 Growth and Projected EFN for the Hoffman Company

Figure 3.1 Grawth and ReJ8ted Financing Needed to, the Hoffman Company

Part I O,'cn'iew

Projected Increase Addition to External Projected Sales in Assets Retained Financing Debt-

Growth Required Earnings Needed, EFN Equity RatiO

0% $ 0 $41.0 - $44.0 .70

5 25 46.2 -2 1.2 .77

10 50 4SA 1.6 .8'

15 75 SO.6 21.4 .91

20 100 52.8 47.2 . 98

25 125 55.0 70.0 1.05

required is simply equa l 10 the o riginal assets of $500 multiplied by the growth rate. Similarly. the addi tion to retained earnings is equal to Ihe original $44 plus $44 times the growth rale.

Table 3. 15 shows that for relatively low growth rates.. HotTman wi ll ru n a surplus., a nd its debt-equity ratio will decline. Once the growth ra te increases to about 10 per­cent, however, Ihe surplus becomes a deficit. FUrihe r more. as the g rowth rate exceeds approximately 20 percent, Ihe debt- equ ity ratio passes its original value of 1.0.

Fie:ure 3.1 illustrntes the connection between growth in sales and external financing need;d in more detail by plouing asset needs and additions to retained earn ings from Table 3.15 against the growth rates. As shown, the need for new assets grows at a much faster rate than the add ition to re tained earnings. so the inlernallinancing provided by Ihe add ition to retained earnings rapid ly disappears.

As this discussion shows. whether a firm runs a cash surplus or deficit depends o n growth . Microsoft is a good exa mple. Its revenue growth in the 1990s was amazin g. averaging well over 30 percenl per year for the decade. Growth slowed down noticeably over the 1000-1006 period, but, nonetheless., Microsofl's combinalion o f growth and

Increase

E 125 in assets

• required ~ c

.~ 100 • ~ EfN > 0 • c (Hficit) .~ 75

~ c • • 50 • Projected ~ • 44 • EFN < 0 addition c (surplus) to retained ~ • 25 earnings • <

5 10 ts 20 25 Projected growth in sales (%1

Olapl"r J Financia l S(;J(cmenIS An!ll)'s is and Financial Modcl$ 71

subslanlial profit margins led to enormous cash surpluses. In part beca use Microsoft paid few dividends. the cash rea lly piled up; in 2008, Microsoft's cash and sha n-term invcstment .ho rde exceeded $21 billio n.

Financial Policy and Growth Based on our discussion just precedi ng, we see that there is a direct link between growth and external financing. In th.is section, we discuss (Wo growth ra les that are particula rly useful in long-range planning .

The Internal Growth Rate The first growlh rale o f interest is the maximum growth rate Ihal ca n be achieved wilb 00 external fi nancing of any kind. We will ca ll Ihis the internal growtb rate because this is the rale the firm can maintain with int ernal financing only. In Figure 3. 1. this internal growth ra te is represented by the poio t where the two lines cross. At Ihis point . tbe req uired increase in assets is exactly equa l to the addition to reta ined earnings. and EFN is therefo re zero. We have seen that this bappens when the growth rate is slightly less tha n 10 percent. With a little a lge­bra (see Problem 28 at the end of the chapter), we ca n define this growth rate more precisely as :

ROA xb Internal growth rate = J ROA x b (3.24)

where ROA is the return on assets we d iscussed earlier, and b is the plowback, or reten­tion, ralio also defined earlier in this chapter.

For the H olTma n Com pany, net income was $66 and total assets were $500. ROA is thus $66/500 = 13.2 percent. Of rhe $66 net income. $44 was retained. so the plow­back ratio, b, is $44/66 = 213. Wilb these numbers. we can calculate the interna l growth rate as:

Internal growth rate = ROA x b

ROA xb . 132 x (213)

1- .132 X (213) = 9.65%

Thus, the Hon'man Company can expa nd at a maximum rate of 9.65 percent per year witho ut external fi mtncing.

The Sustainable Growth Rate We have seen th at if the Hollman Company wishes to grow mo rc rapidly than a t a rat e of 9.65 percent per yea r, external financ­ing must be arranged. The second growth rate of interest is the maximum growt h rate a firm can achieve with no external equity financing while it ma intains a con ­sta nt debt--equity ratio. This rate is commonly called the sustainable growth rate because it is the max imum r.ue of growth a firm can mainta in withou l increas ing its financia l leverage.

There are various reasons why a finn migh t wish to avoid equity s.'l les. For exa mple, flCW equ ity sales can be expensive because of the substantia l rees thaI may be involved. Ah ernatively, the current owners may not wish to bring in new owners o r contribute additional equity. Why a fi rm mi ght view a particular debt-equity ratio as optimal is discussed in later chapters; for now, we will take it as given.

12

EXAMPLE 3.5

ParI J Overview

Based on Table 3.15, the sust ainable growth rale for HotTma n is ap proxi­mately 20 percent because the deb t-equity ra lio is near \.0 at thaI growth rate. The precise value can be calculated as fo ll ows (see Problem 28 at the end of the

chapter):

Sustainable growth rate ROE X b

ROE x b (3.25)

This is identicallO the internal growth rale except that ROE, return on equity, is used

instead of ROA . For the Ho ffman Company, net income was $66 and tolal equity was 5250; ROE is

thus $661250 = 26.4 percent. The plow back ratio. b. is still 2/3, so we can calculate the sustainable growth rale as:

Sustainable growt h rate = ROExb

ROE x b .264 X (213)

1- .264 x (2/3)

Chapter 3 Financial Statements Anal)'sis and Financial Models 73

HOFFMAN COMPANY

Current assets $242.7 -40% Total debt $250.0 ,,],

Net fixed assets 364. 1 60 Owners ' equity 303.4 0', Total assets $606.8 100% Toul liabil ities and $553.4 ,,],

owne rs' equity

External financing $ 53.4 ,,].

needed

As illust rated. EFN is $53.4. If Hoffman borrows this amount, then total debt will rise to $303.4. and

the debt-equity ratio will be exactly 1.0. which verifies our earlier calculatio n. At any other growth

= 21 .36'10, rate. something would have to change.

Thus... the Ho lTman Company can expand at a maximum rate of 21.36 percent per year witho ut external equ ity fi nancing.

Sustainable Growth Suppose Hoffman grows at exactly the sustainabte growth rate of 21.36

percent. What will the pro forma Statements look like? At a 21.36 percent growth rate. sales will rise from $500 to $606.S.The pro forma income state­

ment will look like this.:

HOFFMAN COMPANY Pro Forma Income Statement

Sales (projected)

Costs (80% of sales)

Taxable income

Taxes (34%)

Net income

Dividends

Addition to retained eam ings

$26.7

53.4

$606.S

4S5.4

$121.4

41.3

$ 80.1

We construct the balance sheet JUSt as we did before. Notice. in this case. that owners' equity will

rise from $250 to $303.4 because the addition to retained earnings is $53.4.

Determinants of Growth Ea rlier in this chapter, we saw that the return on equit y, ROE, could be decomposed into its various components using the Du Pont identity. Because ROE appears so prominent ly in the determin ation of the Sllstainable growth rate, it is obvious thaI the factors imponant in determin ing ROE are also important determi nants of growth.

From our previous discussions, we know Ihat ROE can be written as Ihe product of three facto rs:

ROE = Profit margin x Total asset turnover X Equity multiplier

If we examine our expression for the sustainable growth rate, we see that anything that increases ROE will increase the sustainable growth rate by ma king the top bigger a nd the bottom smaller. Increasing Ihe plowback ratio wi ll have the same etTC{:'t.

Putting it all together, what we have is that a firm's ability to sustain growth depends explicitly on the fo llowing four factors:

I. Profit margin: An increase in profit margin \vill increase the fi rm 's abi lity to gener­ate funds internally and thereby increase its sustainable growth.

2, Dividend policy: A decrease in the percentage of nel income paid oul as d ividends will increase tbe retenl lon ratio. This increases interna lly generated equi ty and thus increases sustainable growth.

3. Financial polh:v: An increase in the debt-equity rat io increases the firm's financial leverage. Because this makes additional debt financin g available, it increases the sustainable growth rate.

4 Towl aSSellUrnOl'er: An increase in the firm's total asset turnover increases the sales generated for each dolla r in assets. T his decreases the fi rm 's need for new assets as sales grow and thereby increases the sustainable growth rate. Notice that increasing to tal asset turnover is the same thing as decreasing capital intensity.

EXAMPLE 3.6

Pan' O~'et'V;ew

The sustainable growth nile is a very useful plnnning number. '-'!hat it illustr,ites is Lhe explicit relationship between the firm's four major areas of concern: its operating efficiency as measured by profit margin. its asset usc efficiency as measured by t01<l1 asset turnover, its dividend policy us measured by the retention ratio, and its financial policy as meaSllrcd by the debt--equilY ratio.

Profit Hargins ~nd Sustainable Growth The Sand.ar Co. hu .a debt-equity ratio of .5.30 profit

rrurgin of ) percent, a dividend paYOUt ratio of 'Kl percent. and a capiol intensity ratio of I.What is

iu susuinilble growth rate~ If Sandar de~red a 10 percent sustainable growth "!.t.e and planned to

achieve this gOill by improving profit margins. what would you think!

ROE is .03 X I x I.S = 1.S percent. The ~tentlon ratio Is I - .10 = .60. Sustainable growth is

thus .Q.i5(.60)/[1 - .015(.60)] "" 1.17 percent.

For the company to achieve a I 0 percent growth rate. the profit margin will have to rise. To see

this.. assume that sustainable growth is equal to 10 perceflt and then solve for profit margin. PM:

.10 - PM(l.S)(.6)/{1 - PM(I.S)(.6)]

PM _ .1/.99 = 10. 1%

for the plan to succeed, the ne<:esury illcrease in profit margin is substanwl. from 3 percent to

about 10 percent. This may not be feasible.

Given values for a ll four of Ihese., there is only one growth mtt that can be achieved. This is an important point. so it bears restating:

If II firm d~ not wish 10 sell OtW equit, Ind ils profit marg.hJ, dividend policy. finllDciaJ po l­

icy, and lotlll !ISsei turnover (or C2piraJ mlensily) art all fi lled. !.ben Iht re is only unc possible

growth rate.

One of the primary benefit s of financial planning is that it ensures internal con­sistency among tbe firm's various goa ls, The concept of the sustainable growlh r..ne captures this element nicely. Also. we now see how a financial planning model can be used to test the feasibility of a planned growth nue. If sales are to grow at a rale higher than the sustainable growth rate, the firm must increase profit margins, increase tota l asset turnover, increase financial leverage. iucreasc ea rnings retention, or sell new shares,

The two growth rales. internal and sustainable, arc sumlllarized in Table 3 16.

A Note about Sustainable Growth Rate Calculations Ve ry commonly. the sustainable growth fate is ca lculated using just the numerator in our expression. ROE x b. T his causes some confusion, which we can clea r up here. The issue has to do wi lh bow ROE is computed. Recidlthat ROE is calculated as net iocome divided by total equity. If total eq uity is taken from an cnding balance sheet (as we have done consistcnlly. and is commonly done in praclice), then our formu la is tbe right one. However, if total equit y is from the beginning of Ihe period , then the simpler formula is the correct one.

In principle. you' lI gel exactly the same sustainable $rowth rate regardless of which way you culculale it (as long as you malch up the ROE calculation wilh Ihe right

Table 3.16 Summery of Internal and Sustainable Growth Rates

ChlipUr 3 Fioancia! SUIU.',nenlS Analysis ~nd Financial Models

1. lnternaJ Growth Rate

Internal growth Rile ROA X b

ROA x b

wh.re

ROA "" Rewrn on assets s Net incomeITotal asseu

b "" Plowback (retention) ratio ::: Addition to retained earnings/Net income

The intemal growth n.te is the maximum growth rate tha.t can be achieved with no external financing of .any kind.

II. Suswmlble Growth Rate

ROE X b Sunainoble growth rote "" i ROE x b

where

ROE = Return 0f1 equity = Net incomefTotal equity

b = Plowback (retention) n.tlo = Addition (0 retained earnlngsfNet income

7S

The sustainable growth rone is the mvdmom growth rate that can be achieved with no external equity financing while maintaining a con5Wlt debt--equity ratio.

fonnula). In reality, you may see some differences because of accounting-related com­plications. By the way, if you usc the average of beginning and ending equity (as some advocclle), yet another formula is needed . Also, all of our commenlS here apply to the internal growth mte as welL

3.6 Some Caveats Regarding Financial Planning Models Financial planning models do not always ask tbe right questioos. A primary reason is that they tend to rely on accounting relalionships and not financial relationships. In particular. the three basic elements of firm va lue tend to get left out- namely, cash now size, risk. and timing.

Because of this. financial planning models sometimes do not produce OUiput that gives the user many mcuningful clues about what strategies will lead to increases in va lue. Instead, they diveFt the uscr's atten tion 10 questions concerning the associat ion of. say, the debt-equity ratio and firm growth.

The financial model we used for the Hoffman Company was simple- in fact. tOO simple. Our model, like many in use today. is really an account ing statement genem­tor at heart. Such models arc useful for pointing out inconsistencies and reminding us of financial needs. but they ofTer linle guidance concerning what 10 do abou t these problems.

In closing our discussion . we should add that fina ncial plul11ling is an iterative pro­cess. Plans are created, examined. and modified over and over. The final plan will be a result negotiated between all the different parties to the process. In fact. long-term

ROBERT C. HIGGINS ON SUSTAINABLE GROWTH

Most financial officers know intuitively that it takes money to make money. Rapid sales growth requires increased a$.Sets in the fo rm of accounts receivable. inventory. and fi xed plant, which, in turn, requi re money 10 pay for assets. They a lso know thaI if thei r com pany docs not have the money when needed. it ca n lilCra!1y "grow broke:' The sustai nable growth equa­tion slates these intuitive tru ths explici tly.

Sustainable growth is o ft en used by bankers and other external analysiS 10 assesS a compa ny 's credit­worthiness. They are aided in Ihis exercise by severa l sophisticated computer sortware packages tha t pro­vide detailed analyses of the company's past finan­cial performa nce. includ ing its annnal sustainable growth rate.

Bankers use this informat ion in several ways. Quick comparison of a company's actual growth rate 10 its sustainable nlle tells the banker wilut issues will be at Ihe top of management 's financial agenda. If aclUal growth consistently exceeds sustainable growth. man­agement 's problem will be where 10 get Ihe cash to finance growth. The ba nker thus can anticipate inter­est in loan products. Conversely. if sustainable growt h consistently exceeds aClUaL the banker had beS1 be

prepared to lalk abou t invcstment products beeause managcmenl's problem will be what to do wi th a ll the cash Iha l keeps piling up in the till.

Ba nkers also find the sustainable g rowth equation useful for explaining to financially inexperienced small business owners and overly optimistic entre preneurs that. for the long-run viability of their business. it is necessary to keep growth and profitability in proper ba la nce.

Finally,comparison of actual 10 sustai nable growth rates helps a banker understand why a loan appli­cant needs money and for how long the need might continue. In one ins.tance. <I loan applicant requested SIOO.OOO to payoff several insistenl suppliers and promised LO rep'w in a few rnomhs when he collected some account s receivable that were coming due. A sustainable growth analysis revealed thilt the fi rm had been growing at four to six times its sustainable growth ra le and that this pattern was likely to continue in the foreseeable fut ure. This alerted Ihe banker thaI impa­tien t suppliers were only a symptom or the much more fundamental disease o r overly rapid growth. i1l1d that a $100.000 loan ""'ould likely prove to be only the down payment on a much larger. multiyear commitment.

Roben C.I-I'gin< i< ProIeuor of firww:e ~< tIM U~It)' oIW ashil'l(ton. He p;oneu.,J the u.e 01 w<",ina"'" J'"O""'b as a toOl for ~nan<;bI analysis..

ftnilncial pl<lnning ill most corporat io ns relics on what might be called the Procrustes approach.l, Upper-level management has a goa! in mind. a nd it is up to lhe planning stan' to rework and to ultimately deliver a feasible plan tha t meets that goal.

The fin<ll plan will therefore implicitly contain ditTerent goals in din·erenl a reas and also s<llisfy many conslraints. For this reason. such a plan need not be <I di spa ssionate assessment of what we Ihink t he future will bring; it may instead be a means of recon­ciling the planned activities of different groups and a way of sett ing commo n goa ls fo r

the future.

76

However it is done. the important lhing to remember is that financial planning should not become a pu rely mechanical exercise. If il does.. it will probably focus on the wrong things. Nevertheless, the alternative to planning is stumbling into the future . Perhaps the immortal Yogi Berra (the ba sebal l catcher, no t the cartoon character). sa id it best: "Ya gotta watch out if yOll don't know where you're go in ·. Yo u j ust might

nOl get there.'"

' tn Greek mythology. ProcruSI.eS is a giant who seizes tr;.\,ckrs and lies ~hcm to an iron bed . I'le stre tches them or cuts off thei r legs as needed to mak", tbem fit the- bc:-d.

'\\,,,,'rc nOt,'x(,o(l'sure ..... hat Ihis means. either. bul"~ like the SOUJld or i~.

Sununary and Conclusions

Concept Questions

Chaptu 3 Financial StatCTl'lC'nts Analysis lIml fimlncia l Motkl$ n

This chapler focuses on working wil h information contained in financial slutcmen ls. Spe­cifica lly. we studied standardized fin.mcial st;lIcmen ts. ratio analysis. ;md lonu-term finan-~l~_~ -

I. We e.,<plained Ihm din-erenccs in firm size make it difficult 10 compare financ ial state­ments. and we discllssed how to form cOlllmon-size statements to make comparisons easier llnd more mea nin gful.

2. Evalu;lIing mtios of accounting numbers is ,Hlothcr wa)' of ('omparillg fina nchll state­ment info rmal ion. We ddilled :1 numbe r of the most cOllllllonly used mtios. and we discussed Ihe famous Oil Pont identity.

3. We showl'd how pro forma financial statements call be generated ,1I1d u$("d to plan for future financing neC'ds.

After you have slUclied this chapter. we hope thai you have some persJX'C'tiw on the uses and abuses of financia l statement illfonmu ion. You should also find Ih.1t you r vocabulary o r business a nd fimlllci" l lerms has grown sub:aantially.

I. Fin:lncial Ralio Annlysis A linaneial ratio by itself td ls us li ltle about a comp'lll)' bcC".tuse fi nancial ralios va ry a great deal across industries. There arc two basic methods jor ana lyzing tin.mcial r'Hias for a company: Time trend analysis and lx,-r group analysis. In time trend analysis. YOll find the ratios for the company over some period. say five years. and e.'l:amine how each ratio has changed over this period. In peer group analysis. you compare a company's financia l ratios 10 those of its pee rs. Why might each of these analysis methods be useful'? Whal docs each lell ),ou abollt Ihe company's linancial health?

2. Industr~·-.."pcrific Ratios So-called "same-store sales" are a very important measure fo r companies as diverse ;IS McDonald's and Sears. As the name suggests. examin ing same-store sales means compari ng revenues from the same stores or restaur.Jllts at two d ifl"crcnl points in time. Why might companies foclls on sa me-SlOre sales rather than tOlal sales?

3. Sales Forecast Why do you think most 10ng-tef1\1 fi rwncial plal) n.iog heW ns \I itlt saks fore-cas ts'! Put diflcrcrllly_ why are fUlUr~ sales the key input?

4. Sustainable Growth In the chapler, we used Rosengarten Corporation to demon­st rate how to calculate EFN. The ROE for Rosengarten is about 7.3 percent. ;rnd the plowback ratio is aboul 67 percent. If YOli calculate the sustainable growt h r,ile for RoSt!ngancn. you will find it is on ly 5.14 percent. In ollr cOllcula tion fo r EFN. we used a growth rate of 25 percent. Is this possible? (Him: Yes. How'?)

5. EF:'II and Growth Rale Broslofski Co. rmrintains a positive retention ratio and keeps its debt-cq uity ratio constantl.'\'el)· year. When sales grow by 20 pcn.-cnl. the firm has a negative projecloo I?FN. What doc'S this tell you :tbout the fi rm's sustainabk' growth rate'? Do YOLI know, with ccnainty, if the inlernal growth rate is greatcr tJmn o r less than 10 percent? Wfiy1 \V11al hapiXlls 10 the projected EFN if the retention ralio is increased? ""'hal if the retC'rl1 ion mlio is d(x'Tea~d'? Whal if the re tention mt10 is zero'r

6. Common8Size Financials One tool of firJ;locial analysis is common-size fi nand,,\ statements. Why do you think common-size income slatements and balance sheets are used? Note that the accoull ting statement of cash flows is not conwned into a common-size statement. Why do you think this is?

7. Asset Utilization and EFN O ne of the im plicit assumptions we made in ca lculating the external funds needed was that the company was operating at full capacity. If the company is operat ing utlcss than full capacity. how will this affect the external funds needed?

Questions and Problems

connect BASIC (Question, 1-10)

I':ln I Overview

8. Comp:uing ROE and ROA OOlh ROA and ROE measure prol'itability. Which one is morc useful for comparing two comp;.lnics? Why?

9. Ratio J\nalysis Consider the ratio EBIT D/AsselS. What does this ralio tell us"? Why might it be more useful than ROA in comp:u;ng IWO companies?

10. Return on In,"estment A nuio that is ba.'Oming more widely used is return on invest­ment. Return on investmcni is calculalW as net income divided by long·term liabili-11\,'5 plus equity. What do you think return on invCSlmcn l is intended to measure? What is the relationsh ip betwttn retuOi on investment and return on assets?

Usc the following: information to answer the next live questions: A small business called The Grandmother Calendar Company began selling personalized photo calendar kits. The kits were a hit. and sales soon sharply excet.-ded fOrec:lstS. The rush of orders created a huge backlog. so the company leased more space :tnd expanded capacity. but it still could not keep up with dema nd. Equipment fai led from overuse and quality suffered. Work ins cilpiml was drained to exp;md production, and. at the same time. paymcnts from customers were often ddayed until the product was shipped . Unable to deli\'CT on orders, the com­pany became so strapped for cash that employee paychccks began to bounce. Finally. out of cash, the compa ny ceased operations entirely three years lmer. t t. Product Sales Do you think the company would have sunered the Slime fate if its

product had been less popula r? Why or why not'!

12, Cash Flow The Grandmother Calendar Company dearly had a cash flow problem. In the conte.xt of the cash now :Lnalysis we developed in Chapter 2, what vms the impact of customers not paying until orders were shipped?

13, Corporat(' Borrowing If th.: firm was so successful at selling, why wouldn't a bank or some other lender step in and provide it with the cash it needed to con tinue'!

14. Casb Flow Which was the biggest culprit here: Too many orders. too little cash. or tOO litt le production capacity'?

IS, Cash Flow What are some actions a small COnllXmy like The Gmndmother Ca len­dar Company can take (besides eXIXLIlsion of capaci ty) if it finds itself in a situation in which growth in sa les outstTips produc tion?

I. Du Pont Identity U' Rotcn . Inc .. has an equi ty multiplier of 1.35. total asset turn­over of 2.15. and a prolit margjn of 5.8 percent, what is its ROE?

2. Equity Multipli('r aDd Return on Equity Thomsen Company has a debt-equity r.uio o f .90. Return on assets is ID. I percent. and total eq uity is 5645,000. What is the equity multiplier? Return on equity'! Net income?

3. Using the Du Pont Identity Y3K, Inc .. has SilJcS of 53, 100, total a~ets of 5 1.580. a nd a debt-cquity ratio of 1.20. Ir its return on equity is 16 percent. what is its net income?

4. EFN The most recent !lnanei,,1 statements for Martin, Inc .. are shown here:

Income Statement Balance Sheet

""e, $25.800 Aueu $lll.OOO Debt $ 20,500

COSts t6,500 Equity 92.500

Taxable income $ 9.300 Toml $113 ,000 Toul $ 113.000

Taxes (34%) 3,162

Net income $ 6,138

Gapl"," J Fimmcial SLalO:ITICI ILS An:llysis and Finllncial Models " Assets and costs arc p~ponional to sales. Debt and equity arc not. A dividend of $ 1.84 1.40 was paid, and Manin wishes to maintain a constant payout ratio. Next year'~ sales :lre projected to be 530,960. What external financing is nceded?

5, Sales and Growth TIle most recent financial statemen ts for Fontenot Co. ~re sbown here:

Income Statement Balance Sheet

S<ales $67.000 Cun-ent u seu $ 11.000 long-term debt $ 68.000

COSts ·4),800 Fixed usus 118,000 EqUity 81.000

Taxabte income $23.200 Toul $1-49,000 Total $t49.000

Taxes 01%) 7.888

Net locome $15.312

Asset s.:L~ld costs are prop:<>rtional to sales.. The company maintains a constant 30 per­(;elll dLvLdend payout milo and :t constmll dcbt--cquity mtio. What is the Inll.';1mUm

increase in sales that can be sustained assuming no new (.'quity is issued?

6, Sustai~able Gro:w!h If t~e Layla Corp. h:ls a 15 percent ROE and a 10 perccnt pay­OUI rano, what LS LIS sustamable growth ratc'!

7, Sustainable Growt.h Assuming the rollowing ratios nrc constl.lnt. what is the sus-tainable growth r,ue'!

Total asset turnover " 1.90 Profit margin = 8. 1% Equity multiplier - 1.25 P'.tyout ratio = 30"/ ..

8. Calc:ulating EFN The most l\..'C'ent fina ncial statements for Smdley. Inc .. are shown here (assuming no income taxes):

Income Statement Balance Sheet

S,;:ales $5.700 Assets $14,100 DO<>, $ 6. ]00

COSts 3.820 EqU ity 7.800

Net income $1.880 Toul $1'i. 100 Toul $1-4, 100

Asset s and costs a rc proportional to sales. Debt and equity are not. No dividends arc paid. e."(t year's SlLles are projl'Ctcd to be $6,669. What is the external fi nancing needed'.'

9. Ext«:,rnal Funds NffiI:ct Cheryl Colby. CFO of Charming Florist Ltd .. has created the fIrm's pro forma,balancc sh..:.'Ct ror lhc Ile.-; t fi scal year. Silles are projected to gro\\ by 10 percent to S3<X1 million. Current assets, lixcd assets. and sho rt-term debt are 20 percent . 120 pe~ent, ~nd 15 ~rcc.n~ or sak-s., respectively. Charming Florist pa~ s ~ut 30 percent of LIS net Lncome ILl dLVldends. The compa ll}' currently has 51 30 mil­~Ion of long-term debt and S4S million in common stock par vnlue. The profi t margin IS 12 percent. II, Construct the current b:.lance sheet for Lhe firm using the projected sales figure. b. Ba~ on Ms. Colby's sales growth forecast. how much does Channing Florist

need UI externa l funds for the upcoming liseal year? c. Construct the linn's pro forma balance sheet for the next fi scal \"Car and conlinn

the external funds needed that you calculated in IXLn (b). .

so

INTERMEDIATE (Questlol'l' 11-23)

P:trl I On:rvjcw

10.

II .

12.

13.

14.

Susta inable Growth Rate- The Stei~n ('omp:lIl)' has an ROE of 10.5 percenlltnd a payout roll ;o of 40 pen:cnl. 11. What is the company's sustainable growt h r.\ IC? b. C'Ul the company's actual growth rule be different from ils sustainable growth

r;lte: Why or wby nOl: c. How can the company increase its sustainable growth r.He: Relurn on Equit\' Firm A and Firm n h;.I\'(" debt- total asset mlios of 40 percell t and 30 pcrtX'nt a"nd retums on loml assets of 12 percent and 15 percent. respectively. Whid firm hilS a gre,i1cr return on equity? Raliosa nd foreign Conlpanics PrinC'C Alben Canning PLC had a net loss or £15.834 on S<lles of £167.983. What was the company's profit margin'! Docs the fact that tbese ligures i1rc quoted ill a foreign currency make an), diffefCnce? Why? In dollars. sales were S251.257. What was the nct loss in dollars? External Funds Needed The Optical Scam Company has forecast .. 20 percent sales growth raIl' for next year. The curren t finane; .. l statemen ts are shown here:

Sales

COstS

T~xable ir'Kome

Taxes

N~t income

Divid~nds

Income Statement

$30.400.000 26.710,000

$ 3.680.000 1.288.000

$ 2,]92.000

Addition to retained earnings

$ 956.800

1.0435.200

Balance Sheet

An." Ua bilitles and Equity

Current assets $ 7.200.000 Short-term debt $ 6.'100.000

Long-term debt 4,BOO.000

Mite<! assets 17.600.000

COfl'll'l\Oll stock $ ].200,000

Accumul~ted retained eamings 10.400,000

Toal equity $1 ].600.000

Total ,,"nets $24.800.000 Tou\ liabilities and equity $24,800.000

B. Using the equation from the chapter, ca lculate the external funds needed for ncxt year.

b. Construct the firm's pro forma bahmce sheet for next year and eonfi nnlhe exter­nal funds n\!Cded that you calculated in part (a).

c. Calculate the sustainable gro\'1h rate for the eomp .. n)'. d. Can Optical Sc.un eliminate the na."<i for e.I(tem .. 1 funds by changing its divi­

dend policy? What other options are .. \railable to the company to meet its growth objectives?

Oa,'5' Sales in Receh'ablcs A company has net income of S205.000. a profit margin of 9.3 percent. and an accounts receivable balance of $\62.500. Assuming SO percent of s.o.Ie5 are on credit. what is the company's days' sales in receivables?

Chapler ~ Fin"nt;;11 Smlcmenb AnalYSI$ und Firmnci:ll MooJels " 15.

16.

17.

IS.

Ratios and Fixed ,\ ssels The Lc Sleu Company h,.s a mtio of long-term debt to total assets of .40 aud " current ratio of 1.30. Current liabilities .. re 5900. sales arc S5.3 .W. profit margin is 9.4 percent. and ROE is 18.2 percell!. What is the amoun t of the firm's net fixed assets?

Calculating the Cash Con·r'.Ige Ralio Titan loc.·s net income lor the most recent year ""'as 59.450. The tax rate was 34 percent. The firm ",lid S2.360 in t01a1 inter~s l expense and deducted S3.480 in depredatio n expense. What \\~J.s Titan's cash cover­age ratio for tbe )'ear'!

Cost of Goods Sold Guthrie Corp. has current liabilities of 5270.000. a quick r..llio of 1. 1. inventory turnover of 4.2, and il current ratio of 2.3. What is the cOSt of goods sold for the compan}~?

Common·Sizeand Common-Bas..- Year finaneial$tatcmcnts In adrJ ition tocommon­size financial statemen ts. common- base year financial stau:ments arc oftcn used . Common-base year financia l statements lire constructed by dividing the current year account value by Ihe base yea r account va lue. Thus.. the result shows the growth rate in the account. Using the lollowing fina ncial statements. construct the common-size balance sheet and common base year balance sheet for the company. Usc 2009 ,IS

the b;:lsc year.

Assets

JARROW CORPORATION 2009 ilnd 2010 Billilne.:. Shl'('u

Liabili t ies and Owners' Equity

2009 20 10 2009 1010 Current as~ts Current liabitities

c;,,,, S 8.,436 $ 10.157 Accounts ~ble $ -4].050 • 46.82 1

AccountS receivable 21.530 23.406 NO(H~le 18.38<1 t7,382

Il1'I'eIltory 38.760 42.650 Tow $ 61 .04)4 • 6 .... 20] ---Total $ 68.n6 $ 76.113 Lorog·term debt $ 25.000 $ 32.000

Fixed aueu Owners' equi()'

Net plant and $226.706 $2048,306 Common s(()(k and S 40.000 S oW.OOC equipment ~id·jn $UrplUi

Accumulated reta ined 168,998 188,]16

e.amina:1

Toal $208,998 $228.3 16 Toeal assets $295 .... 3'2. $324.519 Totllll~bilities Vld $295.432 $324.519

owners' equity

, Use Ihe following information fo r Problems 19.20. and 22:

The discussion of EFN in the chapler implicit ly assumed that the company was opcr· ating at full c.1.pilci ty. Often. Ihis is not the case. For example. assume Ihat Rosengarten was openlling at 90 percent c:lpacity. Full-eapacit y s:lles wou ld be 51.0001.90 = 51.11 1. The balance sheet shows $1.800 in fixed asset s. Tbe capital intensity ralio for the com­pany is

Capital intensity rdtio = Fixed :lsset.sJFulJ.-capacity salcs = 51.800fSl. l I1 = 1.62

This means that Rosengarten needs 51.62 in fixed assets for e\'erv doll .. r in sales \\ hen it reaches- full capacity. At the projectcd sales level of SI.25O. it needs 51.250 x 1.62 "" S2.025

82

in fixed ,IsseiS. which is S225 lower Ihan OUf projection of 52.250 in fi .... ed assets. So. EFN

is on ly $565 - 225 = 5340. 19. full-Capacity Sales Thorpe Mfg .. lnc .• is currently opemling at onl~' 85 percent of

fixed usset capacity. Current sales are S630.000. How' much can saks Increase before a ny new fixed assets are necdcd:~

20. Fixed AsselS a lld Capaci~' Usage For the comp;m)' in tbe previous problem. sup­pose fixed lIssel S arc $580.000 a~d s'lles are proj~u .. d to ~ow to ;790,000. How much in new fixed assels are (\.'qutn .. "Xi to support thiS growth In S<llcs.

21. Calculating EFN The most ree;:n! fi n;meial statement s for Moose Tours. Inc .. appear below. Salcs for 2010 arc projccted to .g ~ow by 20 percent. I~teres l cx pen~c will remain constant: the IiIX rale and the d ividend pilyout fate Will also remam constant. Costs. other expenses. currenl assets. lixed OI SSC{S, and accounts payablc increase spontaneously with sales. If the lirm is o~r'lI~ng at full cOIpacity and no new debt or equi ty i$ issued. what extcnml fina nclIlg IS necded to support the 20 percent growth rate in sales'!

22. Capacity Usage and Growth In the prcvious problem. suppose thc firm was operat­ing at only 80 percent capacity in 2009. What IS EFN now?

Currel'lt asse-u

Cash

S.I~

COSts

Other expeo$~

MOOSE TOURS. INC. 2009 Income Statem e nt

u.mifl3s before intemt J.nd UXH

Inta-en expeMe

Ta,x,Ible. ir.c:ome

Taxes

Net income

OiYidel'lds

Addition to reained umil\&s

$33.735

78,7 15

MOOSE TOURS, tNC .

$929.000

nl.OOO 19.000 ---

$197,000

14.000

$ 173.000

6OSS0

$1 12,450

Balancc Shect as of De ce mber 31 . 2009

Asseu Llabilitkl and Owners' Equity

CIJm!l'It Ji~bilitieJ

S lS. lOO AccolJl'l u payabte

AccOVl'lu receiVllble

Invel'ltory

<60.700

86.900

Notes pJ.yable

Toul

Tool St52.900 l Ol'll·term debt

Own(lrs' equity

Fixed usets Common stOCk and paid-lf1 surplus

N et plant MId equipment $4 t l,ooO Reulned earl'linls

1001

Toul USeD $565,900 Toul liabiliti., and O"NN:N' equity

$ 68,000

17.000

$ 85.000

$158.000

$140.000

182.900

$312.900

$565,900

CHALLENGE (Que.IiOM 24-30)

Chllplt'l' .\ Financial SI;\lcm~rU~ I\nul)'sis and Fin:lOcial "'Iodels

23. Ca!eulating H "'N In lirob1em 21 . suppose Ihe finn \\ishes to keep it s debl-cqui lY rallo const:ln!. \Vh:\I is EFN no\\1

24. EFN. ~lnd Internal Growth Redo Problem 21 using saJes growth rates o f 15 and 25 percent in addition to 20 percent. lIIustmte graphicaUy the relationship between EFN a nd the growth rate. and usc this graph to dctermine the relationship between them.

25. EFN and Sustainable Growth RI,.x1o I'roblem 23 using sail-os growth rates of 30 ilnd 35 percen t in addition to 20 percent. Ill ustrate graph ically the relationship between EFN and the ,growtb rolle. and usc this grolph to determine the relationship between them.

26. Conslraints on Growth Bulla Reco rd ing. Inc .. wishes to ll1:1illlain a I!rowth mte of 12 percen t per year and iI debt- equity ratio of .30. Profit margin is 5.9 percent. and the ratio o f tota l assets to sules is constlllll at .85. Is this growth rate possible? To answer. dctermine what t h~ dividend payout ratio must be. How do you interrret the result?

27. E'FN Define the fo llowi ng:

S = Previous year 's sales A = Towl asset s D = Tot,,1 debt E = Total equ ity g = Projected growth in sales PM = Profi t margin II = Retention (plowback) r.u io Show that EFN e,ln be written as:

EFN ::: - P1\'ItS)b + IA - PM(S)b] x g

H im: Asset nC\.--ds .... ill equal A x g. Tbe add it ion to retained earnings will equ,l l PM(Slb x ( I + g).

28. Sustainllble Growth Rate Based on the results in Problem 27. show that the inter­nal and susta inable: growth ra tes can be c:llcu l:llcd as shown in Equations 3.n and 3.24. I-Iillt: Fo r the in ternal I!rowlh rate. set EFN equa l 10 zero lind solve for g.

29. Sustainable Growth Rate In the chaplcr. we discussed one calculation of the sus­tainable growth r"lIe as :

30.

Sustainable growth ratc ::: ROE X b ROE x b

In p,:"<1cticc, probably the most common ly used calcu lation of lhe sustainabll..· growth ralC IS ROE X b. This equat ion is iden tic'l lto the sustainable !,'Towlh ro rle equation prc~ll ted.in the c~llIplh if the ROE iscaleul:ued usi ng the bcgi nnin,g of period equity. Den\'c tillS cquatlon,.from the cqumion presented in the cha pler.

Sust ~ inablc Growth Rate Usc the susta inable growt h nnc equations from the pI'CVIOUS problem to answer the fo llo\\ing quest ions. No Return. Inc .. had tOla l a ssets of S3 10.000 and equi ty o f S 183.0OO at the beginning of the year. At the end o f the yea r. the company had to tal assets o f $355.000. During the yea r the com pany sold no new equity. Net income for the year was 595.000 and dividends were $68.000. What is the sus ta in able g rowth rate for the company? What is the sust.a inable g rowth rdte if you (,:lleu latc ROE based on the begin ning of peri od cqulty'!

S&P Problems

STAN DARD &POOKS

II'WW .mhh(" .comledumarketin ... igbt I. Calculating the Ou Pont IdC1lti~· Find the annual income statmlcnlS and b.l lance sheets

for Dow Chcmkal (DOW) and AutoZone (AZQ). Calculate the Du Pont idcmil)' for each company fo r the most recent three yeaI'$. Comment o n the ciklllges in each compo­nent of the Du Pont identity for each oomjXmy over this period and compare thccompo­nenlS between the tWO camp'lIlies. Are the results what you C." fI\."CIcd'! Why or why not:

2. Ratio Analysis Find and download tbe "Profiulbility" spreadsheet for Southwest Airlines (lUVI and Con tinen tal Airlines (CAL). Find the ROA (Net ROA). ROE (Net ROE). PE ratio (PIE-high and PIE-low). :md Ihe market-to-book r.ltio (Price/Book- high and Price/Book- low) for each company. Bccause ~ Iock prices cha nge daily. PE and m,lrkeHo-book ratios arc often reporlcU as Ihe high('S1 and IOWl!SI values over the year. as is done in this in slam:e. Look at these ra lios for both companies over the past live years. Do you notice any trends in theS\.' rat ios? Which company appears to be operating at il more dTIcicnt kvel based on Ihese fou r ratios? If you were going 10 invest in an airlin~, which one (if either) of these companies would you choose based 0 11 this information':' Why?

3. Sustainable Growth Rate Use Ihe an nual income sliltelllcn ts and balanJ.'C sheels under the "Excel Analytics" link to cu!culMe the suswinable growth rale for Coca­Cola (KO) each year for the past four years. Is Ihe sUSlil inable growth rale the same for every year? What are possible reasons the suslainable growth rate may vllry from

year 10 yea(! .$. External Funds Needed Look up Black & o.."'Cker (DDK ). Under the "Financial

HighlighlS "link you can find a five-year growth rate fo r sales. Using Ihis gro\\lh mte ilnd the most recent income statement and b.."\lance sheet. compute the exten\al funds

needed for BDK nexl year.

RATIOS AND FINANCIAL PLANNING AT EAST COAST YACHTS Dan Ervin was ret:eotly hired by East Coast Yachts to assist the company with its short­term financinl planning and also to c\',llunte the company's lin.mcia l performance. Dan graduated from coUege fi ve years :Igo with it fin(lncc degree. and he bas been employed in the treasury department of a FOr/lll1e 500 company since then.

East Coast Yachts was founded 10 years ago by Larissa Warren. T he company's oper­ations arc located near Hilton Head Island. Sout h Carolina. and the company is struc­tu red ilS 'In LLC. The compuny has m:l nufactured custom midsize. high-performilllce Y:lchts fo r clients over this period. and ils products have received high re" iews for sa fet)' and rel iability. T he company's yachts have also recently received the highest award for customer satisfact ion. T he yachts arc primarily purchased by wcahby individuals for pleasure usc. Occasionally, a yacht is manufact ured for purchase by a company for busi­

ness purposes. The custom yacht industry is fragmented, with a number of manufacturers. As wit h

any industry, there arc market leaders. but the diverse natUTe of the industry ensures thai no manufacturer dominates the market. The competition io the market. as well as the product cost. ensures thaI altention 10 deta il is a necessity. For instance. East Coasl Yachts will spend 80 to 100 hours on hand-buffing the stainless steel stem-iron. which is the metal eap on the yach t's bow that conceivably could coll ide wilh a dock or

anolher boat . To get Dan stancd with his analyses. Larissa has pro\;dcd tbe following financial state-

ments. Dan has gathered the industry nttios fo r the yacht manufacturing industry.

Chapt('r 3 Finantial Statements '\Illll)'~is and FimU14'i:d Models

Sales

C O$( o f goods ,old

Other expense:

Oeprecbtion

EAST COAST YACHTS 10011 Incomo St .... tement

Eaminp beforll ;n(ere:st ~nd ta .... es (EBIT)

Interest

Tvclble Income

TUlls (-40%)

Net income

Oividend5

Addition to RE

$7.537.320

S,024.880

EAST COAST YACHTS Balance Sheet as of December ) 1,10011

$ 167.310.000

117.11 10.000

19.991.000

5,160.000 , 23.9-46,000

J.(I09.000

• 20,937.000

8.371.800

$ 12.562,200

A ... to Liabilities & Equity

Current ~seu Current liabilities

u.h S 1.042.000 Accounts payable S 6.46 1.000

Accounts re<:ei¥'llble 5,473.000 Notes payable 11.078,000

Inventory 6.136.000

Total $ IUS I.OOO To u l • 19.539,000

Fixed asUts Long-term dllbt $ 11.71S.000

Net plant ;lOci equipment S 9),964.000

5lqreholders' equity

Common stock , 5.200,000

Reu.ine<l umin" 50.11 1.000

Total equity S 55.311.000

Total assets $ 108.6 15.000 Total IiIbllities aIId equity $ 108.615.000

.",

Current rat io 0.50 1.4 3 1.89

Quil:k rat io 0.21 0.]8 0.62

Tou.I 3sset turnover 0.68 0.85 1.38 Inventory tu rnover -4 .89 6. 15 10.89

Receiv.ables w moveor 6.27 9.82 11. 11

Oebtratio 0.4< 0.s2 0.6 1

Debt---equity ratio 0.79 1.08 1-56

EqUity multiplier 1.79 2.08 ". Inu ren c~n,e 5.18 ' .06 9.83

Profit m"8in 4.05% 6.98% 9.8~

Return on UUts 6.05% IO.SJX 13.2 1%

Return on equity \l.'H~ 16.54" 26.15%

Part I Q\ ervicw

I. Cl.Ikulnte all of the ratioS listed in the indwn ry lable for EuSI Coost Yachts. 2.' . re the rfonnancc of East Coast Yachts to the indust~y as a \~ho le. For .each

~~;~.P:ommc:; on why it might be viewed as positi \'e or.negam·e rc~a~lve to ~he mdus* I . Su se you create an inventory mt io C<llculil tcd as Inventory dlvld~ b} current I ;;;bil it~~ How do you interpret this rdt io? How docs fil s! Coast Yaclm compare to

the industry aver.lg~? Calculate the susta inabk growth rate of East Coast Yachts. Calculate e;<tern~ 1 fund.s

3, eed 'd (EFN) and prepa re pro lo rmll income statements and balance s~cets assummg ~ro\\~h at pl\.'Cisely this rate. Recalculate Ihe r,lIios in the previous quesnoll. What do

you obscn'e'! . . . As a mctical mailer. East Coast Yacha is unlikely to be ~vll l1l\g t? r.u~ .external,

4. . p . ' . I ' pan bec'\usc the owners don't want \0 dilute theIr cXlstmg ownt:r-eqUIty t:aplhl . 11\' h . I . cO" growth rate I . d llrol positions. Howevcr East CO:lsl Yac IS IS P annlllg I' r.

slIp;tn COl " d dutions '\hout the of 20 percellt ncxt year. What arc your l'onc!usLons <1 11 reeommen ' • fC;lsibility of East Coast's expansion pl:lII s? Most assets can be increased as a percenlUge of sales, For inst.;':"(.'C" cash ~ ... ~ be.

5. increased by lLnV amount. Howevcr.lixed assets often must be LIlcrcased m :;~Lfic amounts becauSe it is impossible, as a practical maner. to bll~, part of a new plant or lll'Lchine. I I) this C'.1se a company has a "staircasc" or " Iumpy fixed cost struct~rc. . ~SUlllC that East Coast YachtS is currently producing il t 100 ~rccnt ~r.capac~t~. As a

f result. to expand production, the company must sct u~ an cntlre ly ne\\ h.nc. at .1 ~?st 0 t S30 million, Calculate the neW EFN with this asslLn~pllon . Whitt does thiS Impl) ahou ci.lpacilY utiliZ<ltion for East Coast Yachts next year !

DiSCounted Cash Flow Valuation

What do baseball players Jason Varilek, Mark Teixeira, and C. C. Sabathia have in common?

AlIlhree athletes signed big contracts in late 2008 or early 2009. The contract values were

reported as $10 million, $ 180 million, and $161.5 million, respectively. But reported figures

like these are often misleading. For example, in February 2009, Jason Varitek signed with

the Boston Red Sox. His contract called lor salaries of $5 million, and a club option 01 $5 mil·

lion for 2010, for a tota l of $10 miUion. Not bad. especia lly for someone who makes a living

using the 100ls of ignorance~ Uock jargon for a catcher's equipment).

A closer look al the numbers shows that Jason, Mark, and C. C. did pretty well. but

nothing like the quoted figures. Using Mark's contract as an example, although the value

was reported to be $180 million, it was actually payable over several years. It consisted of

a $5 million signing bonus plus $175 million in future salary and bonuses. The $175 million

was to be distributed as $20 million per year in 2009 and 2010 and $22.5 million per year

for years 2011 through 2016. Because the payments were spread out over time. we must

consider the time value of money. which means his contract was worth less than reported.

How much did he rea lly get? This chapter gives you the 'ools of knowIedgeP to answer this

question.

4 .1 Valuation: The One-Period Case Keith Vaughn is trying to sell a piece of r:1W land in Alaska . Yesterday he was oITered $ 10,000 for the property. He was abo ut ready to accept the ofTer when another indi­vidual o lTered him S 1 [,424. However, the seco nd alTer was to be paid a year from now. Keith has satisfied himsel~ Ihm both buyers a re honest and financially solvent . so he has no fea r that the offer he selects wiJI fa ll Ihro ugh . T hese two otTers are pic tured as cash nows in Figure 4 .1. Wh ich offer s hould Keith choose?

Mike Tuttle. Keith's financial adviser, points oul that if Keith takes the first olTcr, he could invest the $ 10.000 in the ba nk at an insured ra te or 12 percent . At the end o f ODe year, he would have:

510.000 + (.12 x SIO.OOO) ~ 510.000 x 1.12 ~ 5 11 .200 Re turn of In terest principa l

• i

.. Figure 4.1 Cash flow for Kolth Vaugtln'. Sale

EXAMPLE 4.1

Part J I Va lumion lIIId Capital Bu(]gctinJ!!

Alternative sale prices

Year:

$10,000 $11.424

L __ _ J o 1

Because this is less (ban the Sl l,424 Keith could receive from the second ofTer. Mike reco mmends Ihat be take the latter. Tllis analysis uses Ihe concept of future value (FY) or compound "alue, which is the value of a sum after inve:>ling over one or more periods.. The compound or future value of $10.000 al 12 percent is $11.200.

An al ternative melhod employs Ihe concept of present ,'a1ue (PV). One ca n deter­mine present value by asking the following questio n: How much money, mus~ Keilh PUI in the bank today so that he will have $ 11 ,424 next year? We can wnte IhlS alge­braicallyas:

PY x 1.12 = $ 11 ,424

We wan l to solve for PV, the amo unt of money tbat yields $ 11 ,424 if invested at 12 per­cent loday. Solving fo r PV, we have:

- SII.424 : S IO '00 PV - Ll 2 .-

The formula fo r PV can be written as follows:

Presen t Value of Inrestmen!:

pv "",SL 1 + ,

(4. 1)

where C is cash now al date I and r is the rate of return [hal Kei th Vaughn req uires , 01) his land sale. It is sometimes referred 10 as the (/;$(,011111 mIl!.

Presl!lII mille (lIwl)'sis tells us that a payment o f 51 1.424 to be received next yea r has a present va lue ofsio.200 tod ay. In o ther words. ill <t 12 percent interest rdle, Keith is indifferent between SI0,200 today or $ 11.424 nexl yea r. If you gave him SI0.200 today, he could pUl it in the ba nk and recei ve SII.424 next year.

Because the second offer has a present value of 5 10.200. whereas the first offer is for only $ 10.000, present value analysis also indicates that Keith should take the second o ffer. In o ther words. both future val ue analysis lind present value analysis lead to the sume decision. As it tu rns ou t. present value analysis and future value analysis mUSI always lead to the same decision . .

As simple as this example is. it cont<lin s the basic principles that we will be workIng with over the next few chapte rs. We now use another exam ple to develop tbe concept of net presen t value.

Present Vafue lid<! jennings, a financ~1 :analyst at K.J.\Jfman & Broad, a leading reat estate firm. is

thil'lking abo\Jt re<:ommending that Kaufman & BrOOld invest in a piece o f lal'ld that COsts S85,000. She

is ceruin that next rear ~ land will be wonh $91 ,000, a sure $6.000 gain. Given that the guaran­

teed interest rate in the bank is 10 percent. should Kaufman & Broad undernke the investment in

land! M$. Jennings·s choice is described in Figure 4.2 with the cun flow time chart.

A moment's thooght shoold be all it takes to convince her that this is not an attractive business

deal. By invening $85,000 in the l;and, she will have S91 ,000 ;available next year. S\Jppose. inStead.

Chaph:r 4 Oi:>COlinl ed C .. sh Flow VOl luation .. Figure 4.2 Cash Flows for Land Investment

Cash inflow S!1.000

Time r-- ------ -•

Cash oudlow -S!5.000

that Kaufman & Broad puts the same $85,000 into the bank. Ar the interest rue of 10 percent. this $85,000 would grow to;

( I + . 10) X $85.000 ::: $93,500

nC!Jtt year.

It would be foolish to b\Jy the land when il'lvestlng the same $85,000 in Ihe fi n~ ncial market would

prod\Jce an extra $2.500 (that is. $93.500 fro m the bank mll'1US $9 I ,000 from the land investment). This is a future value calculation.

A1tema~ly. she could cak\Jlate Ihe prese nt VOllue o f the $lIe pr ice next year as:

$91.000 Prelent value'" -'-.1-0- '"' SS2.n1.l7

Beause che presenc value of next year's ules price is less thl1n £his year 's purchase price o f $85,000.

present value l1natys is also indiatH that she should nOt recommend purchasing the property.

FreqUCDl.ly. rinancial analYSIS want todcterrninc the enct cost or be/u1il of a decision. In E:tample 4, 1. tbe decision to buy this year and sell nex t yea r can be eVdluated as:

- S2.273 = - $85.000

Cost of land toda y

$9 1.000 + 1.10

Present va lue of nex i year's sales price

The formula for NPV ca n be written as follows:

Net PresE'nt Value of Investment :

N PV = - Cost + PV (4.2)

Equation 4.2 says that Ih6'value of the invcst ment is - 52.273, after statilllZ all the ben­efits a nd all the cosl$ as o f dale O. We say that - $2.273 is the net prestnt -value (NPV ) of the investment. Th at is. NPV is the prescnt value of fUlUre cash nows minus the present value of the cost of the investment. Because the net present value is neeative. Lida Jennings should not recom mend pun::hasin8 the land. •

Both the Vaugbn and the Jen nings e;<amples deal \\; Ih perfecl certainty. Tha t is. Keith Vaugho knows with perfect certainty that he could sell his la nd for SII.424 nex t year. Similarly. Lida Jennings knows wit h perfeci (."Cnai IllY that Kaufman & Broad could receive $9 1.000 for selli ng its land, UnfOrIUna!ely. bUSinesspeople frequenlly do nor know future cash nowS. This uncertainly is treated in the next exa mple.

90

EXAMPLE 4.2

Part II Valuatioro amI Cllpilal Budgeting

U _. ty and Valuation Professional Artworks. In t., is a firm thal spe<u\ues in modern

nee. ~all'" 000 ' 1\ th· . of paintings. The INnager is thinking of buying an original Picasso for,~'. WIt e ~:~~ In selilng It at the e nd of one year. The manager eKpects that tile palntlng Will be worth .

one year. The relevant cash flows are depicted in Figure 4.],

Figure 4.3 cash Flows tor Investment in Painting

$480.000 Expected cash inflow

\0------- ) Time

Cash outflow -$400,000

Of course this is only an expectation--the painting could be worth more o r less than S480.000.

Suppose the ~uaranteed interest rate granted by banks is 10 percent. Should the firm purchase the

piece of art! . ' . O\Jr first thought might be to discount at the IntereSt rate. Yielding:

$480.000 = $436 364 1. 10 '

Because $4]6,364 is gre.ner than $400.000. it looks at first glance as if me painting should be ~ur.

h d H 10 perceot is the return one can eam on a r iskless investment. Because me polin{·

c ue . owever. f 2S rcent to ing is quite risky. a higher db.count rate is called for. The m<lnager chooses iJ, ~te ~ pe . refte<:t this risk. In other words. he argues that a 25 percent expected return IS fair compensation

for iI.ll investtnent as risky as this painting. The p~senl vlllue of the paintiog becomes:

$480.000 _ $3 .. 000 1.25 '

Thus. the manager believes that the painting is currently overpriced at $400.000 afld does nOt make

the purchase.

The precedinganalvsis is typiC<11 of decision making in loday'scorporations., though real-world examples a're. of courSC. much more complex. Un fortunately, a~y e,;.amplc with risk poses a problem not faced in a riskless exam~le. In an.example wl~h r~~~tl~S~ cash nowS, the appropriate interest rate can be determined by slmpl~ ch~km~'ffi I few banks. The selection o f the discount nne for a risky investment IS qUIte a. I . IC~ I task . We simply don't know at this poin t whether Ihe d iscount rate on the palOllng III Exam le 4.2 should be II percent. 25 pe.rcent. .52 percent. o r some other percentage.

8e~use the choice of a d iscount rate IS so difficult, we ".'-erely wanted t? broach t1~e subject here. We must wait uotil the spec i rl~ material on fisk and return IS covered III later chaplers before a risk-adjusted ana lYSIS can be presented.

Chapter 4 DiscQunted Cash Flow Valll .. tiOIl " 4.2 The Multiperiod Case

The previous ~tion presented the calcula tion or future value and present value for one period only. We will now perfonn the calculations for the multi period case.

Future Value and Compounding s uppose an individual were to make a loa n of $ 1. At the end of the firs t yea r, the bor­rower would owe the lender the principal amount of $ 1 plus the interest o n the loan at the interest rate o f r. For the specific case where the inte rest rate is, say, 9 percen t, Ihe borrower owes the lende r:

$ 1 x (I + r) = $1 x 1.09 = $ 1.09

A t the end of the year, though. the lender has twO choices. She ca n ei ther take the SI.09--or. more generally. (I + r)-out o f the linancial market. or she can leave it in and lend it again for a second yea r. The process o f leaving the money in the fi nancial market and lending it fo r another year is called compounding.

Suppose the lender decides to compound her loan fo r a not her year. She docs this by taking the proceeds from her first one-year loan, $1.09, and lending this amount for the next yea r. At the end of next year. tben. the borrower will owe her:

$ 1 X( I +r)X( 1 + 1')=$1 X(I + 1')2= I + 2r+l,J >I X ( 1.09) X (1.09) = $1 X (1.09)' = 5 1 + S. IS + $.OOS I = $ 1.1SS 1

This is the tot al she will receive two years from now by compounding the loan . 10 other word s. the capital ma rket enables the investor. by prO\'id ing a ready oppor­

tunity for lending, to transform $ 1 today into 5 1.188 1 at the end of two years. At the end of three yea rs, the cash will be SI x ( 1.09)1 = $ 1.2950.

The Illost important point to notice is that the total amount the lender nx:eives is not just the $1 that she lent plus two years' worth of interest on $1:

2Xr=2xS.09 = S.JS

The lender also gets back an amount r, which is the interest in Ihe second year on the interest thai was earned in the lirst year. T he lerm 2 X r represents simple interesf over the two years. and the term r1 is referred to as lhe inlereSI 011 iJllereSI . Tn aUf exa mple, this latter amount is exactly:

,., = 15.091' = S.OO81

When cash is invested at' compound interest, each intere st payment is reinvested. With simple interest. the- interest is not reinvesled. Benjamin Frank lin's statement. " Money makes money and the money that money makes makes more money:' is a colorful way of explai ning compo und interesL The d iJTerenee between compo und interest and sim ple interest is illustrated in Figure 4.4. In th is e,;ample, the d if· fl:rencc does not am ount to much because the loan is for $ 1. If the loa n were for $ 1 million. the lend er would receive $ 1.1 88. 100 in two years' time. Of this a moun t. $8, 100 is interest 011 in terest. The lesson is tbat those sma ll num bers beyond the decima l point can add up to big d olla r amoun ts when the transa ctions are for big amount s. In addit ion. the longer-las ting the loa n, Ihe more important interest o n interest becomes.

92

Figure 4.4 Simple and Compound Interest

EXAMPLE 4.3

Pan 11 V;lluation ;md CHpita\ Bud~eli!1g

$1295 $1.270

$1.188 $1 .180

$1 .09

s ,

1 year 2 years 3 Y .... The dark-shaded area indicates the difference between . compound and simple interest. The difference is substantIal

over a period 01 many years or decadas.

The general formula for <In investment O\'(: f many periods can be wrinen as follows:

Future Va lue of an Inwstmcnl:

FV = CoX (1 +rf (4.3)

whe re Co is the C'.tsh 10 be invested at dat~ 0 (i.e .. toda~) , .r i ~ the intereSt nile per period . a nd T is the number of periods over which the cash IS l1l\ cslro.

IS h Pyo, Ku has put $500 in a savings account at the First National Bank

Interest on nterest U ' K h h d of Kent. The account eams 7 percent. compounded annually. How much wi ll Ms. u ave at teen

of three years? The answer is:

$500 x 1.07 X 1.07 X 1.07 =' $500 X (1.07)1 = $6 12.52

Figure 4.5 illustrates the growth of Ms. Ku's account..

Figure 4.5 S uh·Pyng Ku's Savings Account

$612.52

ssoo

o Z Time

3 10

- ssoo Time

S612.52

t Z 3

EXAMPLE 4.4

EXAMPLE 4.5

ChapleT 4 Discounted Cash F low Valuation 9J

Compound Growth Jay Riner invested $ [ ,000 In the stock of the SDH Company, The com·

pany pa~ a current dividend of $2, which is expected to grow by 20 percent per yeu for !.he ne-xc ry./o years, 'Nhat will !.he divideI'id a f the SOH Compatly be after (WO yearsl A simple calculation gives:

$2 x (1,20)1 "" 52.B8

Figure 4.6 illustrates the increuing value of SOH's dividends.

Figure 4.6 The Growth of Ihe SOH Divldonds

sz.88

t! 52.4&

" D $2.00 f----' Q

o Time

z

Cash inflows $2.40

$2.00

o Time

$2.88

z

The two previous examples can be calculated in anyone or several ways. The computa­tions could be done by hand, by calculator, by spreadsheet , or with the help or a table, We willlntroduce spreadsheets in a few pages. and we show how to use a calculator in Appendix 48 on the Web si te. The appropriate table is Table A.3. which appears in tbe back of the lext. This table presentsfilTllI't' 1'lI/ueo/51 o//he end 0/ Tperiods. lbe table is used by locating the appropriate interest rate on the horizontal and the appropriate number of periods on the venical, For exam ple. Suh-Pyng Ku woukllook at the rollowing portion of Table A3:

Interest Rate

Period 6% 7% 8%

2

3

•

1.0600

1.1236

1.1910

1.2625

1.0700

1.1449

11.22501 J.J 108

She co uld calculate the future value of her $500 as:

$bOO Initial

investment

x 1.2250 Future value

or$ 1

1.0800 1.1664 1.2597

1.3605

$6 12.50

In the example concern ing Suh-Pyng Ku. we gave you both the initial jm'cslmenl and the int erest !""dIe and then asked yo u to calculate the fulUre va lue. Alternatively. the interest rale co uld have been unknown. as shown ill the followiog example.

Finding- the Rate. Carl Voigt, who recently won $10,000 in die lottery, wants to buy a car in five years.

Carl estimates that the Cilr w iU COSt $16, I 05 at that time. His cash flows are displayed in Figure 4 .7.

What interest rate must he eam to be able to "Hard the car! (continued)

PIIII1 II Valualion :lnd C8pitll.l Budgeting

Figure 4.7 Ceah Flows tor purchase of carl Voigt 's Car

Cash inflow $10.000

5 Trme o

cash outflow -$1&.105

The ratio of purchase price to initial cash is:

$16,105 $10,000 = 1.6105

Thus, he must earn an interest rate cl'Iat allows $ I to become $1.6105 in five years,Tabie A] tells us

cl'Iat an interest rate of 10 percent will allow him to purchase the car.

We can express the problem algebraia\1y :u.:

$10.000 X (I + r)l .. $ 16.105

wh~' Is the interest rate neede<l to purdwe the car. Because S\6.105/ $10.000 =

(I + ,)1 .. 1.6105

r = 10%

Either the table. a spreadsheet. or a hand a.1culator lets us solve for r.

1.610S.wehave:

The Power of Compounding: A Digression .. . . Most ople who have had any experience wilh compounding are Impressed "':Ith liS

'er':ver lo ng periods. Take the siock market. for example. Ibbotson and Smque· he~ have calculated what the SIOc\.:. market returned as a whol.e f~om 1926.,th~~~ "008 I They find that one dollar placed in these stocks at the begmnmg or 19_6 0

have 'been worth S2,049.45 at Ihe end of 2008. This is 9.62 percent com~unded annu­ally for 83 yea rs- that is. (1 .0962)83 = S2.049.45, ignoring a small ro undm.8 erro~.

The example illustrates the great difference between eompoun~ and ~lmple mter­est. At 9.62 percent , simple intcrest o n SI i s.9.~2.cents ~ year. ~.mple Interest ~ver 83 ears is $7.98 (=83 X $.0962). That is, a n mdlv.dua l wLlhd rawmg ~ .6~ cen.ts.l!\er~ yea~ would have withdrawn $7.98 (=83 X $.0962) over 83 yea.rs .. TllIS IS ~Ulte a bll below the $2,049.45 tbat was obtained by reinvestment of all pTlnclp~1 and 1nlere:s1.

The results are more impressive over even longer periods. A person With no expene~ce in compounding might think that the value of SI at the end of 166 years would be tWI~ the value of S I at the end or 83 years. if the yea rly rate of return stayed the same. Actu all the value or 51 at the end or 166 years would be the square of the value ~f 51 at the en~ of 83 vears. That is., if the annual rate of return remained the ~me, a Sl1I'lvestmenl ill cornmo~ stocks should be worth $4,200,245.30 (= 51 X (2.049.4) X 2,~9.45)1 .

A few years ago an archaeologist unearthed a relic stating that Julius Caesa r lem the Roma n equiva l~nt of one penny to someOIle. Because there.was no record .of .the

b · rep,·,d 'he archaeologist wondered what the mterest and pnnclpal penny ever emg •

'S/IKks, &rrdJ, Bills. alld lrrflarWn I SBBI J. 1009 Ytarbook. Momin~~ta r, Chicago. 2009.

EXAMPLE 4.6

Chapltr 4 Discounted Cash floI\' Valualion 95

would be if a descendant of Caesar tried to collect from a descendant or the borrower in Tbe 20[h century. Tbe archacologist fell that a rate o r 6 percenl migbt be appropri­ate. To his .surprise, the principal and interest due arter more Ihan 2,000 years was vastly greater than the entire wea lth o n earth.

The power of compounding can explain why the pa.rents or well-to-do ra milies rre­quem ly bequeath wealth 10 their grandchi ldren rather than to their children. That is, they ski p a generat ion. The parents would rather make Ihe grandchildren very rich tha n mak.e the children moderately rich . We have found that in these families the grandchil. dren have a more positive view or the power or compounding than do the children.

How Much for That IslandF Some people have said that j( was the ben real estate deal in his_ tory. Peter Minuit. director general of New Netherlands, the Dutch West India Company's colony In North Arnerte.. in 1626 allegedly bought Manhattan Island for 60 guilders' worth of trinkets from native Americans. By 1667, the Dutch were forced by the British to exchange jt (or Suriname (per­haps the worst real estate deal ever). This sounds cheap: bot did the Dutch really get the btner end of the deal~ It is reported that 60 guilders was worth about $24 at the prevailing exchange rate. If the native Americans had sold the trinkets at a fair market value and invested the $24 at 5 percent (tax free). it would now, ",bout 38] years later. be worth more than $3.1 billion. Today. Manhattan is undQubt~ly worth more than S3.1 billion. so at a 5 percent rone of return the native Americans got the worSt of the deal. Ho~r. it ilWested at 10 percent. the amount of money they received would be worth about:

$2'4(1 ~ r)' = H X I. P" ll!! $1 71 quadrmion

This is a lot of money. In faCt, $171 quadrillion is more than all the real estate in the world is worth today. Noee that 00 one in the history of the world has evilr been able to tim! an ifwtsunenc yietding 10 percent every year for ]8] years.

Present Value and Discounting We now know that an annual interesl rate of 9 per~nI enables the investor to t rans­form $1 today into SI .1881 two years rrom now. In addition , we would like to k.now the rOllowjng:

How much would an inveSlor need to lend today so Ihi:lt she could receive SI IWO years rrom toda~

Algebraically. we ca n wri le Ihis as:

PV x (1.09)' = $1

In the preceding equation , -PV stands ror present value, the amOUnI or money we must lend today to receive.$ 1 in two years' time.

Solving for pv in tbis equation, we have:

$1 PV = IT88T = $.84

This process of ca lCUlating Ihe present value or a future cash now is called discounting. It is the opposite of compounding. The difference betw«n compounding and dis­counting is illustrated in figure 4.8.

To be certain that S.84 is in ract the present va lue of $1 to be received in two years., we must check whether or not , ir we leot S.84 today and rolled over the loan ror IWO years.

.. Figure 4.8 Compounding

and Discounting

EXAMPLE 4.7

ParI II Valuation ~ "t1 Cupitai BudS~lin!

Compounding at 9'10

$2.367.36 Compound interest

$1.soo Simple interest

• ~ $1,000 I-:::::~--------~ $UKlO o

$422.41 Discounting at 9'10

2345678910

Future years

The lop line sttows the growth of $1,(01 at compound interllSt with the funds invested at !I pereent $1,000 x (1.09)" = $2.367.36. Simple inter.st is shOWft on me next line. H is $1.000 + {lD x ($1.000 x .Q9)] = $1.900. The bottom line sflows the discounted value of $1 ,000 if the interest rate is 9 percent

we would get exactly $1 back . If Ihis wen: the case, the capital markets would be say­ing thai 5 1 rC(eivcd in two years' time is equivalent to having $,84 today. C hecking Ihe

exact nu mbers. we gel: $.84t 68 x t.09X t.09 ~$ 1

In olher words. when we ha\'ccapila\ markets wjlh a sure interest rate of 9 perccn t. we are ind ifTerent between receivi ng 5.84 today or $ 1 in tWO years. We have no reason to treat these t WO choices d itTerently from each other because if we h ad $.84 today and le nt it out fo r twO years. it would return $1 to us at the end or that ti me. T he value . 84 I = I I( 1.09)!] is called the present "u luc factor. It is Ihe raclor used 10 calculate the

present va lue or a ruture cash now. In the Tllulti period C.1SC, the rormula ro r pV can be written as rollm,,'s:

Pre5(:nt Va lue of Im'estment: CT

PV = ( I +r)"' (4.4)

Hen::, C.,. is the cash n ow at dale Tand r is the appropriate discount ra te.

Multipe.riod D iscounting Bernard Durms will receive $10.000 three ~ars from now. Bernard can eam 8 percent on his investmenu . 50 the appropriate discount rate is 8 percent.. Whu is the

present value of his fuwre (;Ish flow! The answef' is:

pV "" $10.000 x L .~r = $ I 0.000 x .7938 = $7.938

Figure " .9 Hlustnte.s the aW1ic1l.tion of (he present v",Jue factor to Bernard's investment. When his investments grow at -tn 8 percent r.lote of interest. Bernard Dumas is equally inclined

toward receiving $7.938 now and receiving $ 10.000 in three yean' time. After all. he could cOnYert

the $7.938 he r1!ceives today in to $ I 0.000 in three years by lending it at an in terest rate of 8 per<:ent.

EXAMPLE 4.8

Oapter" Di~ounted Cash FI(>W Valuation

Figure 4.9 Discounting Bernard Dumas's Opportunity

• .!!

. $10,000

" CI $7,938

o Time

Cash inflows

o 2 3

97

$10,000

! 2 3

Time

~rnud DUlnn could have reach«! his present valve. calcu\atiCN'l in one of several way$. The com­puCltlOn could have been done by hand. by cakuJatof". with a spreadshHt. or with the help of TOlbie A I

wh~h a~n in the back of the ~el(t. Thi~ table pre:sents the P(~sent "ICIuc 0{ S f to be rec.cfved ~, ~ periods. e use the table by locaung the appropriate interen rate on the horilO(lW and the. . ate nurnl:>ef- of iod the . appropn· . per son verou.L For example. Bernard Dumas would look at the following po"" bOO of TableAI :

Intere.st Rate

Pe rio d 7% 8% 9%

.9346 .9259 .9174

2 .8734 .8573 .8417 J .8163 [.7938[ .7722

• .7629 .7350 .708<

The appropriate present value factor is .7938 .

In th~ prcced i l~g example we gave bot h the interest ra te and the future cash now. AhernalJvely. Ihe 100erest ra te could h ~ve been unknown.

Fin.dln.&: the .Rate A customer of the Ch",ffkin Corp.. wanu to buy a tugoo..t tod<iy. Rather thin pa: ,"!: 'mmedlate~y. he w/U pay S50.ooo in three years. It will cost the Chaflkin Corp. $38.6 I 0 to

~'Id ~e tugbOat Immediately. The relevant cash ftows to ChafflOn Corp. are displ3yed in Figure .... 10. hn Interest rate would the Chaffkin Corp. charge to neither &.1ln nor lose on the sale?

Figure 4,10 Cuh FlowS' fOfTugboat

Cash inflows sso.ooo

r------ -J Time 0 3

Cash outflows -$38,610

(controe-d)

9S

EXAMPLE 4.9

Learn mOle about using Excel tor time

yalue and other calculat ions at

!fWW §lIIdy1~ MIll,

ParI IJ Valmn ion aru.l Capital Budgeting

The ratio of construCtion cost (present value) to sale price (future \/alue) is:

$38.6 10 = 7722 $50.000 .

We must determine the interest rue that a"OWl> $1 to be r-eceived in three years w have a present

value of $.7722. Table A I tells Ui that 9 percent is that interest rate.

Finding the Number of Periods suppose we are interested in purchasi ng an asset that costs $,50,000. We currently have $25.000. If we cae ea rn! 2 percent o n Ihis $25,000, how long until we have Ihe $50,000? Finding the answer involves solving fo r the last variable in the basic presen t value eq uat ion, the number of periods. You already know how to gCI an approximate answer to this particular problem. Notice that we need to double our money. From the Rule of 72 (see Problem 75 at the end of the chapler), this will take tlbout 72/12 =

6 years a t 12 percent. To come up with the exact answer, wccan aga in roanipulate the basic present value

equation . The present value is $25,000, and the future va lue is $50,000. With a 12 pt r­cen t discount rate, the basic eq uation takes one of the following forms:

$25,000 ~ $50.000/ 1,\2'

$50.000/25,000 ~ 1,\2' ~ 2

We thus have a future value factor of 2 for a 11 percent rate. We now need to solve for I. Jf you look down the column in Table A.I that corresponds to 12 percent, you will see that a future value facto r of 1.9738 occurs at six periods.. It v.ill tbus take about six years. as we calculated. To get the exact answer. we have to explicitly solve for ( (by using a financial calculator or the spreadsheet on the next page). I f you do this, you will see that the a nswer is 6.1163 years. so o ur approximation \vas quite dose in this case.

Waiting fo r Godot You've been !>aving up to buy the Godot Company. The total COSt will be $10 million. You currently have about $2.3 million. If you can eam 5 percent on your money. how

long will you have to wait! At 16 percenl.how long must you wait! At 5 pen:ent.you·1! have to wait a long rime. from the basiC present value equation:

$2.3 mill ion = S I 0 million/ I.OS'

t .OS' = 4.35

L = 30 years

At 16 percent. things are a little better. Verify for yourself that it will take "bout 10 years.

Freq ue ntly. an investor or a business will receive more than one cash flow, The pres­ent value of a set o f cash flows is simply the sum of the present values of the individual

cash flows. This is illustrated in the following two examples.

Cl1aplrr " DiSCQunled Cash Flow Valu,uion " SPREADSHEET APPLICATIONS

Using a Spreadsheet for Time Value of Money Calculations More and more, businesspeople trom many different areas ( . sheets to do a ll the different types of calculations that co oot l.ust~1/larICe and accounting) rely on spread­we INiII show you how 10 use a ~dsheel I handle heme ~p In ~ real world. As a result. in this section. . . ........ ~ 0 t vanous time value of money ,..".,..n ........

In Iris chapter. Wewitl use Microsoft ExcellO. bullhe d .. .....,..........,., .swe present . cornman s are SImilar for othef types of ft W assume you are already familiar with basic spreadsheet ~r so ware. a

As we have .."......~ IOns.

en! value, the cfi=~::~~:: ~:~:rO;: :::c:,~ng :~~=ial unknowns: future \Wue, ~-each. In Excel, lhase are Sho\'m in a nearby box. . a '='I-"OO"S I. lhere IS a separate formtAa to(

In these formulas, pv and tv are present and future value. nper is me number of periods and rate is the discount. or Interest. rate. '

Two things are a litHe tricky here. First. UflIike a financial calculator. the spreadsheet requires that the rala be entered as a decimal. Second as with mosl finandal calctAalors, you have t~ put a negaHve sign on eilher the present value or the M ure value 10 solve for lhe rate or the num·

To Find EnterThis Formula

Future value Present value Discount rate Number of periods

- FV (r.u e.nper.pmt,pv)

- PV (rate.nper.pmt.fv) = RATE (nper.pmt.pv,fv)

'" NPER (rate,pmt.pv.fv)

ber of periods. For the same reason il solve f unless you 'inpUt a _01' f I , you or a present value. the answer win have a negative "inn .~",.... lYe U ure value The same is tn.Je when - ,. To illustrate how . hi h' you compute a fUl ure value.

invest $25,000 at 12~= peruse t e:":°lrmuJas, .te wiB go back 10 an example. in the chapter. If you like this: year. ong unll you have $5O,ooo? You mighl sal up a spreadsheet

EXAMPLE 4.10 Cash flo ..... Va1uation KIM h 10 . f h fl ye ayer as won the Kenwcky State Lottery and will receive tne fol-

wmg sec 0 cas OWS ovoer the next cwo ~ars:

Year Cash Flow

I

2

$20.000

SO,OOO

(continued)

100 ParI II Valualion and Capilal Builgl:' li nl!

Mr. Mayer (40 currently eam 6 percent in his money market account. so the appropriate discount

I70tC is 6 percent. The present value of the ('ash flows Is:

Year Cash Flow x Present Value Factor "" P resent Value

$20,000 x I.~ == $20,000 x I .~ == $18,867.9

2 $50,000 x (_ I_y = $50,000 x (I !",)l == $44.499.8 1.06. . Total $63.367.7

In other words. Mr. ~~r is equally inclined toward receIving $63.]67.7 today and receiving $20,000

;md $50,000 over the next twO years.

EXAMPLE 4.11 NPV Firuonce.com has an opportunity to invest in a new high·speed computer that COstS $50,000.

The computer will generate cash flows (from con ,~ngs) of $25.000 one ~r from now, $20.000

( nd $1 5 000 three""'l"'5 from now The computer will be worthless after mree [WOre .. n rom now, a , ,- . . . years, aod no addilional ash Rows will occur. Finance.com has detenTlIn~ ~t the ip~iI.le discount rate is 7 pen::em for this invesonent. Should Firunce.com make thIS Investment In a new

high-speed computer! What rs the net present value of the Invest~t! The cash fk,w, and present value bnors of the propose<! computer are u follows:

C ash Flows Present Va lue Factor

y..,.o -$SO.OOO I = I

$25.000 I

1.07 = .9H6

2 $20.000 (1.~7Y = .8734

3 $15.000 (,6,)' = .• ,63

The present value of the cash nows is;

Cash Flows x Present value bctor = Present v;due

Year 0 - $50.000 x I = -$50,000

I $25.000 x .9H6 = $23.365

2 $20.000 x .8734 = $17.468

3 515.000 x .8163 = $12.244.5

Total: 5 3.077.5

Finance.com shoukl invest in the new high-speed computer beause me present value of its future

cash nows is greater than its COst. The NPV Is 53.0n .5.

Chap'"' 4 Di.;('ounlN Cash Flow Vlt l o~tion 101

The Algebraic Formula To derive an algebraic formula for the net present \'a lue of a cash now, recall thai the PV o f receiving a cash now one year fro m now is:

PV = C/ ( J ..J- r)

a nd the PV of receiving. a cash now two ye:l rs from now is:

PV = C/O + I')!

We can write lhe NPV of a T-period project as:

C1 CJ

C7

NPV = - Co +T+r+ (I + r): + ... + ( 1 + r)"" (4.5)

The initial n ow. - co' is assumed (0 be negative because i l represents an investment. The Z is shorthand for Ihe sum of the series.

Wc will close out this section by ullswcring the question we posed at the beginning of the chapter concerning baseball player Mark Teixeira 's co ntract. Remember that the COniract reportedly called for a signing bonus of $5 million to be paid immediately, plusa salary or $175 million to be di stributed as S20 million per year in 2009 and 2010 and $2:2.5 million per year for 2011 Ih rough 10 16. If 12 percell! is the appropriate di s· count rale. what kind of deal did the New York Yankees' tirs! baseman snag?

To answer. we can calculate Ihe presenl va lue by discounting each years salary back LO the present as follows (nolice we assumed the futuTe salaries will be paid at Ihe end of Ihe year):

Year 0: 55.000.000 = $ 5,000.000

Year I: S20,000.000 x 1/ l.J2 - $ 17.857, 142.86 Year 2: S20.000.000 X I / 1.I2~ = $ 15.943 .877.55

Year 3: $22 ,500.000 X 1/ 1.1 2' = $16.01 5.055.58

Year 8: 522,500.000 x 1/ 1.1 2' = S 9.087.372.63

If you lill in the missing rows and then add (do il for practice). you will see Iha t Teixeira's contract had a present va lue of aho ul $ 112.55 million. or on ly about 63 percent of the SI80 million reponed va lue, but s till pretty good.

4,3 Compounding Periods So fur. we have assumed that compounding and disco unting occur yearly. Sometimes. coolpounding may occur'lilore frequently than just once a yea r. For example. imagine that a bank pays a 10 percent inle(est rate "compounded semiannually." This me_ans that a $ 1.000 deposit in the bank wou ld be worlh SI ,OOO x 1.05 = $1.050 after six mont hs, and $1.050 X 1.05 = S1.l02 .50 at the end of Ihe year.

The end-of-the-year v,'ealth can be written as:

$1.000 (1 + . iOY = $1.000 X ( 1.05)2 = $1.101 .50

Of course, a SI.OOO deposit would be wo nh $ 1, 100 (= $1.000 X 1.10) with yea rly com­pounding. Note thai the future: value at Ihe end of one year is greater with 'Semiannua l

102

EXAMPLE 4.12

EXAMPLE 4.13

PMI II Valuation and Capi tal BUlJgtling

compounding than wilh yearly compou nding. With yearly compou nding. the original SI.OOO remains the investment base for the full yea r. The origina l $1.000 is the invest­ment base o nly for Ihe fi rst six mon ths with semiannual compounding. The base over the second six months is Sl,050. Hence one gel s inlerf!st 011 il1leres/ with semia nOllOl1 compounding.

Because $1.000 x 1.1025 = $1, 102.50. 10 percent com pounded semiannua lly is the same as 10.2S percent compounded anmmlly. In other wo rds. a nlliona l investor CQuid not care less whether she is quoted a nlle of JO percent compounded scmiaonually or a ralc of 10.25 percen t compounded annua lly.

QUlI rie rly compounding at 10 percen t yie lds wealth at the end of onc year of:

( 10)' $ 1,000 1 +.- = $1.103.8 1

More generally, compounding an investment 1/1 limes a ycar provides end-or-year wealth of:

(4.6)

where Co is the initial investment and r is the stated annual interest rate. The stated annual interest ra te is the annual interest rate wi tho ul considera tion of compou nd­ing. Ba nks a nd other financial institutions may use other names for the stated ,lnnual interest rate. Annual percentage rate (APR) is perbaps the most commo n synonym.

EARs What is the end.o(.year wealth if J3ne Christine reu~ives a stated annual interest rue o f

H percent <:ompounded monthly on a $1 irwoestmeml

Using Equation 4.6. her wealth is:

SI(I + ·::r = $1 X (1.02) 11

:. $1.2682

The annual nte of retUm is 26.82 perc.enL This anno,lf rate 01 return is called either the effect i ... e

annual rate (EAR) or the effe c tive annual yield (EAY). Due to compounding. the effl!CtiYe

anllual interest rate is greater than the stated annual interest rate of 24 percent. Algebraically. we

call rewrite the effective allnual inte~t rate as follows:

Effecti ... e AnnuaJ Rate:

( 1 +-'.)"-1 m

(4.7)

Students 3n!' often bothered by the subtnctlon of I in Equation ... .7. Note that end-of.ye;tr wealth

is composed of both the interest earned over the year lmd the o riginal principal. We remove the:

original principal by subtnCting I In Equation 4.7.

Compounding Frequencies If the stated annual rate of interCH. 8 percent. Is compounded

quarterly, what is the efl"ecti ... e Mlnual rate!

Using Equation 4.7. we have:

(I +;; r - 1 '" (I + '~r - I ... 0824 "" 8,24%

Chapl€"!"4 Discounl¢(l Cuh Flow Vlllu;lIion IOJ

Referring back to our origillal example where C~ - $1.000 and r = 10%. W!! can generate the fol/owing table:

Effecti ... e Annual Rate =

Co Compounding Frequency (m) C, (I + ;r _ t SI.ooo Yearly (m - I) $1.100.00

1.000 Semiannually (m ,. 2) 1,102.50 1.000 Quarterly (m = 04) 1.103.81 1.000 Daily (m ::: 365) 1.105. 16

Distinction between Stated Annual Interest Rate and Effective Annual Rate

.10

. 1025

.10181

.105 16

The dislinction between the stated annual interest rate (SAJR). or APR. and Ihe effec. tive annual rate (EAR) is frequently troubling to students. We ca n reduce the confu­sion by noting that the SA IR becomes meaningful only if the compounding interva l is given. For examplc. for an SAIR of 10 perccnl. thc futu re value at the end of o ne year wilh semiannual compo unding is II + (.IO/2W = 1.1025. T he future va lue witb q uarte rly compounding is II + (.1O/ 4lr = 1.1038. If the SAIR is 10 percent but no compounding interval is given. we c.1nnot calcula te future value. In ot her words we do not know whether to compound semiaol)uully, quarterly. or over some Oth e; interval.

~y conlmst. the EAR is meaningful without a compound ing imerval. For example. a n EAR o'~ 10.25 tx:rcent means th at a $1 iovestmen t will be worth $1.1025 in one year. We can thlllk of thIS as an SA IR of 10 percent with semian nual compounding or an SAIR of 10.25 percent with annual compoundi ng. or somc o ther possi bility.

There can be a bigdirre rencc between an SA IR and an EAR when interest rales ure large. For example, consider '"payday loans." Payday loans are short·term loans made to consumers. often for less than two weeks, and arc oO"ered by companies such as AmcriCash Advancc and Nationa l Payday. T he loans work like this: You wriTe a check today that is postdated. \\'hen the eheck date arrives, you go 10 the store and p<ly the cash for the check. or the company cashes Ihe check. For example. AmeriCash Advance a~ lows you to write a postdated eheck for $125 for 15 days later. In this case. t hey would gIVe you $ 100 today. So. \~'hat are the APR a nd EAR of this arrangemem? First. we need 10 find the interest rate. which we ca n rtnd by the FY equa tion as fo llows:

FY = PV (I + rV $ 125 "" $ ]OO X( I +,.)1

1.25 = ( I + r)

r = .25 or 25%

That doesn't seem too bad until you remember this is the interest rate for 15 doys.' The APR of the loan is:

APR = .25 x 365/ 15 APR = 6.0833 or 608.3311/"

104

EXAMPLE 4.14

EXAMPLE 4.15

PIU1 II Valuation ;anu Up'!al BUdFC'ling

And the EAR ro r this loan is:

EAR = ( I + r i m)'" - I EA R :=. ( I + .25J.k>jf I5 - I

EAR = 227. 1096 or 22,7 10.96%

Now that's a n interest ratc! Just to see what a difference a day (or three) makes. let's look al National Payday's terms. Th is company will allow you (0 write a postdated check for the same amoun t, but will al10w you 18 days to repay. Check for yo urself that the APR of this arrangement is 506.94 percent and the EA R is 9,128.26 percent . This is lower, blu still not a loan we usually reconuncnd.

Compounding over Many Years Equation 4.6 applies for an investUlent over one yea r. For an investment over one or more (7) years. the formula becomes this:

Future Value \\ith Compounding:

FV - C(I + L j·· ' o m (4.8)

MultiyeV' c ompounding Harry DeAngelo is investing $5.000 n a 1uted ,,"n1131 interest

r:lte of 12 percent per yetr. compounded quan erly. for five years. What is his we~lth n the end of five years!

Using Equnion 1.8, his wealth is;

$5.000 X {I + . ~2 r" '" $5.000 X {I.OW' = $5.000 X t.8061 = $9,0)0.50

Continuous Compounding The previo us discussio n shows that we can compound much more frequently than once a year. We could compound semiannually, qua rterly, monthly. daily. hourly. each minute. or even more o flen . The limiling case would be to compo und every infinitesi­ma l insta nl . which is commonly called continuous compounding . Surprisingly. banks a nd ot her fi na ncia l insti tution s some times quole continuously com po unded rates, which is why we study them.

Though the idea o f compounding Ihis rapidly may boggle the mind, a simple fo r­mula is involved . With conti[lUOUs compounding. the value at the end of T years is e;>(pressed as:

(4.9)

where C, is the initial investment. r is the slaled a nnual interest rate. and 7 is the num~r of years over wh ich the investment runs. nu~ number ,. is a constant and is approxima tely equal to 2.7 18. It is not an unk nown like Co' 1" . clnd T.

C o ntinuous Compounding linda DeFond invested $ 1.000 n" COtltinuously compounded /"'lItt of 10 percent fo r one year. Wh~t is tht v~lue of her Wl:.1lth at the end of one yearf

From Equation 4.9 we have:

$t .OOO X e"· = $ I ,000 x 1. 1052 "" $t . IOS.20

EXAMPLE 4.16

EXAMPLE 4.17

Figure 4.11 Annual, S.mlannuat, and Continuous Compounding

Chapler 4 Discounted Cash Flow Valualion "5

This number can easily be read f~ Table A.S. We merely set r. the value on the horizontal dimen. sion. to 10 percent .lind T. the value on the V"ertial dimension. to I. for this problem the releVlo"t portion of ttIe t.1I.ble is shown here:

Continuously Compounded Rate (r) Penod - _

(T) 9% lOX 11 %

I

2 J

1.0912

1.1972

1.3100

[1. 10521

1.2211

1.3-499

I.f 163

1.2"'61

1.3910

Note thilt a continuously compounded roue of 10 percent is equiVlolern: to an annually compounded r:lte of 10.52 percent. In other words. lind" Defend would not care whether her b.JInk quoted .lI

continuously compounded rate of 10 percent or a 10.52 percem rate. compounded annually.

Continuous Compoundin&:. Continued Linda DeFond 's brother. Marlo:. invuted Sl.ooO at ~ COntinuously compounded rate of 10 percent for two ~al"'S.

The appropriate formula here is:

$1.000 x ~ '0'<1 - $1 ,000 X e '» = $1 .221.10

Using the portion of ttt. table of contirovously compounded rates snown in the previous \!l(;Imple. we find the v.:llue to be t .2214 .

Figure 4.1 1 illustrates the relation ship among: annual. semiannua l. and continuous compounding. Semiannual compounding gives rise to both a smoother curve and a high er ending va lue than does annual compounding. Con tinuo us compounding has both the smoothest curve and the highest ending value o f all.

Present Value with Continuous Compounding The Michigan State l onery IS going to pay you S 100.000 at the end of four years. If the annuat c.ontinuously compounded rate of interest Is 8 p&l'tent. what Is the present value of this ~ymen{!

•

o

I I $100.000 x e 'OI." "" $100,000 X 1.3771 '" $72.616.37

Intere,t earned

'\r 2 3 4 5 Years

Annual compounding

•

o

Interest earned

~

2 3 4 5

Years

•

o

earned _______ ___ 1

23. Veers

5

Semiannual compounding Continuous compounding

------~------~~----

10' Part II Valuation and Capital BooSt-ling

4 .4 Simplifications The lirst part of this chapter has examined the concepts of future value and present va lue. Although these concepts allow us \0 answer a host of problems concerning the time value of money. the human etforl involved can be excessive. For example, consider a bank calcu lating the present value of a 20~year momhl), mortgage. This mortgage has 240 (= 20 X 12) payments, so a 10\ of lime is needed to perfoml a con­ceptually simple lask .

Because many basic finance problems are potentially time-consuming, we search fo r simplifications in this section. We provide simplifying formulas fo r four classes of cash flow streams:

Perpetuit y.

Growing perpet uity.

Annu ity.

G rowing annuity.

Perpetuity A perpetuity is a constant stream o f cash flows without end . If you 3re thinking that per· pelUiti('s have no relevance 10 reality. it will surprise you that there is a well·known case of an unend ing cash fl ow stream: The British bonds called w nsols. An investor purchas· ing a consol is entitled to receive yearly interest from the British government forever.

How can the price of a consol be detennincd? Consider a consol that pays a coupon of C dollars each year a nd wi ll do so forever. Simply applying the PY formula gives us:

py_ C + C + C + . .. - ~ (I + rf {I + r)J

where the dots at the end of the formul a stand for tbe inlinite string of terms that con· tinues the formula. Series like the preceding one a rc called geolllt'll"ic ~('ries . It is well known that even though they bave an inlinite num ber of term s. the whole series has a linite sum because each term is only a fraction of Ihe preceding term . Before turning to our calculus books. though , it is worth going back to our original principles 10 see if a bit of linancial int uition can help us lind the PV

The present value of the consol is the present va lue of all of il s fut ure coupons. In other words. it is an amOUIl( o f money that, if an investor had it today, would enable him to achieve the same pattern of expenditures thai the co nsol a nd its coupon s would. Suppose an investor wanted to spend exactly C dollars each year. If he had the consol, he could do this. How much money must he have today to spend the same amount? Clearly, he would need exactly enough so that the interest o n the money would be C dollars per yea r. If he had any more. he could spend more than C dollars each year. Ir he had any less. he would eventually run ou t o f money spend ing C dollars per year.

The amount that will give the inveSlOr C dollars each year, and therefo re the present value or the conso lo is simply:

PV = {;. (4.10) ,. To conrlrm that thi s is the righ t answer, notice that if we lend the amount el l", the interest it ea ms each year will be:

Interest = {;. x ,. = C r

EXAMPLE 4.18

Chaplet"4 Di~ounttd Cash Flow Valulllion 107

wl1ich is exactly the consol Payment . We have arri ved al Ihis rormula fo r a consol :

Formula for Pr~1 Value of Perpetuity:

PV -~ C C . +. - I + r + (I + r)2 + (I + I")J (4.11)

~ £ , It is comforting to know how easily we can use a bit of linancial ill1uition to so lve thi s mathematical problem.

Perpetuities Consider a perpetuity paying $100 a year. If the rele.va.nt interest f1Ite is 8 percent. what is the value of the consol !

Using Equation 4.10 we have;

$100 PV = -:os = $1,2SO

Now ~uPf>Ose mat interest rates (all to 6 pertMt. Using Equation 4.10 the value of the perpewity is: $ 100

F"I = .06 = $1.666.67

Note that the value of the perpetuity rises with a drop in the interest rate. Conversely. the vallie of the perpetuity falls with a rise in the interest ra te.

Growing Perpetuity Imagine an apartment building where cash flows to the landlord after e:rtpenses will be $100,000 next year. These cash flows are expected to rise at 5 percent per yea r. If one assumes that this.rise will continue indelinitely, the cash flow stream is termed a growing perpetuity. The relevant interest rate is I I percent. Thererore, the appropriate discount rate is II percent, and the present value o f the cash flows can be represented as:

PV _ S IOO.OOO ~ I OO.OOO( lo05) SIOO.OOO(lo05)' - loll + (1.11 )' + ( 1.11 ), + ...

+ SlOO,OOO(I.05)N-' (!.ll )": +

Algebraically, we can write the formula as:

PV=~ -.. CX( 1 +g) + C X(l + g }! CX( I + g ).\·- I I + r (l ;trF (l + r)J + ... + (I+r)-\' + . ..

wh7re C is the cash flow; to be received one period hence, g is the rate of growth per penod, expressed as a percentage, and r is tbe appropriate disco unt rate.

Fortunately. this rormula reduces to the ro llowiog simplifica tion:

Formula for Present Value of Growing Perpetuity:

PY =~ ' - 8 (4.12)

From Equation 4.12 the present value or the cash nows from the apartment building is:

5100.000 . 11 .05 ~ $ ).666.667

108

EXAMPLE 4.19

PUrl 11 Yaluation and Capilal Budgelin!!

There are three important points concerning the growing perpeluity formula :

I. Tile numerator: The numerator in Equation 4.12 is the cash flow one period hence. nOt at date O. Consider the fOllowing example.

Payina: Dividends Popovich Corporation Is jusl about to I»Y a dividend of $3.00 per- share. Inves­tors anticipue that the annual dividend will rise by 6 pel'1:em a year forever. The applicable discount

rue is I t pen::ent .. What is the price of the nock today!

The nume~tor in Equatlon ... J 1 Is the cash now to be received next period. Since the growth rate is 6 percent. the dividend neXl year is $3. 1 B (=:$3 .00 x 1.(6). The price of the stock today is:

$66.60 $3.0(1

Imminent

dividend

+ $3.18 . 11 .06

Preient V3lue of all

dividends beginni,,!

a year from now

The price of $66.60 indudes both the dividend to be received immedinely and the present value of

all dividends beginning a year from now. &!uaeion • . 12 makes it possible to ala.date only the present

Villue of all dividends beginning a year from now. Be sure you understand th is example: test questions

on this subject always seem to trip up a rrw of our stvdents.

2. Tht disCOll11l rllfe allli the grOll't" rate: The discount rater must be greater than Ihe gro ..... 'lh rate g for tbe growing perpetuity fomlUla 10 work. Consider the case in wh ich the growth rate approaches the interest rale in magnitude. Then. the denominator in the growing perpelUily formula gets infinitesimally small and the present value grows infinitely large. The present va lue is in fact undefined when r is less than g.

J. The timing lI5SlImp'ioll: Cash generally flows into and out of real-world firms both randomJy and nearly continuously. However. Equation 4.12 assumes that cash nows arc received and disbursed at regular and discrete points in time. In the exam­ple of the apanmenl. we assumed that the nel cash flows of S 100,000 occurred only once a year. In realilY. rent checks are commonly received ever)' monlh. Payments for maintena nce and o lher expenses may occur anytime y,.;th.in the year.

We can apply the growing perpetuity fo rmula of Equation 4.12 on I)' by assum­ing a regular and discrete pattern of cash flow. Although this assumption is sensible beca use the ro rmula saves so much time. the user should ne"er rorget that it is a n m·Jllmpt;Of1. This point will be mentioned agaio in the chapters "head.

A few words should be said about terminology. AUlho rs of financial lcx lbooks gen­erally use onc of two conventions to refer to tUne. A minority of financial writers treat cash nows as being received on exact dates- foT example date O. date I. and so fo rth. Under Ihis convention . date 0 represents the present time. However, beca use a year is an interval. not a specific moment in time, the great majoriry of a uthors refer to cash flows that occur at the end of a year (or alternmively. the end of a period). Under Ihis elld-oJ-the·year convent ion. tbe end of yea r 0 is the present, Ihe end of year I occurs one period hence, and so on . (The beginning of )'ear 0 has a lready passed and is nOI generally referred 10.)~

:SOTTlC'ti!llC1. financial writers merely spc'lI k of It eash 110w in )·c-ar .'f. Although th is terminology is ambigu· ous.. such ... Ti ters ,enerally lfItan the t lltl 0/ )Y'n ,.'f.

Chapter 4 Discounted Cash F10\\' Valua tion ". The interchangeability or the two conventions can be seen from the rollowing chart :

Date 0 = Now

End of year 0 = Now

Date I

End of yel.r t

Date 2 Date 3

End of year 2 End of year 3

We strongly believe that the dflfes cOIII'emion red uces ambiguilY. However. we usc both coovent ions because you are likely to see Ihe l'IIJ·oJ-)"elll' cOIII'emiol1 in )<ller cou rses. [n fact , both conventions may appear in the sa me exam ple for ahe s.'l ke of practice .

Annuity An annuity is ~ I.eve) strcan~ ?f regu lar paymenls that lasts for a fixed number o f peri. ods. No t surpnsU1gly. annuities are among the most common kinds of financial instru­ments. The pensions thai people receive when they retire are often in Ibe form of an annu ity. Leases and mortgages are also often a nnuities.

To rigure o ut the present value of an a nouilY we need to eva luate the ro llowing eq ualion:

.. . + C (I + r)'

The present value of rC(.-eiving Ihe coupons for only T periods must be less Ihan the present \'alue of a conso1. but bow much less? To answer this, we have to look at con. sols a bit more closely.

Consider the rol lowing time chart:

Now

Date (or end ofye.ar) 0 I 2 J T (T+ I) (T + 2) Consoli C C C. C C C .. . Coosol2 C C ... Annuity C C C .. . C

Consol I is a normal canso] wilh its first payment at date 1. The first paymem o r con. sol 2 occurs at dale T + I'.

The presen l va lue of.having a cash flow of C at each of T dates is equal to the prescnl va lue of consol I minus the preselll va lue of coosol 2. The presenl value of consol I is given by:

pv ~ C ,. (4. 13)

Consol 2 is JUSt a consol willl ils -firsl payment at dale T + I . From the pe rpetuity formula. this c0l1s01 will be \vonh Clr at date T.J However. we do not wanl the va lue

'SlIIdenl ~ fTnJuently think that elr is the p~nt \-a lue- at date T + I becau~ the eOAsol's first payment 1$ al datt 7 + I. HO\IIl:\l:T. the formula \'aluC'S the eon~l as of one period prior to the- /irst ~nl .

110

EXAMPLE 4.20

Part n Va]uillioll and Capilal BUdJCt;ng

at dale T. We want the value now. in o ther words. the present vaiue al dale O. We must discount elr back by Tperiods. Therefore. the present value of conso! 2 is:

PV_ C [ I I - r (1+,.)1 (4.14)

The present va lue of having cash flows for 7 years is the present value of a consol with its first payment at dale 1 minus the present value o f a cansol with its fi rst pay­ment at date T + 1. Thus the present value of an annuity is Equation 4. J 3 minus Equation 4. 14. This can be wOllen as:

C CI I I ,- -;:- (\ +r)"

T his simplifies to the following:

FannuJa for Present Value of Annuity:

PV = c[ ~ lit l rf] This can also be written as:

(4.15)

Lottery Valuation Mark Young has JUSt won the state Iottery. p~ing $50,000 a year for 20 years. He is to receive his fin.[ payment ;p, yeilr from I"IOW. The state advertises this u the Million Dollar lottery because $1.000.000 = 550.000 X 20. If the interen roue is 6 percent. what is the present

viltue of the lottery! Equation ~. 15 yields:

Present vatue of Mililon Doll~r lottery

1 - I 06 ~ I ' I = $50.000 x .~) Periodic payment Annuity faCtO(

= $50,000 X 9.8181

= $490.905

Ruher than being overjoyed at winning. Mr. Young 5ues the sate for misrepresentation and fraud. His legal brief sates that he was promised $1 million but rKtlived onty $-490.905 .

The term we use to compute the preseOI value of the stream of level paymenls. C. for T years is called an annuity (actor. The annuity facto r in the current example is 9.8 18 1. Because the annuity factor is used so often in PV calculatio ns, we have included it in Table A.2 in the back of this book. The table gives the values of these factors for a ra nge of interest rates. r. and maturity dates. T.

The annuity factor as expressed in the brackets of Equation 4.15 is a complex for­mula. For simplification. we may from time 10 lime refer to the annui ty factor as:

A:

EXAMPLE 4.21

Chlpler4 DiscountC1J CDsh Flow V. luation 111

This e)(pression s tands fo r the present va lue of $ 1 a year for T years at an interest rate of r.

We can also provide a formula for the future va lue of an an nuity:

FV = e[n +/)7 _ +1 = C((J +r;-' - Ij (4.16)

As with present va lue fac tors fo r annuities. we have compiled future value factors in Table A.4 in the back of thjs book.

Retirement Investing Suppose you put $].000 per year into a Roth tRA. The account ~ys 6 percent interest pel" year. How much will you have when you ",tire in 30 yean~

This question asks for the future value of an annuity of $3.000 per year for 30 years at 6 percent. which we can calculate as follows:

I{I +f) ' -I I It06 1D

FV=C = $3.000 X . , .06 'I = $3.000 x 79.0582 = 5237.1].4.56

So. you'lI have close to a quarter million dollars in the account.

Our experience is that annuity fo rmul as are not hard , but rricky. for the beginning slUdenl. We present four tricks next.

SPREADSHEET APPLICATIONS

Annuity Present Values Using a spreadsheet to find annuity present vakJes goes like this:

, , 3

A • c o • USI" a $preadshfttto lind annuity present yelue'

,

4 Wtkll is!,he sen! val .... 01 $500 ar lor 3 III!. if !he disc:ount "'e _ 10 rcenI?

G

5 we need to soIYe lor !he unknown esent Yalue. so we use !he formula PV rate. n I. tv .

• ~ Payment 3I'O<M.V'II period: S500

a N..mOer 01 3

• " " "

0i500unt rata: ., Ment YlIlue: $1 43.U

13 The formula entered In cal Bl1 i!,-PV(B9.B8.·S7.0); notice that tv i. lI!IfO and lhat \4 has a Uve ' on it. Abo noIiot N t rate is entered as a decimal. not 8 15

" "

II!

EXAMPLE 4.22

Pan II Valuation ~n<I Capit31 Budgetill~

Trick 1: A Delayed Annuity One of the trick s in working wi th annuities or perpe· tuities is gelling the timing exactly righ!. This is particula rly true when an annuit y o r perpetuity begins at a date ma ny periods in the future. We have found that even the brigb lest beginning student can make errors here. Consider the following cxample.

Delayed Annuities Danielle Caravello will receive a four·yellr 1onrouity o f $500 per year. begin.

ning at date 6. If the interest rne is 10 percent. what is the present v.alue of hllf" annuity! This situil·

tion un be graphed u follows:

o 2 J

The aN.lysis involves twO steps:

• 5 , $500

7 $500

I . C.lIculate the p~sent value of the annuity using Equation -i. 15 :

8 • $500 $500

Present Value of Annuity at Date S;

11- (1.10)'1 '

$500 .10 '" $SOO X A ..

= $500 )( 1. I 699

= $1.58-4.95

NOte tNt $1 ,S8-t.,}5 reprC!"Senu the present value ilt date 5.

10

Students freque ntly th ink that $1 ,58-'1.95 is the present value 10t d.a te 6 because the annuity

begins at due 6 . l-Io~er.our formula Y;l.lues the 10 nnuity as of one period prior to the first pay.

ment. This call be seen in the most lYPic,t1 use where the first payment occurs at date I. The

formula values the annuity as of due 0 in that cue .

2. Discount the present value of the annuity b.ack (0 due 0:

Present Value at Date 0:

SI.584.'il5 (1.10)S $981. 13

Again, Il ls worthwhile mentioning that because the Ulnuicy formula brings DlInielle's annuity back

to date 5. the second calculation must discount over the remaining five periods. The two-step pro·

cedure Is graphed in Figure 1. 12.

Figure 4,12 Discounting Danlelle caravello's Annully

I I I Date 0 2 3 4 567 8 9 10 Cash flow $500 $500 $5OO..- S500

,//~ $984.13 _------ $1.584.95

Step one: Discounllhe four pavrnents back to dele 5 bV using the annuity IOfmula. Step two: Discount the present value at date 51$1.584.95) back to present value at date O.

EXAMPLE 4.23

EXAMPLE 4.24

Chapter.. Di~un t l"t.l Ca~h Flow V~ l l.Ia\ion

"' Trick 2: Annuity Due The a nnu ity formula of Equalion 4. 15 assumes that the first annuily paymcnl begi ns a full period hence. This type of a nnuity is somctimes caJled an allnuity in arrellrs or an ordinary (In/w iry. Wbat happens if the annuity begins today- in o ther words. at date O?

A nnuity Du e In a preyj~ enmple. MarkYoo." received $50,000 a yev- for 20 years from the nate lottery. In dut el(ample, he WJ.S to receive the first p,tyment 10 year from the wino; ... , date. let uS

now assume that the first payment occurs immediately. The total number of paymenu remains 20.

Under chis new assumption. we have a 19-date annuity with the first payment occurring at date l-plus all extra payment ~t date O. The present value is:

$50.000 + $50.000 X A~

Payme ... t at date 0 I '}-year annuity

'" S50.000 + (S50.000 x 9.6036)

'" $530.180

$530,180. the present value in this example, is ~ter than $4'i10.905. the present value in the eartier lottery example. This is to be expected because the annuity of the current example begins

ea.rtier. An annuity with an immediate initi,tl p.1yment is c,tlled an omwity in odvonce o r, more com.

monly. an annuity dIN:. Always remember thn Equatioo 1.15 a.nd Table A.2 in chis book refer to an ordinory OfIOOity.

TriCk 3: The Infreq uent Annuity The foUowing example treats an annuity wit h pay. ments occurring less rrequently than once a yea r.

Infrequent Annuities Ann Che ... receives an annui ty of $450, p~ble once every two years. The

,tnlluiry stretches out over 20 yeus. The first payment occurs at date 2-that is. rwo years from today. The ,tnnual interest rate Is 6 percenl.

The crick is to determine the interest rate over a rwo-year period. The interest rate over two years is:

(1.06 X 1.06) - I .. 12.36%

That is , $ 100 invested over tWo years will yield $112.36.

What we want is the pnpent value of 10 $450 aonuit)' over 10 periods. with an interest rate of 12.36 percent per period:

I - ( I + . 1216)'0 ! 1 I $450 . 12)6 ;:;: $450 X A'," ... :: $2.505.57

Trick 4: Equating Present Value of Two Annuities The fo llowing example equates the presen l va lue of in Oows. with the present value of o utflows.

114

EXAMPLE 4.25

Pan II Valu;llion and Gopilal Budgeting

Workina with Annuities Harold and Helen Nash are saving for the college educOIotioo of their

newborn daughter, Susan. The Nuhes estimate that college expenses will run $30,000 per yex

when their daughter ~che.s college in 18 years. The annual interest rate Ollef the next few deudes will be 14 percent- How much money must they deposit in the bank each ye.l r so that their daughter

will be completely suppon:ed through four)'Nn of college! To simplify the cakubtioru. _ usume thn Sus",n is bom texby. Her ~renu will make the rim 0(

her four ,,"nual wition payments on her 18[h birthday. They will make equal bank deposits Oil each

of her fint 17 birthday1:. but no deposit at due O. This is illustnted 'lIS follows:

Dale 0 2 17 18 19 20 21

I I I I I I I Susan's Parents' Parents' P,rents' Tuition Tuition Tuilion Tuition

birth '" ,., 17lhand payment payment payment payment

deposit deposit I •• I , J 4 deposit

Mr . .Inc! Ms. Nuh will be making deposits to the blnk over the nllllt 17 years. l1>ey will be

wi(hcinwing $30.000 per year over the following fCXJr yelIl"I. We GIIn be sun!! they will be a.ble to

withdraw fully $30.000 per year if the present value of the deposits is equal to the present value of

the four $)0.000 wlthdraW3ls. This Qkubtion r!!qulres th~ steps.The first CWO determine. the present v.due 01 the withdl"lWVs.

The fiNI W!p detennines ye~rly deposits that will have a present value eqUl.1 (0 that of the

withdrawals.

I. We ca1culull the present value of the four fUt'S at college using the annuity formu la:

[I-v.hr l . $30,000 x . 1"1 - $30,000 x A ••

"" $)0,000 x 2.9 137 - $87.411

We asSume that SUSAn enters college on hcr 18th birthday. Given our discussion in Trick I.

S87.41 r represents the present value at date 17.

2. We. calculate the present value of the college education at date 0 as:

S87,41 I ('i'14j'i' '" $9,422.91

3. Assuming that Harold and Helen Nuh m ... ke depo$Iu to the bank at the end of each of the

17 ye ... rs, we calculate the annuil.I deposit that will yield a preunt ,-, ... Iut of ... 11 deposiu o f $9.422.91 .

This is c ... !culned as:

Because A:,', '" 6.3729.

C x A',', '" $9.422.9 1

C = $9,422.91 _ $1<7.5° 6.3729 •. ,

Thus deposiu of S 1.478.59 made ... t the end of each of the first 17 years: and In ... ute<! at 14 pen:ent

will provide enough money to make tuitioo pay-menu of $30.000 over the follow ing four years.

EXAMPLE 4.26

EXAMPLE 4.27

(;h3plfr 4 Discounted C .. ~h Flow Vah.llu ion

'" An ah.e:n~live melhod in Example 4.25 would be (0 (I) c-diculate the pre~n! value

of the IUlt.lon payments al Susan's 18th birthday and (2) caiculale annua l deposils so thai t~~ future value of the deposils at her 18th birthday equals Ihe preseOi va lue or Ihe IUIIIOO paymeniS allhat dale. Allhough Ihis lechniq ue can also provide the righ t ansv.'er, we have found Ihat i( is more likely 10 lead to errors. Therefore. we equate o nly present values in our presenlalio n.

Growing Annuity ~ash .flows in busi~ess are likely 10 grow over lime., due either to real grov., h or 10

mO"llon. The growlIIg perpetuity, which assumes an infinite number of cash nowS. provides one fo rmula to handle this growth . We now consider a growing annuity, which IS afilli/f' number or growing c .. sh nowS. Because perpetuilies of any kind are tare. a formula for a growing annuity would be useful indeed. Here is the formula: .

Formula for Presenl Value of Crowing Annuity:

PV ~ e[- I- __ 1_ x (.!....:!:..! )'.j ~ el l -[~r r _ g r _ g 1 + ,. ,. g (4.17)

A~ before, Cis Ihe payment to occ ur at the end of the first period. ,. is the interest rate, g IS the rale o f growth per period, expressed as a percentage., and T is the number of periods for {he a nnu ity.

Growing Annuities SWlr't Gabriel . ... $econd.year MBA $tudent. has just been o ffered a ;ob at

$80.000 a year: He ancicipUe.5 his $;Ilny illcreuing by 9 pert:ent ... yur unol his retirement in

40 yurs. Given ... n interest rue of 20 percent. what is the pre~ent value of his lifetime salary1

We simplify by assuming he will be paid hi$ $80.000 salary exactly one yur from now. and that

his 1.lIiary will conrinue to be pakl in Vlnual inu:l llmenu. The appropriate discount rate i .. 20 percent. From Equ ... tion 4. 17. the calculation is:

[ ' - (~rl Present ...... Iue of SWim's lifetime salary '" $80.000 x .20 ~.~~ :: $711 .730.71

Though the growing annuity formul ... is quite useful. it is more tedious than the other simplifying

formulas. Whereas most $ophiSUGlted calculltON have $pecial programs for perpe tuity. growing

perpewicy. and annuity. there is no special program for ... grOWing annuity. Hence. we must ca.lculate all the terms in Equation 4.17 directly.

More Growing Annuities In a previous example, Helen .ol.nd Huold Nash planned [0 make

17 identiul payment! to fund the coil. eduation of their daughter. Sus.an. Altematively.irm&ine tNt they planned to increll$e their paymenu u ... per'Cetlt per )'Nt: Whu would their first P')'TI'ent be~

The first two nep$ of the previo us Nash fam ily example mowed that the present value o f the college COSts was $9 .... 22.91 .These cwo steps would be the same here. However. the third step must

be altered. Now ..... e must uk. How mU(h should thei r fint payment be $0 that, if payments increue by 4 percent per ye"'f, the present value of all payments will be $9.422.9 11

(continued)

116 ~r1 11 Valuation and Capi!al Budgeling

We sec the growing annuity formula equal to $9.'122.91 i\nd solve for C:

I (I + f )'1 [ ( 1.0<)"1 c I - T+r~ = c I - m = $9.~22.91 r g . 14 -.01

Here.C = $1.192.78. Thus. the deposit on cheif daughter's first birthday i ~ $ 1.192]8. the deposit on

the second birthday is $1.HO.'l9 (= 1.04 X $1.192.78),and so on.

4 .5 Loan Amortization Whenevcr a lender extends a loan. some provision will be made for repayment of the principa l (thc original loan amou nt). A loan might be repaid in eq ual insta llments, l'Or example, or it might be repaid in a single lum p sum. Because the way that the princi. pal and interest are paid is up to the panies involved , tbere a re actually an unlimited number of possibilities.

In thi s seclion, we describe a mortized loan s. Working wilh these loans is a very slraightforward application of the present value principles thai We have al ready developed.

An lIIIIorli:ed loan may require the borrower to repay pa rts of the loa n a moun t over lime. The proccfoS of provid ing for a loan 10 be paid otT by making regular principal reductions is called lmlOrri~i!lg the loan.

A simple way of amortizing a loan is to have Ihe borrower pay the interesl each period plus some fi xed amounl. This approach is common with medium· term business loans. For example. suppose a business takes OUI a S5,000. fi ve· year loan at 9 percen!. The loan agreement calls for the borrower 10 p.'ly the interest on tbe loan bala nce each year and to red uce the loan balance each year by $1.000. Because the loa n amount declines by SI,OOO each year. it is fully paid in five years.

In th e case we are considering, no tice tha t the lo la I payme nt will deeline each year. The reason is that the loan ba lance goes down. resulling in a lower imerest cha rge each yea r, whereas the $1.000 pr incipal reduction is consla 01 . For example, the interest in the fi rs t year will be 55.000 )( .09 = $450. The total payment wi]] be $1.000 + 450 = SI.450. In the second yea r. the loa n bala nce is $4,000, so the interest is $4,000 x .09 := S360. and the total payment is $1.360. We can calculate the to ta l payment in each of Ihe remaining years by prepari ng a simple amorri:arioll schedllle as follo ws:

Begmning Total Interest Principal Ending Year Balance Payment Paid Paid Balance

$5.000 $I.'ISO $ 150 $ 1,000 $<.000 2 ' .000 1,360 360 1.000 3.000 3 3.000 1,270 270 1.000 2.000

• 2.000 1.180 180 1.000 1.000 5 1.000 1.090 90 1.000 0

Totals $6.]50 $1,350 $5.000

Otapler ~ D iscount<!\J C .. sh Flow VlIlu;)lioo 117

N otice.that in each year, the !nlereSI paid is given by the beginning bala nce muhiplied by the m{~res[ rate. Also nOltce th,ttthe beginning balance is given by Ibe end ing bal. ance from the previous year.

~robably the most common way of amortizing a loan is to have the borrowcr ma ke a smgle, fixed paymen t .every period. Almool a ll Consumer loans (such as car loa os) and mortgages .work l~lS way. For example, suppose our fi vc-year. 9 percent, $5.000 10<ln was amortIzed thIS way. How would thc amoniullion schedule loo k?

We first need.to det~rmine the paym.ent . From our discussion earlier in Ihe chapter. we know that thIS loan s cash flows a re III the form of an ordinary a nnuity. In Ihis case, we can solve for the payment as follows:

This gil'es us:

55.000 = C X {II - (1 / 1.09' )1(. 09) = C X «I - .6499)(.09]

C = 55.000/3.8897 = 51,285.46

The borrower wili lherefore make five equal paymenls of $ 1,285.46. Willihis pay 01T the loan? We will check by fillin g in an a mortizati on schedule.

In our previous example, we knew the principal reduclion each year. We then ca l. culated the inte~esl owed 10 gel the IOtal payment . In this example, we know the 100aJ

paymen t. We WIll th us :-a',:u late the interest and then subtract it from the IOta l pay. men t 10 calculate the pnnclpal pan ion in each paymen t.

In .the first year, the interest is $450, as we calculated before. Because IJl e total pa y. ment tS $1.285.46. Ihe principal paid in the first yea r mus t be:

Principal paid := $ 1,285.46 - 450 = $835.46

The endi ng loa n bala nce is Ihus:

Ending balance = $5,000 - 835.46 = 54. I 64.54

The.interest in the second year is $4,164.54 x .09 = S374.81, and the Joan balance dech?cs b.y 51.285.46 - 374.81 = $9[0.65. We ca n summarize all of the relevant cal. culatlons III the rollowin g schedule:

Beginning Total Interest PrinCipal Ending Year Balance Payment Paid Paid Balance

$5,000.00 $ 1.285.'16 $ '150.00 $ 835.46 $1.161.51 2 4.161.5'1

, r .285.'16 371.81 , 910.65 3,253.88

3 3.253.88 • 1.285.'16 29285 992.61 2.261 .27 4 2.261 .27 1.285.16 20351 1.081.95 1.179.32 5 1,179.32 1.285.'16 106. 11 1.179.32 0.00

Totals $6.427.30 $1.427.3 I $5.000.00

B!ec~use the loan. balance d~clines ~o zero, the five equa l payments do pay 0 1T the lOilll . Noltce that t~e tn.tcrest paid declines each period. Th is isn't su rpris ing because the loan bala~l~e IS gO lllg down. Given Chat the total paymenl is fi xed. the principal paid must be mlllg each period.

118

EXAMPLE 4.28

Pari II Valuation and Capilal Rudgeling

If you compare the two loan amonizalions in this section. you will see that the total interest is grealer fo r the equa l total payment case: $1.427 .31 versus $ 1.350. The rea­son for Ihis is that the loan is repa id more slowly carlyon. so the interest is somewhat higher. This doesn't mean that one loan is better tban the other; it simply meanS Ihal o nc is effectively paid off faster than the o ther. For example. the principa l reduct ion in Ihe first year is 5835.46 in the equal tolal payment case as compared to 51.000 in the

first case.

Partial Amorti:r.a tion, or "Bite the Bulle t" A c:ommon arrangement in real esute tending

might call for a S-year loan with, say. a IS-year ;J;mortiution. What this means is that the borrower

makes a paym",t every month of a fixed amount based on a I S-year amortization. However. after 60 months, the borro_r makes iii single, much larger payment called a --balloon -- o r "bullet" to pay

off the loan. Because the monthly payments don't fully pay off the loan. the loan is said to be partially

amortized. SUp{:lo~e we have a $100,000 commercial mortgage wi th a 12 pen:.ent APR and a 20-year

(240-month) amortiution. Furthe r suppose the mortgage has a five-year balloon. W hat will the

monthly payment be? How big wi ll the balloon payment be? Tne monthly p~ent can be Cillculated based on an ordinary annuity with a present v;alue of

$100,000. There are 140 payments. and the interest rate Is I perc:em per month. The payment is:

$100,000 "" C x [I - (1/1.0[1..0)/.01]

:= C X 90.8194

C:= $1,1 01.09

Now. there 15 an easy way and a hard way co determine the balloon payment. The hard way is to

aCtually amorti"le the loan fo r 60 months to ~e what the balance is at that time. T he easy way is

to recognize that after 60 months. we have a 240 - 60 :: ISO-month loan. TM payment is st ill $1.101 .09 per month. and the interest rone i$ $till I percent per month. The loan balance is thus the

prescnt value of the rernaining payments:

loan balance :: $1.l01.09 X [I - ( 1/ 1.01'., /.0 1]

= $1.101.09 X 83.3117

= $91.7+4.69

The balloon payment is a subnantial $91 ,744. W hy is it so large! To get an idea. conside r the fi rst

payment on the mortgage. The interest in the first month is $ 100.000 X .01 = $1,000. Your p;I)'­

ment is $1.1 0 1.09. so the loan balance declines by only $101.09. Be<ause the loan balance declines

50 slowly, the cumulative "pay down" over five years is not greaL

We will close Ihis section with an example Ihal may be of part icu lar relevance. Federa l Stafford loans are an important source of financing for many college students, helping to cover the cost o r tuition , books, new cars. condominiums. and many olher Ihings. Sometimes students do not seem to fully realize that Stafford loans have a seri­ous drawback.: They must be repaid in monthly installments. usually beginning six

months after the student Jc:aves school. Some SlatTord loa ns a re subsidized. mean ing that the interest does not begin to

accrue until repaymenl begi ns (this is a good thing). If you are a dependent under­graduate student under this parlicular option, {he tola1 debt you can rll n up is.

Chaplt r 4 Discounted Cash Flow Valuation 119

at most. 523,000. The maxi~um interest rale is 8.25 percent o r 8.25/12 = 6875 -cent per mon.lh. Under .Ih.e "sta ndard repayment plan:' the i03ns are amo~ized ::;r \0 years (subject to a mlnHUUm paymen t of $50).

S~ppos~ you max oul borrowi ng under this program and also e.el sHIck paying Ihe ma~tnlu.m mterest rale. ~eginning six mo nths aner you gra duale (~r otherwise depart the l~ary tower), what wtll your monthly payment be? How mllch will you owe after ma kmg paymeO(s for fo ur yea rs?

Giv.en our carlier d iscussions. see if you don't agree that you r monthly payment assumlng~ $23.000 tatalloan is S282. 10 per mont h. Also, as explai ned in Example4.28, after making payments far fOllT years. you still owe the present value of tbe remaining payments. There a re 120 payments in all. After you make 48 of them (the fi rst four years), you have 72 to go. By now, it should be easy for you to verify Ihal the present

SPREADSHEET APPLICATIONS

Loan Amortization Using a Spreadsheet Loan amort' r . . lZa I~ IS a cornmon spt"eadsheet application. To illustrate, we wilt set up the problem thai ~ ex~r1'IIned earlier: a five-year, SS.OOO. 9 percenlloan with constant payments. Our ~""eadsheet looks like IhtS: --

no Pari II ValuatiOn lind Capilal Budgeting

value of $282. 10 per month for 72 mOOlhS 011 .6875 percenl per monlh is just under

$16,000. so you still have a long way to go. Of course, it is possi ble to rack up much larger debts. According to the Asso­

ciation of American Medical Colleges. medical slUdents who borrowed w attend medical school and graduated in 2005 had an average student loan balance of $120.280. Ouch! How long will it take the average slUdent to payoff her medical

schoOl loans?

4.6 What Is a Firm Worth? Suppose you a re a business appraiser trying to determine the \·alue of small com­panies. How can you determine what ;l firm is worth? One way to thint< about Ihe question of how much a firm is worth is \0 calcula\e the present value of its future

cash flows. Let us consider the example of a firm that is ex pected to generate net cash nows

(cash inflows minus cash outflows) of $5.000 in the first year a nd $2.000 for each of the next five years. The firm ean be sold for S10.000 seven years from now. The owners of the firm would like to be able to ma ke 10 percent on their investment in

the firm. The value of the firm is fou nd by multiplying the net cash nows by the appropriate

present value factor. The value of the firm is simply the sum o f the present values of

the individual net cash newS. The present value of the. oct cash nows is given next.

The Present Value of the Firm

Net Cash Flow Present Value Present Value of End of Year ofthe Firm Factor (10%) Net Cash Flows

$ 5.000 .90909 • 4.545A5

1 1.000 . 81645 1.652.9Q

3 1.000 .75131 1.502.62

4 1.000 .68301 1.366.02

5 1.000 .62092 1.1041.64

, 1.000 .564047 1.128.94

7 10.000 .513 16 5,131.58

Present value of firm $16.569.35

We can 'llso use the simplifying formula for an annuity:

$5.000 (2.000 X A ',.,J 10.000 ~ 516 569 35 1.1 + 1.1 + (1.1)1 ' . .

Suppose you have the opportunit y to acquire the firm for $12.000. Should you acq uire the firm? The answer is yes because the NPV is positive:

NPV = PV - Cost

$4.569.35 ~ 516.569.35 - $12.000

The incremental value (NPV) o f acquiring the firm is $4 ,569.35.

EXAMPLE 4.29

Oapler 4 O~Oll ntcJ Cash Flow Valualion 121

Firm Valuation The Tro·, PC ' . an Ina ompany IS contemplating investing $1 million in four new outlets In Los Angeles. Andrew La. the firm's chief finan cial officer (CfO). has estimated that the lovestrTlenu Will pay out cull flows of $200.000 per year for nine years and nothing thereafter (The cash (lows Will occur at the end of each year and there will be no cuh flow after 9 ,­Mr. Lo has determined that the relevant discount rate for this investment is 15 percent.. Th~::: th~ rale of re~urn that th~ firm can earn at comparable projeclS. 5hould the Trojan Pizza Com a make the InVeStments In the new outlets? p ny

The decision can be evaluated.u follows:

NPV = _$\ 000000 + $200.000 $200.000 + $200.000 .. Ll5 + (1.1 5)1 + ... (1.15) '

= - $1.000.000 + $200.000 x A'" = - $1.000.000 + $954.3 16.78 = - $45.683.22

The present value of the four new oude.u is onl" ,954 J "78 Th cl th I •.. e ou ets are worth less an they cost.. The Trojan Pizza Company should not make the investment because the NPV .

-$04S.683.2? tf the Trojan Pizza Company requires a IS percent rate of return, the new outlets a:; not a good Investment.

SPREADSHEET APPLICATIONS

How to Calculate Present Values with Multiple Future Cash Flows Using a Spreadsheet :~ti:~:tt up ~ ba~ ~dsheet to calculate the present ualues of !he individual cash IIows as folIO'-'/s.

we ve Slm~l calculated the present values one al a time and added them up·

I

I I

, I

=I -ill+ JI ll 1& (

,

~ ~ ~~ I

".

Summary and Conclusions

Par1 II Valuation and Capital Budgeting

Two b'lsic concepts, filflm! mllfl' a nd pn'J(.'IIr m/ul!. were inlroduccd in the beginning I. of thiS' ~h:lptcr. With a \0 percent inlcreSI rate. an in\'\!st~r wi th SI today ca n generate

'\ future value of S I.10 in a year. S1.21 [- 51 X ( Ll O)!) In two years.. and ~ on. Con­~crse ly present value a nalysis places a current value on a futu re cash now. With I h~ s..'m~ 10 ~nt interest r.lle. a dollar to be recci\'ed in one year has a present va ue 0

S.~ ( = SI/ I . IO) in year O. A dolla r to be received in two ycurs has a pre~nl val ue of S.826 1 : SI /( 1.I0)~ .

. . P percent per y C' tT Howc\'cr. we can 2. We commonly express an mtcrest nne as. say. - •. d ' . I . t.-speak of lhe interest r.ue as 3 percent per quarter. Although the stale . ,umU.l In c~

. . I "> n:ent (=3 ..... n:..'enl x 4). Ihe effective annual Interest rOLle 's est rate remains - pc .... - . ' . • th ~ 1".55 rcc tH (= (I.03t - 1J. In o ther words. th~ ~ompo~lndll\g process In~re.l ses t:

f~ture~al ue of an investment. Th~ limiting ~:l~ IS C~nfIilUOUS compoundmg. where funds are assumed to be reinvested every infimtesl ma l Instant.

3. A basic quantitative tech nique for financial decision m'llking is nCllePs re:~t ;;~~e (~~,; l r~ sis. The net present value fommla for an invcstme!ll t lat gencr.t e , future periods is:

c ' C N PV = - (.~ + (I ~I r) + (I ~1 rf + .. , + (I / r)r - - C~ + 6(1 +' r)'

The formula assumes that the cash fl ow at date 0 is the initial investment (a cash outnow), ,

4. Frequently. the actual calculation of present val,lIe is longhlilnd tediO~s. i;~e"=~~~~l~I~I~ of the present value of a long-term mortgage with mon t y paymen s e • of this. We presented four simplifying form ulas:

Perpetuity: PV "" ;-

Growing perpclUily: PV = r :-g

Annui ty: [I - (11 ,yj

pv "" C r

I - T"+"'r [

( I + g)~ Growing annuity: pv = erg

5. We stressed a few practical considerations in the aPhPlicatihonnOf thlc~~::~~~ 0111'/<,/1 a. The numerato r in each of the form ulas. C. is t e cas ow 0

perim/ /t{'IICt!. . • Id bl . plions b. Cash flows are gener.tlly irregular in practice. TO

I ~volhd. unwlI!booYkPro ... C,,~l~~S~~~ world

to create more regular \:Ush flO\'<"S art made bot llO " ',s lext alK.>, , " .-c. \ umber of present value problems involve <Innlllt tcs (or perpet~lIlcs) beglllllln.g.t

;e; periods hence. SlUdenls sho uld practice combining the a nnUi ty (or perpetUity) formuh with the discounting formula to solve these problems. h

d. Annuities and pcrpeLUit ics may have periods ?f e:ery 11"'0 or e',"a'YsilY" ~::~:~tu~~

than once a year. The annuity and perpetUity lormu as can

circumstances. f 't ' ust be e. We freque",Iy encounter problen;ts where the p~esent value 0 one a nnUl) m

equated with the present va lue o j another annlll ty.

Concept Questions

Questions and Problems

... ,c COuHllona 1-20)

Chapter 4 Di~oun!e.:J Cash Flow V;l luul ion " J

I. Compounding and Period As you increase the length of lime ill\'OI\'ed. wha t hap. pens to future values? What happens to present vn lues?

2. Inter~1 Rate5 " 'hu t happens to the fUlure value of a n annuity if you increase the nue r? What happens to the present value?

3. Present Value Suppose two al hleles sign 10·year contrclelS for 580 mill ion. In one case. we're to ld that the S80 Inillion will be paid in JO cq\1n1 installments. In the olher case. we're told that the 580 million will be paid io 10 insta llm('tlt s.. bu t Ihe install. mCllls will increase by 5 percen t per year. Who got Ihe beller dea l'!

4. APR and EAR Should lending laws be changed to req uire lellders to report EA Rs instead of APRs? Why or why 1I01?

5. Time V&Jue On subsidized Stafford loa ns. a common source of fUl!l.ncial aid foreal­lege students.. interest does not begin to accrue unti l repaymen t begi ns. Who receives a bigger subsidy. a freshman o r a senio r? Explain .

Use the following information to ilnsy"er the next five questions: Toyota Motor Credit Corporation (TMCC). a subsidiary of Toyota Motor Corporation. offered some securities for sa le to the public on March 28. 2008. Under thc terms of the deal. TMCC promised to repay the owner of OIlC o f these sectlritics $100.000 on March 28. 2038, but im'estors would receive nothing until then. Investo rs paid TM CC 524.099 for each of these securities: so they gave up $24.099 on March 28. 2008. for the pro1llise of a S I 00,000 payment 30 years later.

6. Time Value of Money Why would TMCC be willing to accept such a small amou nt loday (524.099) in exchange for a promise to repay about four times that a mount (S 1 00.000) in the future'!

7. CaD Provisions TMCC has the right 10 buy back the securities on the a llni \'l~rsary date at a price established when the securities were issued (this fe:l\ure is a tenn of this pa rt icular deal). What impact does this fe..'llUre have on the desirability of this security as a n investment?

8. T ime VaJue of Money Wou ld you be willing to pay 524.099 today in exchange fo r $ 100.000 in 30 years? What wo uld be the key considerations in answering yes or no? Would you r nnswer depend on who is mak ing the promise to repay?

9. IMestme-ot Coroparisoo Suppose thaI when TMCC oOered the security fo r 524.099 the U.S, Treasury had offered a n essentially iden tical security. Do you think it would hav~ had iI higher or lower price? Why?

10. Length of Jnn'st11l~nf The TM CC securi ty is bought and sold on Ib_e New York Stock Exchange. If you looked a t the price today. do you Ih ink Ihe price would exceed the $24.099 original price? Why? If you looked ill the yellr 20 19. do YOll think the price would be h,igher o r IQ\'ier than teday's price? Why'!

I. Simple Interest \'~rs'9: Compound Interest Fi rst City Bank JXlYS 9 percCIl! simple inlerest on it s !mVings account bala nces. whereas Second City Bank pays 9 percent interest compounded annuull)'. If you made a S5.000 deposit in eac-h bank. how much more money would you earn from your Second City Bank account :It the end of 10 years?

2. Calculating Future Values Compu te the futu re value- of S I.000 COml)()unded annu­a lly for a. 10 )'cars at 6 percen t. b. 10 years 31 9 percent. c. 20 years at 6 percen t. d. Why is the interest earned in part (c) not twice the a mount earned in part (a)?

Part 11 V"lllaliOIl and Capilai llud£cling

3. Calculating Present Vulues For each of the foll owing. compute the present va lue:

4.

s.

6.

7.

8.

9.

10.

V I Years Interest Rate Future Value Present a ue

, , I. 23

7%

15

" I. $ 15.151

51 ,557

886,073

550,IM

Calculating Interest Rates Solve for the unknown interest ra te in each o f Ihe

following:

V I Vears Interest Rate Future Value Present a ue

$ 242

410

51,700

18,750

2 , 15

30

$ 307

'" 162,181

483,500

P ·.. Sol,., '01' the unknown number of years in each Calculating the Number of en S I'

of the following:

V I Vears Interest Rate Future Value Present a ue

$ 625

810 18.400

2 1.500

'" IJ

32

"

$ 1,284

4,].41

402.662

1n.439

Calculating the Number of Periods At 9 percent im"rest. how long docs it take to

double yom moncy? To quadruple it? . .' , Calculating Present ValUl'S Imprudential. Inc .. has an unrwldcd pensIOn .habl ll t~'

f S750 million that must be paid in 20 years. To asSCss the value of the fi rm s stock. ~nancial analysts wallt to discount this liability back 10 t~e !,re~nt.~ If the rc!cv'ant discount fate is 8.2 percent. what is the present value of ,h iS hablhty.

C I "'

;00 Rates of Relurn Although appealing to more refined tasle~, art as a "" fi bl D . "00] Sothebv s sold the collectible has not always performed so pro lUI y. urlng - . . ' .

Ed ar Deg'ls bronze sculpture P('Iile Dallseuse de QI/(lr1Or:(' AilS at auctLo~1 ~o r a pflce of ~ IO,J II :500. Unfortunately for the previous owner. he had pu~ch.~s"d It 1~~, 1999 at

.. f 51' 377 ,·00 Wha t was his anlllm! rate of return o n 11115 sculpture. a pnce 0 _. . . ... • '

Perpetuities An investor purchasing a British con sol ,IS en\lll~ to ~ce,,'C .a nnu:ll a ments from the Bri tish governrne1ll fo rever. What IS tl~e pnce of ~I consul I~"I

~a~s S I20 ,mnually if the next payment occurs olle year tra m today. The mnrkel

intercst rate is 5.7 percent. Com put\! the future value of S I.900 con tinuously cotn-Contiuuous Compounding

pounded for . a. 5 years at a slaled annual interest r:lle 01 12 percent . b. 3 }'ears at a stated anuual interest rate of 10 percent . c. 10 years ill a stated a nnual interest rate ~f 5 percent. d. 8 yean at a SOiled annual inlel'csl rate 01 7 percent.

C~pl~'f" DiocOllll led Ca"h Flow ValU:llion 125

II.

12.

13.

14.

I'resent Value and Multiple Cush Flows Conoly Co, has identilied an investment proj­ect with the following ellsh flows. If Ihe discount ro ue is 10 pen . ."cnt. whill is the present value.of these cash fl ows"? Wbat is thc present value at IS pen,."cm'! At 24 percellt?

YeaI'" Cash Flow

$1,200

2 730

3 965

• 1,590

Present Value and Multiple Cash Flows Investment X offers to pay you $5.500 per yea r for nine years. whereas InvE'stmcni Y offers 10 pay you S8.000 per year lor five years. Which of these c,\sh now streml1S has the higher present v:due if th(' discount rate is 5 percent? If the discount mte is 22 percen t?

Calculating Annuit~' Pn 'Seut Value An investment offers 54.300 per ycar lor 15 years. wilh the lirst paymenl occurring o lle yea r from now. If th" required return is 9 per­cent. what is the v:I[ue of Ihe investment? What would Ih" vallie be if the pnymen ls occurred for 40 years"? For 75 years'~ Forewr?

Calculating Perpetwty Values The Perpetual Life Insurilnce Co. is Iryi ng to sell you all invcstment policy that will pay you and you r hei rs S20.000 per year forever. If the requ ired return on this in\'cstmeot is 6.5 percenl. how much wi l1 you pay for the pol icy? Suppose the Perpetual Life Insurancc Co. told yo u the policy costs S34O.000. At what interest rate would this be a fai l' dea l?

15. Calculating EAR Find the EA R in each of Ihe fo\lowingcases:

16.

17.

18.

Stated Ra.te (APR) Number of Times Compounded Effective Rate (EAR)

8% Q uarterly

18 Monthly

12 Oaily

14 Infinite

Calculating APR Find the APR. or stated rate. in each o f the followi ng cases:

Stated Rate (APR) Number of Times Compounded Effective Rate (EAR)

Semiannually 10.]%

Monthly '.4 Weekly 7.' Infinite 15.9

Calculating EAR First N.llioll:ll Ban k cha rges 10.1 percent com pounded mOnlhly o n its business 101lns. First Un ited Ban k charges 10.4 percent compounded semian· nUllny. As a polential borrower, to which bank would you go for a new loan?

Interest Ra tes Well-known lina ncial writer Andrew Tobias aTl!ues that he can earn 177 percent per year buyi ng wine by the (,'aSt:. Specifically. he -assumes that he will consume one SIO bottle o f line Bordeaux per week for the next 12 weeks. He l'an either pay S IO per week or buy a caliC or 12 bottles today. If h" buys the case. he

INTERMEDIATE tauesllons 21-60)

Pari II Valuation and Capital Budg\'ling

receives a 10 percent discount and. by doing so. cams the 177 pcr~nt. ~SSUDlC ~~ buys the wine and consumes the first boule loday. Do you agn.--c wLth hIs analysIs . Do you sec a problem with his numbers? ,

Calculating Number of Periods One of your customers is delinquent all hIS accounts 19. payable balanee, You've mUlUally agreed toa repayment schedule of ~ ~r month,

You will charge ,9 percent per month interest on the overdue bal,anee, .. ) I e current balance is 518,400, how long will it take for the account to be paid oft.

Calculating EAR Fricndly's Quick Loans. Inc .. offers you "tbree for four ~r I 20. knock on 'our door." This means you gCt 53 today and repay 54 w~en yo.u get :your

paycheck i~ one week (ore\se). What's the effective annua l return Fnendl~ ~e~rn~t~ this lending business? If you were brave enough to ask. what APR waul nen ys

say you were paying? . '.. 21. Future Value What is thc futurevdlue in seven years ofS I,OOO Invested In an .Iccount

with a Slated annual interest r.ue of 8 perttnt. a. Compounded annually? b. Compounded semiannually? e. Compounded monthly? d. Compounded continuously? . ..) e. Why docs the future value increase as the compoundmg peTJod shortens . .

Sim Ie Interest ,'crsus Compound Interest Fi rs t Simple Dank pays ~ percent Slr:n' 22. pIe rnterest on its investmcnt accoun ts. If Firsl Complex Rao k . p~ys tnterest on t~

accounts compounded annually, what mt~ should the b:m?k set If It wants to matc First Simple Rank over an investmen t honzoo of 10 years.

C I I r Annuities You are planning to Sllve for retiremcnt overthe ne;(t 30yc.ars. 23. T;~: ~hl~g~'Ou will invest 5700 a month in a stock account and S300 a montltdJllha

bond accou~l. The return of the stock account is e.'tpect.ed to be. 10 percent. an . t e bond account will pay 6 percent. Whcn you retire. you WIll ~ombtne your moneYrtnto

. h 8 ""rcenl rentm How mueh ca n you Withdraw each month rom an account WII an I~ : '00' vour account assuming a 25·year wuhdrawdl pen .

Calculating Rates of Return Suppose an investment offers to quadruple y~ur 24. money in 12 months (don't believe it), \\'hat ratt of return per quarter are you betng

offered? d 'ff, , t Calculating Ra tes of Rcturn You're trying to choose between two 1 erent 1Il\'es·

25. ments. botb of which have up.fron t costs of 575.000. In\'cst~ent G re tu~s ,SI35,000 . . '1m nt H returns S195 000 in 10 years. \\'hlcb of these tn"estmeOls to 51;( yea rs. .nves e ,

has the higher n:lUrn1 . '. . I. Growln Perpetuities Mark Wcinstelll has been worktng on .tn advanced techn.o.

26. 0 in I~ser eyc surgery. His tcchnbiogy wilt be .wailable in the near term. ~~ anll~,I . ~;es his first an.nual cash flow from Ihe technology to bc .S215,OOO, .recel\ed t~ ~ pa, 00 S L_quenl .nllu·LI cash flows will grow at 4 percent III perpetult). years lrom t ay. u~ • . . 0 ? What is the present value of the technology if the d iscount rale IS I ~rcellt.

Perpetuities A prestigious in\'estment ballk desi~n.ed a new seeunt)· that pays a 7.7. uarterl ' dividend of $5 in perpetuity. The first dIVidend ~curs one q~arter from

~ay. \~'ha t is the price of Ihe security if the stated annualmterest rate IS 7 percent. compounded quarterly?

Annwh' Present Values Wbat is the present value of an annuity of $5.000 per ~ear. 7.8. with the first cash now received three yea rs from today and the last one receIved

25 years from toda.y? Use a. discount rate of 8 percent. .

\n ' t'.' Prescnt ValDes \\'hlll is the value today of a 15·year annUIty that pa~'s S7SO 29. ~ y:a~ The annuity's first payment occurs six years from today. The annualmterest

rate is 12 percent for years Ilhrough 5, and 15 percent thereafter.

ChapleT 4 Discounled Cash Flow ValU31ion 127

30. Balloon Payments Audrey Sanborn has just arranged \0 purchase a 5450,000 vaca. lion home in the Bahamas with a 20 percent dmo,'11 payment. The mortgage has a 7.5 percent stated annual interest r.ue. compounded monthly. and calls for equal mouthly payments o\'er the next 30 years. Her first payment will be due one mottlh from now. However. the mongage has an eigh t·year balloon payment. weaniog that the balance of the loan must be paid 00' at the end of year 8. There were no o ther transaction costs or finance ebarges.. How much will Audrey's balloon payment be in eight years?

31.

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CaJcuJatiog loterest Expense You receive a credit card application from Shady Banks Savings and Loan offering an introductory rate of 2.40 percent per year. compounded monthly for Ihe first six months. jnc~asing thereafter to 18 percent compounded monthly. Assuming you transfer tbe S6.000 balllnce from your existing credit card and make no subsequent p.'lyments. how mueh interest will you owe :tithe end of the first yeur?

Perpetuities Barrett Pharmaceuticals is considering a drug project that costs S 150,000 today and is expected to generate end·of-year annua l cash flows of S 13,000, forever. At what d iscount rate would Darrell be indifferent between accepting or rejecl.ing the projcct?

Gro1\;ng Annuity Southern California Publishing Company is trying to decide whelher to revise its popular textbook. Fill(mcia/ Psycl/Oolltll)'Sis Af(lde Simple, Thc company has estimated that the revision will COSt 565.000. Cash nows from increased sa les will be 5 18.000 the first year. These cash flows will increase by 4 percent per year. The book will go out of print the years from now. Assume that the initial cost is paid now and revenucs are received at the end of each year. If the company requires an II percent return for such an investment. should it undertake the revision'!

Growing Annuity Your job pays you on ly once a year for all the work you did over the previous 12 months. Today. December 31. you just received your slliary o f 560.000. and you plan to spend all of il. However. you want to start saving for retirement beginning next year. You have decided that one year from today ),ou will begin depositing 5 percent of your annual salary in an account that will carn 9 percent per year. Your salary ~'ill increase at 4 percent per year throughout your career. How much money will you have on the date of your retirement 40 years from today?

Present Value and Interest Ra tes Whnt is the relationship between the value of an annuity and the level of interest rates? Suppose you just bought a 12.year annuity of 57.500 per year at the cu rrent interest rate of 10 percent per year. What happens to the value of your investment if interest rates suddenly drop to 5 percent? \Vhm jf interest rates SUddenly rise to 15 percent?

Calculating the Number of Payments You're prepared to make monthly payments of 5250, beginning at the end of this mont h. into an account that pays 10 percent interest compounded Q"lontbly. How many payments will you have made when your account balaoce reac~s S30,00Q'?

Cakulating Annuity Present Values You want to borrow S80.000 from yOllr local bank to buy a new sailboat You can afford to make monthly payments of SI ,650, but no more. Assuming montbly compound ing, what is the highest APR you can afford on a 6O-month loan?

CalcuJating Loan Paym('nts You need a JO·yea r. fixed ·rate mortgage to buy a new home for 5250.000. Your mortgage bank \vill lend you the money at a 6.8 percent APR for this 360·month loan. However. you can only afford monthly payments of SI,200. so you offer to payoff any remaining loan balance al the end of the loan in the form of a single balloon payment . How large \villthis bnlloon paymeut have to be: for you to keep your monthly payments at SI. 2OO?

tlS Par! II Valuation and Capillli Budgeting

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Present and Future- Values The present value of the following cash flow s~rc~m is 56.453 when discounted at 10 percenl annually. What is the value of the mlssll'lg

cash flow?

Year Cash Flow

I

2 J ,

$1 ,200

2.0\00 2.600

Calculat ing Present Values You just won the TV~1 Lon cry. You will recei,\'c $1 million today plus another 10 annual payments that IIlcrease by S350.00? ~r ye.lT. ThUs. in onc year you receive $1.35 million. In IWO year:" you gel $1.7 Imlhon. and so on . I f Ihe appropriate inlcresl ratc is 9 percent. what IS the present \'alue of your

winnings"? EAR \'I~rsus A.PR You have just purchased a new warehouse" To Ii ,~ance the pur­chase. you've arranged for .. 30-year mortgage for SO percent 01 the S~.600.000 pur­chase price. The monthly payment on Ihis loan will be 514.000. What IS the APR on Ihis loan'! The EAR? Present Value and Break.[,·en lntcrest Consider il firm with a contmct to sell :m aSSl:: t for SI35.000 three years from now. The asset costs S96.000 t~ produce loday. Given a relevant discount I""dle on this assel of 13 percent per year. \",11 the firm make a profil on this asset? AI what ratc does the finn just break cveo"! Prl.'Sent Value and Multiple Cash Flows What is the ~resen~ vtlluc of $4.000 per year. at a discounl mte of 7 percen!. if the first payment IS ra'Clved 9 years from now and the last payment is received 25 years from no\\~! Variable Interest Ratcs A 15-\'c:ar annuity pays S1.500 per mon th. and payments :are made ill the cnd of each m·onth. If the interest r,lIe is 13 percent compounded monthly for the lim seven years. and 9 percent compounded monthly therea fl er. what is the present \'alue of the annuit)t! Comparing Cash Flow Streams You have your choice of twO in\"esunelll accounts. Investment A is a IS-year annuity that features end-of-Illo nlh 51,200 ~Ylllents and has an interest nne of 9.8 pen:ent compounded monthly. 100·estmenl n IS a 9 percen t continuously compounded lump-sum investme~t . also good for 15 years. H~w much money would you need to invest in B today for II to be worth as mudl as Im estment

A 15 years from now? Calculating present Value of a Perpetuity Given an interest rate of 7.3 percent per \"ear. what is the value at da te t "" 7 of a perpetual stream of S2.100 unnual payments ihat begins at date t = IS? Cakulating EAR .A. local finanC(: company quotes a 15 percc:n~ interest rate on one­year loans. So. if you borrow S26.000. the interest for the year Will be S3 .9O? Bec.IUse ;.ou must repay a totlll of S29.900 in one yea r. the finance company ~qu~ you to pay 529.900/ 12_ or S2.49 1.67. per month over the ne:(t I ~ mon ths. IS.lhls a I) pen.:e~1 loan? What rate would legally ha\'e to be quoted? What 15 the effective annual nile.

Calculating Present Values A 5-year annuity of len ~.5~ semi,mllu,,1 payments will begin 9 yen rs from now. wit h the first payment comlll~ 9.) yea rs fro~ I~OW. If t.he discount rate is 12 percent compounded monthly. what IS the value o~ thiS annUlty five \"ears from no\\i ! What is the value three years from now? What IS the current value of the annuity?

CHALl.ENGE (Que_lions 51-76)

ChYpll'r 4 Discounled Clish Flow Va!Ull.l ion 129

49.

so.

5 1.

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53.

54.

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56.

Calculating Annuities Due Suppose you are going to recei\'e SIO.OOO per yea r for fh·e years. The appropriate in terest rate is II percent. a. \V'!lat is tbe present value of the payments if they are in the form of an ordinary

annuity? What is the present value if Ihe payments are an annui ty due? b. Suppose you plan to invest the paymellls for fi ve years. What is the future value if

the payments are an ordinary annuity? \Vhat if the p"yments arc an Hnnuity due? e. Which has Ihe highest present value. the ordinary annuity or annuity due? Which

has the highest fUlUre value? Will this ulwuys be \rue?

Calculating Annuities Due You want to buy a new sports ca r from Muscle Motors for S65.000. The contmct is ill the form of a 48·l11onth annuity due at a 6.45 percent APR. What will your monthly payment be?

Calculating Annuirics Due Vou wan t to lease a ~t or golf clubs from Pings ltd . The lease contract is in the form of 24 equal monthly payments at a 10.4 percent stated annuill inlerest rate. compounded monthly. Ik:c:ause the clubs cost S3.500 retail . Pings wants the PV of the lease payments to equal $3.500. Suppose that you r first payment is due immediately. What will your mOllthly lease payments be?

Annuilies VOli are saving for the college education of your two children. They are twO years apart in age: Oile will begin college 15 years from today and the other \\iIJ

begin 17 years from today. You estimate your children's college expenses 10 be S35.OOO per year per child . payabk at the beginning of each school year. The annual interest rote is 8.5 percent . How much money must you deposit in an account each year to fund your children·s education? Your deposits begin one yellT from today. You will make your last deposit when your oldest child enters college. Assume four Years of colleboe.

Growing Annuitics Tom Adams h:ls received a job ofTe r from a large investment bank as a clerk 10 an associate banker. His base salary will be $45,000. He will recch·c his first allnual salary paymcnt one year from the day he begins to work . In addi tion. he will get all immediate $ 10.000 bonus for joining the company. His salary will grow at 3.5 percent ellch year. Elich year he will receive a bonus equal to 10 perceot of his salary. Mr. Adams is c:.;pected to work for 25 years. What is the present value of the ofTer if the discount rate is 12 percent?

Calculating Annuities Vou have recently won the super jackpot in the Washington State l onery. On reading the fine print. you discover thai you have the following 1\\ 0

options: a. You will receivc 31 annual payments of SI75.000, witb the first payment being

deliwred roday. The income will be taxed at a r:Ue of 28 percent. Taxes will be withheld when the checks are issued.

b. You will receive S530.000 now. lmd you will not have to pay taxes on this amount. In addition . beginning one year from today. you will receive $125.000 each year for 30 years. The eash flows from this annuilY will be taxed at 28 percent.

Using a discount mte of 10 percent, which option should you select?

Calculating Growing .,nnuifies You have 30 years left until ret irement aud wanl to retire with SI .5 millioo. Vour sa lary is paid annually. and you will receive S70.000 al the end of the curren'"t year. Your salary will increase at 3 percen t per year. and )ou can earn a 10 percent retum Oll the money you im·est. If you save a constant pcn.'cnt­age of your salary. what percentage of your salary must you save each year'?

Balloon Payments On September I. 20(H. Susan Chao boughl a motorcycle for 525.000. She paid SI.OOO down and financed the balance with a five-year loan at a stated annual interest rate of 8.4 percent . compounded monthly. She started the monthly payments exactly one month after the purchli se (i.e .. October 1.2007). Two years later. at the end of October 2009. Susan got a new job and decided to pay ofT the loan . If the bank charges her a I percent prepaymen t penalty ba:>ed on the loan blilance. how much must she pay tbe bank on November I. 2009'?

Part n Valuation and Capital Budgeting

51.

58.

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60.

Calculating Annuitv Valoes Bilbo Baggins wants 10 save money to ~eel thre~ objec­tives. First he wo~ld like to be able to retire 30 years from now wlth .a ;~rement income of 520,000 per month for 20 years, with the first paymcnl.re~elv. 0 yea~s

d I h f S-ond he would like to purchase a cabm In Rlvendell 11\ an mont rom now........ • h d [ h , ed t f 5320 000 Third afler he passes on at teen 0 t e 10 years al an estlmat cos 0 " , . f 5 I 000 000 to his 20 years of withdrawals, be would like to leave an inhentance a , 0 ' If h ne hev.' Frodo. He can afford to save SI ,9oo per month for the next I years. . e

p II EAR be'ore he retires and an 8 perceOI EAR after he rellres. can earn an percent I' ? how mucb will he have to save each month in years 11 throug.h 30. . Calculating Aunuity Values After deciding. to buy a new ~ar, you c,an either lea~ h h 't w'th a three )'ear loan The car you wish to bu) costs S38,OO .

I ecarorpurc Mel I -. Siod a dS5'Oper The dealer has a special leasing arrangement where you pay. t ~y ffn. - hi month for the nel'i.t three years. If you purcbase the car, you Will P'ay It a III mO~ltl ~

avments over the next three years at an 8 percent APR. You believe that you "WI

~bi~ to sell the car for $26 000 in three years. Should you buy or lease the car. W?at bre:k-even resale price in' three years would make you indilTerent between buymg

and leasing? Calculating Annuity Values An AII-~ro defensive line~an is in contract negotia­tions. The team has offered the followmg sala ry structure.

Time Salary

0 $7,500.000

1 "1.100.000

2 5.100,000

) S.900.000

• 6.800.000

S 7,400,000

6 8,100.000

All salaries are to be paid in a lump sum. The pla~er has asked you as his agent to renegotiate the terms. He wants a S9 million sigl1lng bonus payabl: today a~d a contract value increase of S750,OOO. He also wants an equal sal.ary paId e,'e.ry _t fee

months, with the first paycheck three months fr?m now. If the lO~erest rate IS :> per· cent compounded daily. what is the amount of Ius quarterly check. Assume 365 days

in a year. . .

61.

Discouot Interest LoaDS This qut'stion illustrates what is known as (IISWI/III tnle',;sl.

Imagine you are discussing a loan with a somewh~t unscrupulous ie]~der. You .w~nt to borrow S20,000 for one year. The interest rate]s 14 percent. You and the len er a ree that the interest on the loan will be .14 x S20,000 ~ S2,800. So, the lend~r d~ducts this interest amollnt from the loan up front and g.ves you SI7.200. 111 thIS case, we say that the diseount is S2.800. What's wrong here'? . . ., . , Calculating '\nnulty Value> You are serving on a jury. A plalOuff. ]s sumg the Clt~ for injuries ~usta in~ after a freak street sweeper accident. In the 10011, doctors t~Stl­fied that it will be live years before the plaintiff is able to return to work. "The JU1 has already decided in favor of the plaintiff. You are tht' foreperso? of the Jury an. propose that ·thejury '!ive the plaintiff an award to cover the followlllg: (I) The pre!>­ent value of two yea~· bllck pay. The piaintiO·'s annual salary for the last twO ["roars

Id' h .- S42000 and S45000 res ......... tivel\'. (2) The present value a Ive

wou ave ,-"""n. , . 1'-- , (3) 5150 000 r. 'ears' future salary You assume the salary will be 549,000 per year. ,or

) , d ~' '(4) $25 000 for court costs. Assume that the salary payments;lfe pam an sUllenng. ,

Cbapter 4 Discounted Cal;h I-low yatuauon 131

62.

63.

64.

65.

equal amounts paid at the end of each month. If the interest rate you choose is a 9 percent EAR. what is the size of tbe settlement? If you were the plaintiff, would you like to see a higher or lower interest rate?

Calculating EAR with Poi.nts You are looking at a one-year loan of S I 0,000. The interest rate is quoted as 9 percent plus three points. Apo;", on a loan is simply I per­cent (one percentage point) of the loan amount. Quotes similar to this one are very common with horne mortgages. The interest rate quotation in this example requires the borrower to pay three points to the lender up front and repay the 101ln later with 9 percent interest. What rate would you actually be paying here? What is the EAR for a one-year loan with a quoted interest rate of 12 percent plus twO points? Is your anS\\o'er affected by the loan amouot?

EAR l'C($US APR Two banks in the area offer 30-year, 5200,000 mortgages at 6.8 perceot and charge a 52,100 loan application fee. However, the application fee charged by Insecurity Bank and Trust is refuodable if the loan application is denied. whereas that cbarged by I. M. Greedy and Sons Mortgage Bank is oat. The current disclosure law (equires that any fees that will be refunded if the applicant is rejected be included in calculating the APR, but this is not required wi th nonrefundable fees (presumably because refundable fees are part of the loan rather than a fee) . What are the EARs on these two loans? What are the APRs?

Calculating EAR with Add-On Interest This problem illustrates a deceptive v.'Uy of quoting interest rdtes called add-on il/teresr. Imagine that you see an advertisement for Crazy Judy's Stereo City that reads something like this: "$1,000 Instant Credit! 16% Simple Interest! Three Years to Pay! Low, Low Monthly Payments!" You're not exactly sure what all this means and somebody has spilled ink over the APR on the loan contract, so you ask the manager for clarification.

Judy e;t;plains that if you borrow SI,OOQ for three years at 16 percent interest. in three years you will OUl::

$\.OOO X 1.16) = SI,OOO x 1.56090 = $1,560.90

Judy recognizes that coming up with $1,560.90 all at once might be a strain, so she lets you make " low, low monthly payments" of SI ,56O.90/36 = $43.36 per month. even though this is extra bookkeeping work for her.

Is this a 16 percent loan? Why or why not? What is the APR on this loan? What is the EAR? Why do you think this is called add-on interest?

Calculating Annuity Payments Your friend is celebrating her 35th birthday loday and wants to start sID'ing for her anticipated retirement at age 65. She wants to be able to withdraw Sl JO,OOO from her savings account on each birthday for 25 years following her retirement; the first withdrawal will be on her 66tb birthday. Your friend intends to invest her money in the local credit union, which offers 9 percent interest per year. She wants to make equal annual payments on each binbday into the account established at the credit union fo r her retirement fund. a. If she startS making these deposits on her 36th birthday and continues 10 make

deposits until sher- is 65 (the last deposit will be on her 65th birthday). what amount must she deposit annually to be able to make the desired \\ithdrawals at retirement?

b. Suppose your friend has just inherited a large sum of money. Rather than making equal annual payments. she has decided to make one Iwnp-sum payment on her 35th birthday to cover her reti.c:ement needs. What amount does she have to deposit?

c. Suppose your friend 's employer wiII contribute $1,500 to the account every year as part of the company's profit-sharing plan. In addition, your friend expects a S50,OOO distribution from a family trust fund on her 55th birthday, which she will also put into the retirement account. What amount must sbe deposit annuu lly now to be able to make the desired withdrawals at retirement?

IJ2 (;rl U Valull1ion and Capital Budgtting

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Calculating the Number of Periods Your Chrislmas sk i vacalion was great. bul il UJ) (onunalely ran a bit over budget. All is not lost : You just received an OHef in the mail to transfer your S9.000 balance from your currenl credit card. which charges an annual rate of 18.6 percent. 10 a new credi t card charging a rate of 8.2 percent. How nluch fa ster could you pay the loan off by making your planned 1U00uhly payments of $200 with the new card? ,"'hat if there was:t 2 percent fee charged on ;l ny balllnces

transferred? FulUrt Value and Multiple Cash Flo",s An insurance company is offering a new policy to its customers. Typically tht: policy is bought by a parent or grand par. ent for a child at the child's bi rth. The details of the policy arc as follows: The purchaser (say. the paren!) makes the following six payments to the insurance

compaoy:

First birthday: Second birthday: Third birthday: Fourth birthday: Fifth birtbday:

S 800 S 800 S 900 S 900 SI.OOO SI,OOO Sixth birthday:

After the. child's sixth birthday. no more payments are made. When the child reaches age 65, be or she recei\'es S350,OOO. If the relevant interest rate is II per­eent for the first six years and 7 perceot for all subsequent years. is the policy worth

buying? Annuitv Present Values and EITec:til'e Rates You bave just won the lottery. You will ~\"e S2.ooo.000 today. and then receive 40 payments of S75O.000. These payments wiIJ sta rt one year from now and will be paid every six months. A rep­resentative fro m G reenleaf Invest ments has alTered to purchase all the paymelllS from you for $ 1 5 million . If the appropriate interest rate is a 9 percent APR com­pounded daily, should you take the offer? Assume there are 12 months in a year.

each with 30 days. Calculating Interest Ra tes A finllncial planning service offers a coUege savings pro­gmm. The plan calls for you to m.,ke six annual payments of S8.000 each, with the first pilyment occurring today. your child's 12th birt hday. Beginning on your child's 18th birthday. the plan will provide 520,000 per year for four years. What return is this investment offering! Break.El"el1 IOl'estment Returns Your financial planner offers you two different investment plans.. Pla n X is a S20.000 annual perpetuity. Plnn Y is a lO·yea r. S35,OOO annual a nnuity. Both plans will make their firsl payment one year from today. AI what discount mte would you be indifferent between these IWO plans'? Perpc.tual Cash flows What is the value of a n investment that pays $8,500 every other yeu.f forevcr, if the first payment occurs onc yeur from today and the d iscount rate is 13 percent compOllllded daily? What is the value today if the fi rst payment occurs four years from today? Assume 365 days in a year.

Ordinary Annuities and Annuities Due As discussed in the text. ao annu ity due is ide ntical to an ordinary annuity except that tbe periodic payments occur ut the b.=gioningof each petiod and not at the end of the period. Show that the relationship between the value of an o rdinary annuity and the \'aluc of an o therwise equivalent

annuity due is:

Annuit)' due value _ Ordinary annuity value X ( I + r)

Show this for both present a nd future values.

S&P Problems

STANDARD &POOKS

Appendix 4A

ChApfc-r 4 Discoumed Cash Flow Valuation l.l.l

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74.

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76.

Calculating EA R A ~heck-cashing store is in lhe business of mak ine personal ~oans \ 0 walk-up customers. The store makes only one-week loans a t- 9 percent IOten;st per wuk. a. What APR must the store report to its customers? What is tbe EAR that the cus­

tomers a re actually paying? b. Now suppose the Slo re makes one-week loans at 9 percent discount interest per

week (see Question 60). Whal's the APR now? The EAR? e. ~he ehec~-cashing store also ma\t~ one-month add-on interest loans at 9 percent

dl~unt IIlte~t per week . Thus. If you borrow $100 fo r one month (four weeks), the mterest WI ll be (SIOO X I.~) - 100 = S41.16. Because this is d iscount interest your net loan proceeds today will be $58.84. Yoo must then repa)' the store $100 a~ !he end of the month. To help you out, though. tbe store lets )"ou payoff thisSIOO in IOstallments of S2:5 per ""'Cek . What is the APR of this loan? What is the EAR?

Present V~lue of a G~wi~g Perpetuity What is the equation fo r the present value of a growmg perpetUIty with a payment of C one period from today if the payments grow by C each period?

R~le o~ 72 A useful rule of thumb for the time it takes an in .... estment 10 double \~It~ dIscrete COJ~poul)ding is the "Rule of 72." To use the Rule of 72, )'01,1 simply dIVIde 72 by the mterest tate to delermine the number o f periods it takes for a va lue to:<lay to double. For example, if the interest !"dte is 6 percent, the Rule of 72 says it will take 72/ 6 = 12 years to double. This is approximately equal to the actual answer ~f 11.90 years. The Rule of 72 can also be applied to determine what interest rdte IS o~ed to double money in a specified period. This is a useful a ppro:<..imation for many IOterest rates a nd periods. At what mte is Ihe Rule of 72 exact?

Rule of 69.3 A corollary to the Rule o f 72 is the Rule of 69.3. The Rule o f 69.3 is exactly correct except for rounding when interest rates are compounded conlinu· ously. Prove the Ru k of 69.3 fo r continuously compounded interest.

www.mhhe.comJedumarketins.igbt

I.

2.

Under the "Excel Analytics" link find the MMthly. Adj. Price" for Elizabeth Arden (RDEN) stock. What was your a~nuaJ ~turn O\'er the last four years assuming yo u pu~ha~ the stock at the close ~nce ~our ~ears ago? (Assume no dividends were paid.) USlllg thIS same return, what pnce wlil Ehzabeth Arden stock sell for five vears from now? Ten years from no\\1 What if the stock price increases at II percent ~r year.'

Calculating t~. Number of Periods Find the monthly adjusted stock prices for ~outh west.,Alrilnes (lUV). You find an analyst who projects the stock price will Increase I ~ percent per year for the foreseeable future. Based on the most rl'Cent monthly stOCk. p~ice. if Ihe projection holds true, when will the stock price rt',Lch $150? When will It reach S200? . ,

• Net Present Value: First Principles of Finance To access the appendix ror tbis chapter, please go to www.mh he.comlrwj .

Appendix 4B Using Financial Calculators To access tbe appendix for this chapter. please go to www.mhhe.com/rnj.

134

THE MBA DECISION Ben Bates graduated from college six years ago with a finance undergraduate degree. Although he is satisfied with his current job. his goal is to become ao investment banker. He feels that an MBA degree would allow him to achieve this goal. After examining schools, he has narrowed his choice to either Wilton University o r Mount Perry College. Allhough internships are encouraged by bolh schools, to get class credit for the internship, no salary can be paid. Other than internships, neither school will a llow its students to work while enrolled in its MBA program.

Ben currently works at the money management firm of Dewey and Louis.. His annual salary at the firm is S60,OOO per year, and his salary is expected to increase at 3 percenl per year until retirement. He is currently 28 years old Rnd expects to work for 40 more years. Hiscu rrentjob includes a rully paid heal th insurance plan. and his currenl average tax rate is 26 percent. Ben has a savings accou nt with enough money (0 cover the entire cost or his MBA program.

The Ritter College or Busioess at Wilton University is one or the top MBA programs in the country. The MBA degree requires two yeaN or full-t ime enrollment at the university. The annual tuition is 565,000, payable at the beginning or each school year. Books and other suppl ies are estimated to cost S3,OOO per year. Ben expects that after graduation rrom Wilton, he will receive ajob offer ror about $110,000 per year. with a S20.000 signing bonus. The salary at this job will increase at 4 percent per yea r. Because or the higher sal­ary. his average income tax rate "'>ill increase to 31 percent.

The Bradley School or Business at Mount Perry College began its MBA program 16 years ago. The Bradley School is smaller and less well known than the Ritter College. Bradley offers an accelerated, one-year program, with a tui tion cost or $80,000 to be paid upon matriculation. Books and other supplies ror the program are expected to cost 54,500. Ben thinks that he will receive an offer or S92,OOO per year upon graduation. with an $18.000 signing bonus. The salary at this job will increase at 3.5 percent per year. His aver­age tax rate at this level or income will be 29 percent.

Both schools offe·r a health insurance plan that will cost 53,000 per year, payable at the beginning or the year. Ben also estimates that room and board expenses will cost S2,OOO more per year at both schools than his current expenses, payable at the beginning or each year. The appropriate discount rate is 6.5 percent .

I. How does Ben's age affect his decision to gel an MBA?

2. What other, perhaps nonquantifiable ractors affect Ben's decision to gel an MBA?

3. Assuming all salaries are paid at the end or each year, what is the best option ror Bell-rrom a strictly financial standpoint?

4. Ben believes that the appropriate analysis is to calculate the ruture value or each option. How would you evaluate this stalement?

5. What initial salary would Ben need to receive to make him indifferent bet\\-een attend· ing Wilton University and staying in his current position?

6. Suppose, instead or being able to pay cash ror his MBA, Ben must borrow the money. The current borrowing ralC is 5.4 percent . How w()uld this affect his decision?

5.1

"" .. """' .... """ iIaIlludgeting lOr small businesses al

Wl!I!t!!! ' ,." 1_ m

Net Present Value and Other Investment Rules

In 2008, with gasoline prices reaching reeord levels. companies began developing aiter­

native energy sources, and finnish company Neste Oil was no exception. In June 2008,

Neste announced plans to spend $1 billion building an 800,000-ton biodiesel plant in the

Netherlands. The plant, which wJll be one of the largest biodlesel projects in the world,

will produce Neste's proprietary NExBTL biodiesel. The only comparable project is the

800+ billion ton plant in Singapore that Neste announced In January 2008. Decisions such

as these, with price tags 01 up to $1 billion, are obviously major undertakings, and the risks

and rewards must be carefully weighed. In this Chapter, we discuss the basic tools used in making such deciSions.

In Chapter 1. we show that increasing the value 01 a company's stock is the goal 01 finan.

cial management. Thus, what we need to know is how to te/I whether a particular investment

will achieve that purpose or not This chapter considers a variety of techniques finanCial analysts routinely use. More importantly, it shows how many ot these techniques can be

misleading, and il explains why the net present value approach is the right one.

Why Use Net Present Value? This chapter, as ~IJ as the. D~t two, :ocuses on C"Opital budgeting. the decision-making pr~ss ror acceptlD~ or reject ing prOJects. This chapter develops the basiccapitaJ bud­geting methods,. leaVing much of the practical applicalion to subsequent chapters. But we don't have to .devt.lop these me~hod.s from scratch. In Chapter 4, we pointed out that a dollar ~rved In the ruture 15 worth less than a dollar received today. The rea­son, of cou rse, IS that IOOay's dollar can be reinvested, yielding a greater amount in the future. An~ ~e showed in Chapter 4 that the exact worth or a dollar to be received. in the ruture IS liS present value. Furthermore. Section 4 .1 suggested ca lculating the net present I'allie of any project. That is, the section suggested calculating the difference between tbe sum or lhe p(esent va lues or the project 's ruture cash nows aod the initial cost of the project. ..

The net .present ~alu.e (NPV) method is the first one to be considered in this chap­ter. We begJO by reviewing the approach with a simple example. Then, we ask why the method leads to good decisions.

JJ6

EXAMPLE 5.1

P9rl n Valuation and Capital Budg.:liug

Net PrEsent Value The Alpha Corporation is cO!'ISlderlng investing in a riskless project (oSt­

ing $100. The project receives $107 in one year and has no other cuh flows. The discount rate i~

6 perl:ent. The N PV o f the project can usily be calculated as:

$107 $.94 :: - $100 + 1.06 (5.1)

From Chapter 4. we know that the project should be. ac.cepted because its NPV is positive. Had the

NPV of the project been negative. as would have been the case with an interest rare greater than

7 percent. the project should be rejected.

The basic invest ment rule can be generalized to:

Accept a project if the NPV is greater than zero.

Reject a proje<:1 if l'\rpv is less than zero.

We refer 10 Ihis as the NPV rule. Why does 'he NPV rule lead to good decisions~ Consider the following two strate­

gies ava ilable to the managers of AJpha Corporation:

I . Use $100 of corporate cash to invest in the project. The $107 will be paid as a dividend in one yea r.

2. Fo rgo the project and pay the $100 of corporate cash as a dividend today.

If strategy 2 is employed, the stockholder might deposit Tbe dividend in a bank for one year. With an interest rate of 6 percent , slrategy 2 would produce cash of $ ]06 (=$ 100 x 1.06) at tbe end of the year. The stockholder would prefer strategy I because strategy 2 produces less lhan S 107 a t the end of The year.

OUT basic poin t is:

Accepting posith'tl NPV projects benefits the stockholders.

How do we interpret the exact NPV of S.94? This is the increase in the value of the lirm from tbe project. Fo r example. imagine that the firm today has productive assets wort h SV a nd has $1 00 of cash. If the fir m forgoes the project, the value o f the firm today would simply be:

$V + $ 100

If the finn accepts the project, The firm will receive $107 in one yea r but "'"i ll have no eash today. T hus, the firm's value today would be:

$V + $ 107 1.06

The di fference between these equations is just $.94. the net presenl va lue of Equa­

tion 5. 1. Th us:

The- \'II,lue or the firm rises by the NPV of the projw.

NOle that the value of the firm is merely The sum o f the values of tbe dilferent proj­ects. divisions., or other entities within the firm. T his property. called yalue addithity, is quite importanl. It implies that the comribution of any project to a fi rm's va lue is

Chapler 5 Nel P=nl Value and Other Investment Rules 137

simply the N PV o f the proj~t. As we will see later, alternative methods discussed in thjs chapter do not generally have this nice property.

One detail remains. We assumed that the project was riskless, a rather impla usible assumption . Future cash flows of real-world projecTS a re invariablv riskY. In other words, cash flows ca n o nly be estimated, ratber tban known. Imagin~ that {he manag­ers of A lpha exp~cl the casb flow o f the project to be SI07 next year. That is, the cash flow could be higher, say $1 17, or lower. say 597. With this slight change, the project is risky. Suppose the project is about as risky as the stock market as a whole, where the expected return Ihis yea r is perhaps 10 percent. Then 10 percent becomes the discount rate, implying that the NPV of the project would be:

Sl07 - $2.73 ~ -$100 + T.lO

Because the NPV is negalive. the projec t should be rejected . This makes sense: A stockholder of AJpha receiving a $ ] 00 dividend today could invest il io the slock mar­ket , expecting a ] 0 percent return . Why accept a project with the sa me risk as the market but with an expected return of only 7 percent?

SPREADSHEET APPLICATIONS

Calculaling NPVs wi th a Spreadsheet Spreadsheets are commonly used to calculale NPVs. Examining Ihe use of spreadsheets in this context also allow s us to issue an important warning. Consider The follo\.ving:

A , o , U. 'n a ~_IO~clIlM. noM preoHnt VlluK

a A '(OSI " 10000. The tuh 11_ I'e 12 000 "' tor the lit,t two e~,, 1, 5 S<l 000 t at lor t ile next IWO "rod SS 000 In th4r In1 The d lKount ,.tt II 6 10 c .... """-l"Ilh<I NPV1 , , Yee' "'" ,-• · SIOOOO 1)i'l<0lInt. ,,,Ie .. , .. .. , , ... , , .. "~ . $l.102.72 (, ... .,., .... _ r) " " " " "

, .... "~. 52.312." ,. r ......... ,)

• . .. , , .. Iii The for ........ flIlfl..! in <oMI FII " .. NP'V{F9. ( 9:(1 • . ~ tflll til, w' .n,w., b«.I o,rw the 17 NPV l\WICtion an_I ""<"'.1,", .,..,." "alues, t'oOC nel h.'...,.. " 19 Theformul ..... tottfllin ct/I FI2k .. N ' 9 (10:(1 •• C9. n.i-I iYHltla, ' I"" n w,t>«"uwthe 20 NP'V function" uvd 10 'ak ..... te !.peenl .... I~ 01 ~ caoh,..........nd ,,,",,, the 1",, '., toll il 21 wblt.KIed \0 </lkulne the .. >I>I.~' Notice 111 81 we lidded ,ell C9lMuuse I." .I,u . ' i~. ,

In our spreadSheef example. notice that we have provided two answers. The first answer is wrong even though we used the spreadsheet's NPV formula. VI/hat happened is that the "NW funclion in our spread­sheet Is acrually a PV function; unfortunately, one of the original spreadsheet programs many years ago got lhe definition wrong, and subsequent spreadsheets have copied it! Our second answer shows how to use lhe formula property.

The example here illustrates lhe danger of bjindly using calculators or computers withOut underslandulg "'mat is going 00; we shudder 10 think of how many capital budgeting deciSions In the real worfd are based on Incorrecl use of thiS particular function.

138 P:.rt II Valuation and Cephal Budgt1inl!

Conceptually, the discount rate on a risky project is the return tha~ one can expect to eam on a financial asset of comparable risk. This discoun l rate IS often referred to as an opportunity COSl because corporate investment in Ihe project takes away Ihe stockholders opportunity to invest the dividend in a financiaJ asset. If the actual ca l­eulalion of the discount rate strikes you as extremely difficult in the real world , you are probably right. Although you can call a bank to find OUI the current imerest rate. whom do you call to find the expected return on tbe market thi s year? And , if the risk of the project differs from that of tbe market. how do you make the ~dju~lme.nt? How­ever, the calculation is by no means impossible. We forgo the calculation In thiS chapter but present it in later chapters o f the text. .

Having shown that NPV is a sensible approach, how can we tell whether altematlve methods are as good as NPV? The key to NPV is liS three atlributes:

l. N P V uses cash flows. Cash nows from a project can be used fo r other corporate purposes (such as dividend payments, o tber capital budgetin~ p~ojects, or pay. ments o f corporate interest). By contrast. earoings are an artificial co~struct: Although earnings are useful 10 account.ants, they should not be used 10 capItal budgeting because they do not represent cash.

2. N P V uses all ihe caslrflows of the project. Ot her approaches ignore cash nows beyond a particular date; beware of these approaches.

3. N P V disco/nlls the cash floll's properiy Other approaches may igno re the time value of money wben handling cash flows. Beware of these approaches as well.

Calculating NPVs by ha_nd can be tedious. A nea rby Spreadsheet Applications box shows how to do it the easy way and also illustrates an important cUI'eat colculator.

5.2 The Payback Period Method

Figure 5.1 Cesh FloW1i of en Investment ProJect

Defining the Rule One of the most popular alternatives to NPV is payback. Here is how payback works: Consider a project with an initial investment o f - 550,000. Cash nows a~ $30.000. S20.000, and $ 10,000 in the first three years, respectively. These flows ~re .)lIu~trated in Figure 5. 1. A useful way of writing down invesLmenlS like the precedmg IS With the

notation:

(-550,000, $30,000. 520,000. S IO.oool

The minus sign in front of the $50,000 reminds us that this is a cash outflow fo r the investor. and the commas between the different numbers indicate that they are

""oo - ,,_ Casal illflew

ro. 0 , 3

Cash oUlftow -......

Table 5.1 Expect&d Cash Flow. lor ProJects A lhrough C (S)

Chapu~r 5 N~l Present VRlu~ :lnd Other h1Vnlm~nl R.uln "9

received-or if they are cash outflows, that they a re paid out-at different times. In this example we are assuming that the cash nows occur one year apart. ""ith the first onc occurring the moment we decide to take on the investment.

The firm receives casb Oows of 530.000 and $20,000 in the fim two years, which add up to the $50.000 o riginal invesunent . lnis mea ns that the firm has recovered il s investment within two years. In this case two years is the payback period of the investment.

The payback period rule fo r ma ki ng investment decisions is simple. A particular cutoff date. say two yea rs.. is selec ted. All investment projects that have payback peri­ods o f two years or less are accepled, and all o f those tbat pay ofT in more than lWO

years-if at a U- a re rejected.

Problems with the Payback Method There are at least three problems witb payback . To illustrate the first IWO problems, we consider the three projects in Table 5. 1. All three projectS have the same three·yea r payback period. so tbey should all be equally attracti ve- right ?

Actually. they are not equally attractive, as can be seen by a compariso n of different pairs of projcels.

Problem 1 : Timing of Cash Flows within the Payback Period Let us compare project A with project B. In years I through 3. Ihe cash nows of project A ri se from S20 to $50, wh ile the cash flows of project B fall from $50 to 520. Because the large cash flow of 550 comes earl ier wit h project B. its nel present value must be higher. Nevertheless, we just saw that the payback periods of the I\VO projects are identical. Thus. a problem with the payback method is that it does nOl consider the timing of the cash nows withjn thc payback period. This example shows that the payback mel hod is inferior to NPV because, as we poiLlied out earlier. the NPV method discmlllis lhe cash flows properly.

Problem 2: Payments after the Payback Period Now consider projects Band C, which have ident ical cash flows within the payback period . However. project Cis clearly preferred because it has a cash now of $60.000 in the fourth year. Thus, another problem with the payback method is that it ignores all cash flows occurring a fter the paybac k period. Because of the short-term orientation of the payback method, some valuable long-term projects are likely to be rejected . The NPV method docs not have this flaw because, as we pointed out earlier, this method Ilses all the cash fl{JII·.\· (~r the project. . ,

• Year A 8 C

0 - $100 - $100 - $100

20 50 50 2 30 30 30 3 50 20 20

• 60 60 60.000 ~~ck period (years) 3 3 3

140 Part n V(llualion ~IlLl Capiwl all(j~l i n~

Problem 3: Arbitrary Standard for Payback Period We do not need [0 refer to

Table 5.1 when considering a third problem with the payback method. Capital markets help us estimate the discount rate uSCd in the NPY method . The riskless rate. perhaps proJtied by the yield on a Treasury instrument, would be the appropriate rate for a ri sk­less investment. Later chapters of Ihis textbook show how to use hislOrical returns in the capita l market:>. to estimate the discount rate for a risky project. However, there is no comparable guide for choosing the p,ayback cutoff date. so the choice is somewhat

urbitrary.

Managerial Perspective The payback method is often used by large. sopbisticated companies when making relatively small decisions. The decision to build a small warehouse, for example. or 10

pay for a wne-up for a Iruck is the sort of decision that is orten made by lowcr-level management. Typically. a manager migbt rea son that a Hme-up wou ld cost. say. 5200, and if it saved Sl20 each year in reduced fuel costs. it would pay for itself in less than two years. On sllch a basis the decision would be made.

Although the treasu rer of the company might not have made the dl'Cision in the smne way. the compa ny endorses such decision making. Why would upper manage­ment condone or even encourage such retrograde activity in its employees? One answer would be that it is easy to make decisions using payback . Multiply the tune-up decision into 50 such decisions a month. and tbe appeal of this simple method becomes clearer.

The payback method also has some desirable features for managerial control. Just as imponant as the invest ment decision itself is the company's ability to evaluate the manager's decision-making ability. Under the NPV method. a long time may pass before one decides whether a decision was corrCel. With the payback method we know in two years whether the manager's assessment of the cash flows was correct.

It has also been suggested that firms with good investment opportuni ties but no avuilable cash may j us tifiabl y use payback. For example. the payback method could be used by small , privately held firms with good growth prospects but limited access to the capita l markets. Quick cash recovery increases the reinvestment possibilities for

such firms. Finally. practitioners often I.Irgue that standard academic criticisms of the payback

method overstate any real-world problems with tbe method. For example. textbooks typically make fun of payback by positing a project with low cash innows in the early yea rs but a huge cash inflow right aner the payback cutoO' date. This projcct is li kely to be rejccted under the payback method. tho ugh its accepwllcc would. in truth. ben· efit the firm. Project C in our Table 5.1 is an e.''<.ample of such 1.1 project. Practitioners point out that the pattern of cash flows in these textbook examples is much too styl­ized to mirro r the real world. In fact. a number of executives have told us that for the overwhelming majority of real-world projects, both payback and N PV lead to the sa me decision. In addition, these executives indicate that if an investment like project C we re encountered in the real world, decision makers would a lmost certainly make ad hoc adjustments to the payback rule so that the project would be accepted.

Notwitbstanding all of the preceding rationale. it is not surprising to discover thai as the decisions grow io importance. which is to say when firms look at bigger projects. N PV becomes the order of the day. When questions of controlling and eva luat ing the manager become less imporlant than making the right investment decision. payback is used less frequently. For big-ticket decisions. such as whether or not 10 buy a machine. build a factory. or acquire a company, the payback method is seldom used.

Chapter 5 Ntl Pn:'>en[ Vulu<, lind OdIn Invt~\melu Rults 141

Summary of Payback The payba.ck method differs from N PV and is therefore conceptually wrong. With its arbitrary cutolT date and its blindness to cash flows after that date. it can lead to some nagrantly roolish decisions if used too litcrally. Nevcrtheless. becauSC' or its simplicity. as well as ils ot her mentioned advantages. companies often use it llS a screen for mak­ing thc myriad of minor investmen t decisions they continually face.

Although Ihis means that yOll shou ld be wary or trying to change approaches such as the payb<lck method when you encounter (hem in companies. you should probably be carerul not to accept the sloppy finuncial thin king they represent. After this course, you would do your company a disservice if you used payback instead of NPV when you had a choicc.

5.3 The Discounted Payback Period Method Aware of the pitralls of payback. some decision makers use a \'ariant called the diSCOUnTed payback period mefhod. Under this approach. we first discount the cash flows. Then we ask how long it ta kes for the discounted cash nows to equal the initial investment.

For example. suppose that the discount rate is \0 percent and the cash nows on a project are given by:

(-$100. $50. $50. $20]

This investment has a payback period or two years because the investment is paid back in that time.

To compu te the project 's discounted payback period , we first discount each or the ,ash flows at the 10 percent rale. These discounted cash flows are:

[- $100. $5011.1. $501( 1.1 Y. $201(1.1 11 - (-$ 1 00. $45.45. $4 1 .32. $15.03]

The discollnted payback period of the original investment is simply the payback period fo r these discounted cash nowS. The payback period for the discounted cash nows is slightly less than three years because the discounted cash flows over the threc yea rs are $101.80 (=S45.45 + 41.32 + 15.03). As long as the cash nows and discount rate are positive. the discounted payback period will never be smaller than the payback period because discounting reduces the value of the cash nowS.

At first glance discounted payback may seem like an attractive alternative, but on closer inspection we sec that it has some of the same major flaws as payback. Like payback, discounted payback first requires us to cboose an arbitrary cmoO' period. flnd then it ignores all cas~ flows after that date.

If we have already gone to the trouble of discoun ting the cash flows. we might just as well add up all the discOitnted cash nows and use N PV (0 muke the decision. Althoueh discounted payback looks a bit like NPV. it is just a poor compromise between the payback method imd NPY.

5.4 The Internal Rate of Return Now we come to the most importilnt alternative to the NPV method: The internal rale of return. universa lly known as the IRR. The IRR is about as close as YOIl can get to the NPV without actu<l lly being the NPY. The basic rationa le behind the IRR method

142

Figure 5.2 Casl'l Flows tor 8 Simple Project

CHh inflow $110

o

easll outfl_ - $100

is thai it provides a single number summarizing the merits of a project. That number does not depend on the interest rate prevailing in the capital market. Thai is why it is ca lled the interna l rate of return; the number is imemal or intrinsic to the projcct a nd does not depend on anything except the cash nows of tbe projecl.

For example, consider the simple p roject (- 5100, SIlO) in Figure 5.2. For a given ra le, tbe nct presen t value of Ihis project can be described as:

NPV ~ - $100 + B..!Q. I+R

where R is the d iscount rate. What must thc discount rate be to make the NPV of the project equal to zero?

We begin by using an arbit rary discount rate of .08. which yields:

$ 1 85 ~ - $100 + ~ '6~ Because the NPV in this equa lion is positive. we now try a higher discounl rate. such as . 12. This yields:

-S1.79 - - $100 + ~III~

Because the NPV in Ihis equation is negative, we try lowering the disco unt rale to . 10. This yields:

o~ - $100 + $ 11 0 1.1 0

This trial-.lOd-error proced ure lells us that the NPV o f Ihe project is zero when R equals 10 percent. ! T hus, we say that [0 percent is Ihe project's internal rate of return (lRR) . In general. the IRR is the rate that causes the N PV of the projecllo be zero. The implication of this exercise is very simple. The firm should be equally wi lling to accept o r reject the project if the discount rate is 10 percent. The firm sho uld accept the projcct if the discount rate is below 10 percellt . The firm sho uld reject tbe project if the discount rate is above 10 percenl .

The genera l investment rule is clear:

Accept tbe project ir the IRR is grea ter thsn the d iscount ~te. Rejecr Itt<' project ir the IRR is less

than tbe discount rtte.

'or course. .... e could h;r.·c di rec tl )' solved ror R in this eumpJt after senin! NPV ~ual 10 ttro. However. .... ilh II long St.- riel of cash nowj. one cannot generally soh'e for R directly. Instead. one is forced to uS(' tria l and em>r for let a machine use trial and error).

Figure 5.3 ca.h Flows for e More Complex Prolect

Chapfer 5 Net Present Value and Olher In''CSlment Rules 143

cadi inftow $I" " .. " .. lima o , ,

C .. II olltflow -S200

We refer to this as the basic lRR rule. Now .... -e can Iry Ihe more complicated example ( - $200. $100. 5100, $ 100) in Figure 5.3.

As we did previously, let's use l ria l and erro r 10 ca lculate the internal rate o f retum. We try 20 pe rcent and 30 percell!. yielding the following:

Discount Rate NPV

20% 30

$10.65

- 18..)9

After much mo re trial and error, we fin d Ihat the NPV of the project is zero when the discount rate is 23.37 percen!. Thus, the IRR is 23 .37 percent. With a 20 percent dis­count rate, the NPV is positive and we would accept it . However, if the discount rate were 30 percent , we wo uld reject it .

Algebraically, LRR is the unknown in the following equation:!

0- S200 + 5100 SIOO $100 - - I + IRR + ( 1 + IRR)l + (I + IRR))

Figure 5.4 illustrates what the IRR of a project means. The figure plots the NPV as a funct io n of the discount rate. The curve crosses the horizontal axis at tbe IRR o f 23.37 percent because this is where the NPV equals zero.

It shou ld also be clear that Ihe N PV is positive fo r discoullt rales below Ihe lRR and negative for di scount rates above the IRR. If we accept projects like Ihis one when the d iscount rate is tess tha n Ihe IRR, we will be accepting positive N PV projccts.. Thus, the IRR rule coi ncides exactly with the NPV rule.

If this were alli here were to it, tbe TRR rule would a lways coincide with the NPV rule. But the world of fin CJ:nce is not so kjnd . Unfortunately, the I"RR rule and the NPV rule a re consistent with ~ach other only fo r exam ples like the one just di scussed. Sev­eral pro blems with the lRR approach occur in more complicated situations. a topic to be examined in Ihe next section.

The IRR in Ihe previous example was computed through trial and error. This labo­rious process can be averted through spreadsheets. A nearby Spreadsheet AppliC-Ufiolls box shows how.

'Onc can den"c Inc IRR diteClly for a problem with an inilial cash out flow and up to (our !ubsequcnl innO\'o'S. In the case of two subsequent inllowt, fo r example. th~ quadratic fonnula is needed. In general. howc\'Cr. only trial and error will W\)rk for an outflo ..... and five or more subsequen! inflows.

1'''

Figure 5.4 Net Present Value (NPV) and Olscount Rates for a More Complex Project

Pari \I Valu(lIion and C<lpHa l Bud~l i Jl g

$100

$10.65 • 23.31

SO I-----:,~O ---:20~/'i..=-c;! .. '-----":. - $18.39 IRK

Oiscount Illite (%1

The NPV is positive for discount rates below the IRR and negative for discount rates above the IRR.

SPREADSHEET APPLICATIONS

Calculating IRRs with a Spreadsheet Because lARs are so tedious 10 calculate by hand . financial calculators and. especial ly, spreadsheets are generally used. The procedures used by varIOUS financial calculators are too different fOf us to illustrate here, so we will fOCUS on using a spreadsheet. As the follO\ving example illustrates, using a spreadsheet

is very easy

, ~ ,

~ ~ " "

~

iJ:i ; " .~ i ; I

5.5 Problems with the IRR Approach

Definition of Independent and Mutually Exclusive Projects An independent project is one whose acceptance or rejection is independent of the acceptance or rejection of o ther projects. For exam ple. imagine that McDona ld's is considering putting a hamburger outlet on a remote island. Acceptance or rejection of

ChapUT S !'leI Present Value' and Other In''e''Sun~ nl Rules 14'

this unit is likely to be unrelated to the acceptance or rejection of any other restaurant in its system, The remoteness of the outlet in question ensures th at it will not pull sales away from·other outlets.

Now consider the other extreme, mutualJy exclusive m\'estments. Wh at does it mean for two projects, A and B, to be mutually excl usive? You can accept A or you can accept B or you ca n reject both of them. but you can not accept both of them. For example, A might be a decision to build an apa rtment house on a corner lot that you own, and B might be a decision to build a movie theater on the same lot.

We now present IWO gene ral problems with the JRR approach that affect bot h inde· pendent and mutually exclusive projects. Then we deal ,,,;th two problems affecting mutually exclusive projects only.

Two General Problems Affecting Both Independent and Mutually Exclusive Projects We begi n our discussion with project A. which has the fo llowing cash nows:

( - $ 100, S130)

The IRR for project A is 30 percen!. Table 5.2 provides other relevant informati on about the project. The relationship between NPV and the discount raTe is slJown for this project in Figure 5.5, As you can see, the NPV declines as the discount rate rises.

Table 5,2 The tntemal Rate of Return and Net Present Velue

___ ProJ!~ A _ _ ~ ___ Proje~tE

Dates: 0120 1 20 1 2

Cash flows - $100 $130 $100 - $130 - $100 $230 - $132

IRR 30% 30% 10% and 20%

NPV @IO% $18,2 - $18.2 0 Accept if market rate < 30% > 30% > I 0% but <20%

Financing or investing Investing FinanCing Mixture

Figure 5.5 Net Present Value end Discount Retes for ProJocls A, B. and C

Project A Project B Project C

$30 -, •

•

~ 0 Discount ~ Discount ~ Discount z .. rete 1%1 z .. ra"I"Io1 z 'Ite 1%)

-sz Approlches

-S>I -$tOO - 100 when R~ ~

Project A has e cesh outflow at date 0 followed by e cash inflow at date 1. Its NPV is negatively related to the discount rete. Project Shes 8 cash inflow at date 0 followed by e cesh outflow 8t date 1. Its NPV is positively ralated to the discount rate, Project Chas two changes of sign in its cash flows. h ltas an outflow at date 0, an inflow at date 1, and an outflow at date Z. Projects with mora than one change of sign can have mUltiple rates of return,

, .. Pari n Valuation and Capital Budgeting

Problem 1: Investing or Financing? Now consider project B, with cash flows of:

($ 100, - $1 30)

These cash flows are exactly the reverse of Ihe news (or project A. In project B. tile firm receives funds first a nd then pays out funds later. Whi le unusual, projects of this type do exisl. For example. consider a corporation conducting a seminar where the participants pay in advance. Because large expenses are frequently incu rred at the seminar dale, cash inflows precede cash outflows.

Consider our trial·a nd-error method (0 calc ulate IRR :

S130 -$4 ~ +5 100 - TiS

$130 53.70 ~ +$100 - 1.35

S130 SO ~ +$100 - 1.30

As with project A. lhe internal rale o f retum is 30 percenl. However, notice that Ihe net present value is negative when the discount rate is below 30 percent. Co nversely. the net present va lue is positive when the discount ratc is above 30 percent. The decision rule is exactly the opposite of our previous result. For this type of project. the foUow. ing rule applies:

Ac:«pl the project when the JRR is less than the diKount tate. Reject tbr project when the IRR Is greater t han the discount rate.

Th is unusual decision rule follows from the graph of project B in Figure 5.5. The curve is upward sloping. implying tha I NPY is posiliw!iy related to the discount rate.

The graph makes intuitive sense. Suppose the firm wants to obtain $100 imme­diately. 1t can either (I) accept p roject B or (2) borrow $100 from a bank . ~~he project is actually a substitute for borrowing. In fact. because the 1RR is 30 percent, taking 0 '0 project B is equivalent to borrowing at 30 percent. If the firm ca n borrow from a ba nk at , say. only 25 percent, it should reject the project. However, if a firm cae borrow from a bank only at, say, 35 percent, it shou ld aC(;ept the project. Thus proj ­ect B will be accepted if and only if the discount rate is abo'l'e the lRR.l

This should be contrasted with project A. If the finn has $ 100 cash to invest, it can either ( I) accept project A or (2) lend $100 to the bank . The project is actually a substitute for lending. In fact , because the lR R is 30 percent: taking on projcct Xis tantamount to lending at 30 percent. The firm should accept project A if the lending rate is below 30 percent. Conversely, the firm sho uld reject project A if the lending ratc is above 30 percent .

Because the firm initially pays out money with project A but initially receives money with project B , we refer to project A as an in'l'esling type project and project 8 as a financing type prqiect. Investing type projects arc the norm. Because the IRR rule is reversed for fina ncing type projects., be careful when using it with this type o f project.

'This paragraph implicitly aMWI\($ that the r;ash n OW5 of the project are risk· free. In tbis way we can trrat the borrowing rate as the discount (alt for a fi rm nceding 5100. With risky cuh flow s. another diKounl rale would be: chosen. Howe·'er. the iotuition bchi rw:lthc decision (0 acoepl when t~ IRR isirM than Ihe diKount rille would still apply.

Chapter 5 Net Prcs(lII Value and Other Inves tment Ruk-s

'" Prob lem 2: Mult iple RateS of Return Suppose the cash nows fro m a project are:

( - 1 100, $230, -11 32)

Because this project has a negalive cash now, a posi tive cash now, and another ~e~tive ca~h now, we sa~ that the project's cash flows eKhibit two changes of sign, or nl~nopS. ~lthough thiS pattern of cash nows might loo k a bit strange at tirst, many

pr?J~ts ~ul re outflows of cash after some innOws. An example would be a strip­mmm~ project. The first stage in such a project is the initial investment in excavating the mme. Profits from operating the mine are received in the second stage. The third sta~e involves a further investment to reclaim the land and satisfy the requirements of envlro~mental protection legislation. Cash nows are negative at this s tage.

Projects fmanced by lease arrangements may produce a similar pattern of cash ~~~s. ~eases oOen provide substantia l tax subsidies, generaticg cash innows a fter an mlual. InveStment. ~o\.\'ever, these subsidies decline over time, frequently leading to negative cash nows 10 later years. (The details of leas ing will be discussed in a later chapter.)

It is easy to verify that this project has not one but two IRRs, JO percent and 20 per­cent.~ In a case like this. the IRR does not make any sense. What IRR are we to use-- IO percent o r 20 percenl? Because there is no good reason to use one over the other, IRR simply cantlo t be used here.

. Why does this project have multiple rates of return? Project C generates multiple ~ nternal rates of ret urn because both an innow and an out now occur after the initial Investment. In general. these nip-nops or changes in sign produce multiple IRRs. In theory. a cash now stream with K changes in sign can have up to K sensible inter­na l rates. of :em,:" (IR Rs above - 100 percent). Therefore, because project C has two changes In sign, 11 c~n have as many as two IRRs. As we pointed out, projects whose cash nows change sign repeatedly ca n OCCur in the real world.

NPV Rule Of course, we should not be too worried about multiple rates of return. After all. we can always fall back on the NPV rule. Figure 5.5 plo ts the NPV of proj­ect C~ - Sl00, 1230. - SI32) as a function of tbe discount rate. As the figure shows, the NPV IS zero at both JO percent and 20 percent and negative outside the ra nge. Thus, the NPV rule te lls us to accept the project if the appropriate discount rate is between 10 percent a nd 20 percent. The project should be rejected if the discount rate lies out­s ide this raoge.

Modffied I~R As a n alternative 10 NPV, we now introduce the modified IRR (MIRR) method . which handles the multiple IRR pro blem by combining cash nows unti l only

'1""he calculations arr: ~

- 5 100 + S2JO _ S I31 1.1 O .lf

- 5100 + 209.09 - 109.09 _ 0

-SIOO + S230 _ S Il2 1.2 fU r

-S IOO + 191.67 - 91.67 _ 0

Thus. we h.ave multiple rales or relum.

148 Pur n Valuation ond Capilal Budgtlint!

one change in sign remains. To see how il works. consider project C a~ain . With a dis­coont rate of. say, 14 percent, the value of the las\ cash now, -SI32. IS:

-S I3211.14 ~ -SII 5.79

as of dale I . Because 5230 is a lready received at that time. the "adjusted" cash n ow at dale I is S1 14.21 (=5230 - 115.79). Thus. tbe MIRR approach produces the following

twO cash flows for the project:

(- SI()O, SII4.2I)

Note that by discounting and then combining cash flows. we are lert with only one change in sign. The IRR rule can 0 0\\: be applied. The IRR of, these lWO cash 00':"5 is 14.21 percent, implying that the prOject should be accepted gIVen our assumed diS­count rate of 14 percent .

or course, project Cis relalively simple to begin with : It has o nly (bree cash flows and two changes in sign . However, the sa me procedure can easi ly be applied to more comple., projects- that is., just keep d iscounting and combining the later cash nows until only o nc change of sign remain s.

Although tbis adjustment does correct (or multiple lRRs, .i t appears,. at IC~l st to us. to violate the "spirit" of the IRR approach. As stated earher, the baSIC ratlonale behind thc IRR method is that it provides a single number summarizing the merits o f a project. Th at number does not depend on the .discount rate. .In ~act.' that is why ~t is called the internal rate of return: The number 15 ;nremal. or mtnnSlc, to the project and does not depend on anything except the project's cash nowS. By contrast . MIRR is clea rly a function of the disco~nt rale. Howev~r, a firm using thi~ adju~tIr~e~t will avoid the multiple IRR problem, Just as a firm usmg the N PV rule WIll aVOId It. '

The Guarantee against Multiple IRRs If the fi rst eash now of a project is negative (because it is the initial invesrment) and if all o f the remaining nows are positive, tbe~ can be o nly a single, unique lRR, no matter how many periods the project lasts. Thl.S is easy to understand by using the concept of the time value of money. Fo r exampl~, It is simple to verify that project A in Table S.2 has an IRR of 30 percent because usmg

a 30 percent discount ratc gives:

NPV ~ - $100 + SI30/( 1.3)

~ SO

IThere is more than one '~ r5 ion of modified IRR. In the discussion above. MIR R combines the presoi' nt values of the lattT cash flow:>. !ea\ing a set of cash flows "'ith only OM' chan~ in sign. Alternatively. invcs, IOU oft en combine the fu ture ,'Ilues of the cash flo .... 'S3S of the termination dale of the project . In our

uample. the sum of the fu ture \·ahles., as of dale 2. it: , Dale of cash now

Future "alue as of Date 2 S13011.14) - S262.20 - SI32

Under this '·e~ion. lhe MIRR of the project b:romes:

130.02 -Ion + {I + MIRRf

Soro S 130.021=262 .20 + ( - 112)

impMng an MI RR of 14.11 percent . TheM IRR here differs from the MtRR of t4.21 percent in the tell!. Hov.~n. both MfRR $ are above the

di$COunt rate of 14 percent. implying IK"Cl:ptOI'lCt of Inc projCCt. This consistency should aJways hold bet~ the tWO ,'Snants of modirlcd IRR. And. as in tnc version in the le.u . the muhipk IRR probkm is a"o'Olded.

Chapter 5 Net Present Value Md Other In\'C$lmtnt Rults '49

How d o we know lhal this is the o nly IRR? Suppose we were (0 try a discount rate greater Ihan 30 percen!. In computing the NPV. changing the discOUIll rate does not change the value o f the initial cash n ow or - S IOO because that cash now is not disco unted . Raising the di scount rate can only lower the present value of tbe ruture cash n ows. In other words. beeause the NPV is zero at 30 percent. any increase in the rate will push the NPV im o the negat ive range. Similarlv. ir we LTya diseou nt rate or less IhaD 30 percent. thc overall NPV of the project 'will be positive. Though this example has only one positive n ow, the above reasoning s till implies a single, unique IRR if there are many innows (but no o utnows) after the in it ial inves tment .

If the initial cash flow is positive-and if a ll or the rema ining nows are negative­there can only be a single, unique IRR . This result follows from simila r reasoning . Bmh these cases have o nly one change o f sign o r nip-no p in the cash nowS. Thus, we are safe from multiple IRRs whenever there is only one SigD change in the cash fl ows.

General Rules The following chan summarizes o ur rules:

Number Flows o f IRRs tRR Crtterton NPV Criterion

fint cash now is neg.;t.tive and all remaining cash Hows are positive.

Fint cash now is po.sltive and all remaining cash flows are negative.

Some cash flows after flrst are positive and some cash nows after first are negative.

Hoy be

""'" thilln I .

Accept if IRR > R. Reject if IRR < R.

Accept if IRR < R. Reje<:( if 1RR > R.

No valid IRR.

Accept if NPV > O. Reject if NPV < O.

Accept if NPV > O. Reje<:t if NPV < O.

Accept if NPV > O. Reject if NPV < O.

Note that the NPY criterion is the same fo r each or tbe three cases. In other words. NPV analysis is always appropriate. Converse ly, tbe TRR can be used only in certain cases. When it comes to NPV. the preacher's words, " You just can't lose with the slu/T T usc:' clearly apply.

Problems Specific to Mutually Exclusive Projects As mentioned earlier, two Qr more projects a re mutually exclusive if tbe firm can accept only onc of them. We no\\> present two problems dealing with the application of the lRR approach to mutua lly exclusive projects. These two problems are quite similar, though 10gicaUy d istinct.

The Scale Problem A professor we know motivates class discussions o f this lo pic with this sta tement: "Students, I am prepared to let one of )'OU choose betWeen two mutualty excl usive ' business' proposi tions. Opportunity I-You give me $ 1 now and I'll givc you SI. SO back at the end o f the class period . O pponunity 2- You give me SIO and I' ll give you $ 11 back at the end o f the class pe riod . You can choose o nly o ne of the tWO o pponunilies. And you cannot choose e ilher opponuniry morc than o nce. I' lt pick the fi rsl voluOIeer. "

150

EXAMPLE 5.2

Part II Valuation and Capilal Budgeting.

Which would you choose? The correct ansv.-er is opportunity 2.6 To see this, look at

the following chart:

Cash flow at Cash Flow at End of Class Beginning of Class (90 Minutes Later) NPV' IRR

Opportunity I

Opportunity 2

-$ 1

- 10

+$ 1.50

+ 11.00

$ .SO

1.00

50% 10

As we have stressed earlier in the text, one should choose the opportunity with the higbest NPY. This is opportunity 2 in the example. Or, as ooe of the professor's stu­dents explained it. "I'm bigger than the professor, so I know I' ll gel my money back. And I have $10 in my pocket right now so I can choose either opportunity. At the cnd of the class. I'll be able to buy one song on itunes with opportunity 2 and still have my original investment , safe and sound . The profit on opportunity I pays for only onc

half of a song." This business proposition illustrates a defect with the internal rate of return crite-

rion. The basic IRR rule indicates the selection of opportunity I because the IRR is 50 percent . The IRR is only 10 percent for opportunity 2.

Where does IRR go wrong? The problem with lRR is that it ignores issues of scale. Allhough opportuni ty I has a greater lRR. the investment js much smaller. In other words, the high percentage return on opportunity I is more than offset by the ability to earn at least a decent returns on a much bigger investment under opportunity 2.

Because IRR seems \ 0 be misguided here, can we adjust or correct it? We illustrate

how in the next example.

NPV versus IRR Stantey Jaffe and Sherry unslng nave lust purchased the righu to Corporate Finance: The Motion Picwre. They will produce this major motion picture on either a ~mall budget or

a big budget. Here are the estimated cash now~:

Small budget

Large budget

Cash Flow at Cash Flow at NPV Date 0 Date I @2S% IRR

- $10 million

- 25 million

$40 million

65 million

$22 million )00%

27 million 160

Because of high risk, a 25 percent discount rate is considered appropriate. Sherry wants to adopt the large budget because the NPV is higher. Stanley wants to adopt the small budget because the

IRR is higher. Who is right!

"The professor uses real money here. Though many students ha'·c done poorly on the pro(cssor"s cxams over the yean;, no slDdenl cver chose opportunity I. The professor claims that h i~ students are -money

players. -"'We assume a zero rale of interest because his clau lasted only 90 minutes. II juSt seemed like a 101 longer.

'A 10 percent return is more than decent over a 9O-minute interval!

Chaplet 5 Net ~nt Value and Other In\'estment Rub 151

FO; the re.asons espoused in the classroom example, NPV is correct.. Hence Sherry is right. How_ ever. tanley IS very stubborn where lRR is concemed. How can She ·u ·J.. ch I Stanley using.the IRR approach ! rry I roOT e arge budget to

. This Is. where inaemenrollAA comes In. Sherry calculates the incremental cash Rows fro h Ing (he large budget instead of the small budget as follows: m coos-

Cash Flow at Date 0 Cash Flow at Date I (in $ millions) (in $ millions

Incremental cash flows from choosing large budget Instead of small budget

- $2S - (- 10) = - $15 $65 - ..0 = $25

'

This chart snows that the incremental cash flows ue - $IS million at date 0 and $25 million at ate I. Sherry calculates incrementllllRR as follows :

Formula (Or Calculating the Incremental IRR:

0= -$IS mill · .... $2S million IOn I + IRR

IRR equals 66.67 percent in this equation. implying that the incremental IRR · 6667 1",c_7mentaI IRR it the JRR on the incremental investment from choosing the liJ.I"g~S prolec('::::~· o me small projKt.

In addition . we can calculate the NPV of the incremental ash flows:

NPV of Incremental Cash Flows:

$15 .. $25 million

- mtil lOfl + 1 "" $S million .25

N;:.e kno~ the sm;lll-budget picture would be acceptable as an independent project because iu IS pos.ove. We W<lnt to know whether it is beneficial to invest an additional $15 mill"

ma~ the large:,~dget Picw~e . inStead of the small-budge t pitture. ln other words, is it be~::;'c~: t~ Invest an addltlon~1 $15 mIllIon to recei~ ~n additional $25 millio n next yearl First k 1 (Ions show the NPV th . . 0 our ca u a-. on e IfIcrementaJ in~stment to be positive. Second, the incremental IRR of ~6.67 percent Is higher than the discount n ee of 25 percent. For both reasons th . 1 Investment can be . s ·fi d the I ' e tncrC!menta JU tl Q • so ~rge-budget movie should be made. The second reason is what Stanley needed to hear to be convinced.

h In review, we can handle, th is example (or any m utually exclusive example) in one of

tree ways: •

I. Compare ,he N PVs of ;"e 111'0 choices The NPV of the la'ge b d . . h h

. - u ge t plcture IS

greater t an t e NPV of tbe small-budget picture That i S27 ·11' . tba n $22 million . s, nu Ion IS greater

2. Calculate the i~cremenral A'P VIrom making the large-h I/tiger picture iI/stead of the small-budget plClllre. Because the incremental NPV equals S5 ill" h the large-budget picture. m lon, we c oose

J. :~~pare rhe incremelllal ~RR 10 the discoullt rat£'. Beca use Ihe incremenlallRR s. .67 percent and the discount rale is 25 percent , we lake the large-budgel

p Ictu re.

EXAMPLE 5.3

PaN n Valuation and Capita! Budgeting

All three approaches always give the same decision . However. we must I/ot compare the IRRs of the two pictures. If we did . we wou ld make the wrong choice. That is., we would accept Ihe small-budget picture.

Allhaugh SlUdents frequently think that problems of scale are relatively unimponanl. the trut h is JUSt the opposite. No real-world project comes in one clear-cut size. Rather, the fi rm has to determine the best size for Ihe project. The movie budget of $25 million is not fi xed in stone. Perhaps an extra $ 1 million to hire a bigger star o r 10 IiIm at a better location will increase the movie's gross. Similarly, an industrial fi rm must decide whether it wants a warehouse or. say, 500,000 square feCI or 600,()(X) square feel. And, earlier in the chapler, we imagined McDonald's opening an outlet on a remote island. If it does this. it must decide bow big the outlet should be. For almost any projcct. someone in the firm has to decide on its size, implying that problems of scale abound in tbe real world.

One final note here. SludcnlS o ften ask which project should be subtracted from the other in calculating incremental flows. Notice that we a re subtracting the smaller proj­ect's cash flows from the bigger project"s cash flows. This leaves an olltflow at date O. We then use the basic IRR rule on the incrementa l fl OWS.9

The Timing Proble m Nex t We illus trate another, somewhat similar problem with thc IRR approach to eva luating mutually exclusive projects.

Mutually Exclusive Inv@stments Suppose (hat the Kaufold Corporation has twO alternative uses for a wa~house. It can store toxic waste containers (investment A) or electronic equipment (i""estmint 8). The tash flows are as follows:

C ash Flow at Year NPV -- ----- --- - --- --

Year: 0 I 2 1 @ O% @ IO % @ IS % IRR

Investment A ~$ IO.OOO $10.000 $1.000 S 1.000 $2.000 5669 $109 16.04%

Investment 8 -10.000 1.000 1.000 12,000 "',000 7S1 -"'84 12.9'"

We find that the NPV of inve.umem B Is higher with low discount rates. and the NPV of invest­ment A is higher with high discount rates. This is not surprising if you look closely "'t the cash flow patterns. The cash flows of A occur early. whereas the ash flows of 6 occur later. If we assume a high discount rate. we favor investment A because we ",re implicitly assuming thac the early cash flow (for example. S I 0,000 in year I) can be reinvested ;!,( that race. Because most of investment 8's cash flows occur in year 3. 8's value is relatively high with low discount rates.

The palterns of cash now for both projects appear in Figure 5.6. Project A has an NPV of $2.000 at a discouDt rale o f zero. Thi s is calcul ated by simply add ing up the cash nows without discounting them. Project B has an N PV of $4,000 at the zero rate. However, the N PV of project B declines more rapidly as the discount rate increases

°A!tem:ll i\-cly. we could havc subtrac ted Ihc largtr proje.. .. (s cash 110w!; from thc smalieT projrc($ ca~h flows. This would have left an ;"jfo .... al dale O. making i1 necC')SDr}' to use the IRR rule (or financing situation:!.. This would work. bu. we find il more confusing.

Figure 5.6 Net Present Value and the Internal Rate of Retum for Mutually ExclusIve Projec ts

Chapler.5 NC'1 Present Value and Other In~tment Rules 1>3

......

o~--~~~~~~ __ _ -484 18.55 1

Project A

Project 8 Discol/nl r818 (%oj

than does the NPV o f pro!ect A. As we mentioned. this occurs because the cash nows of B occur late r. B~:Hh projects have the same NPV at a disco unt rate of 10.55 percent. The.IRR for a pr~jcctls the rate al w hich the NPV equal s zcro. Because the NPV of B declines more rapIdly, B actually has a lower IRR .

As with the movie exa mple, we can select the bette r project witb o ne o f three dUrer­e nl methods:

I. Compar!' ~PVs of the 111'0 projects, Figure 5.6 aids our decision. If Ihe discount rate is belo:, to.5) perCCnt, we should choose project B because B has a higher NPY. If the rate IS above 10.55 percent, we should ehoose project A because A has a higher NPv,

2. Compare increnll!lIfa/ J RR 10 discOllflf I'me. Method I employ>d N P V A Ih . fd . . . ... . no erway o etcrmmmg that B IS a better project is \0 Subtract the cas h nows of A from the cash flows of B and then to ca lcula te the JR R. This is the incrementallRR app roach we spoke of earlier.

Here are the incremental cash nows:

NPV of Incremental Cash Flows --- - --- - -- ---- - ------ --------

Incre m e ntal Year : 0 I 2 1 IRR @ O% @J O% @ JS %

B- A o - $9.000 o $ 11.000 10.55% $2,000 $83 - SS93

This chart sh.ows that Il'Ie. incremcnlal JRR is 10.55 percent. 10 other words. the NPV on th~ mcremenr,a l Investment is zero when tbe discount rate is 10.55 per­cent. Thus. I ~ the rcle,vant discount rate is below 10.55 percent, project B is prc­~erred to project A: II the relevant discollnt rate is above to.55 percenl, projecl A IS preferred to project B.

F~gure 5.6 shows thai the NPVs of the IWo projects are equa l when Ihe discoullt ~ale IS 10.55 percent. In other words. the crOSSOl'f!r rOle in the figure is 10.55. The lO::remental cash flows chan shows Iha tlhe incrementa l lRR is also 105' I . 'd . J perceD1.

l iS not ~ comel. ence that the crossover rale and the incrementallRR are Ihe sa m.e: this equa lity mUSI ahra)'s hold . The incremenlallRR is the ratc that ca uses the mcremental cash flows 10 have zero N PV. The incremental cash nows have zero NPV when the two proj(,.'CLS have the same N I:'V

IS .. P:m IT Valuation aod Cap;181 BI.Jd~lioi

3. Ca/culme N PV on in('remental cash floWs. Finally. we co uld calculate the NPV o n the incremental cash nows.. The chart that appears with the previous method d isplays these NPVs. We find that the incremental NPV is positive when tbe discount rate is e ither 0 percent o r 10 percent. The incremental NPV is negative if the discount rate is 15 percen!. If the NPV is positive on the incremental nows, we should choose B. If the NPV is negative, we should choose A.

In summary, the same decision is reached whether we ( I) compare the NPVs of the two projects., (2) compare the incremental lRR to the reie"Bnt discount rate, or (3) examine the NPV of the incremen tal cash nows. However, as mentioned earlier, we should not compare the IRR of project A with the IR R of project B.

We suggested earlier that we should subtract the cash n ows of the smaller project from the cash nows o f the bigger project. What do we do here when the two projects have the same initial investment? Our suggestion in this case is to perform the subtrac­tion so that the first nonzero cash now is negative. In the Kaufold Corp. example \ve achieved this by subtracting A from B. In this way, we can st iB use the basic IRR rule for eva luat ing cash nO\\'5.

The preceding examples illustrate problems with the JRR approach in evaluating mutually exclusive projects. Both the professor- student example and the motion pic ture example illustrate the problem that arises when mutually exclusive projects have different initial investments. The Kaufold Corp. example illustrates the problem tbat arises when mutuaUy excl usive projects have different cash now timing. When working with mutually exclusive projects, it is no t necessary to determine whether it is the scale problem or the timing problem that exists. Very likely both occu r in any real-world situation. Instead, the practitioner should simply use eitber an increroentalLRR or an NPV approach.

Redeeming Qualities of IRR IRR probabty survives because it fi lls a need that NPV does oot. People seem to want a rule that summarizes the information about a project in a single rale of return . This single rate gives people a simple way of discussing projects. For example, one manager in a firm might say to ano ther, " Remodeling the nor th wing has a 20 percent IRR."

To their credit, however, companies that employ the IRR approach seem to under­stand its deficiencies. For example, companies frequent ly restrict managerial proje<:tions of cash nows to be negative at the beginning and strictly positive later. Perhaps. then, both the ability of the IRR approach to capture a complex investment project in a single number, and the ease of communica ting tha t number explain the survival of the IRR.

A Test To test your knowledge, cons ider the following two statements:

I . You must know the discount rate to compute the NPY of a project , but you com­pute the IRR witho ut referring to the discount rate.

2. Hence, the IRR rule is ea sier to apply than the NPV rule because you don't use the discoun t rate when applying lRR.

The firs l statement is true. The di gcount rale is needed to compure NPY. The IRR is comploed by solvi ng for the rate where the NPV is zero. No mention is made of the discount rate in the mere computation. Howeve r, the second statement is false. Toapply IRR, you must compare the internal rate of return with the discount rate. Thus the discount rate is needed for making a decision under either Ihe NPV or lR R approach.

Chapll'f 5 Net Present Value and Other In \,C'Slrntnl Rilles IS'

5.6 The Profitability Index

EXAMPLE 5.4

:r"~:eer mcthod IUSCd ;0 evaluate projects is cal led the profitability index. It is the ratio present va ue 0 . the fmure expected cash nows after ini tial investment d ivid

by the amount of the mitia l investment. The profitabililY ;ndc- be d ed .... can represente as:

Profitability index (PI) = PV of cash flows subsequent to initial investment Initial illVeStment

Profitabi lity Index Hira Fi I m nnepn "c. (HFI) ;!,pplies a 12 percent discount .-ate to two invest_

ment opportunities.

Project c,

Cash Flows ($000,000)

c ,

- 10 IS

c,

.'

PV@12 % o(Cash Flows Subsequent

to Initial Investment ($000,000)

$70.5

45.3

Profitability Index

] .5)

4.5]

NPV @ 12~

($000,000)

$50.5 ]5.3

Calculation of Profitability Index The profitability index is calculated for project I as follows. The prese t I f cas h flows after the initial investment is: n va ue 0 the

S70.5 ~ $70 + ~ 1.12 ( 1.12),

The profitability index is obta ined b div·d· h· $20 Th ' . Id Y I mg t IS resuh by the inilial investment o f . IS Y1C s:

3 53 ~ 570.5 . 520

Appl.ication of the Profitability Index H d conSIder th ree sit uations: ow 0 we use tbe profi tability index? We

1. fI1dependellt projects: A~sume that HFl' . . to the NPV rule bot h pro· t h Id ~ two prOjects are mdependenl. According

Th . . . . )CC S S o u accepted because NPY is positive in each case. e profitabIlity Index (PI) is greater tban I whenever the NPV ·s .. Thus, the PI decision ru/~ is: t poslllve.

• Accept an independent project if PI > I . • Rejcct it if PI < I .

2. MIIII/ally exc!usil·e projecrs: Let us now assume tha t HFI I its two . N PV can o n y accept o ne of bi er pro~CC t s. ao~lysis says accept project I because this project ha s the

.hgcgwroNP ' I~use project 2 has the higher PI, t he pro fitabilit y index leads to ng se eClLon.

156 PlIrt II V~\ lI<1(ion and Capital Budgel illS

. '. h rolitabilitv index sutTers from the scale For mutually exclusive ~roJe<::b, ( e p . .,', s~1al1er than project I . Because

problem IhallRR also suflers.from: ~rOJect. - ~; 'lmeot Thus-like IRR, PI igno res the PI is a ratio, it igs\Ores project 1 s ,,:ger 1Il~ :. .

differences of scale for mutually ~X.hCIUlsl"peJProp~p~Ch can be corrected using inere-l'k lRR the Oaw WIt I Ie a < • 2

However, I e , '. . . \ 'h (lows afte r sublra<:ting proJecl mental analysis. We wnte the Incrementa ca~

from project I as foHows:

.. .' the incremental cash nows is greater tlum . Because the profitabihty ,mdex o n . Ib I is. project \. This is the same decl-

1.0, we should choose the bigger proJect- a

sion we get wi~h the NPV approac~ .. im licil\ assumed thai HFI could always 3, Ctlpital ralio/1/ng: ~he first t~O ~ascs ror~able ~nvestments, Now consider the case

auract enough capnal to rna c any ~ ' tal to fund all positive NPV projects. when the firm does not have enoug capl

This is the case of capital ration:gd 'eet as well as the fir st tWO, Project 3 has

Imagine that the fir m has a t If proJ . ,

tbe following cash n ows:

, s of Hinm Finnegan Inc , are independent. Further, imagine that 0) the pr~J~ct , '. Because projcct I has an initial but (2) the firm has only $20 million to Inves I- _I bo' Ih this pmJ'ect and another

- 520 '11" the firm cannot se ec . . investment ot ml Ion,. ') d 3 h ve initial investments of $10 ffillhon one. Conversely. bec~use projects - an I a h words,. the cash construint forces

each both these projects can be chosen .. n ot er d 3 • . I rop;ts 2 an

the firm \0 choose either project. ?~ p 11 ojects ') ~nd 3 have lower NPVs than What should the firm do? indl~~~~ y/rrojl.'<:ts-2 a nd 3 are added together.

project I has. However, when the I, ~ 0 f Thus common sense dictates thai the sum is higher than tbe N PV 01 proJect. ,

ro'ectS ') and 3 should be accepted . p ~ - , sa ' aboullhc N PV rule or the PI rule? In the case What does our conclUSion have (0. ) d - 1 their NPVs. Instead we should

. t rank proJccts ac<:or tng 0 . . PI of limited funds. ~ canno . f sent value to initial investment. ThIS IS the rank them accordlllg to the .ratlo 0 pr~. h PI ratiOS than does project I. Thus they

:~~~1~0~ ~:~t: ;I~~~ ~rt~:j:c~~v:h;~ ce;pital is rationed .

Chlll'ltr 5 Nel Pres.cnl Vnluc ;jnd Olher II1\"es imenl Rulc-s J~7

T he usefulness o f Ihe profitability index under C<lpilUI rationi ng ca n be explained in military terms. The Pelllagoll speaks high ly of a weapon wilh a 10 1 of "bang for the bllck."·!n capital budgeting, the profitabilit y index measures the bang (the dollar return) for the buck invested. Hence it is lIseful for capita l rationing,

It should be noted that the profitabi lity index does not wo rk if funds arc also lim­ited beyond the in itial time period. Fo r exa mple, if heavy cush outflows elsewhere in the firm were to occu r at date 1. project 3, which also has a cash outflow at date I, might need to be rejected , In other words, the profitability index cannot hand le capital rationing o\'er multiple time periods.

In addition. what economists term imlil'isihililic~s mClY reduce IhcelTeclive ness of the PI rule. Imagine that H FJ has $30 million available for capital investment , not just $10 mill ion, The firm now has enough cash for projects I and 1. Because the sum of the NPVs o f these two projecls is greater than the sum of the NPVs of projccts 2 and 3, the fir m would be better served by accepting projects I and 2. But because projects 2 and 3 still have the highest profitability indexes, the PI rule now leads to the wrong decision. Why d oes the PI rule lead us astray here? The key is that projects I and 2 USe up all of the $JO million, whereas projects 1 and 3 have a combined initial invest­ment of only $20 million (= SJO + 10). If projects 2 and 3 a re acrepted. the remaining SIO million must be left in the ba nk .

This sit uation points out thai care should be exerci sed when using the pro fitability index in the rell l world, Nevertheless. while not perfe.c\. the profitabilit y index goes a long way toward handling capilnl ralioning.

5.7 The Practice of Capital Budgeting

Table 5_3 Percentage of CFOs Who Always or Almost Always Use a Given T&Chnlque

So fa r this chapter has asked "Which capita l budgeting methods should companies be using?" An equally importa nt question is this: Which methods tire companies usi ng? Table 5.3 helps answer this question, As c;.m be seen from the table. approximllte ly three-quarters of U.S. and Canadian companies use Ihe IR R and NPV methods. This is not surprising, given the theoretical adva lliages of these approaches. Over h .. tf or these companies use the payback method. a rather surprising result given the concep­tua l problems with this approach, And while discounted payback represents a theoret­ical imprOvCmeJlI over regular payback , the us.."1.ge here is far less. Perhaps companies are attracted to the user-fri"endly nature of payback . In addition. t he naws of this approach, lIS mentioned in the: current chapter. may be relatively easy 10 correct. For

Internal rate of return (IRR) Net present value (NPV) Payback method Discounted pilyback Accounting rate of retum ProfitabiUty index

·1. Always or Almo!;t Always

75.6% 74.9

56.7 29,5

]0.3

tl.9

SOURCE: F~ llrom}oho R. G,.."h3m Ind Campbell It. Horvey, ' "The TileOf")' arod P,.."ctke 0( ~,e ""'.11",.: Evidc n,,. from m. FI.Id.~ Joumd o{F"monciol €corIomIa 60 (1001). &sed on a w ..-...y 01 392 CFOs.

IS'

Table 5.4 kequHlcy of Use of Vartous Capita' 8udgeling Methods

Pan II Valuat ion arid Capilal Bu~sc l i nG

exa mple. wh.ile the payback met hod ignores all cash flows after the payback period . an alen manager ca n ma ke ad hoc adjustments for a project with back·loaded cash flows.

Capital expenditures by individual corporal ions ca n add up to enormous su ms for lheeconomy as a whole. For exaOlple. in 2007, Ex;c;ooMobil announced that it expected to spend about $20 billion per year in capital outlays from 2007 to 2010. 1l1is was about the same ilS the company's capital spending in 2006. which had totaled $ 19.9 biJ lio n. Abo ul the same time, competitor ChevronTexaco announced Ihat it would increase its capilal budgcting fo r 2007 10 $ 19.6 billion. up from $16 billion in 2006. Olher companies with large capital spending budgets in 2007 ~re Ford . which projected ca pita l spending of about $6.5 billion , a nd semiconductor company SaOlsung, which projected capital spending or about $6.7 billion.

La rgc~scale capital spending is often an indusu ywide occ urrence. For exa mple. in 2007, capital spending ill the 25 la rgest sem iconducto r comp<lOies was eXpe1:ted to reach S48.3 billion . This tidy sum represented a 2 percent increase over the industry capital spending in 2006. which was $47.2 billion. This relat ively slow growth was in stark contrast to thc 18 percent increase from 2005 to 2006.

Acco rding to inrormation released by the Uni ted States Census Bureau in late 2007 and early 2008. capita l investment ror the economy as a wbole was S1.3 1 tri llion in 2006. S1.I 5 trill ion in 2005. and $ 1.04 trill ion in 2004. The to tals for the three years Iherefo re equaled approximatcly 53.5 trillion! Given Ihe sums at stake, it is not too surprising that successful corporatio ns carefully analyze capita l expenditures.

One might expect the capital budgeting methods or large firms to be more so phis­ticated than the methods o f small firms. After all, largc fi rms have Ihe financial resources to hire more sophis ticated employees. Table 5.4 provides some su pport for this idea. Here firms indicate rrequcncy of use o f the vario us c.lpita l budgeting me thods o n a sca le or 0 (never) to 4 (a lways). Both the IRR and N PV methods are used more frequently. and payback less frcquently. in large firm s than in sm(ll l firms. Conversely, la rge lind small firms employ the last three approaches about equally.

The use of Quantitative techn iques in capital budgeting va ries with Ihe ind ustry. As one would imagine, firms that are better ablc to estimatc cash nows are more likely 10

use NPY. For example. estimation o f cash flow in certa in aspects of the oil business is quite feasible. Bec;lUSC of this. encrgy~related fi rm s werc among the rust to usc NPV analysis. Conversely. the cash flowS in the mOl ion picture business are very ha rd to project. The grosses o f great hits like Spidernwn. Harry POller, and Slar Wars were far. rat' greater than anyone imagined . The big fa ilures likc AI(lmo and Waterll'orfd

Large Firms Small Firms

Internal rate of return (IRR) 3.-41 2.87

Net present Vil lue (NPV) 3.42 2.8]

Payback method 2,25 2.72 Discounted payback 1.55 1.58

Accounting r.ue of return 1.15 1.41

Profitabilil)' Index 0.75 0.78

finns indic;:ne fr.quenq of use on ~ scM from 0 (ne-_) 00" (>lw3ys). Numben III I3bIe are ~ _, ~enu.

SCII.AI.CE: T~ 1 '-' GrWIn and Har....y (200I).Op.dt.

Summary and Conclusions

C'b:lpftr 5 NCI PreS(nl Va luc.and O(~r Inw5tmcn( Rules 159

bwe~ unexpe<'ted as well. Because of (his. NPV analysis is frowned UpOIl in the movie USlOess.

How does Holl~ood per.fo~m capital budgeting? The info rmation that a studio uses to accepi or reJcct a mOVie I~ca comes frOID the pitch. An independent movie ro­ducer ~hedul:s ao ex tremely bnef meeting \"';th it st udio to pitch his o r her ide:for ah'"°hv1e. ConSider .Ihe rollowing fou r paragraphs or quotes concerning Ihe pilch from t e l oroughly delightfu l book Red POwer:"

"They (st udio executi\"eSJ don'I waOIlO know 100 much " Sl Ro S· " y k . a15 n Impson . hey wanllo

h" owconccPI: . .. They want 10 know what the three~lillcr is. because Ihcy want ill o suggest

t e ad campaIgn They Wan t a t'11 Th ' d ' • • J C'.... (:) on I wanl to h(:3r any esoterica And if the

m:.~ng lasts mor~ tha n ri lle mi~u~es, t ll~y're Probably not gOing 10 do the proj~I." guy co~es in"and says thiS IS nt~ I~ea : '1(111'5 on a spaceship,'" says wriler Clay Froh­

man (U~u/~r :11'1"). And Ihcy say, ·8nlhant . fantastic.' Becomes .,IIiI'll. That is 1au·.( on II space~hlp. u l~ lmalely . .. : And thai's il. That's all they wanl to hear. Their 311itude is ' Oon't confuse us wu h thc d(:lalls of Ihe s10ry ... ·

. .. ... Some high:onccpt stories are more appealing to Ihe st udios than ot hers. The ideus hked. ~st are sulliclent ly originalthallhe audience will not r~1 it has already seen the movie. yet slnlliar enough to past hits to rellSsure executives \\~dl')' or an)1.hing 100 rar-oul. Th h rrequentl), used ShOrthand: It's Flashd(Jnt'1' in Ihe COUntry (Foolloosf') or H ' h N . us. t e Sp'ICC (Ollllalld)." Ig IJIJI/ III outer

b' .. . One ga mbit not to use during a pilch," saysexccutive Barbara Boyle. "is to talk aoom i~g oox.~Ollict gro~ your story is sure 10 make. Execut ives know as well as anyone Ihal it 's , po5.sl~le to predict how much money II Olo\'ie will make. rtOd declardliOlls to the cOnlrary are conSIdered pure mala rkey."

'-Marl;: Lit ...... k. RN1 POln~ TJ.e S'Tl--l fi /" /S . W·tr ~ .I ' . "'" t' or "'.I .... ' (C'mu uut'$.J 1II111(! Nj'''' H vll)"II'I)O(/(Ntvo· Yon. . I lam .. orrow and COmpilny. lnc .• (986). pp. n. 74. and 77. .

I . In this chaplcr. ~\'(' COvered differelll ill\'cstmeol decision rules. We CV·llu·tted the rno t popU lar othernatl\,(,s 10 the NPV: The p',yb'lek pcn·od II d' . d" . s Ih~ . I ". le tscountc payback pcnod a~~~t(c;~l~ ~~te of relun1. and the prolitabilit y index:. III doing so we le,amed mo~

2. ~Vhilc ~e found thaI Ihe al ternat i\'cs ha\'c som!! redeeming qualilies. \\ hen all is said and O"~dl ey arc nOI the NPV rule: for those of us in fi rHillce. Ihat makes them docidcdly

SCCon ~ntle. .~

J. Of Ihe competitors to ~PV, IRR must be ranked aboVe payback in raci I'RR I ~e~ches ~he S~tme decision a~ NPV in the normal ca5C where the i'll itiai 0~ 1t10wSa ;~~~ III epen ent IflVcstment proJCCt a re followoo only by 11 series or inflows.

4. We cI.assificd the. flaws of IRR into two Iypes. Firsl. wc considered the general case fl pplYlllg to both Independent and mUI ua lly excluske projccts. Therc '11'PC'lrcd 10 be I ' problems here: " \\ 0

a. ~Olll!! projccls have cash inflows followed by one or more outflows. Th IR.R I ~' ~n\'ened h.cre: One should accept when the IR R is helOlI' the discount r:te. ru" IS

b. Ii~;;c ioro~CC l s h~\'e ~n. number of chnnges of sign ill thcir cash nowS. Hcre. Ih(:rc an.: Yod.' d':lultlPk IIltcrna l ra les of return . The praclitioner must use ei ther NPV

or mIl le Inlernal ratc of return here.

""

Concept Questions

I'll" II Valuation and C:lpilal lJudgt:1inll

S. Next. wcconsidcn:d the specific problems with the NPV for mutually exclusive proj«ts.. We showed Ihal. due to diO"crcn(;es in either size or timing. Ihe proje<:\ wilh the highest IRR need not have the h ighest N PV. Hence. the IRR rule sho uld not be applied. (Of coun~c. NPV can still be lIpplicd .)

Howc\'cr. we then cllkulatcd incrcl\lcnl3\ cash flows.. For case of cakulmion. we sug­gested subtracting Ihe cash nows of the smaller projC'C1 from the cash fl ows of the larger project. In lhal way the incrementa1 initial ('ash flow is negat ive. One C,IIl .. lways rc<tch a corn..-ct decision by un'Cj)ting the larger proj .... 'Ct if the incrcment:l llRR is gl\!<llcr than the discount r;nc.

6. We described capita l rationi ng as thccasc where funds arc limitoo 10 a lixed tlollar mllount. Wilh capilal mlioning Ihe profiwbi1it~ index is a userul met hod of adjusting the NPY.

I . Payback Period and Nef Prl"SCnt Value If a projcct wilh com'cntional cash 110ws ha s a payback period less than the projIX'fs lire. can you detlnitively st:IIC Ihe algebraic sign or the NPV'! Why or why nol? Ir you know thallhe disco unted p'lyback period is less than tlte projt..'CI's lire. wltat ColO you say about thc NPV? Explain.

2. Net Present Value SuppoS!! a rroj~"C t has conventional cash nows and a posi th'c N I~V "'.'hm do you know about its pll}back? lis discoulltoo payback'! Its profitability index? It s IRR? Explain.

J .

<.

5.

6.

7.

8.

Comparing Inn.':Stml'lII Criteria Define each or the rollowing invcstment rules and discuss any pot('ntial shorlcomings or each. In your definition. stale the criterion for lIcccpting or rejecting independen t proj~"C t s under each rule. a. Payback period. b. hllernai ralc or return. c. Profitabilit y index. d. Net pr~nt value.

Pa~'baek :H1d Internit l Ra te of Return A project has perpetuli l cash nows of C per JXriod. a cost of I . ;:lIld a requin.--d relurn of R. What is the relationship between the I)roject's payback and its IRR? What implications doe~ your answer have ro r long­lived projects with rel,lIively constant cash nows?

International InH!'stmcIII Projects In January 2008. automobile manufacturer Vol kswagen announc(.'d plans 10 build an aU lOlIlat k transmission and cng.ine plan t in South Carol ina. Volkswagen app:l rently felt thai it would be beller :tble to compete ilnd creilll." "li llie with U.S.-based f:t cilities. Other companies stich as Fuji Film :tn'" Swiss chemic;11 compiln)' Lonzil ba\e reached si mihlr conclusions and taken similar actions. \Vhat are some o r the reasons that io reigll manufacturers o r products itS

dh'ersc as automobi les. Iil lll, and chemicals might arri\'e at thi s S~\llle conclusion'!

Capital Budgeting Problems Wh at a rc !K)mc of the d ifficul ties thm might come up in actual applicat ions or the v:tr:ous criteria wc discussed in Ihis ehupter? Which one wou ld be the caSil!St to implement in actual applications? The most dillicu lt?

Capilal Budgeling ill Not-for-Profit Entiti l'S Are the I:apital budgeli ng criteria we discussed applicabk to not-ror-prolit corpor.uions? How should such entities m:t ke capilal budgeting decisions'! What about the U.S. government? Should it ev,lhmte spending propoS<lls using these tcchniqucs?

N{'.t Prl'Seflt Value The inveslrm:nl in project A is SI mi llion, and Ihc in\'cstment in proj ... 'Ct B is S2 million. Both proj~"C l s have a uniqUl.' iruenl:.1 rate or t\.'lUrn of 20 peT­cent. Is the rollowing statcmel11 true or ralsc-!

!-"'or any disco un t r:tte from 0 percent to 20 percent, project B has an NPV twice as great as that or project .4.

Explain your answer.

Chllprrr 5 Nel Pn:wJlI ,VaJuc: aud Otbn lon'Sl.M?l1 l Ruin 16'

9.

10.

II .

12.

1J.

14.

Net Present Value \'crsus Profitabilih' 100 . C ·d ." . I

. ' . . ex o nsl er ule ,0110\\ IIlg two mutuallv e.'\c USI\'(' projects avm lable to G loballnveslmen ts.. Inc.: .

Profitability Co C , C t Index NPV

A

• -$1.000

- 500 $1 .000

500 $500

'00 1.32 1.57

$J22

2.5

:he appropriate disco~nt r.tte for the projccts is 10 penxnl. Global !J\\'CSlmenl chose to undertake prolttt A A,·, lu ,ehe ' h h Id ' . ~ . • I on ,or s are 0 ers, Ihe manager or a pen-~~O~l :und .that O~\11S a substaJl~illl amoun t o r ~hc firm's stock asks you wby Ibc lirm

St: proJecl A tIlstead of proj\.'Ct B when prOject B has a higher protl tability index How would )'Otl the CFO )."" .,'). )"OU r: '.. . " .. . - . . . " . r , Irm ~ .Iel lon , , ... re Ihcre any Cln:Ulllstances

under whIch Global Inv('Stments should choose projecl B?

Internal Ratc of Return Projects A and B have the fo llowing cash 110ws:

Year Project A Project 8

0 - $ 1.000 - 52,000 I C IA CI. 2 C2A C2. 3 C3A C3.

II. Ir the ca.sh nows rrom the projCCts arc ident k aL which of the two projects would have <l hIgher IR R'! Whv!

b, IfCIB =2C IA.C2B ';2C2A. andCJ B =2CJA.thcnis IRR - IR R '! Net Preseflt Va lue Yo . • • I . " . • II )Cri . -.. u.tTe evol I.talmg ~roJecllllll\d proJect B. Projl!'Ct A hilS <l sho rt I .od or rUlure. \,;a~It l1ows. w~l~e ProJl.'ct 8 h'ls rela tively long rUlure c:lsh nO\\ S,

WhIch project wtll be more SCnStl1 VC to changes in the required re!llm·.' Wh,,? Moo 'fled I I R . . : I 1 ,nt{'rna ... ate o~ Rc(ur~ Onc 01 the less Oaltering interpretatio ns or the ~\cron y.1l1 t-.l1 R R IS mellllmglcs.s mtern,,1 n ile of ret urn ." Why do you thi nk t his term IS Ilpphcd 10 MIRR:'

Net PfeS('nt Valuc It · . d . IS somenmes stme Ihat " the nel presen t value a ppro'leh assumes rCmYl.'Stlllelll or the intermedimc cash Oo\\'s at tho: req " d .. I ·h· chi n ? To Ire relurn. s t IS

• I correct. 0 answer. suppose you calculale Ihe NPV of a project in the usual way. Ne; .. t. suppose you do the lol lowing: a, Calcu late the ruture value (as of Ihe cnd o f the p.....,; .... ,) of ··II ,h h n h I h" . .v~.... " e cas O\\S ot CT

~ lUll I . e In It ~a l o utl,;!y assum ing they arc reinYl'sted at the required return. prod uc­mg a slllgle luture \ 'alue figure (or the proj ... oct.

b. Calc.ulatc the NPW or the project using the single future \~J.lue ealculmed in the p~e\'!~u~ .step and lI,'e. initial o utlar It is easy to veriry that you will gct the same N~\ ,IS 111 your ~Tlgmal ('alculallon only if you usc the rcquin.'tl ret urn as th' reuwestrnent role til the previolls step. e

Interna l Rate of Rel.urn It is sometimes slated thill "the internlll rate or return approach assumes rell1\,csmlCnt or t.lte intennedi'l!C ("Ish OOWS "I\ ,h · I f ret " I I· . . 1" . . " • e IIlterna n ile 0 . urn. s 11b C .1111l correct '! To ilJl:.·W(·r. suppose you caicuhue the IRR of a ro· ... "Ct 11\ the usual way. Ne_xt. suppose you do the rollowing: P ~ u. Calculal~ I~~ fulure value (as of the cnd or the projCl..·1) of al l the CilSh nO\\ S olher

than the IOllIal outlav asstlm inl.! they are rei",·" ,_·' ·" ,h, IR R d· . I f

- - I.'U • • pro ucmg a smg e tlture value figure for Ihe project.

162

Questions and Problems

connect BASIC (Ou .. lions 1-8)

Parr II V;lluation ~ml Capi tal Blldge1inS

I.

b. Calculate the IR.R of the project usi ng the single future " '.tItle calculated in the previous slep and the initial o utlay. It is easy to verify that you will get the same IRR as in your original calculation o nly if you use the IRR as the reinvestment ratc in the previous step.

Calculating Payback Period and i\PV Fuji SoftWl.lre. Inc .. has the followil.lg mutu­ally excl usive projects.

Year Project A Project 8

o

2

J

-$10,000

6.500 4.000

1.800

- s 1 2.000

7.000

'.000 5.000

a. Suppose fuji 's payback period cutoff is two years. Which of these two projects should be chosen?

b. Suppose Fuji uses the NPV rule 10 rank these two projccts, Which projcct should be chosen if tbe appropriouc discount rate is 15 percent?

2. Culculaling Payback An investment project provides cash inOow'S of S970 per yCilr for eight yea rs. What is the project payback period if the initia l cost is S4,IOO? What if the initial cost is S6.200'1 Wh:l t if it is S8.000?

3.

4.

s.

Calculating Discounted Payback An investmen t projcct has allnual cash inOows of S6.000, S6500, $7,000, and $8.000. and a d iscount rolte of 14 percent. What is tbe d iS(.'Qunted payback period for these cash Ilows if the init ial cost is S8,0Q0? What if the initial cost is S13,000? What if it i5SI8.0001

Ca lculating Discounted Paybatk An in\'t."S tmelll project COSt s SIO.OOO and has annual cash flows of S2.600 for six yea rs. Wlll1t is the discounted payback period if the d iscount rate is 0 percenl'! Whal if the discount r".lIe is 10 percenl? If it is 15 percent?

Calculating IRR Teddy Bear Planel , Inc .. has a project with the foll owing cash 0 0W5:

Year Cash Flows ($)

0 - $11.000

5. 500

2 4.000

J 3.000

The company e\<tluates all projects by applying Ihe IRR rule. If the appropriatc interest rate is 8 percent. should Ihe company accept the project?

6. Calculating IJt.R Compute the internal r'.ate of return for the cnsh flows of the 1'01· lo"~ug twO projects:

INTERMEDIATE (Quetllon. "20)

Chllpl"r 5

7.

8.

9.

10.

'6]

Cash Flows ($)

Year ProJect A Project 8

0 -$3.500 -$2.300

' .800 900 2 2.-400 '.600 3 ' .900 1.400

Calcu~aling Profitability .lndc-x . Bill plans to open n sel f·serw groomin ' t.'Cntcr in a storefron t. The groomlll£ equipment will cost $190 000 ' 0 be -d' g d- 1 Bill ex . fi . . •. pal Imme late y. J. • peels a tCr1ax c~sh mnows of S65.000 annually for seven yea rs. after which he

p .IIlS ~~ scra,P the eq Ulpn~ent and retire to the be:lcbes of Ncvis. The fi rs t cash inOow ~cul"'s ~II I~C end of the ~lr$t year. Assumc the required return is 15 percent Whal is 1 1e project s PI? Shou ld It be a(.;cepted? .

Calcu.Jati~~ I)rofi l abili~)' Index Suppose Ih(' fol lowing two independent in\'(';;t1l1ell t o pportunities lire aVillhlble to Greenplain Inc The 'IPProp','" d · '­to percent. . . < "e Iscount ral(' IS

Year Projett Alpha Project Beta

0 - SI.500 - $2,500

• 800 SOO 2 '00 1,900 J 700 2,100

a. ~o~pute t~e profi tabili ty index for C'dch of the Iwo projCCts, b. Vhlch proJect(s) shou ld Gn.'en p/Ilin an'Cpt bllscd on the ruie? p rofi tabil ity index

Cashd' ~low Inluition A proja:t hilS an initial cost of I. has a required return of R

,111 JXlYS C annually for N years. .

a, Find C in (('rms of 1 and N such thm Ihe project h'l$ '\ n..1ybaek pc -"" . . 1 10 its life. • • y' fI Just cquil

b. Fhind C in tc~n~s of I. N. and R such t1mt this is it profililble project 'lccordinl!: 10 I e NPV dt."Clslon rule. ' -

e. Find C i~l t('rms of I. N. and R suc h that the projcct hilS;1 bcnefit-cost ra tio of 2. Problems " 'llh IRR SUPPO'"' '11'·--, 58 1

. you an.: 0 ell':'" .000 today but musl make the 101 owmg payments: . , .

Year Cash Flows ($)

• 0 $8.000

• - -4 .-400

2 - 2.700 3 - 1,900

• - 1.500

a. What is the IRR of this offer? b. If the app' ' . d ' . opr~a e ~scou nt nile IS 10 jX'1'CCnt. should you accept this ofrer? c. If the appropnate discount rate is 20 percent. should you accept this offer?

'" Pari II Valtl:llion and Capiml Budgeting

d. What is the NPV of the oller if the appropriate discounl r.lle is 10 percent'! 20 percenl'~

c. Are the decisions under Ihe N PV rule in P"ft (d) consistent with those of the IRR rule?

II. NPY "crsus IRR Consider the followi ng cash nO\\S on IWO mutually exclusive proj<.'Cts for the Bahamas Recreation Corpor..ltion ( BRC). BOIh proj(.'Cts require an annual relUm of 14 perce ll!.

Year Deepwater Fishing N ew Submarme Ride

0 - $750,000 - S2.1 00,000

I 310.000 1.200.000

2 430,000 760,000

3 330,000 850,000

As a financia l :1I1:I IYSI for BRe. ),011 an: ltskcd th(' following questions: s. If you r decision rule is \0 al,.'(:ept the proj\.'C1 wjah the greater I RR, which project

should ),Oll choosc'~

b, Because you are fully aware of the IRR fulc's scale problem. you ca1culute thc incremental IRR for the cash tlows. Based on your compul.'\(ion. which project should you choose?

c. To be prudent. you compute the NPV for both projects' Which projcct should you choose? Is it consistent with the incremcntal lRR rule?

12. Problems with Profit abi lity Index The Robb Computer Corporat ion is trying to choose bet\.\"eCn the fo llowing two mutually exclusive d l"sign projects:

Year Cash Flow (I) Cash Flow (II)

0 -s-iO,OOO - $15.000

I 2 1,000 8,500

2 1 1.000 8.500

3 1 1.000 8~()()

a. If the req uired return is 10 percent and Robb Computer applies the profitability index decision rule. which projcct should the firm ,KCept?

h. If thc company applies t he NPV decision rule. which projcct should it ta ke'! e, Explain why your anS\vcrs in (a) and (b) a rc d ifferenl.

13. Problcms with I RR Cutler Petroleum, Inc,. is trying 10 evaluate a generation proj­ect with Ihe following cush flows:

Year Cash Flow

o I

2

- $32.000,000

57.000,000

- 9.000.000

:l. If the company requires a 10 percent return on its investmen ts. should it accept this project? Why?

b. Compute the IRR for th is project. How many IRRs 011\' there? If you apply the IRR decision rule. should you acceptl he proj~'Ct or not '! \Vb.u 's going on here'.'

Chapin 5 Nel Present Value and Other hwC'St lllcnl Ru1c$ 165

14. Comparing Inwslmcnt Critcria Mario Brothers. :t game manufacturer. has 11 new idea for an adventure game. II can mHrket the game either as a traditional board game or as an interactivc CD·ROM. but not both. Consider the folJowingc:lsh flows of t he two mutually exclusive projects for Mario Brothers.. Assumc the discoun t rate for Mario Brothers is 10 percent.

Year Board Game CD. ROM

o I

2

3

- $600 700

ISO 100

- $1 ,900

1.400 900

400

a. BaSt.'d 011 thc p..ytxlck period rule. which project shou ld be chosen? b. Based on the NPV, which project should be chosen? c. Based on the lR R, which projcct should be chosen? d. Based on the incrementa ll RR, which project should be chosen?

15. Profitabil il~' Index \-eTSliS NP V Hanmi Group, il consumer elcctronics conglomer­~lIe. is rcvi~\~ing its annual budget in wireless h.'Chnology. I t is considering invest ments III lhree dlflerent technologies to develop wireless communication devices. Consider the following cash flows of the three independent projects for Hanmi. Assume the d iscoun t rate for Hanmi is 10 pereent. Furthcr. Hanmi Group has only $15 million to invest in new projects this year.

0 - is - $10 - SIS I IJ 10 10

2 7 15 20

2 30 SO

a. Based on lhe profitability index decision rule. ran k these investments, h. Based on the NPV. rank these im'est rnents. e. Based 01) you r findings il) (iI) and (b). whm wou ld you ro.:.'commend to the CEO of

H:lIlmi Group and why'!

16. Comp~ring 1I~\'csnncDt Criteria Consider the following cash fl ows of two mutua lly exclUSIVe proy •. 'Cts for AZ-Motorcars. Assume the discount rate for AZ-Motorcars is 10percenl. ~

Year AZM Mrni-SUV AZF Full-SUV

0 - $)00.000 -$600.000 I 270.000 250,000

2 180.000 -400.000 3 150,000 )00,000

a. Based on the payback period. which pro~"'Ct sho uld be accepted? b. B:lscd on the N PV. which project should be accepted?

... rul U V:llualion and Capiml Budl!c:ling

c. Based on the IRR. which project should be accepted? d. Based on this analysis. is incremenlal lRR analysis mx:essary? If yes.. please con·

d uct the analysis. 17. Comparing Imcstmcnt Criteria The treasurer of r\maro Cnnn,--d Fruits. Inc .. has

projected Ihe cash flows of projccts A. B. and C as fo llows.

Year Project A Project B Project C

o • 2

-$200.000

140.000 1'10.000

- $400.000

260.000 260,000

- $200.000 150,000

120.000

Suppose the relevant discount rate is 12 perccnl a year. a. Compute the profit;tbility index for each of the three projects. b. Compute the N PV for each of the three projects' c. StlPPOSC these three projccts :I re independent. Which proj~'C t( s) should Amaro

accept based on the profilahility index rule? d. Suppose these lbree projects are mUlUally exclusive. Which projccl(s) should

Amaro accept based on the profitabili ty index rule? c. Suppose Amaro's budget fo r these projects is $600.000. The projects ,Ire not divis­

ible. Which project(s) should Amaro ,Icccpt? 18. Comparing Investment Crilerilt Consider the following casb nows of twO mutually

exclusive projects for Tokyo Rubber Company. Assume the discount rate fo r Tokyo Rubber Company is 10 percen t.

19.

Year Dry Prepreg Solvent Prepreg

0 - S 1.400.000 - $600.000

900.000 ]00.000

1 800.000 500.000

J 7CO.OOO <100.000

u. Based on the payback period. which project should be taken? b. Based on the N PV, which project should be taken'! c, l3ascd on the IRR, which project should be taken? d, Based on this analysis, is incremc1I1aliRR analysis necessa ry? If yes. please con-

duct the analysis. Comparing In,'estmellt Criteria Consider two mutually exclusive new product launch projects that Nagano Gol f is considering. Assume the discount rate fo r Nagano G olf is 15 percent.

Project.1: Nagano IP_30. Professiona l clubs that will take an initial in\'Cstmenl of S450.000 at

time 0, Next five ye:lfS (years 1- 5) of :;.'1Ies will generate a consistent ellsh

now of S 160.000 per year. Introduction of new product at year 6 will terminate further cash

!lows from this projccl.

Project B: Naga no NX·20. High-end amateur d ubs that \\~J1lakean inili:.1 invcstment of $200.000

al timcO.

CHALLENGE (Oue.lioos 21- 28)

03plt'l'" 5 Nl:'t Prc:lC' llt VlI lut' :Inti Other h1l'C:Slrnt'1lI Rules 167

10.

21.

Cash flow at year I is S80,()(X), In each subsequent year cash flow v.~11 grow at 15 percent per yea r,

Introduction of new product at )'car 6 will terminate furt her cash flows from Ihis project.

Year NP-30 NX·20

o •

2 J

• S

- $450,000

160,000

160.000

160,000

160.000

160,000

-$200.000

80.000

92,000

105,800

121 .670

139,92 1

Please fill in the fo llowing table:

NPV

'RR In( re.menuIIRR

PI

NP-30 NX-20 Implications

~o~paring I"" cs~mel'lt Criteria You are a sen ior manager at Poeillg Aircra ft and h'l\e ,bee~ authOrized to sPC.nd up to $400.000 fo r proj(.'(;ts. The three projects you arc consldenng have the follo\\,1I1g characteristics:

Project A: Initia l investment of S280,?O:O. Cash flow of $ 190.000 at yea r I and ~ 1 70.000 at yea r 2. ThiS IS a plant cxpansion proj(.'Ct. where lhe reqUired mte of relUm is 10 pereent.

Project B: Ini;ial investment o~ S3~.DI?O. Cash flow of S270,000 al year I and S_40.000 at ye.ar _. 11l1S IS a new produl;t development projtct. where the reqUIred mle of return is 20 percent.

Projc<:t C: Initia l investment of S230.000, Cash Aow of $ 160.000 at \'car I llOd SI90:000 at yeur 2, This is a market expan sion project. ~'hcrc the reqUIred rate of return is 15 percent.

Assume the corpo rate discount .. lie is 10 perceo t.

Please offcr your recommcndations. backed by you r analysis: ,

Paybac.k IRR ~

NPV

ABC Implications

:ay~a('k and N llV An j~vestment ,under eonsider.ltion has a paybac.k of six years and ,~ cost of $574.000. II tbe reqUired ret urn is 12 percent . what is the worst -c:asc N PV , The best-c:asc N PV? Explain. Assume the cash fiows are conventiona l.

'68 P:irl II Vlllluallon and Capital UlLd~Clinb

22.

23.

24.

25.

Multiple IRRs This problem is usefuJ for tcsting the abili ty of financial c.alcula­tors and computer software. Consider the following cash flow s. How Ill:!ny dlfTe(ent IRRs arc there? (H im; Search between 20 percent and 70 percent.) When should we take this project'l

Year Cash Flow

o

2 ]

•

- $ S04 2.862

-6.070 5.700

- 2.000

NPV Valuation The Yurdo ne Corporation wants to set up il pri\"itlc cemetery busi­ness.. According 10 the CFO. BaIT)' M. Deep. business is " looking up.'· As a result. the cemetery project will provide a net cash inflow of $1 15.000 for the firm during the first yea r. and the cash flows are projected to grow at a mtl! of 6 percent per yea r forever. The projCCt requires lin init iol l investment o f S I.400.000. a. If Yurdone requires:1 13 percent rcmrn on such undertak ings. should the cem·

etery business be sia n ed? . b. The company j ~ $() l1lewhat unsure abou t the aS~U1UptlO11 of a 6 perce~t growth

rnte in itscush nOWS. At what const:lnt growth rate would the company Just break even if it still required a 13 percent re turn o n investment?

Calcula ting IRR The UHth Mining Corpor.uion is set. 10 0v<:n.a gold mine ne:lr Provo, Uta h. According to the treasurer, Monty G o ldstCIIl. " ThiS IS a golde.n oppor­tunity." The mine will cost 5900.000 to open and will have an economic hfe of II yea rs.. It will ~encmte a cash innow o f S I75.000 at the end of the first ye .. r. and the C:lsb in nows :Ire projected to grow at 8 percent per yea r for the next 10 years.. After I I years. the mine will be abandoned. Abandonment COSts will be 5125.000 at the end of year I I. a. What is the IRR fo r the gold mine? . b. T he Utah Miniog Corporat ion requ ires a 10 PCR.'Cnt return on such undertak ll1g5.

Should the mine be opened?

NI'V and IRR Anderson Lntern:lt ional Limited is e\'aluati ng a project in Erewhon. The project will creatc the fo llowi ng cash nows:

Year Cash flow

0 -$750.000

205.000

2 265.000

) 3-46.000

• 220.000

All c;lsh nows will occur in Ercwhon :tnd are expresscd in dollars.. In an iltlempt to improve its economy. the Ercwhonian governml!n t has declared that all cash nows created by a fore ign company are "blocked" ilnd mllst be reinvested with the govern­ment for o ne yea r. TIle reinvestment nile for these funds is 4 percen!. If Ande~soll uses an II perttnt required relurn on this project. \\'hat arc the N PV and IRR 01 the p roject? Is the IRR you calculated the J\IflRR of the project'? Why o r why no t'!

Chapll'r!li Nct l'rt'SCnl Vutuc anu Olher InWSl1lh.'nt Rules

'" 16. Calculating LRR Consider Iwo streams of cash flows. II ilnd B. 5tn.:am A's first cash

now is S8.900 and is received three ycars from today. Future cash flows in strellm A grow by 4 percen t in perpetui ty, Stream 8's fi rst cash now is - SIO.OOO. is received two yea rs from today. and will con tinue in perpetuity. Assume that the appropriate diScou nt rate is 12 percen t. H. What is the prescnt va lue of each strea m?

b, Suppose that the IwO streams are combincd int o one project. called C. What is the IRR o f project C?

e. What is the correct IRR rule for project C'?

17. Calculating Incrementa l Cash Flows Darin C lay. the CFO of MlIKeM oney.com. has to decide between the fo llowing two projects:

28.

Year Project Million Project Billion

0 - $ 1.200 - SIc '0 + 160 '. + 100

2 '60 1.200 ] 1.200 1.600

The I.:Xpccted rate of return for either of the two projects is 12 percen t. What is the rdllge o f initiil l invcstment (/0) for which ProjCCt Billion is more lillancinl1y all r: lclive than Project Million?

Problems with IRR McKcekin Corp. has a project wi th the following cash flows:

Year Cash flow

o

2

$20.000

- 26.000

13.000

What is the IR R of the project'.' Wh;lt is happen ing here'!

BULLOCK GOLD MINING

Selh Bullock . the owner o f Bullock Gold Mini ng, is evaluat ing a new gold minc in South Dakota. Dan Dority_ the comp;my's geoloyisl. has just fini shed his ana lysis of the mine site. He has esti mated that the mine would be prod uct ive for eieht years. after which the gold would be completely nli ned. Dan has t;tken an estimate of ihe gold deposits to Alma ~arrell. the co~p:my's lil\illlcial officer. Alma has been ilsked by Seth to perform an :ma l),­SIS of the n.e ..... mlllc and preSCll! her rccommCJld iUion on whether the com p.ln)' should open the new mme.

Alma has used the estimates provided by Dan to det~rllline the revenues that co uld be expected from the mine. She has also p rojccted the expense o f opening the mine and the ann~al ~perdti ng expenses. If the company OpellS the mine. it wi ll cost $400 million today. and II Will have a cash out now of $80 million nine years from today in costs associated \\ith closing the mi nc and rt."'CI:liming the area surrounding it, The expected cash nows each ,car from the minc arc shown in the following table. BuJ lock Mining has a 12 percell! required return o n all of its ~o ld mines..

170 Part II Valuation <lml Capit,lI Budg':ling

Year Cas

0 - $400.000.000

I 85.000,000

2 90,000.000

3 140,000,000

4 180,000.000

5 195.000,000 , 130,000,000

7 95.000,000

8 60,000,000

9 -95,000,000

\. Constfllct a spreadsheet to calculate the payback period. intcrnadl ra~c of return. modi­fied internal ralc of return . and net present value of the propose mine.

2. Based on your analysis. should the company open the mine? 3. Bonus question : Most spreadsheets do not have a built-in fonnu.l~~ caleutal,e the pay-

back period. Write a VBA script that calculates the payback pen or a project.

Making Capital Investment Decisions

Is there green in green? General Electric (GE) thinks so. Through its "Ecomagination" pro­

gram, the company plans to double research and development spending on green products.

from $700 million in 2004 to $1.5 bill ion in 2010. With products such as a hybrid railroad

locomotive (described as a 2oo-ton, 6.oo0-horsepower "Prius on rails~), GE's green initiative

seems to be paying off. Revenue from green products was $14 billion in 2007, with a target

of $25 billion in 2010. The company's internal commitment to reduced energy consumption

saved it more than $100 mi!lion from 2004 to 2007, and the company was on target to reduce

its water consumption by 20 percent by 2012, another considerable cost savings.

As you no doubt recognize from your study of the previous chapter. GE's decision

to develop and market green technology represents a capital budgeting decision. In this

chapter, we further investigate such decisions-how they are made and how to look

at them objectively. We have two main tasks. First, recall that in the last chapter, we

saw that cash flow estimates are the critical input into a net present value analysis; but

we didn't say much about where these cash flows come from. We will now examine this

question in some detail. Our second goal is to learn how to critically examine NPV esti­

mates, and. in particular, how to evaluate the sensitivity of NPV estimates to assumptions

made about the uncertain future.

6.1 Incremental Cash Flows: The Key to Capital Budgeting

Cash Flows-Not Accounting Income You may not have thought about it, but there is a big difference between corporate finance courses and financial account ing courses. Techniques in corporate finance generally use cash nows,'whereas financial accounting generally stresses income or earnings numbers. Certainly our text follows this tradition: Our net present value tech­niques discount cash no"ws, not earnings. When considering a single project. we dis­count the cash nows that the fi rm receivcs from the project. When valuing the firm as a whole, wc discount dividends-not earnings-because dividends are the cash flows that an investor receives.

III

172

EXAMPLE 6.1

EXAMPLE 6.2

Part n Valuation lind C.:.p;\l11 Budltlin £.

Rele .... ant Cash Flows The Weber-Dec.ker Co. juSt paid $1 million in cash for a building as part

of a new capital budgeting project.. This entire $1 million is an immediate cash outflow. However,

assuming straight-line depreciation over 20 years. only $SO.OOO (= $1 million/20) is considered an

accounting expense in the current year. Current earnings are thereby reduced by ooly $50.000. The

remaining $950,000 is expensed over the following 19 years. For caph:al budgeting purposes. the relevant cash ovtflow at date 0 is the fun $1 million. not the reduction in earnings of only $50.000.

Always discount cash nows. not earnings. when perforn~ing a capital budg~ling calculation. Earnings do not represent real moncy. You canOl spend ~Ul or eamL,ogs. you can't eat OUI of earnings. and you ca n't pay dividends out of carrungs.. You can do these things only out of cash flow. _ .

In addition, it's nol enough 10 use cash nows. In l.:a\Cu lating the NPV 01 a project­onl" cash flows that are incrementa/ to the project should be used . These cash fl~ws are the'changes in the firm'scash flows Ihal occur as a direct consequence of accepung the project. ThaI is. we arc iOlerested in the dilTercnc~ between the .c<lsh nmV$ of Ihe firm with the project and the cash flows of the firm WIthout the pro)ec.t. .

Tbe use of iocremental cash flows sounds easy enough, but pufalls abound 111 the real world. We describe how to avoid some of the pitfa lls of determining incremental

cash fl ows...

Sunk Costs A sunk cosl is a cost that has already occurred. Because sunk costs are in the paSt, they cannot be changed by the decision to accept or reject the projec.t. Just as we " let bygones be bygones." we should ig.nore such costs. Sunk costs are not mcremenlal cash

outflows.

Sunk Costs The General Milk Company (GMC) is currently evaluating the NPV of esublishing

a line 01 chocolate milk. As part of the evaluation. the company paid a consulting firm $100,000 last

year lor a test marketing analysis. Is this con relevant for the capiul budgeting dec isJ.on now con­

fronting GMC"s management! The answer is no. The $100,000 is flot recoverable. so me $100.000 expenditure is a sunk cost.

or spilled milk. In other words. one muu ask. "What is me difference between the cash flows of

the encire firm with the chocolate mitk project and the cash flows of me entire firm without the

project!"' Since the $100.000 was already spent, acceptance of the project does not affeCt this cash

flow. Therefore. the cash flow should be ignored for capiQ.! budgeting purposes. Of course, the dedsiofl to spend $100,000 (or a marketing aflalysis was a capital budgeting

decision itself and was perfectly relevant before It was sunk. Our point is that once the company

incurred the expense, the cost became irrelevant for any luture decision.

Opportunity Costs . . Your firm may have an asset that it is considering sellin~. leasmg.. o.r emplOying else­where in the business.. If the assel is used in a new proJcct, potentIal revcnucs from alternative uses are lost. These lost revc:nues can meaningfully be viewed as costs.

EXAMPLE 6.3

EXAMPLE 6.4

C":lptt>r 6 Making C:lri1al hWCii HllCnt D .. :cisions 173

They ure called opporlUni~' costs because. by taking Ihe project. the firm rorgoes other opportunities for using the assels.

Opportunity Costs Suppose the Weinstein Trading Company has an empty warehouse in

Philadelphia that can be used [0 store a new line of electronic pinball machines. The company hopes

to sell these machines to affluent northeastern consumers. Should the warehouse be considered a

cost in the decision to sell the machines?

The answer is yes. The company could sell the warehouse if the firm decides not to market the pinball machines. Thus. the sales price of the warehouse i ~ an opportunity cost in the pinball machine

decision.

Side Effects Another difficulty in determining incremental cash nows comes from the side effects of the proposed project all other pans of the firm. A side etTect is classified as either erosion or s)'nergy. Erosion occurs when a new product reduces the sa les and. hence. the cash flows of existing products. Synergy occurs when a new project increases the cash flows of cxist ing projects,

Synergies Suppose the Iflnovative Moton CO'"9oration (IMC) is determining the NPY of a new

convertible sportS car. Some 01 the would-be purch;),sen art ownen of IMe's compaCt sedans.Are

all sales and profits from the new convertible ~ports car incremenul!

The answer is no because some of the cash flow represents transfers from other elements of

IMC's produCt line. This is erosion. which muSt be included in the NPV calculation . Without ak­ing erosion into account. IMe might erroneously calculate the NPV of the sports car to be. say, $100 million. If half the customers are transfers from the sedan and lost sedan sales have an NPV

of - $ISO million. the true NPV is - $50 million ( =$100 million - $150 million) .

IMC is also contemplating the formation of a racing team. The team is forecast to lose money for the foreseeable future, with perhaps the best projection showing an NPY of - $]5 million for

the operation. However, IMC's managers are aware that the team will likely generate great public­

ity for all of IMCs produCts. A consulunt estimates that the increase In cash flows elsewhere in

the firm has a present value of $65 million. Assumin8 that the consultant's estimates of synergy are truStwOrthy. the net present,'value of the team is $30 million ( : $6S million - $]5 million). The

mafl~en should form the team.

Allocated Costs Frequently a parlicular e:<pendilure benefits a number of projeels. Acco unta nt s a llo­cate this cost across (he dinerem projects when determining income. However. fo r capital budgeting purposes. this allocated cost should be viewed as a cash outflow or a project only if il is an incremental COSt of the project.

'"

EXAMPLE 6.5

6.2

P.r1 U Valuation and Capital Budgeting

Alloc.ated Costs The Voetmarm Consulting Corp. devotes OO~ wing of iu suite of offices to a library requiring a cash outflow of $100.000 a year in upkeep. A proposed capital budgeting project is expected ( 0 generate revenue ~ual to 5 percent 01 the overall firm's ules. An e)(ecutive at the

firm. David Pedersen, argues that $5,000 (",,5 per-cent X $\00.000) should ~ viewed as the pro·

posed projen's share of the li brary's cosu. Is this appropriate for apical budgeting!

The answer is flO. One must ask w!\at the difference is between me ash flows of the entire firm with the proj&t and the tuh flows of the entire firm without the projKL The finn will spend

$100.000 on library upk~p whether or not the proposed project is accepted. Beouse accepu.nce of the proposed project dOe1o not affect this ash now, the c;un t\ow should be ignored when altu­bting the NPV of the project.

The Baldwin Company: An Example We next consider the e:a:.ample of a proposed investment in machinery and related items. OUf example involves the Baldwin Company and colored bowli ng baUs.

The Baldwin Company, originally established in 1965 to make footballs, is now a Jeading producer of tennis balls,. b.'\scballs. footballs. and golf balls. In 1973 the com­pany introduced " High Flile," its first line of high-performance golf balls. Baldwin management has sought opportunities in whatever businesses seem to h .. vc: some potential for cash now. Recently W. C. Meadows., vice president of the Baldwin Com­pany, identified anotber segment of the sports baJl market that looked promising and that be felt was not adequately served by larger manufacturers. That market was for brightly colored bowling balls, and he believed maay bowlers valued appcamnce and style above performa nce, He also believed that it would be diflicult for competitors to take advantage of the opportunity ~use of bOlh Baldwin's cost advantages and its highly de\'eloped market ing sk ills.

As a result . the Baldwin Company iovesligated the marketing potential of brightly colored bowling balls. Baldwin sent :t questionnaire to consumers in Ihree markets; Philadelphia, Los Angeles, and New Haven, The results of the three questionnaires were mueh better than expected and supported Ihe conclusion that the brightly col­ored bowling balls could achieve a 1010 15 percent share of the market . Of course, some people at Baldwin complained about the cost of the tcSt marketi ng. which was $250,000. (As we sha ll sec later. this is a sun k cost and should not be included in proj­ect eVl:lluatio n.)

In any case. the Baldwin Company is now considering investing in a machine to produce bowling baJIs. The bowling balls would be manufactured in a building owned by the firm and located near Los Angeles. This building, which is vacant, and the land can be sold for $150.000 aner ta xes.

Working with his staff. Meadows is preparing an analysis of the proposed new prod­ucl. He summarizes his assumptions as fo llows; The cost of the bowling ball machine is SIOO,ooo. The machine has an estimated market value at the end of five yea rs o f $)0,000. Production by year during the five-year life of the Dluchine is expected to be as follows; 5,000 units. 8,000 units. 12.000 uni ts, 10,000 units, and 6,000 units. The price of bowling balls in the first year will be $20. The bowling ball ma rket is highly competi tive. so Meadows believes that the price of bowling balls will increase at only 2 percent per year. as compared to the anticipnted general ionalion nne of 5 percent.

Cnaplff 6 Making Capi tal ln~!1n~nt t::Jecisions

'" ~on"erse ry. the pla.slic used i~ produce bowling ba lls is rapidly becoming more expen­sIve. ~aus.e of thIs, pr?ductlon c~sh out nows arc. expected to grow at 10 percent per yea r. Flrs~ ~~ear prod~lctlon costs Will be $1 0 per umt. Mendows has determined. based on Ba ld;.vrn s taxable Income. that the appropriate incremental corporate lax ra te in the bowling ba ll project is 34 percent.

. ~~I . wor~g capitaJ is defined as the difference between current assets and current !,abrIHies. L~ke any ~ther ~anufacturing firm, Baldwin finds that it must maintain an mvest',ll~nt I~ worlong Cl:Iplta l. II wi ll purchase raw material s before produclio n and sale. glvrng nse to ~n inveslmen.t in inv~ntory. It .will maimain cash as a buffer agains t unforeseen expenditures. And. liS credu sales w,1I Dot generate cash until payment is made at ~ later ~ate. Management determines that an initial investmenl (a t yea r 0) in net wQrkrng caPita! of $10.000 is required. Subsequently. net working capita l at Ihe end of ~ch year wlll .be equ~1 to 1.0 perc~ot of sales for that yea r. In the final year o f the project , nel work 109 capllal Will decline LO lero as the projcct is wound down, Jo o ther words. the investmen t in workiogcapita l is to be completely recovered by the end o f the project's life.

Projections bct sed 0 11 these assumptions and Meadows'saoalysisappear in Tables 6. 1 through 6.4. In these tables all ~sh nows a re assumed to occur al the elld o f the yea r. Because of the la rge amount of rnforma lio n in these tables. it is important to see how the lables arc related . Table 6. 1 shows the bas ic data for both in\'esimcill and income. Supplemen tary schedu les on operations nnd depreciation, as presented in Tables 6.2

Table 6.1 The Worksheet fOr Cash Flows of the. Baldwin Company ($ in thousands) (All cull nOWS occur ill the end ot the year.)

tnvestments:

(I) Bowling ball machine

(2) Accumulated depredation

(3) Adjusted basis of machine after depreciation (end of year)

(i) OpportUnity COst (warehouse)

(5) Net working capital (end of year)

(6) Change in net working capital

(7) Total Ci1sh now of investmem [(I) + (') + (6»

Income:

(8) Sales revenues

(9) Operatlng cosu

(10) Depreciation

(II) Income before taxes [(8) + (9) + (10))

(12) Tax at 3 ... percent

(13) Net income

Year 0 Year I Year 2 Year J Year 4 Year 5

- $100.00 $21.77*

$ 20.00 $ 52.00 $ 71.20 $ 82.70 91.20 80.00 " .00 28.80 17.30 5.80

- 150.00 150.00

10.00 10.00 16.32 21.97 21.22 -10.00 - 6.32 - 8,65 3.75 21.22

- 260.00 - 6.32 - 8,65 3.75 193.00

• $100.00 $163.20 $219.70 $212.2'" $129.89 - 50.00 - 88.00 - 1"'5.20 - 1)3.10 - 87.85 - 20.00 - )200 - 19.20 - I 1.50 - 11.50

JO.OO 13.20 85.30 67.6-i Jo:s5 - 10.20 - 1 .... 69 - 29.00 - 23.00 - 10.19

19.80 28.51 56.30 44.64 20.16

'76

Table 6.2 OperatIng Revenues and Costs of the Baldwin Company

Table 6.3 Depreciation (in percent) under Modified Accelerated

Cost Recovery System (MACRS)

ParI I[ Valuation and Capi tal Bud~ting

w w ~ w w (1). Sales Cost Operating

Quantity Year Sold Price Revenues per Unit Costs

, 5.000 $20.00

2 •. 000 20.10

J 12,000 20.81

• 10,000 21.22

5 6.000 21.65

.~d coot>

1 .333 .200 .143

2 .+4, .320 .245

J .148 . 192 . 175

• .074 .115 . 125

5 .115 .089

6 .058 .08' 7 .089

• .0<5 , 10

" 12-15

16

17-20

21

$100,000

163.200

249.696

2 12,242

129,892

.100

.18(l

. 1+4

.115

.092

.074

.066

.066

.066

.066

.033

$10.00

11.00

12.10

13.31

14.64

.050

.095

.0&

.077

.069

.062

.059

.05'1

.05'1

.059

.059

.059

.030

$ 50.000

".000 145,200

133.100

87,846

.072

.067

.062

.057

.053

.0<'

.0<5

.0<5

.0<5

.0<5

.0<5

.0<5

.045

.022

and 6.3, help explain where the numbers in Table 6.1 come from . Our goa l is to obtain project ions of cash now. The data in Table 6.1 are all that arc needed to calculate the relevant cash flows, as shown in Table 6.4.

An Analysis of the Project For most projects. cash nows follow a common pattern . First. firms inves~ at the becinning of the project , generating cash out fl ows. Seco~d, product sales provIde cash inflows over the life of the projecl. Third, plant and eq~lpmellt are ~o!d ofT at Ihe en~ of the project , generating more cash inflow. We now dISCUSS Baldwlll s casb nows fo

each of these three steps.

Chapter 6 Making C;lpi t:. l lnves!",,,", Decisions 177

Table 6.4 Incremental Cash Flows for the Baldwin Company ($In thouaands)

Year 0 Year I Year 2 Year 3 Year 4 Year S

(I) Sales revenue [line 8, Table 6.1)

(2) Operating costs (line 9,Table 6. 1}

(3) Taxes [line 12.Table 6.1]

$100.00

- 50.00

- 10.20

$163.20

-88.00

- 14.69

$249.70 $212.24 $129.89

- 1~5.20 - 133.10 - 87.85

- 29.00 - 23.00 - 10.3'1

(4) Cash flow from operations [( t) + (2) + (3)]

(5) Toul cash flow of investment [line 7, - $260.00

39.80 60.51

- 6.32

75.50 56.14 31.66

- 8.65 J.75 193.00 Table 6.1]

(6) Toul cash flow of project (4) + (5» - 260.00 39.80 54.19 66.85 59.89 224.66

NPY @ ~% $123.M

'0% 15%

15.68%

20%

$ 51.5'1

$ 5 .... 7

$ 0.00

($ J !.l5)

Investments The investment ou tlays for the project" are summarized in the top segment of Table 6.1. They consist of three pans:

I. The bowling b(/II lIIad,ill£': The purchase requires an immediate (year 0) cash ournow of $100.000. The firm rea lizes a cash inflow when the machine is sold in year 5. These cash 110ws arc shown in line I of Table 6.1. As indicated in the foo\· note to the table. taxes are i.ncurred when the asset is sold.

2. The QPpoTllmi,y cost oj not selling the warehouse: If Baldwin accepts the bowling ball project, il will use a warehouse and land that could otherwise be sold . The estimated sales price of the warehouse and land is therefore included as an oppor­II/f/i,y cost in year O. as presented in line 4. Opponunity costs are treated as cash outflows for purposes of capital budgeting. However, note tbat if the project is accepted, management assumes that the warehouse will be so ld for $150.000 (after taxes) in year 5.

The test marketing cost of $250.000 is not included. The tests occurred in tbe past and should be viewed <IS a slIlIk COSI .

3. The illl'I!Sf1/1el1l illll'orkillg copital: Req uired working capit al appears in line 5. Working capital rises over the early years of the project as ex pansion occurs. However, all working capital is assumed to be recovered at the end, a common assu mption in capita l.budgeting. In other words, all invento ry is sold by the end , the cash ba lll nc~maintained as a buffer is liquidated, aDd a ll accounts receivable arc co llec ted. Increases in working capital in th e early years must be runded by cash generated elsewhere in the firm . Hence. these increases are viewed as cash OW(lOifS. To reiterate. it is the illl"rellSI! in work ing capital over a yea r that leads to a cash outnow in that yea r. Even if working capi ta l is al a hjgh level. there will be flO cash out now over a year jf working capita l stays constaot over th at year. Converse ly, decreases in working capital in the later years are viewed as cash in flows. All of these cash nows are presented in li ne 6 of Table 6.1. A more complete discussion of working capital is provided later in this sect ioD.

17& Pa.r1 II Valuat ion and Capilal Rudgel!"' !!

To recap, thc~ are three investments in this e'(ample: the, bowling ball machine (line 1 in Table 6. 1), the opportunity cost of the warehouse (I me 4). and the,changes in workin g capi tal (line 6). The total cash flow from these three investments IS shown in line 7,

Income and Taxes Next the determination of income is presented in th,e haltom segment of Table 6. 1. While we are ultimately interested in cash flow- not Income­we need the income calculation to determine taxes. Lines 8 and 9 of Table 6.1 show sales revenues aud operating costs, respectively. The project ions in these lines are based on the sales revenues and operating costs computed in columns 4 and 6 of Table 6.2. The estimates of revenues a nd costs fo llow from assumptions made by the corporate planning staff al Baldwin. In other words.. the estimates critically depend on th~ raC! that product prices are projected to increase at 2 percent per year and costs per UOII a re projected to increase at 10 percent per year. . .

Depretiation or the SI00,OOO capita l investment is shown In ILOe 10 or Table 6:l. Where do these numbers come rrom? Depreciation for tax purposes ror u.s. compam<:, is based on tbe Modified Accelerated Cost Retovery System (MACRS). Each asset IS assigned a useful life under MAC RS, with an accompanying depr~iatio~ sc~edule as shown in Table 6.3. The IRS ruled that Baldwin is to depreciate ItS capJtalmvest­ment over fi ve years, so the second column or the table applies i? this case. ~use depreciation in the table is expressed as a percentage or t~e .asst.! s cost, multIply the percentages in this colwtln by $100.000 to arrive at depreciation In dollars.. . .

Income berore taxes is calculated in Ii.ne II o r Table 6. 1. Taxes are prOVided In line 12 of this table. and net income i$ calculated in line 13.

Salvage Value When selling an asset, one must pay taxes o n tbe di.tTerenc~ between the asset's sa les price a nd its book value. Therefore. taxes must be estImated If the sa.le of an asset is part or a capilal budgeting project. For example, suppo~ that Ba.ldw~n desires to sell lhe bowling ball machine a t the end or year 5, rorecastmg that It will receive a sales price of $30,000 a t thai lime.

At the end of the fifth year, the book value of the machine would be S5,800. as shown in line 3 of Table 6.1 . If the company sold the machine ro r $30,000. it wo~ld pay taxes on the difference between this sales price and the book value o f $5,800. Wllh a 34 percent tax rate, the tax liab ility would be .34 x (S30,OOO - S5,800) = 58,228. The aftertax salvage va lue of the equipment , a cash innow to the company, wou ld be $30000 - S8 228 = $2 1 772, as indicated in line I of Table 6. 1.

Alternativ;ly, ir the ~ok value exceeds the market value. Ihe difference is treated as a loss for tax purposes. For eltample, ir Baldwin sold the machine for S4.000, the book value eltceeds the market value by S I.800. In this cnse, taxes or .34 x £,1,800 = S612 are saved.

Cash Flow Cash now is finally determined in Table 6.4. We begin by reproduc­ing lines 8, 9, and 12 in Table 6. 1 as lines I. 2, and 3 in Tabl: 6.4. <:=ash .no~' rrom operation~ which is sales minus bot h operating costs and taxes, IS proVIded III IUle.4 of Table 6.4 . Total investment cash flow, taken from line 7 of Table 6.1. appears as hne 5 o f Table 6.4. Cash flow from operations plus (olal cash flow or the investmen t eq ua ls total cash flow of the project , which is displayed as line 6 of Table 6.4.

Net Present Value The NPV of the Baldwin bowling ball p~oject can be ca\Culate~ from the cash flows in Jine 6. As ca n be seen at the bottom of Table 6.4. the NPY IS

Chapter 6 Making Capil li t hl '"c~'meni Decisions 179

551.590 ir 10 percent is the appropriate discoUlI1 rate and - $31,350 ir 20 percent is the appropriate discount rate. If the discount rate is 15.68 percent. the project will have a zero N PY.1n other words. the projcct's internal rate or re turn is 15.68 percent . If the diseount rate o r the Baldwin bowling ball project is above 15.68 percent. it sho uld not be accepwd because its NPV would be neg.ll ive.

Which Set of Books? Corporations musl provide a computation of pro lit o r loss to bo th thei r own stock­holders and lax lluthorities. While you might th ink that the numbers going to both parties wou ld be the sam e. Ihis is not the case. In actual fact . U.S. firms keep two sets o r books. one ror the I RS (ca lled tax books) and another for their annual reports (ca lled stockholders' books), with the numbers differing across the two sets.

How can this be the case? The two sets of books differ because their rules were developed by two separate bodies. The tax books fo llow the fules of the IRS and the stockholders' books follow the rules of the Financial Accollllling Stalldards BOllrd (FAS O), the governi ng body in accounting. For eltllmplc. int erest o n municipa l bonds is ignored for ta>.: purposes while the FASB treats the interest as income. As an ot her example, companies typically usc accelerated depreciation rOf their taxes and straight­line depreciation ror their stockholders' books.

The differences almost always benefit the firm : the rules permit income on the stock­holders' books to be higher Ihan income on the tax books. ThUs. management can look profi table to its stockholders wilhout having Io-pay taxes 0 0 all of that reported profil. In ract, plenty of large companies consistently report posi tive earnillgs to their stock­holders while reporting losses to the IRS. A cynical interpretation is that members of Congress., who collectively make tax policy, develop ravorable rules to help their con. stituents.. WhetJler or not this interpretation is true, one thing is clear: Companies are ronowing the law, not breaki ng the law. by creating two sets o r books.

Which set of books is relevant for the present chapter? The numbers in the tax books are the relevant o nes.. since you ca n on ly calcu late cash flows aner subtracting o ut taxes. While the stockholders' books are relevant for accounting and financial a nalysis. they are not used ror capital bUdget ing.

F inally, while U.S. firms are allowed two sets or books. this is not the case in a ll, o r perhaps even a majority, of other CoullIries. Knowledge of local rules is needed befo re estimating internatio nal cash n ows..

A Note about Net Working Capital The investment in oet working capita l is an important part or any capita l budgeting analysis. While we considered net working capital in lines 5 a nd 6 of Table 6. 1, st u­dents may be wondering wllefc the numbers in these lines came rrom . An investment in net working capital arises whenever ( I ) inventory is purchased, (2) cash is kept in the project as a buffer against unexpected eltpenditu res. and (3) sa les arc made on credit. generat ing acco unts receivable ratber than cash. (The investment in nel working capi . ta l is reduced by credit purchases, which generate accou01S payable.) This investl1lent in net working capital represents a cash outflow because cash generated elsewhere in the firm is tied up in Ihe project.

To see how the investment iUne! working capital is built rrom its componenl parts. we focus on year I. We see in Table 6.1 that Baldwin's managers predict sales in year I to be S IOO,OOOand operating costs to beS50,OOO. If both the sales and costs were cash tran sac­(ions, the firm would receive $50.000 (=$100.000 - S50.000). As staled earlier. this cash flow wou ld occur a t the eml of )'C<lr I.

18<1 Part LI \llIlu:UIOO and upita! Budgt:ting

Now lei 's give you more information. The managers:

F ecast that $9 000 of the sa les will be on credit. implying that cash receipts at. I. tho: end of year i will be only $91.000 ( = $ 100.000 - $9,000). The accouots reeCt\!·

able of $9,000 will be collected 31 the end of year 2. . I '

2. Believe tbat Ihey cao defer payment o n $3,000 ,of tbe S50.000 of C~IS. ~~~g that cash disbursements at the end of ye<lf 1 wIll be only $47.000 ( - 55 , ') $)'.000). Baldwin will payoff the $3.000 of accounts payable at the end of year _.

3. Decide that inventory of S2,500 should ,be len o n hand at the eod of year I to avoid srQckOlw (that is, running out of loventory).

4. Decide that cash of S I,500 should be eannark.ed for the project 31 the end o f year 1 to avoid running out of cash.

Thus. net working capi tal at the end of year 1 is:

52 500 ~ S 1.500 59,000 53,000 + , ' Accounts Accounts rnventory Cash receivable paYdble

$10,000 Net working

capital

of cash enerated elsewhe re in the firm must be used to o llset this BecR.use $10,000 ' k' g ca ital. Baldwin's m:magers correctly view the invest~ent ~eq ulremen~ fo~e~t:lo;s ~n!.shPoutnow of the project. As the project grows over tIme,

~n:~~ ~~~r~~gwo~ki~g ~~PI ;ntal i,ncre~~i;:::~~~;' li~e :~t~\~~:!;:r:~;~~~~~~l~ rire::~et\~ year represent furthe r C.ts \ O\"s. as ID . . . I k' Ig

Ii e 6 of Table 6. 1. However, in the dechnmg years of the proJcct. ne wor II .

yea~ ~~ nd ced- ultimately to zero. That is. accounts receivable are finally coll~t~. capIta ~:C7s ~sh buller is relUrned to Ihe rest of the corporation, and a ll ~.mallllllg ~he proJ. Id ofT This frees up cash in the later yea rs, as indicated by posit ive num-mventory IS so . hers in yea rs 4 and 5 on line 6. . . I

. rate worksheets (such as Table 6. 1) treat net work..ing capita as a Wh!rt~~I?;'n~~:~ual components of working capi tal (re<:eivhab les..dinve~to~~ ~en~et~~ 1",-) d'O nOI generally appear in the worksheets.. However. t e rea er s ou f h' , IN:; . k h not pulled out 0 t In air. ~:t~~~.\~~~ ~~~~~Of~oc~P~t~e~i~~~:: ;;;::s~~~ t~ee:~~l::nents.ju s t as we ilJustrated ror year 1.

A Note about Depreciation , , ' The Baldwin case made some assumptions about depreciation. Where dId th~

assum;tions come from? Assets are current ly deprcdated .for ta~1 pu rpo7~:::~~I~ to the provisions of the 1986 Tax Reform Act. Tbere are sevcn c asses 0

property: .

The three-year class includes certain specialized short-Iiv~ pro~rt~. T~ac to;h~nils and racehorses over two years old art among the very few items mlllg IOtO tS class. .

The five-year class includes (a) cars a~d Hucks: (b) co~pu.tersda~~ ~r~fA~~~~ms equipment, as well as calcu lators. copiers, and typewnters. an c pe used for researcb. . The seven year class includes office furniture, equipment, book s.. and smgJe­

urpose a~riCUltural structures.. It is also a catchaU category beca use aoy asset not ~es ignated to be in another class is included bere.

Gaptl'!' 6 M~ldng Capit"'tn~·r.ilme"l Decisions

The IO-yea r class includes vessels. barges. lUgs. a nd similar equipmenl related to water transportation.

1,81

The 15-year class encompasses a variety of spedali.zcd items. Included are equip­ment' of telephone distribution plants and sim ilar equ ipment used for voice and data communications, an d sewage Ire-alment plants.

The 20-year class includes farm buildings, sewer pipe, and other very long-li ved eq uipment.

Rea l property that is depreciable is sepa rilted into two classes: residentia l and nonresideotiaJ. The COSt of residential property is recovered over 27 Y2 years and nonresidentia l property over 39 years.

Items in the three-, fh:e- , and seveo-year classes are depreciated using the 200 per_ cent declining-balance method. with a SWilch to stf'oJight-line depreciation at a poin t specified in the Tax Reform Act. Items in the 15- and 2()..yea r classes nrc depreciated using Ihe 150 percent declining-bala nce method. wi tb a switch to straight-line depre­ciation al a specified poin!. All real estate is depreciated on a sir-dighl-line basis.

All calcu lations of depreciation indude a half-yea r convent ion. which treats a1l property as jf it were placed in service at midyea r. To be consistent. the IRS a llows half a year of depreciation for the year in which property is disposed of o r retired . The effect of Ihis is 10 spread the deductions for property over one year more tha n the name of its class- for exam ple. six lax years for five-year propen)'.

Interest Expense It may have bothered you thnt interest expense was ignored in the Baldwin example. After all. many projects are at leasl part ially financed with debt. particularly a bowl­ing ball machine that is likely 10 increase the debt capacity of the firm. As it lurns OU I, o ur approach of assuming no debt financing is rather standard in Ihe rea l world. Firms typically calculate a project's eash flows under the assumption that the project is financed only with equity. Any adj ustments for debt financing are renected in Ihe discount rate, not the cash flows. The treatment of debt in capital budgeting wi ll be covered in depth later in Ihe Ie .. ..:!. Suffice il to say at this time (hal the full ramifications o f debl fina ncing are well beyond our curren l discussion.

6,3 Inflation and Capital Budgeting Innation is a n important faci of economic life. a nd it must be considered in capi­lal budgeting. We begin obr exa mination of innation by considering the relationsh ip between iolerest rates anc1 innation.

Interest Rates and Inflation Suppose a bank offers a one-yea r iJJteresl rate of 10 percem. This means thai an indi­vidual who deposits S 1.000 will receive SI.IOO (= SI.OOO X J .10) in one yea r. Although 10 percent may seem like a handsome return. ooe can PUt it in perspective only after examining Ihe rale of in nal ion.

Imagine that the rale of innalion is 6 percem over the yea r and il affects all goods equa lly. For example. a re~i1aurant that charges $1.00 for a hamburger today will cbarge $ 1.06 for the same hamburger OIl Ihe end of the year. You ca n usc you r SI.OOO to buy

"" Figure 6.1 (;aleut8Uon of Real

Rate of Inlerest

Pan n Va iulill ion ;md O lpi llil Budge tin,

Today (Dale 0)

Irwiil'idWII in\'eslS - - - - - 10% - - - -_ S 1.000 in bank.

~ Intcrest r.lle (1k'C3Use ha01bu~ers sell ---.....

fur S I al d:uc O. $1.000 3.8%~ would ha,'c purchased --.........

1.000 h:lIl1burgers.)

[)o.le 1

Indi" idual n::ceive,.; Sl.IOO frum bani.: .

I Inflation mte ha.-< + been 6% nYC'! )'car.

Because each hamburger sells for S 1.06 :11 dale I. 1.038 (,. 51 .100IS1 J )6)

hamburgers can be pun:l\ased.

H nlburgers arc used as 111'1 ilIuwali W' ,ood. 1.0)8 hamburgm clll be ptlKh:lSCd on dale I ~nSU~ad of 1.000 hamburgers :1I daleO. Real intt rcsl rate _ I,OW I,OOO - I = 3.8~.

1000 hamburgc(s today (date 0). Ahernalively, if you put your m~ne~ in the bank, y~u can buy 1.038 (= £1, 100/ SI .06) hamburgers al dale I. Thus. lending mcreases your hamburger consumption by only 3,8 percent. . ' , •

Because the prices of all goods r ise al Ihis 6 percent rate. lendmg lets you mcrea!)c our consumption of any single good or any combination of go~s by 3.8 percenl. ~h s. 3 8 percent is what you are really earning through your saVings accoLLn~, ancr ad ·~sti~ for innation . Econo mists refer to the 3.8 percent number as the ret!' mlNeSI

J g . r to the 10 percent rate as the lIominal ilI/eT(WI rale or simply the r(ll(' . Economists rel cr . . inl f!resl rate . This diSClission is illustrated In Flgu.re 6 .. 1. . . _

W h e used an example with a specific nonunalmterest rate and a specific mn~ tio n ;ate~Vl n general, the formula between real and nominal interest rates can be Writ­tcn as follows:

I + Nominal interest rate =- (I + Real interest rate) x (I + Innat ion rate)

Rearranging te rm s. we have:

I + No minal interest rate Real interest rate = I + Innation rate (6.1)

The fonnula indicates that the real interest rate in our example is 3.8 percenl (= I ICV

1.06-1). . Thr.n . · fi lais an Equation 6. ' determines the real interest fa le precisely. e 0 oWing orm u

approximation:

Real interest rate '= Nominal imerest rate - Cnnatio n rate (6.2)

The symbol ;;. indicates that the equat.ion is. approximately true. This latter formula calculates the real ratc in our example hke thiS:

4% = 1(1'/0 - 6%

The student sho uld be awa re that. allhoug.h Equation 6.2 may s~em ~or~ intuitive than Equation 6.1, 6.2 is o nl y ao approximation. This approXlmatloo IS re~son­ably accura te for low rates of interest and inflation. In our e~amplc the differ;

b tween the approxi mate calculat ion and the exact one IS onl y .2 percen ~~': pe~ent - 3.8 percent). Unrorlunatel y, the approximation becomes poo r when rates are higher.

EXAMPLE 6.6

EXAMPLE 6.7

D.pltr 6 MlI. king C:lpi lallnve!llJlCnl Decisions J8J

Real and ~ominal Rates The little-known monan::!-ty of Gerberovi.t recently had <l nomln<ll interest r-ate of 300 percent <lnd an inflation rate of 280 percent. According to Equation 6.2, the real interest r.ne is:

300% - 280% '" 20% (Approldmate formula)

How(!Ver. according to Equation 6.1. this rate is:

I + 3()()% I + 280% - I >0; 5.26% (Exaa: formula)

How do we know that the s«ond formula is indud the exact onel Lets think in terms of hMn­burgers again. Had you depos ited $1,000 in a Gerberovian bank a year <lga, the account WOIJld be

worth $4.000 [= $1 ,000 x (I + 300s)] today. However, while a hamburger COSt $ t iI yellr ago, it

COstS $3 .80 (= I + 280%) tooit)'. Therefore. you would now be ilble to buy 1.052.6 (=$i,OOOjJ.80) hilmburgers. implying a real interest rue of 5.26 percent.

Cash Flow and Inflation The prev10us analysis defines two Iypes o f interest rates. nominal rates and rea l rates, and relales them thro ugh Equation 6.1. Capital budgeting requires data on cash nows as well as on interest rates. Like interest rates, cash nows can be expressed in either nominal or real terms.

A nominal cash now refers to Ihe actual do llars to be received (or paid out). A rea l cash now rerers to the cash now's purchasing power. These definitions are best explained by examples.

Nominal versus Real Cash Flow Burrows Publishing ~ lun purchased the rights to the next

book of filmed romantic novelin Barbilra Musk.. Still unwritten. the book should be available to the public In four years. Currently, romantic novels sell for $10.00 in softcovet". The publishers believe that inflation will be 6 percent a year over the next four )'eilrs. Because romantic novels are so popu­~r. the publishers anticipate that their prkes will rise About 2 percent per yur more thlln the infl<l­don fate over the next four years. Bur~ Publishing pl.tns to sell the novel ilt $13.60 I'" (1 .08)' x $1 O.OOJ four ye.11"S from now, anticipating sales of 100,000 copies..

The expected ash flow in the fourth year of $1 .36 million (=$11.60 X 100,000) is <l lIOtrIino/ cosh ffow. That is, the firm expecu tb receive $1.]6 million at that time. In other words, a nominal cash Row refers to the acrual dolbp to be received in the future .

The purchasing power of $ 1.36 million in four yurs is:

. . $1 .]6 million $1 .08 mIllion = (1.06)'

The figtJr"e of $ 1.08 million is a reol cash (/fNIf beause it is expressed in terms of purchasil"lg power. Extending our hamburger eXllrnple. the $1.36 million to be reuived in four years will only buy 1.08 million h<lmburgen; becllU$e the price of a hamburger will rise from $1 to $1.26 (= $1 x ( 1.06)",] over the period.

,,,

EXAMPLE 6.8

EXAMPLE 6.9

Part II Valufllio n ~nd C!tpi!al Budgc:1inll

Depreciation E08l1 Publisners, a competitor of Bu~. recently bought a printing press for $2.000,000 to be depre<:iilted by the Slr'aight-line method over five ye<lrs. This implies yearly de~.

ciation o f $400.000 (= 52,000.000/5). Is th is $0400.000 figure a real or a nomin,) j quanti ty?

Depredation is a nominol quantity because $400.000 is the Jew .. 1 tax de duction over eac.h 01 the

next five years. Depredation becomes it real quantity if it is <ldjuSted for purchuing power. Hence. $3 J 6.837 (=$400,000/ ( 1.06),] is depreciuion in the fourth year, expressed as a real qUilntity.

Discounting: Nominal or Real? Our previous discussio n showed that intcresl rales ca n be expressed in either nominal or rca\lerms. Simila rly, cash nows can be e . .;presscd in eit her nominal or rea l terms. Giveo these choices. how shou ld one express interest fales and cash nows wben per­forming capital budgeting?

Financial pract it ioners correctly stress the need 10 maintain cOfuil f('ncy between cash Ilows and discount rates. That is:

Nom inal cash nows must be discounted at the /lomillol nue.

Reol cash nows must be discounted at the real rate.

As long as one is consisten t. ei ther approach is correct. To minimize computational error. il is genera lly advisable in practice to choose lhe approach that is casiesl. This idea is il1ustraled in the following tWO examples.

Real and Nominal Discounting a particular proj~ct:

Shields Electric forecasts the (ollowing nominal cuh flo~ 00

o - $1.000

I

$600

2

$650

The nomirt31 discount nne is 1<4 pet"<:ent. and the innuion rate is foreoSl to be 5 percent. What is

the Y1I lue of the projec t!

Using N ominal Quantities The NPV tan be ulculued u:

$600 $650 $26.47 = - $1 ,000 + Ti4 + ( 1.14)1

The project should be accepted.

Using Real Quantities The real cash flows are these:

o - $1.000 $571.43

- (~':)

2

$589.57

( 56SO ) = (1.05)1

According to Equation 6.1. me real discount rue is 9571-4] percent ( == 1. 1-4/ 1.05 - I).

The NPV can be cakulued u: $571.·0

$26.47 '" - $1.000 + 1.085714] +

EXAMPLE 6.10

Q\Hp.tr 6 Making C:lpu,11 I n\'t'Stm~n ' Decisions IS' ~~e NPV is the same whether cash nows are expressed in nominal o r in real quan­tilles. It must a/ways be the case lhat the NPV is the sa me under the two diflerent approaches.

Beca use both app~ac1.\es always yield the sa me result , which one should be used? Use the a~proach that IS Simpler beca use the simpler approach genera lly leads to re ..... er com~ut allonal .c~rors. The ShicJds Electric example begins wi lh nomina l cash nowS. so nommal quantlt lcs prod uce a si mpler calculat ion here.

Real and Nominal NPV A1tsh I I ed u er. nco generac the following foreust for II capiol budgeting project:

Year 0 Year I Year 2

Capinl expenditure $1 ,210

Revenues (in real terms) $ 1,900 $2,000

Cash ~Xpen5es (in re<lll tenns) '150 1000

Depreciation (strajght.Ii~) 60S 605

The p~e.sident. D<II~id Altshuler,estimates innation to be 10 percent per year over the next tWO years. In <IIdd lnon, he believes that th~ c<lSh flows at the projKt should be diSCOunted at th~ nominal rate or 15.5 percent, His firm's ax rate is 40 percent.

Mr. Altshuler rorecasu all ca:!h flows in nominol lef'ms. leading to the following table:

Year 0 Year I Year 2

Capial expenditure - $1.210 Reyenues $2.090 ( ,= 1.900 X 1.10) $2,420 [= 2.000 X ( 1. 10)1)

- Expenses - I,()4S (= '150 X 1.10) - 1210 (=1,000 X (1.10)1) - Depreciation - 60S ( <= 1210/ 2) - 605

Taxable income ... 0 60S - Taxes ! 4~~ -176 - 242

Income after taxes 264 363 + Deereciuion , 605 60S

Cash flow 86' , .. $869 $968

NpV = - $1.210 + 1.155 + ( LI SSY:: $268

(continued)

lB' Pari II V~ l tJal ioo .. no Capilal Budg~ling

. f workin in rea! terms. He fi~t alculates the rea l Mr, Aluhulers sidekick 5wut Weiss. p~ eN h g tes the foUowin& table to rt:oI quantities: rate lObeS percent(::I.ISSj l .IO - 1).Next. egenera

v 0 Year I Year 1 ,ear

Capital expenditure

Revenues - Expenses - DepreciatiOtl

Taxable income

Tues (40%)

Income after taXes

+ Depreciation

Cuhfl~

-$1.210

$1.900

- 950 - 5S0 (- 605/ 1.10) ..,. - 160

2<0 SSO 790

$2,000 - 1000

- SOIl [- 605/( I.IO)~

SOIl

- 200 300 SOIl

800

. $790 S8OO:: $268 NPV = -$1 ,210..,. 1.05 + ( 1.05)1

In expbining his calculations to Mr. Altshuler, Mr. WeIss points out these b cu:

) . n miNiI value and Its real value are L The capital expendilu.-e occurs at dlt.e 0 (coday . s.o Its 0

eqw.1 _ I . by 2. Beca~se ~rly depreciation of $605 is a nominal quantity. one converts It co a rea quantItY

discounting at the inflation nte of 10 percent.

. . th SOIme NPV I"lIJmber. Both It is no coincidence that both Mr. Altshuler and Mr. We,n unye 3t e

methods must always generate the ~me NPV.

6.4 Alternative Definitions of Operating Cash Flow .

in the exa mples of this chapter. proper calculation of.cash now~ IS As ca? be seeo. . ber of different definitions of project operatmg essential 10 cap~tal budget mg. A nu~. fr uenlly bedeviling corporate fina nce stu­cash nows are III common usa~e,,~ ta~~~ ~elinitions are eonsistelll with each other. dent - Howeve r the good news IS a 0;; • bl We

Thatis, if used ~orrect ly. they will all dle~d ~~ the s~~:~~~~~~r ;.~:~~ r::1 t~~~ are now consider some of thc common e,m1l1ons, s

identi~1 ~~Ih e~~h o~~:;. lfOIlOWS. keep in mind thaI when we spc~\k of cash now. w: In tIe ISCUSSlon Th ' . all we a re concerned wilh . In thJS

liler.ally mean d.ollalrs inb l~ss. d~lIa~:tfo~ 'abo~~ ~~ I es, cOSts, depreciation. and taxes to secl1on, we mall1pu a te aS1C iOJ orn calculate cash now.

, For simpl ic;i t)'. working capital is igooT"W in [his discussion.

Ctt.pttt 6 Mllking Capita lln~tmenl D«i~ons 18'

For a pa rticula r project and year under consideratio n, suppose we have the fOllow­ing estimates:

Sa les = 1 1,500 Casn costs! = $700

Depreciation = $600

With these esti mates., earnings before taxes (EBT) is:

EBT = Sa les - Cash costs - Depreciation - SI.l00 - 700 - 600 = $200

[6.3)

As is customary in capita l budgeting, we assume that no im erest is paid, so the tax bill is:

Taxes = (Sa les - Cash cos ts - Depreciat ion»(" = EBT x " ($1,500 - 700 - 600) x .34 - 5200 x .34 _ 568, (6.4)

where ' " the corporate t aJ( rate, is 34 percent .

Now that we have calcu lated eamings before: taxes in Equat ion 6.3 a nd taxes in Equation 6.4, how do we determine operating cash now (OCF)? Below we show three different approaches. all of them consistcnt with each other. The first is perhaps the most commonsensical because it simply asks. " What cash goes into the owner's pock. CIS and what cash goes out of his pockets?"

The Top-Down Approach Let's fol low the cash. The owner receives sales o f $ 1.500, pays cash costs of $700 and pays taxes of $68. Thus, operating cash now must equal :

OCF = Sales - Cash cos ts - Taxes - 51,500 - 700 - 68 - $732

(6.5)

We call this the Wp-dlll fll approach because we sta rt at the lOp of the in come state. ment a nd work ou r way dOwn to cash flow by subt ract ing costs, taxes, lmd o ther expenses.

Along the Way, we left out depreciation . Why? Because depreciation is not a casb outllow. T hat is- the owner is not writing a S600chcck to any Mr. Depreciation! While deprecia tio n is an accounting concept, it is not a cash flow. Does dcpreciat ion play a part in the cash flow calculation? Yes. but only iodirect ly. Under current tax rules. depreciat ion is a deduction t lowering taxable income. A lower income number leads to lower taxes. which in turn lead to higher cash flow.

The BoHom-Up Approach This is the approach you would have had in an account ing class. First , income is ca l. culated as:

Project net income = EBT - Taxes = $200 - 68 = $132

~Ca$h costs ignon:: deprmallo ... .

188

Next. depredation i ~ added back, givi ng us:

OCF = Net income + Deprecia tion = $132 + 600 ~ $732

(6.6)

Expressing net incom!! in terms of ils component s, we could wril t OCF mo re com· pletelyas:

OCF = (Sa les - Cash costs - Depreciation) ( I - r) + Depreciation

~ ($1500 - 700 - 6001(1 - .34) + 600 ~ $732 (6.6 ' )

This is the bouo/ll-IIf' approach. whet her written as Equation 6.6 o r Equatio n 6.6' . Here we stan wi th the accountant 's bollom li ne (nct income) and add ,back a~~ noo­cash deductions such as deprecialion. It is crucial to remember tha~ thiS dC,fio m? n of operating cash now as net inco me pl ~s deprecia~ion is correct o nly If there IS no mter· est expense subtracted in the ca lculUllon of net Illcome.

A' Iypical man or woma n ofT the street would geoerall7 find the lop-down approach easier to understand. and that is w~Y we presented It firs!. The lo p-d own approach simply a sks what cash flows come 10 a nd what cash flows go out. Ho:,",­ever. anyone with accounti ng tra ini ng may find th~ bottom- up approach ~as ~er because accountants use this hLller approach all the lime. In fact, a slUd~n l.wll~ an accountin g co urse under her belt knows from force o f habi t that depreclau on IS 10

be added back to get cash fl ow. . . ?

Intuitively. can we explain why one shou ld.a~d back. de~r~lCItlon. as \\~dS done here . Accouming te:< ts devote a lot of spa~e expla ll.ung the ,.ntuIIJon behind the b~t~oln-u~ a pproach . and we dOIl't want to duplicate the l ~ efforts In a fin~nce text. ~~\\leH:r, let s give a two-sentence explanation a try. As mentIOned above, whde depreclat.lol~ red~ces income. depreciat io n is /lUI a cash o mOow. Thus. one must add depreclUtlon back when going from income to cash flow.

The Tax Shield Approach . The tax shield approuch is just a vnriant o f the top-down a.pproacl~. as present.ed I.n Equation 6.5. One of the terms comprising OCF in Equatio n. 6.5 ~ s tax~ which IS

defined in Equatio n 6.4. If we plug the fo rmula for taxes provided III 6.4 IOtO Equa­tion 6.5. we gCt:

OCF == S<l les - Cash costs - (Sa les - Cash COsls - Depreciation) X I,.,

which simplifies to:

OCF :::: (Sa les - Cash cost s) X (1 - I ) + Depreciat ion x r . , (6.7)

where I is again the corporate tax rate. Assumi ng. that " == 34 perceut . the OCF works OUt to be:

OCF ~ (SI.500 - 700) X .66 + 600 x.]. = S528 + 204 ~ 57]2

This isj ust as we had before. . This approach views OC F as having tWO cOlOpo~e~t s. The first part IS what the

'r 1 d at 0' expense In Ihis (""$C. this project's cash now would be I I u~rc were no epret:l. I I .

would-have-been cash now is 5528.

189

The second plitt of OC F in this <lpproach is the depreciation ded uct io n mult iplied by .he ta x ra te. This is called the depreciation tax shield . We know that dcprecim ion is a no ncash expense. The o nly cash flow elTect of deducting depreciation is 10 reduce ou r taxes.. a benefit to us. At .he current 34 percent corporate , .. x nlle. every doUar in depreciation expense saves us 34 cents ill taxes. So. in o ur example. the $600 deprecia ­tion ded uction saves us $600 x .34 :::: 5204 in taxes.

Students o ft \!n think thai the tax shield a pproach contradicts the bottom-up approach bcc<.! usc depreciation is added back in Equation 6.6. but only the lax shield o n depreciation is added back in Equatio n 6.7. Howevcr, the two form ulae a rc per­fect ly consis tent with each erher. an idea most e..1si ly seen by compa ring Equation 6.6' to Equation 6. 7. Depredation is subtracted out in the first term on the righi -hand side of 6.6'. No comparable subt raction OCCurs on the right- ha nd side of 6.7. We Cldd the full amount o f depreciation al the end o f Eq uation 6.6' (and at the end of its equiva­lent , Equation 6.6) beca use we subtracted OUt depreci'll ion ea rlier in Ihe equa tion.

Conclusion Now that we've seen that all o f these Clpproaches a re the same. you 're probably won ­dering why everybody doesn't just agree on one of them. One reason is that different approaches arc useful in d ifferent circumstances. The best one to use is whichever IHIP­pens to be the most convenient for the problem at hand .

6.5 Investments of Unequal Lives: The Equivalent Annual Cost Method Suppose a firm must cboose bel't\"een two machines of unequullives. Both machines Can do the sa me job. but they have dilTerent operating costs ,Ind will la st for different time. periods.. A simple appl..iCOltion of the NPV rule suggcs ts t.aking th e machine whose costs have the lower prescfll va lue. This cho ice migbt be a mistake, however, because the lowe r-cost machine may need to be replaced before the o ther one.

Let's consider an example. The Downtown Athletic Club must choose between two mechanical tennis ba ll throwcrs.. Machine A costs less Ihan machine B but will not last as long. The cash outflOIl"S from the twO machines are shown here :

Da(e

Machine 0 I 2 1 4

A

B $500

.$600 $120

$100 $120

$100 $120

$100 $100

Machine A costs $500 lind lasts three years. There wi ll be maintenance expenses o f S l 20 to be paid at the end of each o f the Ihree years. Machine B COSts $600 and las ts ro ur years. There will be ma intenance expenses of $100 to be pa id ;.11 the end o f each of the fo ur yea rs. We place a ll costs in real te rms. a n assumptio n greatly Si mplifying the ana lysis.. Revenues. per yea r are assumed to be .he same. regardless of machine. so they a re igno red in the Ilnalysis. Note that a ll numbers in the previ ­ous cha rt <ire outflQws.

'''' P.r' II Val ... ation ,md Capilal Budgcling

To gel a handle on the decision. let's lake the present va lue of the costs of each of the tWO machines. Assuming a discount rate of 10 percent. we have:

$ ' 20 $ '20 + $ ' 20 Machine A: $798.42 = 5500 + - ,-.,- + ( I.I )~ (1.1))

$'00 $,00 S ' OO S 'OO Machine B: $9 16.99 = $600 + -,-.,- + (l.l)! + ( 1.1 )' + (I.I)~

f n A naive approach would be to selcct Machine 8 has a highe~ present value 0 ou, t O~~"cver machine B has a longer life, so machine A because of ItS lower present va ue. •

perhaps it s cost per year is aClu~~IY 10;C\he difference in useful life when compar­. Hohw might 0hn.:~~ore;~apas ~~:tc:;est approach involves calculat ing something m 2. t e IWO mac I . . Th ' roach puts cost S on a per-called the l'q llil'{I/ell ( (flll/ual cost of each machmc. IS app

year ba sis. r{$500 S I20 $ 1')0 SI20)areequiv-The prc~ious equation showed that paYa%C~t~e now ~ish t; eq~a~e the single pay-

alent to a slIlglc payment of S?98 .42hat d . " uilY Using techniques of previous

ment of $798.42 at date 0 with a t rce-~ear ann .

chapters, we have: 5198.42 = C X A'lo

~ three years. discounted at 10 percent. C is the A ~,o is an annuity o~ $ 1 a year or ear such that the present value of all payments unknown- the annUIty pay~eot ~~/2 4869, C equals $321.05 (= 5798.42/2.4869). equals $798 .42. Because ,A('bijsooc<J S'20 '$120 $120) is equivalent to annuity payments Th a payment stream 0 ~, . ' S32' OS the m. d h 10'· each year for three years. We refer \0 , as o f $321 .05 rna eat teem equivalent annual ('QS' 0T rna.chi ne A. . .

This idea is summarized to the followtng cbart .

Cash outflows of machine A

EqUivalent annuat cost of machine A 321.05 321 .05 321 .05

. h uld be indifferent between cash o ull10ws of ($500, The Downtown Athletic Club s 0 f ($0 $321 05 $32 J 05 $3"") I 05). Ahernatively.

S 120. $120. SlhI2tO~h~lpdu~~~~~u~~:Sn~achil;e is r~an~ially ~~ivaiel~t to a rental agree-one can say a · "") 05 men t callin.g for <lnnualleh~:ee paB Y;::~~cO~!~~i~~ equ ivalent annual cost from:

Now let sture to mac h. .

$916,99 = C x A~11I

~ I 3 1699 Cequals$9 169913.1699,or S289.28. Be~~~eAd:d e~~~~aCilille A, we can creat~ the fo llowing chart fo r machine B:

Cash outflows of mllchine B

Equivalent lI/lnual cost of machine B 289.28 289.28 289.28 289.28

EXAMPLE 6.11

Cb.:Ipl(·r 6 Making C"pilal I.n ves lment Dcch;ons 19'

The decision is easy once the ch<t rts of theTwo machines are compared. Would you rather m:.tke an nual lease payments of $32 1.05 or $289.28':' Put this way, the problem becomes a no-bra iner: A rational person would rather pay the lower amou nt. Thus, mach ine·S is the prererred choice.

Two final rem arks are in o rder. Firsi. it is no acciden t that we specified the costs of the tenllis ball machines in real terms. Although 8 would still have been the preferred machine had the costs been stated in nominal terms. the actual sol ution would have been much more d ifficult . As a gencfCl I rule. always convert cash flows to real term s wheo workin g th rough problems or this type.

Second, such analysi s applies onl y ir one anticipatcs tbat both machines ca n be replaced. The analysis wou ld dilTer if no replacement were possible. For example, imagine that the only company that manufactured tennis ball throwers JUSt went out of busIness and no new producers are expected to eorer the lield. In this case, machine B would generate revenues in the fourth ycar whereas machine A wou ld no\. Here, simple net present value analysis for mutually exclusive projects including both revenues Hnd costs would be appro priate.

The General Decision to Rep/ace The previous ana lysis concerned the choice between machine II and machine B. both of which were new acq uisitions.. More typically firms must decide when to replace an existing machine with a new o ne. This decision is aCTually quite straightforward. One should replace if the annua l cost of the new machine is less than the annua l cost of the old machine. As with much else in finance, an exa mple clarifies this approacb bener tha n further ex planation .

Replacem e nt Decisions Consider the slt.uation of BIKE, which must decide whether to ~Iace

an existing machine. BIKE P'lYS 00 ta)(cs. The replacement machine COSts $9,000 now and requires maintenance of $1.000 at the end of ~ry year for eight years. At the end of eight years. the machine would be sold for $2,000.

The existing machine requires increasing arTIounts of maintenance each year. and io. salvage value

falls each year. as shown:

Year Maintenance Salvage Value

Present $ 0 $4,000 , ' .000 2.500

2 2,000 1,500

3 h

3,000 1.000

• '.000 0

This chart tells us we the existing machine can be sold for $4.000 now. If it is sold one year from now. the resale price will be $2.500 after t<PI:es. and $1,000 must be spent on maintenance during the year [0 keep it running. For ease of calculation, we assume that this maiOlenance fee is paid at the end of the ~ar. The machine will last for four rTIOI'"C years before It falls apart. In other words, salvage value will ~ l.ero at ttle end of year 4. If BIKE faces an opportunity cose of capical of 15 per· cent. when should it reptace tke machine1

(continued)

ParI II V .. lual ion and Capiml BuJ.gcling

o ppro;r,ch is CO compare the annual COSt o f the replacement machine with the annu<tl con of theu~l~ machine. The annual COst of the replacement machine is simply iu equivalent annual caS(

(EAC). Let's olcula te that flrst.

EquivalentAnnual Cost of New Machine The pre~ent value of the COSt of the new replace.

mel'll machine is:

! $2,000 pv",." '" $9.000 + $1 .000 X A I ~ - ( 1.15)'

= $9.000 + $1,000 X (4.4873) - $2.000 X (.3269)

= $12,833

. , . .. a nPoaUve number in this equation Notice that the $2.000 t.1I Ivage value is an ,"flow. t IS treat ar. .. ~. becaus~ it offsel5 the COSt of the machine.

The EAC of a new replacement machine equals:

. _ PV _ $12.83 3 :- $2.860 PV/ 8·ye:tr annuIty factO\" at 15% - AI - .. 4871 " .

This Gl.lculation implies that buying a replacement machine is financially equiv;r, lem to renring this

machine for $2,860 per year.

C t f Old Machine This calculation IS a It e mc er. . ·nJ . k.i If BIKE keeps the o ld machine for one os 0 . r $1 000 a year from now. But this is not BIKE's only COSt Year. the firm must pay maIntenance costs 0 • h. . k

. . to BIKE ill receive $2,500 at date I if the old mac Ine IS ept from keeping the machIne r one year. w . Th' d for ooe year but would receive $-1.000 today if the o ld machine were sold ImmedIately. IS re uc·

lion in sales proceeds is clearly a COSt as wetl. . . . Thus the pV of the costs of keeping the machine one more year before selling It equals.

$1.000 $2.500 =- $2696 $4,000 + ITS - I. IS .

d ive the $4000 tOday. This That is if BIKE holds the o ld machine for one yea r. BIKE oes not rece , f $4000' be thought of as an opportunity cost. In addition. the firm must pay $1,000 a year rom

r'tO~. Fi:17y, BIKE does receive $2500 a year from now. This last item is treated as a negative num·

W be<:ause it offsets the othe r twO costs. . . Although we normally express cash flows in terms of present value, the ana~S iS to come 15 .e~Sler

jf we express the cash ow In terms I , . of'ts future value one year from now. ThIS future value IS.

$l.696 X 1.15'" $3.100

In other words, [he cOSt of keeping the rt"\<Ichine for one year is equivalent to paying $3.100 at the

end of the year.

Making the Comparison Now lec's review the cash flows. If we replace the machin.e imme.,

2 860 ~. , a the end of the year ThIS annua diately, we can view our annual expense as $. . gllll'lltlg [ . .

expense occur.; forever if we replace the new machine every eight year~. ThIs cash flow stream can

be written as follows:

Expenses from replacing machine immediately

Year I Year 2 Year 3 Year 4 ., ,

$2,860 $2,860 $2.860 $2,860

If we n! ace the old machine in one year, our expense from using the o ld machine for that final

ye~r can b::iewed as $3 .100. payable at the end of the year. After replacement. our annual expense

Summary and Conclusions

Chapter 6 Making Capiutf Im cslment Decisions J9J

is $2.860. beginning at the end of two )'tars. This annUilI expense occur.; forever if we replace the new machin~ every eight years. This cash flow Stream Ciin be written as:

Expenses from using old machine for one year and then replacing it

$3,100 $2.860 $2.860 $2,860

Put this way, the choice is a no-br.liner. Anyone would I"ilther pay 52,860 at the ~d of the year than

$3. 100 at the end of the year. Thus, BIKE shoold rep/ace the old machine immediately to minimize the expense at year I.]

Two final poinu should be made about the decision to replace, First. we have examined ii sitl,la. tion 'oYtlere both the old machine and the replacement machine generate the same revenues. Because

revenues are unaffected by the choice of machine. revenues do not enter our analySiS. This Si tuation is common in busine55. For example, the decision to replace either the heating system or the air conditioning system in one's home office will likely not affect firm revenues. However. sometimes

revenues will be greater with a new machine. The approach here can tuily be ametlded to handle differential revenues.

Second, we want to Stress the importallce o f the current approach. Applications of this approach are pervuive in business because every machine rnun be replaced ;n some point.

lOne caveat is in order. Pt:-rltups the old maehine's maintcnllncc is high in the 1;0;1 ytar but drops llrter thaI. A decision 10 repl3~ immedi:llely might be premature in that case. Therefore, we need tQ check Iht COSt of the old machine in futu re years..

The COSIOI' keeping: .hc e.~ i$t i ng mao;-hine H S<."'Cond ye."l f is:

. 51.000 SI,500 • py of COSts at lime I ,. S2.500 + - -- - __ '" $1,9)) J.I 5 1.1 5

which has a fUlu re v" lul." of S3.375 ( =52.935 x 1,151. a COst gretner thaI! the allnua] COSt (51.860) of Ihe old machine.

The costs o r kttping the e:tist ing mHehine for years ) and 4 are also greater than the EAC of buyinll a ntw machine. Thus.. BI K E's decision to replace Ih" old machine jmm«iialely is still \'alid.

This chapter discus$(."'C! a number of pruclical applications of capital budgetjng.

I. Capital budgeting mllst bl' placed on an incremental busis.. This means thiu sunk costs must be ignor\."d, whe~as' bolh opport unity costs lind side effects must be considered.

2, In the Baldwin case we c~mputed NPV usi ng the foUowing two steps: a. Cn lculate the net cash now from aB sources for each period. b. C:llculale the NPV using these clIsh fl ows..

3. Inflation must be handled consistently. One approach is 10 ex press both cash flows and the discount nile in nomi(wl terms. Th,' ot her approach is to express both cash flows and the discount ratc in real terms. Because ei lher approach yields the same NPV cal~ eu lalion . the simpler method should be used. The simpler method will ,gencr.uly depend on the type of capital budgeting problem.

4. A firm should use Ihe eq uiva lenl lIn nual cost approllch when choosing between two machines of unequal lives.

, .. Concept Questions

P.rI 11 V:lIualion and Capital Budge ting

I. Opportunily Cost In the context of capital budgeting. what is an opportunity cost?

2. Incremental Cash Flows Which of the following should be treated as an incremen­\a l cash now when computing lhe NPV of an i!wcSIOlcnt?

3.

4.

5.

a. A reduction in the slIles of a comp.·my's other products caused by the investment b. An expenditure on plant and equipment Ihll1 has not yet been made and will be

made only if the project is accepted. c. Costs of research and development undertaken in conncction with the product

during thc past three years. d. Annual depreciation expense (rom the investment. c. Dividend payments by the firm. f. The resale value of plant and equipment;1I the end of the project's life. g. Salary and medica l costs for production personnel who will be employed only if

the projcct is accepted . Incremental Cash Flows Your company currently produces and sells steel sha n golf clubs.. The board of directors wants you to consider the introduction Qf <I new Hoe of tilanium bubble woods with grnphite sha fts. Which of the foIlO\ .. ;ng costs are /10/

relevant? II. Land you alrc:ldy own that will be used for the projcct. but o therwise will be sold

for $700,000. its market value. b. A $300.000 drop in your s.:lles of steel shan clubs if the titanium woods with

grnphite shafts are introduced. c. S200.ooo spent on teSl."3rch and development last year on graphite shafts.

Depreciation Given the choice, would a firm prefer to usc MACRS depreciation or straight-line deplttialion? Why'? Ncr Working Capital In our capital budgeting examples. we assumed thai a firm would recover all of the working capital il invested in a project. Is this a reasonable OIssumption? Whcn might it not be valid?

6, Stand-Alone Principle SUppose;l financial manager is quoted as saying. "Our firm uses the stand-alone principle, Becl.luse we treat projects like minilirms in our C'VOIlu­ation process, \vc include financing costs because they arc relevant l.I t the firm level:' Critically cvahll.lte this statemcn t.

7. Equh'B.ienf Annual Cost When is EAC anl.llysis appropriate for comparing two or more proj«ts? Why is this method used? Are there any implicit assumptions required by this method that you find troubling? Explain,

8. Cash Flow and Depreciation "When evaluating projccts. we're on ly cOIl(:~rncd with the relevant incremental aftertax cash flow s. Therefore. because deprcciation is :t

noncush c: .. pcnse, we should ignore it s eflects when evaluating projects." Critically evaluate this statement.

9. Capllal BLKlgeting Considerations A major college textbook publisher has an exist­ing IinOln,-"C textbook, The publisher is debating whether to produce an "essential­izoo " \'crsion . meaning a shorter (and lower-priced) book , What arc some of the considerations that should come into play?

To answer the ne:'1t three questions. refer to the following example. In 200), Porsche unveiled its new spons utility vehicle (SUV). the Cayenne, With a price lag of over S40.000, the Cayenne goes from zero to 62 mph in 8.5 ~nds. Porsche's decision to enter the SUV market w:tS in response to the runaway success of o ther high·prkcd SUVs such as the Mer· ttdes-l3enz M dass. Vehicles in this class hud genentted years of very high profits. The Cay­enne certainly spiced up the market. and, in 2006. Porschc introduttd the Cayenne Turbo S. which goes from zero to 60 mph in 4,8 seconds and has a top speed of 168 mph. TIle base price for the Cayenne Turbo S? Almost SI 12.000!

Questions and Problems

connect .... c ('>_t'~ 1111- 10)

Cbaptn 6 Making Capilal lnvt'Slmenl Deci$ions

'" ,

Some analysts questioned Porsche's en tr int I I "-ere CQt,1cerned because not onl W' pya. t Ie uxu~y SUV market. The unalysts introduction of the Ca enne mr tS orsche H late ~ntry IIlIO. the market. but also the performance automobil%s. gh damage Porsche s reputation as a maker of high-

10.

II.

12.

I.

2.

Erosion In evalu'uing the Ca . Id ' Porschc's reputati~n as erosionr~nne. "all you conSider the possible damage to

Capital BLKlgetfug Porsche was f h I utility vehicle market Why Id

onc 0 t e ast mm~ufacturcrs to enter the sports

, wou one company decide to proceed \~ . h whe~ other co~pal1ies.:II least initially. decide not to en ter the market;t a product

~aplta l 8udge~mg In evaluating the Cayenne, what do W'>U th'nk n • d assume regarding the s bst 'I fi' ;- I .-orsc c nee s to that they will be mainta~neda:st;~ pro ~ m~l ns tllat e.'(iSI in lhi~ ~arket? Is it likely be able to maintain the profit m:~~~r ~au:m~ m?te compet itiVe, o r will Porsche the Cayennc? 0 us Imagc and the performance of

Calculafing Project NPV Rapl ' I R ' . " $12000 m" l.ae estaumnt IS conSIdering the purchase of . . sou 0;; maker The souflle make h' ' " .1

be ~I!y depreciat~ by the stra ight_liner m~~~~~~~;~~~~~f ;~~ :~:;en~ ~ ~u es per y~ar. With each costing $2.20 10 make and priced :II S5 Assume th'; h

Iscount tate IS 14 percent and the taJ!: nile is 34 S.· .1 t e purchase? • percent. ould Raphael make the

Calculating Project NPV The Best Manufactu' C ' . investment. Financial pro,'octions fi ,. . rTOg ompany IS conSIdering a lIew . ' or e Investment are tabulated here. Th

;;~~;:~~t:,~:~!! ~:~;t;.:~n~~ :~~:~l~n~:~~ue i~ ~iVCd in ~Ish , a ll o~~~~ year, All net working capital is reeovered at the enc~~f t~;~=t: at Ihe end of the

Year 0 Year 1 Year 1 Year) Year 4

Investment

Sales revenue Operating (oro

Depreciation

$1t.,000

$8.500 t,9oo

' .000

$9.000 $9.500 $7.000 2.000 2.200 1.700 '.000 '.000 <.000

Net working capital spending

200 250 300 200

a. Compute the incremen tal net income of tbe investmen t for ea 'h b. Compute the inc remental cash flows of Ihe investment for e.:c~ year.

c. ~~~:t~ the apprq'priate discount nile is 12 percent. Wha't is ;~:r'NPV of the

3. Calculating Projcct NPV Down U dB · . , ~ear expansion projOCt that requi:S ~~ i::fr~~:d 1~~~:lIi~~nStdering;t nC\\'.thre:­hon, The fixed asset will be de ' cd " estment of S2.4 nH/­life, after whii:h it will be wort~:'I';!-h str.t!ght~hn~ ,to zero over its three-year tax in anllual sales. with costs of $950 000 e -F~oJCCt IS est,lmated to generate $2,050,000 return is 12 percent. What is the pr~jec;'s ~~~ nne IS 35 percent and the required

4. Ca~ting ,Proje<:t, <;~sh.Flow from Assets In the previous problem su ~roJect.requlres an mnlal mvestment in net workingcapitaJ of $'85 000', :~~ the .Issel WIll have a market va lue of S225 000 t th .~' an, I t IXed

OCt's year 0 net cash flow" Year I? Yi:a'r 2? ~I''' " 3~n\~~f I~e p.roJcct. What IS the proj-• • .... 1 " 'Hlat IS t e new NPV?

196

INT£RMEDlA.TE (Ouestlol'ls 11- 27)

Put 11 Valuation ,md Capil:11 Budgeting

5.

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NPV and Modified AC RS In the previous problem. suppose the fixed asset ac':Ually faUs into the three-year MACRS class. All the ot her facts are the same. What IS tbe project's year I net cash now now'! Year 2'? VenT 3? What is the new NPV"!

Project [l'31uation Your firm is conlcmplilling t~e purchase, of a nc\~' $85:0.000 computer.based order entry system. T he system wJlI be depreciated sl!'ught-lmc ~o zero over its fi vc-ye,tT life. It will be worth $75.000 at the end of that tll!lC, You W ill

solve S320,000 before taxes IXf year in order processing cOSts.. .md you Will be able t~ reduce working capital by SI05.000 (this is a one-time reduction), If the tax rate IS

3S percen t. whal is the IRR for this project?

Project E"aluBtion Dog Up! Franks is looking :11 a new .saus:~ge system with an installed cost of $420.000. This cost will bedcpn.'"Clutcd stmlgh t-hnc to zero ovcr the project"s fIVe-year life. at the end of which the silusOlge system C:dTl be scrapped ~or $60.000. The sauS<lge system will save the firm S13~.OOO per y~a r III p~ta.'I: operatmg costs. and the system requires aD initiOlI investment In net workmg capital of S28.000. If the tax rate is 34 percent and the discount ratc is 10 percent. what is the N I)V of this project? Calcularing Sah'age Value An as~t used in it four-ye,.lr. ~rojcci fall s in the live-year M ACRS class for tax purposes. The asset has an lIcqUlsltlon cost .of ~8.400.000 and will be sold fo r 5 1.900,000 at the end o f the project . If Ihe tall rale IS 3) pen:enl . what is Ihe a fterlax salvage value of the llsse!'!

Cillculating NPV Howell Petroleum is coosidering a new project that cOl~ ~lcments its c,'l: ist ing busincss. The machine required for the proj~t cos.tS $1.8 nlll1!o.n . Thc marketingdcpClrtment prcdiclS that S<lles related 10 the .proJect Will ~ S I.I millio n J.>Cr yea r for the nCllt fo ur years.. after which the markct Will cea:-c ~o eXI~L The ma~hllle wi ll be depreciated down to zero o\,er its fo ur-year economic life uSlllg the s ~nughl­line method . Cost of goods sold and operating expenses related to t~e proJ,,:t arc predicted to be 25 percent of sales.. Howe-lllliso needs ~o ad~ nct work-lIlg ~pltal of $ 150.000 immediately. The additional net work ing capital Will be recove~d m full 011 the end of the project's lifc. The corporate lall mte is 35 pereent. The reqUIred ra te of retu rn for HO\\."e1l is 16 perceol. Should Howell proceed with the proj\."Ct?

Calculating EAC You are evaluating two different silicon wilfer milli ng n~achincs. The Tcchron I costs $270.000, has II three-year life. and hilS pre tall opcratlllg costs o f S45.000 per ycar. The Techron II costs 5370.000, has a fi ve-year life. ~Illd .has p.re­tax operating costs of 548.000 per year. Fo r both milling machines. use s tra Ight-lin: depreciation to zero o\'cr the projecf~ life and as~ulll c a S<llvage value of 520,000 . .u your tall mte is 35 percent and your d iscount ratc IS 12 percent. compute Ihe EAC lor bol h m,tchines. Which do you prefer'? Why?

Cost-Cutting Proposals Massey Machine Sho p is consid~ring a four- yellr projt.:-t to improve its production elliciency. Buying a new machLlle press for S530.~ 15

estimated to result in S2)0.000 in annual pretax cost S<l\'ings.. The p ress fa lls.1Il the­MAC RS five-year class. and it will have a sa lvage v,due .at the end of tl.\e project of S70,000. The press also requires an init ial invcstment III spare part~ mventol)' o f S20.000. alo ng witb an itdditional S3.000 in invcn to,:y fo r each s~ec\.'Cd ll1g year of the project. If the shop's tax rate is 35 percen t :md its discount rate IS 14 percellt. sho uld M,ISSCY buy and installthc machine press? Compariog Mutually Exclush"e Projf'C ts Haga r Industri .. 1 Systems Company (HI SC) is trying to decide between two din'ercnt conveyor. belt systems.. Syst~m :\ costs 5360.000. has a fo ur-year life. and requires $ I05.(}(X) 10 pretax annual operat­ing costs.. ~ys tem 8 costs S480.000. has a sill-yea r life. ~Illd re() ui,rcs ~5.000 in pretax a nnual oper.tting costs.. Bo th systems arc to be deprecIated strm~ht-hnc to .zeT<? owr their li\·C'S and will have zero salvage value. Whichever system IS eho~n. It WlIl ,,~t be rcplact.-d when it wears Ollt. If the tax r.ttc is 34 percent and the dIscount r.tte IS II percent. which system shou ld the linn choose?

Chaplet" 6 Making Capilal I nw~llIIcll1 Deci.~ions 197

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Compa ring Mu1uallr Exdusin Projccts Su ppose in the previous I>roblem that HI~C ahwys ne!!ds a cooveyor belt system: when o ne W("ars ou t. it must Ix replaced. Whleh system shou ld the firm choose now!

Comparing Mutually ~xclusi\"e Projects Vandalay Industries is considering the pur­chase ~f a new machme for the product ion of lale:c Machine A costs S2.400.000 and will last for si.'I: yea rs. Variable costs a re 35 perttnt of sales, and fi xed COSts arc S180,000 ~r year .. Machine 8 costs 55.400.000 and will/ast for nine years. Variable L"OSts for thiS machlllc ilre 30 percen t and filled costs an' S I IO.OOO per "ear. The sales for each ma~hi ne will be S10.5 millio n per year. The required relUJn is io percent and the lax rate IS 35 percent. 8 0t h machines will be depri.:cilll<.-d on a str.tight-line basis. If the eompttny plans to replace the machinc when it wears o ut on a perpetual basis. which machine should you c hoose? .

Capital Budgeting ",ilh Inflation Consider Ihe fb llowing cash flows on I\VO mutu­ally excl usive pro~"Cts:

Year Project A Project 8

o I

2 ]

- $50.000

lO.OOO

25.000 20,000

- $65.000

29.000

l8.ooo "1,000

The cash flow,S of p~jec t II are expressed in real terms. whereas those of projcx" B are e-xpr~ssed.'n noml~alterl1ls. The appropria le nominal discount mle is 15 percen l and the mflatlo n •• 1Ie IS 4 percent. Which p roject shou ld you choosc'!

Innalion .aod. Compan~' Val1M.' Sparkling Water. Inc .• ellpects to sell 2.1 mill ion bot­~Ies of drJllktng water each year in perpetuity. This year each bottle will sell fo r $1.25 III real terms ;tn~ W~ 1l COSI S.75 in real term s, Sa les incom.e and costs Ot.:cur at year­end . RC"enues w,lI nse at a real mte o f 6 percent a nnually. while real COSls will rise at a real r.I~e of 5 perc("nt annually. The real discount nile is iO percent. The corpOrllte ta ll r.lle 15 34 percen t. What is Sparkling worth today?

Clllculat in.g Nominal <:ash Flow Eton ic Inc. is co nsidering an investment of S305.~ JIl an assel wllh an economic life of five years. The firm estimatcs that the nOlllmal anoua l cash re"e~lUes and ellpenses at the end of the firs t year will be $230.000 and ~.~. respectIVely. Bot h re\'enues ilnd expenses wi ll ~row thcl"\!a fter at the ~n n~al mnatlOn mte of 3 percent. Etonic wi ll usc the siraight-line method to deprecia te us a.sset 10 zero over five years. The salvage \~dlue of the ilSset is cst imated to be $40,000 inl~omim~llc~s at l~at time. The one-lime net working capi tal i nw~l_ melll of 5 10,000 IS reqUired Immedl~tely and will be ra:overed at the end of the proj­ect. All co.rporate cash fl ows are subject to a 34 percent tax rate. What is the projt.'Ct·s Iota I nOllllOal cash fll1W from assets for each year?

C~ Flow Valua.lion .. Phillips Industries runs a small manufacturing opemtion. For thiS fi~1 1 year .. It expecls real n~ t .cash flo ..... s of 5 155.000. Phillips is 811 ongo ing operdllon . bur 1\ expects competrtlve pfCS!lures 10 erode its real net cash nows at 5 percent per year in perpetuity. The .appropriOlte real disco unt ratc for Phillips is II pert'elll. All net cash nows are rece1\led al yea r-end. What is the presen t value o f the net I.'ash flows fro m Phillips's operations?

Equiv:a lenl Annual Cost Bridgto n Golf Acitdemy is e\'"dluatingdiffercnt golf pn.ctiCl' equIpment. The "Dimple- Max" equipment costs $63.000. has a three-year life. and COSIS S7:500 J.>Cr year to.o~r..tte. The relevan t discount rale is 12 percen t. Assume thai Ihe s t rillgh t - ll ~e depreocmtlon method is used and that th e- equipment is fully depreci­ated to zero. l-unhermo(C, assume the equipmclJt has a salvage va lue of 515.000 a l

'98 Pirl II Valuation and Capital ROOIl(\ing

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the end of the projcct's life. The reiev-.mt lax rate is 34 percent. All cash nows occur at the end of the year. What is the equivalent a nnua l cost (EAC) of this equipment?

CaJcuJatiog Project NPV Scott Investors. Inc., is considering the pure,hase of a $450.000 computer wilh all economic life of fi ve ye'drs.. The computer will be fully depreciated over live yC'.tJ"S using the slmight-linc method . The m;trkct value of the computer wil l be $80.000 in five years. The computer v.1.~1 rcp~ace f~ office, employees whose combined annual salaries are $140,000. The machme will also Immcchalcly lower the fi rm's required nel working c-otpi tal by $90,000. This amo unt of net ~rldng capital will need to be replaced once the machine is sold. The corporate tax rate IS 34 percent. Is it \\'Orlhwhile to buy the computer if the appropriate discount rate is 12 percent?

CalcuJating NPV and I RR for a Replacement A fir~ is c~m~idering ~n inveslmenl in a new machine wilh a price of $12 millio n 10 replace li S eXlst1ng machIne. The current machine has a book value of 54 million and a market value o f $3 million. The new machine is expected to have a four-year life, and the old machine has fou r years .left in wh ich it can be used. If the firm replaces the old machine with the new machme, it e;>;.pects to save $4.5 million in operaling costs each yea r ovcr Ihe !lCXI fo ur years. BOlh machines will have no salvage value in fo ur years. If Ihe firm purchases the new machine. it will also need iln jnvcstment of 5250.000 in net work ing capital. The req uired relUm on Ihe in~tmelll is 10 percent, and the tax mle is 39 percenl. What are Ihe NPV and IRR of the decision to replace the o ld machine'!

Projcct Analysis und Inflalion Sanders Enterprises. Inc .. has t>ct:~ co~sidering tbe purchase of a new manufacturing facility for $ 150.000. The fac lhty IS to be fully depreciated o n a stmight-1inc basis over seven years. It is cx~ted to have no resale va lue after the seven years. Opemting re\-cnues from the faellllY are expected to be S70.000. in nomi nal terms. .1.1 the end of thc fi rst year. The revenues a re eXpei:ted to increase a t Ihe innatio n rate of 5 percent. Producrion costs at the end o f the fi rs l year will be S20.000. in nominal terms. and they arc expected to increase tit 6 percent per year. The real discount rate is 8 percent. The corpomtc tax nile is 34 percent. ~anders has other ongoing profitable operations. Should the company aceept the project?

CaJcuJating Project NPV With the growing popularity of casual surf print clothing. twO recent MBA graduates decided to bro.'1den this casual surf concept to encompass a "surf lifestyle for the ho me.·· With limited capital, they decided to focus on surf print table ilnd noor lamps to accent people's bo mes. They projected uni t sales o f these lamps to be 6.000 in the first year. with growth of 8 percent each year for the next five yeMs. Production of these lamps will require $28.000 in nCI wo rking c.1pital. to start. To t.a! ijxed costs are S8O.000 per year. variableproduclion costs are S20 per unll .and the UOltS are priced at S48 e<lch. The equipment Deeded to begin production will cost $145.~. The equipment will be depreciated using the strd.ight-line method over a fi ve-year life and is not e;>;.peeled to have a salvage value. The effeclive laX nHe is 34 percent. and the required rdte of rei urn is 25 pen.."ent. Wh"t is the N PV of Ihis projcct'?

Ca1cuJating Project NPV You have been hired as a consulta nt for Pristine yrb.1~­Tech Zi ther. Inc. (PUTZ). manufactu rers of fine zi thers. The market for l.llhers IS growing quickly. The (;Qmpany bought somc land three years ago fo r $ 1 million in anticipation of using it as a toxic waste dUmp site but has ~ntly hired another ,:om­pan)' to handle alllOxic materials. Based on a recent appraIsal, the company beheves it (;Quid sell the land for $800.000 o n a n a ftcnax basis. In four years. the land could be sold for $900.000 after taxes. The company also hired a market ing firm to a nalyze the zither market. at a cost of $ 125,000. An e.xcerpt of the marketing report is as follows:

, 'he zither induslr)' wi11 have ~ I rdpid expansion in the ne;>;. t four years. With lhe brand name recognilion that PUTZ brings to bear. we feci that the comp.1ny wil~ be able t.o sedl ~.I~. 3.800. 3.600. and 2.500 units e:lch year fo r the nexi four years. rcspccll\'ely. Again. capltahz· ing on the name recogni tion of PUTZ. we feci thai a premium price of S7SO C3n bccha~ed for each zi ther. BecaLL'Ie ri thc:rs appear to be a fad. we fed 9t the end of the four.year penod. sales should be discontinued.

CHALLENGE (Ouesllons 28-38)

Ch:apttt' 6 "- laking Capilal hl"estment Ikcisions '99

P~TZ feels that fixed ~osts fo r the proj.ttt will be 5425,000 per yea r. a nd va riable co~ts a~c. 15 pcrce~1 of sa les. ,!"he eqUIpment necessa ry for production will cost 54.2 mllho n and W]Il. be deprecl~ted aCCOrding to a th ree-year MACRS Sclll.-rlule. At the end o f the pro)CCt . the cqulpment CU ll be scrapped "0' • • ~ 000 N, . k ·

. I f $ . '. .rtVV, . e \Ioor mg

25.

capita 0 1.20,000 Will be requt~ l~lmedimely. PUTZ has a 38 percent tax nUe, a nd lhe reqUired return 0 11 the proJect IS IJ percent. Wlmt is Ihe NPV of the project? ASsume thc Company has olher profitable projects.

Calc:ulafio.g ~roject NPV Pilot Plus Pens is deciding when to replace its old machine. ~he machmescurrent Silh',tge value is SI.8 million. lIsclirrent book V'.duc is $ 1.2 mil­lIon. ff not sold . the o ld machine will require maintenance costs of S520.000 at the end of the year fo r Ihe ne.x t five years. Depreciat io n o n the o ld machine is 5240.000 per year. At the end of five years, it will have a salvage \'alue of S200,OOO and a book value of SO. A rep la~melH machine costs $3 million fl OW and req uires maintenance costs of S35O.000 3l the end o f each yea r during its ecooomic life o f fi ve years. At the ~nd of the five )'~ars. the new machine wi ll have a sa lvage va lue of 5500.000. It .\\'1I~ be ~~IIY depreciated by t~e str~ight - linc method. In five years a replacement ma.clune ~\I IJ .COS I S3.500.000. Pilot WIll need to purchase this machine regard less o f wh.lI .cholcc II Ill,~kes today. The corporate tax rate is 34 percent and lhe appropri_ :He d Iscount rale ' ~ 12 percen!. The company is assu med to eam surrlCient revenues to ge~lerate tax shIelds from depreciation. Should Pilo t Plus Pens replace the o ld mac hme now or ilt Ibe end of five years'!

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28.

EAC and Innafion Office Auto matio n. Inc .. must choose between two copiers. the "-:"40 or. the RH45. The XX40 COSIS S I.500 and will last for three years. The copier wll! req UIre a real a~lCrtax COSI o f $ 120 per year afier all rclev"nt expenses. The RH45 costsS2.300 and WIU last fi ve years. The real a ftenax cost fo r the RH45 will be SI50 per year. All cash nows occur al the end of Ihe year. The mnanon rate is expected to be 5 percent per year. aod the nominal discount ratc is 14 pereent . Which copicr should the company choose?

~roject ~ldJsis and Inna tion Dick inson Brothers. Inc .. is considering investing III a maehlllc ~o prodUce computer keyboa rds. The pri(,:e of the m'lchine will be S53O.00:0. an~ liS economic life is five years. The machine will be fully depreciated by th~ strdlght-IJIle method . :rhe mach.ine will produce 15.000 keyboards each year. The pn~ of each key~ard will be $40 111 Ihe fi rsl yea r and will increase by 5 percen t per year. The production COSI per keyboard will be S20 in the first year and wi ll increase by 6. pcrce~t per ~ear .. The projecl wi ll havc an a nnual fixed cost of $75.000 and r~qUlre an ImmedIate IIIv.est ment of 525.000 in net working capital. The corporate lax rate for the COmpa ny IS 34 pe rcen t. If Ihe 'Ippropriale discount rolle is 15 pen.'Cnl what is Ihe NPV of Ihe invcstment? '.

Projcct Enluation Ag uilera Aco ustics. Inc. (AAI). projects unit sales for a lIew seven-octave voice emula tion imp l~nl as follows:

Year Umt S,lles ,

87.000 2 904.000 3 r 18,000 4 109.000 5 95.000

Product~o.n of Ihe imphmts will req uire S I,500.ooo in oet working capital 10 stan aOd. add lt]Onal .net working capital investmen ts each year ;:qual to IS percent of the Pro!cctcd sales In.crease for the following ye~r. Totnl fixed (;Qsts 'Ire S700.000 per year. vanable productIon costs are S240 per unll. and Ihe unils are priced at S325 each.

hrl II VlIlu;l\ion ;md C"pit:1i Budgeling

29.

30.

31.

32.

The equipmen t needed to begin production has an installed cost of SI8: 000.0?0. Ba:ause the implan ts arc inlcnded fo r professional singers. this equipmcnlls consId­ered industrial machinery and thus qualifi es as seven-yea r MACRS property. In five years. this equipmen t can be sold fo r abou t 20 percen t .of its <lcquisition.cosl. ~AI is in the 35 pe-rcenl marginal tax bmckct and has a requ ired rcturn on all Its proJccts of 18 pen:cnl. Based on these preliminary projcct estimates. what is the ' PY of tbe project'! What is the l RR?

Calculating Required Sa\'ing5 A proposed cost -saving device has ;111 installed COSt o f S540.000. The devk-e will be used in a five-year project but is classified as three­year MACRS propeny for tax purposes. The required ini tial net working c;:'1pilal investment is $45.000. the margin" l laX rate is 35 percent. and the project discount rate is 12 percent. T he devicc has an estimated year 5 sa lVllgC \'alue of S50.000. What level o f pretax cost saviogs do we require lor this project to be profitable'!

Calculajing a Bid Price Another utiliZiit ion of cash flow analysis is sell ing the bid price on a project. To calculate the bid price. we set the project N PV eq ual to zero lind fi nd the required price. Thus the bid pri(.-e represents a financial break-even Icvel fo r the projet:t. Guthrie Enterprises needs someone to supply it wit h 130.000 cartons of machine screws per year to support its nwnufacturing needs over the next five years. and you've docid(.-d to bid on the contmcl. It will cost you S830.000 to ins~a ll the equipment 1l(.'CeSS<lry to start product ion: you'lI depreciate this cost stntigh t- lmc to zero ovcr the project's life. You estimate thai in fi ve yea rs this equipment clin be S<'1lvdged for 560,000. Your fixed production (.'O$ts will be $2 10.000 per year. a nd your variable production costs should be S8.50 per cilrton. Y~u also need an initial illv~t. ment in net working c'l pit al of $75.000. If your tax mte IS 35 percent and you require a 14 perctnt retum 0 11 your investment. what bid price should you submit?

Financial Break-E"cn Analysis The technique for calculating a bid price C;1Il be c.1Ii.tendcd to many o ther types of problems. Answer the fo llowing qucstions using the same technique as selt ing a bid pri<:e: that is. set the proj«t NPY to zero and solvc for the variable in question. a. In thc pre\'iolls problem. assume that the price per carton is $ 14 and find th(.'

projCl.'t N PY. What docs you r ans\\'Cr tell you about your bid price" What do you k.now about the number o f cartons you ca n sell and stili break c\'cn? How .. boUl your level of costs? . .

b. Solve the p revious problem ag:.!in with the price soU a t S l4- but fi nd the quantity of canons per ye;l r that you I.·an supply and still break even. (H illt: It's less than 130.000.)

e. Repeal (b) with a pricc of S I4 a nd a quanti ty of 130.000 cartons per year. and find the highest level of fixed costs you could afford and still break even. (H int: It 's more than $2 10,000.)

Calculating a Bid Price Your company h:ls been approached 10 bid on a contract to sell 9.000 voice rt.'Cognition (VR) computer keyboa.rds a year for fo ur years. Due to technological improvements. beyond that time they will be outdated and no saks will be possible. The equipment necessary for the product ion will cost S3.2 mill~on a nd will be depreciated on a straight-line basis to a zero salvuge va lue. Production will requi~ an investment in net working capital o f S75.000 to be relUrned at the end of the project. and the equipOlent can be sold for $200,000 at the end of pro­duction. Fixed costs ;lre $600,000 per year. and va riable costs are $ 165 per un it. In addi tion to the contract. you feel your comp;my ca n sell 4 .000, 12.000, 14.000. and 7.000 additional units to compan ies in o ther countries over the next four ye.lrs. respecth·dy. at a p rice of S275. This price is fi:-:ed. The tax m te is 40 percent . and the required return is 13 percent. Additionally. the president o f the company wi ll undertake the project only if it has an NPV of $ 100,000. What bid price should you set for the contr.tct?

ChapUf 6 Makinll Capilal ln\ tSlmenl De..."i ~iolb 20 1

33.

34.

Replaceml'nl Decisions Suppose we <Ire thinking about replacing an o ld computer wi th II new one. The old one cost us S65O.000: the new one will cost $780.000. The new madline will be depreciated stfllight-Iine to zero over its !i\'e-ye;tr life. It \\; 11 probubly be worth abou t S140,000 .. fler fi\"~ years.

The o ld compu ter is being dcprl.ocitltoo at a rllte of S130.000 per year. It will be completely written on' in thn..'\: ycars. If we don't replace it now. we will have to replace it in two yea rs. We can sell it now fo r $230.000: in two years it \\;U probably be worth S9O.000. The nl.'"\\· milchine wi ll SlI\'C us $ 125.000 per year in operating costs. The tax ra,,' is 38 perCCIlt. and the diSl'OUlll r:ltc is 14 percen t. u. Suppose Wo! r;,.'cognize that if we dOIl't replace thl' computer now. wc will be

replacing it in two years. Should W\': replil(',(, now or should ,",,'C \\';.Iit? (iii",; What we cflectively have here is a decision eit her to "invest" in the old compu ter- by not selling it- o r to invcst in the new one. Notice that the two im'estmcnts h .. vc unequalli\"cs')

b. Suppose we considcr only whether ..... e shoult.l replacc the o ld computer now wi1h­ou t worryi ng about what's go in g to happen in two ycars. \Vhlll arc thl' relevan t cilsh nows"? Should we replacc it o r not'? (H i",: Con sider the net chllnge in the fi rm's aftertax cash nows if we do the replaCCmelll.)

Project Amllysis BenSOIi Enterprises is e" .. luiuing alternative U S\..'S for iI three-story manufacturing ~nd .... 1uehousing building that it has purchaSl.-d for $850.000. The comp."1ny can con tinue to rent tbe bu ilding to the pn..'SCnt (x:cupallls for S36.000 per ye .. r. The p~nt occupan ts hnvc indicated an interest in stayin g in the building for .. t least another 15 years. Alternat ively, the (.·omp.'lny could mod ify Ihe ex isting struc. lure to use fo r its Own Illlllilifactu ring ilnd w:lrchousing m:cds. Benson's production engint.~r feels the building cou ld be adapted to hilndk olle of two ncw product lines. The cost and revcnue data for the two product a lternat ives arc :IS follows:

Ini tial cash otJuay for building modifications

Initial cash outlay for equipment

AnnUill pretax cilsh revenues (generated for t 5 years)

Annual pretax expenditures (generat.d for 15 yeilrs)

Product A Product 8

$ <45,000

t65.000 135.000

60.000

$ 65.000

205.000

165.000

75.000

The building will be used for on ly 15 years for either product A or product 8 . Afte r 15 years the building will be too small for efficient production of either product line. At that time. Benson plans 10 ren t the building to firms similar to the current occup.'ln ts.. To rent th~ building ag;! in . Benson will need to restore the build ing 10 ils present layout . Tbe estimated cash cost of restoring the building if product A has been undertaken is S49.OOO. If product B has been manufactured. the cash cost .... ill be S35.000. These casf. costs can be deducted for tax purposes in the year the e)l;pen. d itures occur. ..

Benson will depreciate the original building shell (purchased for $850.1)00) m er a 30-year life to zero. regardless o f which alternative it chooses. The bu ilding modi. fiC"'.uions and equipmeut purchases for ei ther product are estimated 10 h:.!ve 11 IS-vcar life. They will be deprecia ted by the straight-l ine method. The fi rm's tax nne is 34 ·per. cent. a nd ils required ... te of ret urn 0 11 such investments is 12 percent.

Fo r simplici ty. assume all cash nows occu r at the end of the \'ear. The initial out­lays for modifications and equipment will occur today (year 0): and the restoration ou tla}'s will occur at the end of yea r 15. Benson has other profitable ongoing operd­tions that a rc sufficien t 10 cover any losses. Which use of the build ing would YOli recommend to management?

ZU2 Part II Valuation and Capillil Dudgcling

35.

36.

37.

Project Analysis and InOation T he Biological Insect Control Corporation (D ICC) has hired you as a consultant 10 evaluate the NPV of its proposed toad ranch. BICC pl.llls to bn.-ed toads and sell them as ecologically desirable insect co)1lrol mcchanisms. They an ticipate that the business will continue in to perpetui ty. Following the neg.ligible start-up costs.. DICC expects the following uominlll C<lsh flows at the end of the year:

Revenues labor COSts

Other COSts

$225.000

175,000 45,000

The company will lease machinery for $25.000 per year. The lease paymen ts start at the end of year I and are expresSl..'"d in nominal terms. Rc,renues will increase by 5 percent per year in real terms. L lbor costs will increase by 3 percent per ycar in real terms. Otber costs will increase by I percent per yea r in real terms. The rate of infla­tion is expected to be 6 percent per yea r. BICe's requi\"\.--d rate of return is 10 percent in real terms. The company has a 34 percent lax rate. All cash 110ws occur at year­end. What is the NPV of BICC's proposed toad ranch today?

Project Analysis and Inflation Sony luternation"l has an investment opport unity to produce" new HDTV The required investment on January I of this year is 5175 mi l­lion. The fi rm will depreciate the investment to zero using the straight-line method ovcr four years. The investment has no n..'Salc va luc after completion of the project. The fi rm is in the 34 percent tax bracket. Thc pritt of the product will be $550 per unit. in rca.! terms, and will 110t change over the life of the projcct. Labor costs for year I will be 516.75 per hour, in real terms.. and will increase:ll 2 percent per year in relll terms. Energy costs for year I will be $4.35 per physica l unit. in real terms. and will increase at 3 percent per year in rea l terms. The in fl ation rale is 5 percent per year. Revenues are received and costs are paid at year-end. Refer to the following table for the production schedule:

Physical production. in units

labor input, in hours

Energy ·llIput. physical units

Year I Year 2 Year 1 Year 4

150,000

1,800.000

175.000

160.000

2.000.000 195,000

180.000

2.100.000

205,000

170.000 1.800,000

200,000

The real discount rate fo r Sony is S percent. Calculate the NPV of Ihis project .

Project Analysis and InOation After extensive medical and markcti ng research. Pill, Inc .. believes it can p.::nelTate the pain relievcr market. It is considering two alter­native products. The first is a medication for headache pain. The second is a pill for headache and arthritis pain. Both products would be introduced at a price of $5.25 per package in real terms. The hcadache-only mediCAtion is projec ted to sell 4 million packages a year, whereas the headache and anhrit is remedy wouJd sell 6 million packages a year. Cash costs of production in the first year arc expected to be 52.45 per package in real tenns for Ihe headaChe-on ly br.t nd . Production costs are CXIX'CtOO to be 52.75 in real terms for the heu.dache and arthritis pill. All prices and costs arc expected to rise at the general in Oatioll rate of 5 perceill.

Either product requires further investment. Thc headache-only pill could be pro­duced using equipment costing SIS million. That equipment would last three years and have no resale va lue. The machinery required to protluce the broader remedy would cost 521 million and lasttitrc(: years. The finn expects that equipment to have a 51 million resale value (in rcalterms) atlne end of year 1

Pill. Inc .. uses straigh t-Iinc depreciation. The firm faces a corporate tax rate of 34 percent and believes thatthc appropriate real discoullt r.:lle is 13 percent. Which pain reliever should the linn produce?

t.lIlIpll'r 6 Making COlpi lal hm."Slmcnt Deeisions 203

38. Calcu.latin~ ~roject NPV J. Smythe, Inc., manufactures fine furnituTC. The com­~n~ IS dccldmg wl~ether ~o introduce a new mahogany dining room table sct. The SCt ~11I sell fo~ S5/,()(), I~cludlllg a sct of eight chairs. The company feds that sa les will be ,8~, 1,9.)0. _.5~. _.350, and 2,100 SCts per year for the ne.'\t five years. respttt i\'dy.

Vafl.lble costs WIU amoun t to 45 percent of sales. and fixed cosls arc Sl 9 ." . ye'lI": Th " bl '11 . . . Illl IOn per

, : . c nc\\ ta. es ~I reqUIre I~Ventory amounting to 10 percelll of sales, pro-duced .md s.tockptled III the year prior to sales. It is believed that the addition of the new table wtll cause a loss of 250 L"1blcs per year of the- oak tables the company pro­~u:cs. These ta~les sell for ~.500 and have variable costs of 40 percen t of sales. The JO\t:!lI01j' for thls.oak table IS also 10 percent of sales. J. Smythe current ly has excess produ~t l.on capacJty. if t.he company buys the necessary equipment today. it wiU cost $16 ~mllhon . H.oweve~, the exce~s production capacity means the COmpany can pro­~~cc I~e oew table wllhout buylO~ the n(:w (:q uipmcnL The compa ny COntroller has ~al~ that the cur~ent excess capaclly will cnd in two years with current production T?IS means tbat If the company uses thc current excess capacity for the new table. i~ wil l be ~orccd to spend the S I6 million in two years to accommodate the increased sales of l t~c~rrc.n t products.. In fi ve years. the new eq uipmen t will have a market valuc of ~3. 1 mll ~lon If p~rchascd today, and S7.4 million if purchased in two years. The ~U\pmelll IS deprecIated on a s~ven-year MACRS schedule. The company has a ta.'\ rate of 40 percent. and the req UIred return for the project is 14 percellt. a. Should J. Smythe undertake the new projcct? b. Can you perform an fRR analysis on this projL'"Ct? How many IRRs wou ld vou

cxpectto find? • e. How would you interpret the profitability indcx?

BETHESDA MINING COMPANY

Bethesda ~i ning is a midsizcd coal min ing company with 20 mines 10C'lted in 01 . Pc~nsy~vanl<l_ West Virginia . 'lI~d K~ntuck)'. The company operalCs decp mtnes as WCI;I~~ stnp nllnes. Most of the coal mlO<!d ts sold under contract. wi th excess productio 'd thl' spot market. n so on

. The cOil l. mini~g indtlst~y, especi'l lly high-sul fur coal operations such as Bethesda. h.,s. beCIl. h.ud-h n by envlronrncntal regulations. ReceDlly, however. a combination ?f mcrca:.t."'(! demand for coal and new pollution reduct ion tecbnologies has led to an lrn'provc~ marke~ dem and for l?igh-sulfur coal. Bethesda has just been ap,;roached b ~td-OhlO Elect nc Company wlI.h .a request to supply coal for its elet.:tric genenllors IO~ ~ e n~.'\t four yea rs. Bethesda MlnlTlg does not have enough excess capacity a t its exis t­~ns m.llles to guarantee tb~ contract. The company is consideril)S opening a strip millc ~n O~~o. on 5,0(}() acres of lan.d purchased 10 yea rs ago for 56 million . Based 011 a reccnt .tppraIStll, the company feels It cou ld receive $7 million on an aftertax basis if it sold the land today.

:trip mining is a pr.ocess where the layers of topsoil above a coa l vein om: rem oved an th.e ~xposed coal tS L'Cm~)\'ed. Some ti me ago. the com pany would simply remove the C~.ll ,llId leave the land HI. an unusable condition. Changes in mining regulations ~o~ o rce a company to reclaUl1 the land; that is, when the mining is completed the an must be restored to. n~ar it s original condition. The land can then be used fo r

ot her pu.r~o~es. .B~ause It IS curreml.y operating at fu ll capacity. Bethesda will need to purc!la:;c addltl<>.nal necessary equIpment. which will COSt $85 million . T he c ui _ l~lent WIll be depreera.ted on a seven-year MACRS schedule. The COnlract ru ns fo rqonf , ~our years. AI th~t tune the COil1 from the site will be entirely miJled. The corupa ll~' ~: I s th at t~e, eqUlpment can be sold for 60 percent of its initial purchase price in four

::.e.l ~s. Ho\\e\er. Dethesd~ plans to open another strip mine at tha t time and will use the t:qlllpment at the new mme.

2 .. P1lrl n Valmuion amI Carll", RuJ~c!iI1S

The contract ca lls for tbe delivery of 500.000 tons of coal per yc .. r i ll a price of 595 per Ion. Bethesda Mining fecls that coal production will be 620,000 IOns. 680.000 Ions. 730.000 Ions. and 590,000 Ions. respectively. owr the nc;u fou r y~·ars. The. excess produc< lion will be sold in the spot markcl at an avcmgc of $90 PC-f Ion . Variable costs amount to $3 1 per ton. and fi xed I..'Osts arc S-l.300J)()() per yea r. The mine will require a net work­ing Cap1I;!1 invl!Sl mcni o f 5 pe rcent o f sales. The NWC will be buil t up in the year prior to the SOlie:>.

Bethesda wi!l be responsible for n.:daiming the land III term inatio n of the mining. This will occur in year 5. The comp.1.ny Ll SCS an outside company for [1,.'\:1<lI11<1\iol1 of al1 the company's strip mines.. 11 is estimated the COSI of rccl;lIllalion will be- $2.8 million. After the land is rl.'daimcd. the company plans to donate thc land to Ihe sUI te fo r use aS :I public park and recreation area . This will ()(."Cur in ye:tr 6 and result in a ("htlritable c.'I;pcnsc deduction of S7.5 million. Bethesda faces a 38 percent tax rate and has a 12 percent required retum on new strip mine projects.. Assume that a loss in auy year will result in a tax credit.

You h:we been approached by the president of the comp:l n)' with a request to analyze the projf..'Ct. Ca leulate the payb:lck period. prolitabilily index. avcrage accounting return. tlet present "a[ue. internal r:lte of ret urn. and modilied internal rate of return lor the lIew strip mine. Should Bctbewa Mining (;Ike Ihl;' contmct and open the minc'!

GOODWEEK TIRES, INC. After extensi\'e resean:h :md development. Goodwcck Tires.. Inc .. has rL-ccnt [y dcyc\opt..'<i a new ti re. thc SupcrTread. and must docide whcther to make the in\'(.'S tment nf..'CeSSl:lry to produce and market it. The ti re would be ideal for d ri\'ers doing a l:trge :!lnount of wei weather and ofY·mOl d drivi ng in addi tiol1 to norm:ll freew:'IY us-Ige. The research and deve[­opment COSIS so far have totaled about SI O millioll. The SupcrTread would be put 011 the mnrket beginning this yea r. and Goodweck ~;(pecl$ il to slay on the market for a to tal of four years. Test marketing costing S5 million has shown Ihal Ihere is a significant market for a SupcrTread.type tire.

As a financial an:llyst al Goodwcek Tires.. yo u ha" e been ask(.'<i by yo ur CFO. Adam Smith . to e\'.aIU:lIe the SuperTread projcct and pro\ ide a recommendation on whcther to go ahead with the in\'est ment . Except for the initial in"estmenllhal will occur immediately. assume:all cash nows wil [ occur:1I vear--cnd.

GoodwlXk must initially iOVCSl SI40 million in production equipment to make the SupcrTread. This equipmcnt can be sold for 554 million at the end of four years. Good­w(."Ck intends 10 sell the SuperTread to two distinci markets:

I . Tht' original eqllil'III('1/f IIwmljiu'wrer ( OEM) /I1(1rl..-(' I: The OEM market consists pri­mari ly of Ihe large automobile companies (like Gencr.u Motors) that buy tires for new ca rs. III the OEM market. the SuperTread is expected to sell for 538 per tir(·. The vari­able COSI to produce each lire is $22.

2. The rep !m·ell/('lII l1/ar/..'('f: The rep!;lccment ma rket consists of alilires purchased after the au tomobile has left the factory. This market allows higher margi ns: Goodw(.'Ck cxpects to seHlhe Supt.'rTread for S59 per ti re there. Variable costs are th.e same as in the OEM ll1iJrket.

Goodweek T ires intends to raise prices iJt I percent above the innalion rate: variable COSts will a lso increase at I percel1t :thovc the inflation mte. In addilion. the SuperTread project 1;\;11 incur S26 mill ion in markcring :tud general :tdminist r.Jtion COSIS the firsl year. This cost is expected 10 increase a t the inflation r.tte in the subsequent years.

Goodwcek's corporate tax rate is 40 pen:em. Annual inflation is eX(X'Cled 10 rem:lin conslll nt at 3.25 percent. The company uses a 15.9 percent discount rate to eva luate new produc t decisions. Au tomotive industry analYSIS expecl au tomobile manufaclurers to produce 5.6 million new cars this year and product ion to grow at 2.5 percenl per year

2'"

thereafter. Each new Cllr needs four tires (the SJXlre ti res are undersizt.'<i and are in a diOer­em eme!!'ory). Goodw«k T ires expects the SupcrTrcad to capturc II percent of the OE M market.

. Industry ana lY~ls e~ t imate that Ihe rcplaccment ti,re market size will be 14 million ti res thiS year and Ihalll wlllgTow at 2 ~rceru annually. GoOOwf..'Ck CXJX.'Cts Ihe SuperTread to capture an 8 perf..-cnt market share.

The. a~propriatc depnxiation sched llie for the equipmcnt is the sc\"cn-\'car MAC RS deprecl:lllon schedule. -r:he i ml~'<ijatc initial working capita l rcquiremcllt 'is $9 million. Thereafter. the nel. work.lIlg capJlal requi rements will be 15 pert:ent of sales.. Whal are toe NPV, payback penod. discounted payback period. I RR . and Pion this projcct:'

2116

Risk Analysis, Real Options, and Capital Budgeting In the summer of 2008. the movie Speed Racer. starring Emile Hirsch and Christina Aied,

spun its wheels al the box office. The Speed Racer slogan was ~Go Speed Racer, Go!" but

critics said, "Don'l go (see) Speed Racer, Don't go!~ One crilic said, "The races fell like a

drag.~ Others were even more harsh, saying the I1"I<Me "was like spending two hours carom·

ing through a pinball machjne~ and ~a long, dreary. migraine-inducing slog."

Looking al the numbers, Warner Brothers spent close 10 $150 million making the movie,

plus millions more lor marketing and distribulion. Unfortunately for Warner Brothers, Speed

Racer crashed and burned at the box office. pulling in only $90 million worldwide. In fact,

about 4 of 10 movies lose money in theaters, though DVD sales often help the final laity.

Of course, there are movies thaI do quite well. Also in 2008. lhe Paramount movie Indiana

Jones and the Kingdom of the Crystal Skull raked in about $780 million worldwide at a pro­

duction cost 01 $185 million. Obviously, Warner Brothers didn't plan to lose $60 or so million on Speed Racer. but it

happened. As the box office spinout of Speed Racer shows. projects don't always go as

companies think they will. This chapter explores how this can happen, and what companies

can do 10 analyze and possibly avoid these situations.

7.1 Sensitivity Analysis, Scenario Analysis, and Break-Even Analysis One main point of 1his book is that NPV ana lysis is a superior capital budgeting technique. In facl. because the NPV approach uses cash flows rather than profits.. uses a ll the cash nows. and discounts the cash flows p roperly. it is ha rd to find any theoretical fault with it. However. in our conversations with practical businesspeo­ple, we hear the phrase " a f~ lse seose of security" frequently. Tbese people poim o ut thai the documeOiation for capital budgeting proposa ls is often quite impressive. Cash nows are projected down to the last thousand dollars (or even the last dollar) for each year (or even each moot h). Opportunity costs and side errects are handled quite properly. Sunk costs are ignorcd-also quite properly. When a high ne t present value appears at the bottom. one's temptation is to say yes immediately. Neverthe­less. the projected cash now o ft cn goes unmet in practice. and thc firm ends up with a money loser.

Sensitivity Analysis and Scenario Analysis How can the firm get the net present value te(hnique to live up to its potential? One approach is sensith'i!y altalysis, which exami nes how sensit ive a particu lar NPV

Ta ble 7.1 cash Flow Forecasts lor Solar Electronics Corporatlon's Jet Engine: Bue Case (millions)'

OOplff 7 Risk AnalySIs, Reli t Op(ions. and Capilill 8ud!!.:"1;1I!

, Revenues

Vilriable casu

Fixed COSts

Depredation

Pretax profit

Tax (t, .. .304)

Net profit

ea.h /low Inidal Invenmeot cosu

Year I Years 2-6

$1.500

$6.000

3.000 1.791

....lQQ S 909

309

S 600 $ 900

~As~. ( I ) Itwutment" depo'eci:oted In ~ 2 tftrouch (j \IlIn.c mcltn!&ht·IM method: (2) WI "". Is l~ poI't .... t:(l) <he compIl1)'..., ....... no <aX bmc-lits lor Inklal deveiopmenttosu.

calculati?n is to ~hanges in undcrlying assumpt ions. Sensitivity ana lysis is a lso known as wharf analYSIS and ,hop (best. optim istic. and pessimistic) analysis,

Consider the rollowlng e~ample: So lar Electronics Corporation (SEC) ha s recemly ~evel0JXX! ~ ~o lar-powe:,:,-d Jet engl~e and wan.ts. to go ahead with full-scale produc­tion. The lnilml (yea r I) InveSlmentls S I.500 million. followed by production and sales over Ihe next fi ve yea rs. The prelim inary cash now projection appears in Table 7.1. Sh~uJd SEC go a head with investment in and production of Ihejet cngine, the NPV at a dlscouol rale of 15 percent is (in millions):

NPV _ - $ I 500 + ± $900 . ,.d I.l 5)"

= - $1.500 + 5900 x A'u "" SI ,5 17

Bec~ use the NPV i ~ po~itive. baSi: financia l theory implies that SEC should accept Ihe prOJect . However. IS thiS atl there IS to say about the venture? Before actual funding, we ought to check out the project 's underlying assumplions about revenues and costs.

Revenues Let's assume that the markeling department has projecled annual sa les to be:

Number o f jet engioes Ma rket share Size of jet engine

so ld per year x market per year

J.OOO .30 x 10.000

An.nual sa les Number of jet Price per revcnuc,s engi nes sold x

eng:inc . $6.000 mj.ll.ion 3.000 x S2 millio n

Thus. it turns out tbat the revenue estimates depend on three assumption s:

I , Market shu re.

2. Size of jet engine market.

3. Price per engine.

• Fin:IIK:ial cU~lom. generan>' d('Si~alC'S )'.:":If 0 as - Ioday." How~'ff . .... 1; use year 1 ItS lod;!)' in Ihis ('.':'Imple' be-cltuS(' taler In (hIS cha pTer we Will consid~ r :lnolh.:"r dccis i('>n mllde a year earlier. Thill deciSion will have occurred 1;11 )'("oIr O.

208

Table 7.2 Different Estimates

lor Solar Ellctronics' Solar Plant Engine

P;lrt II Valuation anu Capital Budg~lin!!.

Variable Pessimistic Expected or Best OptimistiC

Market size (per year) 5,000 10.000 20,000

Market share 20% 30% 50%

Price $1.9 m11lion $2 million $2.2 million

Variable cost (per plane) $1.2 million $1 million $.8 million

Fixed COSt (per year) $1,891 million $1.791 million $1.741 mill ion

Investment $1,900 million $' ,500 million $1.000 million

Costs Financial analYSIS frequently divide costs illlo two types: Vari'lblc costs and fi xed costs. Variable costs change as the OUipUI changes. and they are zero when pro­duction is zero. Costs of direct labor and raw materials arc usua lly variable. It is com· mon to assume that a variable cost is constant per unit of output. implying that tolal variable costs are proportional 10 the level of production. For example. if direct labor is variable and one unit of fina l output requires SIO of direct labor. then 100 units of final output should require S 1.000 of direct labor. . .

Fixed costs are not dependent o n the amount of goods or services produced durmg the period. Fixed costs are usually measured as costs per unit of time, such as rent per month or salaries per yl!ar. Natura lly. fi xed costs arc not fixed fore ver. They are fixed

only over a predetermined time period . . . . The engineering department has estimated variable costs to be SI million per cngUle.

Fixed costs arc Sl , 791 million per year. The cost brca kdowns are:

Variable Variable cost Number o f jCt engines per unit

x sold per year cost per yea r

53.000 mi llio n S I million x 3,000

Tala I cost before Variable COSt Fixed cost per yea r = +

taxes per yea r per year

$4.791 millio n $3.000 million + $1. 791 million

These estimates for market size, market share. price. variable cost, a nd rtxed cost, as v,>ell as the estimate of initial investment, are presented in the middle column of Table 7.2. These ngures represent the firm's expectations or best estima~es .o~ the difren:nt . p~rameters. For comparison, the finn 's analysts also prepared both OptlllUStlC and pessmusuc forecasts for each of the different variables. These forecasts are provided in the table as well.

SUindard sensitivity analysis calls for an N PV calculation for all three possibilities of a si ngle va riable. a lo ng with the expected forecast fo r all olher vari~b\es. This proc<;d~ is illustrated in Table 7.3, For example, consider the N PV calculatIOn of $8, 154 mllho n provided in the upper right corner of th is table. This NPV occurs when t~e optimistic forecast of 20,000 units per year is used for market size while all other vanables are set at their expected fore;asts from Table 7.2. Note thaI each row of the middle column ~f Table 7.3 shov,'s a value of $1.51 7 million. This occurs because the expected forecast IS

used for the variable that was singled out. as weU as for all other va riables. Table 7.3 can be used for a number of purposes. First, taken as a whole, the table

ca n indicate \vhether NPV analysis should be trusted. In other words, it reduces the false sense of security we spoke of earlier. Suppose that NPV is positive when the e.'\,pccled forecas t for each variable is used . However, further suppose. that ever~ n~~­ber ill the pessimistic colwnn is highly negative and every number 111 the opt101ISt iC

Table 7.3 NPV calculations (S In millions) lor the SOlar Plane Engine Using Sensitivity Analysis

Chilpler 7 RI.sk Analy).i •. Real Oplions.. and Capilat Budgeting 209

PessimistiC Expected or Best OptimistiC

Market size - $1 .802· $1 ,517 S9, I S4\ Market' share - 696*' 1.517 5.942

Price 853 1.51 7 2,844

Variable cost 18' 1.517 2.844

Fixed cost 1,295 1.5 17 1.628

Investme nt 1.208 1,5 17 1.903

Under sensitivity analysis. one input is varied while all other inputs are assume<! to meet their expectation. For example. an NPV of - $1.802 occurs when the pessimistic forecast of 5.000 is used for market size. while all other variables are set at their expected forecasts from Table 7.2.

'We ... ume tha, the odIer djyjsoons of the form'n! pror'<Jble. lmpIyin& that a lau on this prol« , can ofloe, income eh.e·..t.e ... in the ~rm .• herd»' reducinJ: dIC <M:r.III <Jxes of the form.

column is highly positive. A change in a single forecast greally alters the NPV eSlimate. making one leery o f the net present value approach . A conservalive manager might well scr<lp the entire N PV analysis in this situat ion. Fortunately, the sola r plane engine does not exhibit this wide di spersion because aU but two of the numbers in Table 7.3 are positive. Managers viewiog the table will likely consider NPV analysis to be userul for Ihe sola r·powered jet engin e.

Second. sensitivity analysis shows where mo re informal ion is needed . For example. an error in the estimate o f invest men I appears to be relatively unimportant \x."Causc, even under lhe pessimistic scenario. tbe N PV of $1,208 million is still highly posi­tive. By contrast, the pessimistic forecast for market share leads to a negative l\.rpv of - $696 million , and a pessimistic rorecast for market size leads to a substaniialJy nega­tive NPV of -$1,802 million. Because the effect of incorrect estimates o n revenues is so much grealer than the effect of incorrect estimates on COSIS. more info rmation about the factors determin ing revenues might be needed.

Because of these advantages. sen~it ivity analysis is widely used in practice. Graham and Harvcy~ repon that slightly over 50 percent of the 392 firms in their sample subject their capital budgeting calculations to sensitivity analysis. This number is particularly large when one considers Ihal only about 75 percent o f the firms in their sample use NPVanalysis.

Unfortunately, sensitivity analysis also suffers from some drawbacks. For example. sensi tivity an alysis may unwittingly il/uellSt' the false sense of security among manag­ers. Suppose all pessimist ic forecasts yield positive NPVs. A manager might feel th at there is no way the project can lose money. Of course, Ihe forecasters may simply have an o ptimistic view of a pessimistic forecast. To combat this. some companies do not treat optimistic and pessi.,niSlic forecasts subjectively. Rather. their pessimist ic fo rc· casts are always, say, 20 percent less than expected. Unfortunately, the cure in thi s case may be worse than the dfsease: A deviation of a fixed percentage ignores the fact that some variables arc easier to forecast thao otbers.

In addition, sensitivity a na lysis trcats each va riable in isolation when, in reality, the different variables are likely to be related. For example, if ineffective management allows costs to get out of control. il is likely that va riable costs, fixed cost s, and invest­ment will all rise above expectation al the samc·time. lf the market is nOI receptive to.1 $.Olar plane engine. both market share and price should decline togelhl!r.

~ See Figure 2 of John Gmham and Campbell Han·ey. "The Theory .. nd Practice of Corporate Finane.!': Evidence from the Fitld:' IQltrl1/I/ Q.( Firll/llcilll E CQIIQI/li<'s (Ma}'l'June 20(1).

21' Table 7.4 cash Flow Forecast ($ In millions) under th. Scenario of a Plane Cruh"

ParI IJ V~ l u;l lion and Capilal BudgO/ lin@

Year I Yca~ 2-5

Revenues Variable t osU

Fixed costs

Depreciation

PretaX profit

TilX (1, - .3-4)1

Net profit

Cuhflow

Inltill investmerlt cost

• AswmptlonS are:

- $1 .500

Harbc.a. 1.000 (70 pet'C_ 01 expeowiofl)

I"'tarbc w r-e ~ (VJ of ~ali<lfl)

forK>,. tI for" od'>u ~aria~ .. . re <1M ~ed IonasU'1 pn in Tabk ? l­

'T.,. loss olbeu ""0_ ~t in r.nn.

$2,800

1.400

1.791

300

- 691

~ - $456 - $156

Managers frequently perform sceuario ana lysis. a va riant of sensitivity analysis. to minimize Ihis problem. Simply pUI. this approach examines a number of diffe rent likely scenarios. where each scenario involves a confluence of factors. As a simple example, consider Ihe effect of a few airline crashes. These c ra shes a re likely 10 reduce nying in total. thereby limiting the demand fo r any new engines. Furthermore. even if fhe crashes do not involve solar-powen...~ <l ircrart , the public co uld become more averse to any inno-­valive a nd comrover'Sla ltcchnologics. Hence, SEC's market share might fall as well. Per­haps the cash no", cal<.: ulatio ns would look like those in T:'lble 7.4 under thc scenario of a plane c rash. Given the calculations in the table, the NPV (in millions) wo uld be :

- S2,023 = -S I,5OO - S I56 x I\ ~I~

A series of scenarios like Ihis might illuminate issues concerning the project better than the standard application of sensitivity analysis would .

Break-Even Analysis Our discussion of sensitiviry a nalys is and scenario analysis suggests lh at there are many ways to examine va riabililY in forecasts. We now prescnt anot her approach, break~\'en ana lysis. As its name implies. this approach determines the sales needed 10

break even. Thl! approach is a useful complement to sensitivity analysis because it also sheds light o n the severity o f inco rrect forecasts. We ca lculate the brca k-even point in terms of both accounting pro fit and present value.

Accounting Profit Annual ne t profit under four di fferent sales fo recasts is as follows:

Net Profit Annual Unit Sale.. ($ in millions)

o 1.000

3,000

10.000

- $1.180 - 720

600

5.220

Chap"~r 7 Risk Analyst!\, Real Oplion::;.. ilnd Capila l Budgtling

'" ,

Table 7.5 Revenues and Costs o f Project under Olfferellt Sales AssumpUOll9 (S in millions, except unit sales)

Year I Year'S 2~

Initial Annual 0 perating NPV Invelit· Umt Variable Fixed Depreci. Taxes· Net Cash (evaluated ment Sale.. Revenues Co .. t.. Costs atlon « - 34) P fi. FI

$1500 1,500

1.500

o 1,000

3,000

1.500 10.000

Figure 7.1 Bl'Nk·Even Potnt U-'ng Accounting Numbers

,- . ro ow .. date I)

$ 0 2,000

6,000

20,000

$ 0 - $1 .791 - $300 $ 711 - $1 .380 - $1,080 - $ 5. 120 - 1,000 - 1.791 - 300 - 3.000 - 1,791 - 300

- 10.000 - 1.791 - 300

Annual revenues

371 - 309

- 2,689

- 720 - 420 600 900

5.220 5.520

Variable costs per year

- 2.908

1.517 17,004

S2,1191 Fixed costs per vear (including depreciation)

2.091 Output (in terms of annu,l sales units)

The prelal( contribution .... 'gin per pillne is $1 million. n.e finn can recover its an?uIII'ixed c~ts of$2.091 million by selling 2.091 plenes. Hence, the brellk-.ven poun occurs WIth annual slles of 2.091 plll .. es.

A more complete prese nt ation of costs and revenues appears in Table 7.S . . ~c plot t he revenues. COsts. and profil s under the d ifferenl ass umptio ns aboUI sales 10 Flgu~e 7.1. The. revenue\and COSI curves cross at 2.091 jet engines. This is the break ­evcn point- th aI IS. the pomt where the project generates no profits or losses. As long as a n~ua l sales a rc above-2,09 1 jet engines. the project will ma ke a profit. . ThIS brea~-eve n point can be calculated very easily. Beca use the sales price is S2 mil­

hon pe:~ engine and the variable COSI is $ 1 million per engine,) the diffe rence between sa les Price an d variable cost per engine is:

Sales price - Varia ble COS I = $2 million - S I milli on = S I million

'Th.ough I ~ p!'e~'ious seclion (onsidcrC'd bolh optimistic and pessimiSl1c foro:caSIS for §.:lies pric-c- and "~lOable COSI. break-c-\'C1l anal)·si.$ US¢$ just the e~pecl«l or bes, eslimales of these \'s ri3b1es.

212 Part II V~lualjon and Capilal Budgeting

T his difference is called the preta x con lrioolioo ma rgin beca use each add itional engi ne contributes this amount to pretax profit. (Contribution margin ca n also be expressed on an aftertax basis. )

F ixed costs are 51.791 million and deprecia tion is $300 mHlion. implyi ng that the sum of lhese costs is:

F ixed costs + Depreciation = $1.79 1 million + $300 million "" $2,09 1 million

That is. the lirm incurs costs o f $2.09 1 mill ion per year, regard less of the number of sa les. Because each engine contributes $1 million. annual sales must re<tch Ihe follow· ing level to o ffset the costs:

Accounting Profit Break·Even Poi nt:

F ixed costs + Depreciation $2.09 1 million Sa les price Variable costs $1 million

2,09 1

Th us, 2,09 1 engines is the brea k-even poin t required fo r an accoun ting profi t. T he astute reader might be wondering why ta)ltes havc been ignored in the calcula·

lio n of break·even accounting profi t. The reason is that a firm with a pretax prolit of SO will a lso have a n aftertax profit of $0 beca use no taxes are paid if no pretnx profit is reported. Thus. the number of units needed to break even on a pretax basis muSI be equal to the nlllnber of units needed to brea k even on an .. flertax. basis.

Present Value As we have stated many l imes, we are more interested in presenl va lue tha n we arc in profit . T herefore. we should calculate breakevell in terms o r pres· ent va lue. Given a discoun t rale of 15 percent . Ihe solar plane engine has Ihe following Ucl present v .. lues for d irferent levels of annual sales:

Annual U mt Sale~ NPV ($ m illions)

o 1.000 3,000

10.000

- 5.120

- 2.908

1.5 17

17.004

T hese N PV calculations are reproduced rrom the last column of Table 7.5. F igure 7.2 relales the net presenl value o f bOlh the revenues and the costs to o ut put .

There are at least two di lTerenccs between Figure 7.2 and Figure 7.\. one of which is quite important a nd tbe other is much less so. First the less important poinl: T he dollar amounlS on the vertical dimension of Figure 7.2 are greater tha n Ihose o n the vertica l dimension of Figure 7. 1 because the net present va lues are calculated over five years. More illlporta nl. accounting breal<even occurs when 2,09 1 uoils are sold annually. whereas NPV breakevcn occurs when 2,3 15 uni ts are sold annually.

Of course. the NPV break-even point ca n be calculated directly. The firm origina lly invested SI.500 million . Th is initial investment can be expressed as a rive-year eq uiva­lent annual cost (EAC). detenni ned by dividing the ioi tial investment by the appropri· ate fi ve· yea r annuity factor:

EAC Initial investment Initia l investment - 5-yea r annuity factor at 15% A~"

$1.500 million . . - 3.3522 = S447.5 mIllion

Figure 7.2 BrH k·Even Point u sing Nat Present Value'

O apfl'r 7 Ris l; Ana lYS~ Rcal OplJOO5. and Capllal 8udgC:lillg

J ~ $10.244 M

Net pruent value of revenuas

Net present value of total costs

Net presant value of yariabla costs

$5,120 I""-----;-,£--::~"------~ Net present v. h,e 0' fi xed costs (includin.g

""'-___ --:-:!:;;-________ L depracialionl

2.31' Output (in tenns 0' annual sales units)

• Net present nlues of both revenues and costs are calculated on an aftertax basis.

Breakev.en i.n lanns of NPV occurs at a higher leval 0' sales than does breakaven 'or accou~ng Income. Co~anies thet just break even on an accounting basis ara not rtcoyenng the opportunity cost of the initial investment.

2JJ

Note t?3.t Ihe ~AC o r $447,5 million is greater than the yea rly depreciat ion of $300 rOll ho n. TIllS mUSt OCCur because the calcula tion of EAC 'mpr ' I h tl e $ 1 500 'li' . I lCIl Y assumes ( al

1 • ml Ion Investmen t could have been invested at 15 percent. Aflertax costs, regardless of OUl pUI. can be viewed lik e th is:

$ 1,5 28 $447.5 SI.791 million + million x .66 million

$JOO X .34 million

EAC + F ixed costs x ( I - f) - Depreciatio n X I

That is. in addil io n to the ini tial investmen~ 's equ iva lent annua l cost of S447.5·mill ion. the fi r~ ~ys rixed ~osl s. each. year and receives a depreciation tax shield each year. T he deprec la t ~on lax. shield IS wnth~n as a negative nu mber beca use it o ffsets the costs in the eq~atlon . Each plane cootnbutes 5.66 million 10 afierlax pro fi1. so i( will take the rollowlng sales to offset the COSIS:

P rescnt Value Brta k· E~·en Point:

EAC + Fixed costs X-{ I - t) Depreciation X 1

(Sa les price \!~riable~costs) x ( I I) C

$ 1.528 million $66 'II ' =2.315 . ml Ion

Thus, 2.~ 15 planes is th.e break-even poinl from Ihe perspect ive of present va lue. .W~y IS the account lllg b,:ak-evcn point different rroOl the fi nancia l break -even

POint .. When ~ u.sc accounl l~g proli t as the basis ror the break·even calculation. we subtract deprecIat ion . DeprecHHlon fo r tbe sola r jet engines project is $300 mi llion year. Ir 2.09 1 solar ~et. engines are sold per year, SEC will generate sunicient reven~~ :ov cover t.he ~300 ~1~~lon depreciation expens~ pl us other costs. Unfo rt unately. a t this , ~ el o.f Stiles SEC ".111 not cover the economic opportuni ty costs o f the $1.500 mil. 10~ laid O~ I fo r the mvestment. If we take in to accoun t that the $1500 million could ~a\c been Invest~d. al 15 percent. the true a nnua l cost of the investment is $447.5 mi l. hon, not S300 mIllion . Deprecia tion understates the true COSts of recovering the initial

"' P.n Tl Valuation aDd Capia..1 Budgcli"g

investmenl. Thus companies that break even on an accounting basis are really losing mo ney. They are losing the opportuni ty cost of the ioiliai investment.

Is break·even analysis importan t? Very much so: All corporate execUlives fea r losses. Break-even analysis determines how fa r down sales can fa ll befo re the project is losing money. either in an accounting sense or ao NPV sense.

7 .2 Monte Carlo Simulation Both sensitivity a-nalysis a nd scenario analysis anempl to answer the question " What if?" However. while both a nalyses arc frequently used in the real wo rld, each has its own limitations. Sensi tivity analysis allows o nly o ne variable 10 change at a limc. By cont rast , many variables are likely to move al the same lime in the rcaJ world. Scenario ana lysis fo llows specific scenarios, such as changes in inflatio n, government regula­tio n, or the number of competito rs. Although this methodology is often quite helpful . it cannol cover all sources o f variability. In fact , projects are likely to exhibit a lot or va riability under just one economic scenario.

Monte Carlo simulation is a further allem pt to model real-wo rld uncertainty. Th is approach takes its name fro m tbe famous European casi no beca use it analyzes proj­ects the way o nc might analyze gambling strategies. Imagine a serious blackjack player who wonders if he sho uld ta ke a third card wbenever his fi rsl two ca rds lotal 16.

Most likely, 8 formal mathematical m odel would be too complex to be practical here. However, he could play thousaods of hands in a cnsino, sometimes drawing a third ca rd when his first two cards add to 16 and sometimes not drawi ng that third card . He could compare his win nings (or losings) under the two strateg.ies to determine which were better. He would probably lose a lot of money performing this test in a real casino. so simulating the results from the two strategies on a computer might be cheaper. Montc Ca rlo simulation of capital budgeting projects is in this spirit.

Imagine that Backyard s.,rbeques. Inc. (BBI), a manufacturer of both charcoal and gas grills, has a blueprint fo r a new grill that cooks with compressed hydrogen. Tbe CFO, Edward H . Comiskey, dissatisfied with simpler capital budgeting techniques, wants a Monte Carlo simulation for this new grill. A consultant specializing in the Mo nte Carlo approach. Leste r Mauney. takes him througb the five basic steps of the method.

Step 1: Specify the Basic Model Les Mauoey breaks up cash flow io to th ree components: annua l revenue, annual cost~ and initial investment. Tbe revenue in lI ny year is vicwed as:

Num ber of grills sold Market share of BBl's Price pe r by entire industry x hydrogen grill (in percent) x hydrogen grill

(7.1)

The cOSt in any yea r is vif!\ved as:

Fixed ma nufacturing costs + Variable manufacturing costs + Marketing costS + Selling costs

Initial investment is viewed as:

Cost of patent + Test marketing costs + Cost of production faci li ty

Step 2: Specify a Distribution for Each Variable in the Model Here comes the hard part. Let's start with revenue. which has th ree components in Equa­tion 7.1. The consuit llnt first models overa ll market size-that is. the {lumber of grills sold

Figure 7.3 Probability Distributions jor Indu S1tywlde Unit Sales, Market Shllre of BBI'8 Hydrogen Grill , and Price ot Hydrogen Grill

Clutpler 7 Risk Anelysis. Real Oplions.. and Capilal Budgeling

60%

~ .... :a • ~ e ~

"""

Panel A

60%

""" """

10 11 12 Next year's industrywide

unit sales (in millionsl

Penele

.... ~ 30%

:a • ~ e """ ~

'''''

$'''' ~O<----"~-:''=O-CIOL.,~I'-, Next year's indvltrywide

vnit sales (in millions'

Panel B

30%

25"

""" ''''' '''''

'" 1% 2% :J% 4% 5% B%

The market share of BBI', hydrogen grill next year

Positive random drawing (50% probability)

Expected

Negation ralldom drawing (50'% probabilityl

Fo! each of !h~ three variables, a drawi"" il generated by computer simulation. In addition. pnce per gnlllS dependent on industrywide vnit sales.

lIS

by' the entire industry. The trado'publicat ion Outdoor Food (Of) reponed thai 10 million gnlls of a~l t.)"peS were sold in the cont inental United States last yea r. and it forecasts sales of 10.5 ml.lIlon .ne~t y~r. Mr, Mauney. using OF's forecast and his own intuition , creates the follOWing dlslnbu llon for next year's sales of grills by the ent ire induslry:

Probability 20% 60% 20% NextYear's fndustrywide Unit Sales 10 million 10.S mUlion II million

The tight d.istributio.n. her~ re.nec~s t~e slow but steady hislOrical growth in Ihe grill market. ThiS probablilly dlstnbutlon IS graphed in Panel A of Figure 7.3.

ll6 PH" II Va l u~ti()n nnd CapiUlI 6ud!t1intE

Lester Mauney realizes that estimating the mark.et share of OBrs hydrogen grill is more dinkulL Nevenhelcss, after a great dea l of ana lysis. he determines the d istribu­tion of next year's market share :

Probability 10% 2Q';\; 30% lS'X. 10% S'X.

Market Share of BBI's Hydrogen Grill He.tYe at' 1% 2% 3% -4% 5% 8%

Whereas the consult an t ass umed a symmelrical distribution for industr)'\\,idc lInit sales, he believes a skewed dis tribution makes more sense for the project's market share. In his mind there is always tbe small possibili ty that sales o f the hydrogen grill wi ll rea lly take 01T. This prob"bility distribution is graphed in Panel B of Figure 7.3.

These fo rec'lsts assume thaI unit sales for the overa ll industry are unrelated to the project 's ma rket share. In other words, tbe two va riables are indc:p(,lItiem of each ot her. Mr. Ma uney reason s that alt hough an econo mic boom might increase industrywide grill S<lles and a recession might decrease them. the project 'S market share is unlikely to be related to economic condit ions.

Mr. Mauney must determine the distriblllion of price per grill. Mr. Comiskey. the CFO, informs him that the price will be in the area of $200 per grill. given what 0 1 her competitors are charging. However. the co nsultant believes that tlle price pe r hyd rogen grill will a lmosll:ertain ly depend on the si7.e o f the overall market for grills. As in any business. you can usually charge more if demand is high.

Aner reje~ting a number of complex roodels for price. Mr, Ma uney SC llles on the following specification:

Next year 's price Industrywide unil sales per hydrogen grill = $ 190 + $ 1 X (i n millions) +/- S3

(7,2)

The g.ri ll price in Equation 7.2 depends o n the un it sales of the industry. In addition. ra ndom variation is modeled via the term " +/ - S3:' when.~ a drawing o f +$3 and il

drawing of -S3 each occur 50 percent o f the lime. For example. if industrywide unit sa les are I I million . the price per share would be either of the following:

$ 190 + $1 1 + 53 = $204 (50% probability)

£ 190 + $11 - $3 = SI98 (50% probability)

The relat ionship between the price o f it hyd rogen grill and indu strywide unit sales is graphed in Pane l C of Figure 7. 3.

The consultant now has distributions for each o f the Ihree compQnenl:i of next yea r's revenue. However, he needs distribu tions for future years as well. Using fore<:aslS fro m OUldoor Food and o lher publication s. Mr. Mauney forecns ts the distribution of growth rates fo r the entire indust ry over the second year:

Probability 20% 60% 20% Growth Rate of Industrywide Unit Sales in Second Yea,. 1% 3% 5%

Given both the distribution of next year's industrywide unit sa les and the di stribution of growth rates for this va riable over the second year. we cao generate the di stribu­tio n o f indust rywide unit sales fo r Ihe second yea r. A sim il<l r ex tension sho uld gi,'e Mr. Ma uney a distribution for later years <IS well , though we woo't go into the detail s

ChapIN 7 Risk A n.ly~i$. Reli t 0 plions. ;,nd C;,pi tal Bud~lIn! lf7

h~re. A~d juSt as the consultan t e;( tended the first Component of revenue (indusIfY­Wide UI.ltl s?lcs) 10 later years.. he wou ld wa nl 10 do the same thi ng for market share and u mt pnce.

The preceding discussion shows how the Ihn .. "C components of revenuc can be modeled',Slep .2 ~ould be complete once the components of cost and investment are mo?el ed III a Simi la r way. Sp'-~ i al attention must be paid to the interactions between \'imables he~ because ineffective management will likely allow the dilTereni cost COIll ­

po,nenl s to rISe lo~elher. However, YOll are probably gelling the idea now. so we will skIp the rest of thiS step.

Step 3: The Computer Draws One Outcome ~s we said , next yea r's revenue in our model is the product of Ih ree component s. Inug­mc that the computer randomly picks industrywide unit sa les of 10 mill ion. a market share for ~Bl's hydrogen grill of 2 percent. and a + 53 random price variation. Given these d ntwlIlgs. nex t year's pr ice per hydrogen grill will be:

$ 190 + $10 + $3 = $203

and next yea r's revenue fo r BBrs hydrogen grill will be:

J 0 million X .02 X $203 = $40.6 million

Of cou~se , we are nOt d.o ne with the emire olltcome yec We would have to pcr­:orm drawmgsfor revenue In each future year. J n addit ion. we wo uld perform draw­mgs for cost s In each future yea r. Fi na lly. a drawin g fo r initial inve.stment wou ld have 10 ~ ma?, as well. In th is way. a single outco me. made u p of a drawing fo r each va ri able III the model . would generate a cash flow from the project in each future year.

. How likely is it that the specific Outcome d iscussed wou ld be drawn? Wc can a nswer thiS ~?use we know the probabili ty of eac h componen t. Because industry sales of SID million ~l~I S a 20 percent prob~ bi l ity. a market share of 2 percent a lso has a 20 per­ceut ~r~?ablhty. and a random 'price va riati o ~ of +S3 has a 50 percent probability. th e probabIli ty of these thn..'C draWings logether In the same o utcome is:

.0.2 = .20 x .10 x .50 (7,J)

Of course the pro ba?il.it.y ,;ould get even smaller once drawi ngs fo r future reve nues, fut ure Costs. and the IIlltlallllvest ment are included in the outcome

Thi~ step g~nerates the cash n ow fo r each yea r from a single ~Ulcome. What we are ultimately 10tcrested in is the tilslriburirll/ of cash n ow eac h year across many out­c~m:s. \ye ask ~he ~~mputer to randomly draw over a nd over again to give us this d lSln butlon. wh tch IS JlISI what is d ohe in the next step.

Step 4: Repeat the Procedure !he fir st th ree steps generale one ou tcome. but the essence of Monte Ca rl o simul ation IS repealed o utco mes. Dependi ng o n the si tuation, th e co mputer may be ca l!t:d on to g~?e~ate .thousands o r even millio ns of o utcomes. The result o f a ll these drawings is a d lstnbullon o f cash now fo r cach future yea r. This distribution is Ihe basic output of Monte Carlo simula tio n. . Consider Figure 7.4. Here, repeated drawings have produced the simulated d is tribu­~Ion ?f the third year's cash now. There would be. of course. a dist ribluio n like the one In thIS Cigure for each future year. This leaves us wi th j ust one more step.

218

Figure 7.4 Simulated Distribution 01 the Third Year 's Cosh Flow tor BBl's New Hydrogen Grill

7.3

Pnt II Valuation and O'piutl Budgcling

I

o ClISh rIow

In Monic Cario simulations. rcptau:d sampling or alllhl' variabks rrom a $pedlic mod~1 gcocMes a st:diSlical distribution.

Step 5: Calculate NPV . . . Given the distribution of cash now for the third year In Figure 7.4. one can dct~nlll~e (be expected cash flow for Ihis year. In a si mililr manoer. one can al so detcrnune t he expected cash flow for each fU lure year and lhen calculate the ~et present value o f t c project by discounting these expected cash flows at an appropn,.ue rate. . . . I _

Monte Carlo s imu\;.lI ion is o rten viewed as a slep ~yond cuher ~nsn lv l ty. ana ~ sis or scenario analysis. Inte ractions between the vanabl~s are explicitly speC1fie~ I~ MonIc Carlo: so (aileasl in theory) Ihis met hodology provides a more com plete a nal~ sis. And, as ~ by-product. having to bui ld a precise model deepens Ihe forecaster s

understanding of the proje<.:L . h Because Monle Carlo simulations have been around for at l eas~ ~5 years,. you mig t

think that most firms would be performing I~em by now. Surpnsll1g!y, thiS does no~ seem 10 be the cuse. In our experience. executives are frequentl r skeptica l ~f Ih.C .c~m

kxit v. II is difficuh to model either the distribulionsof e~ch variable or. the mteractlo~s ~e(w~n variables. In addilion, the computer output IS often. devOid .of econo mIc . .. Th s while Monte Carlo si mulations are used 111 certam rea l-world mtultlon. u . . t"; " 1 r I G raham . . 'the approach is not likely to be "the wave of the IUlUre. n ac. . snuallOns. r: . h· Ie t"'~ eapnal and HalVcyJ report that o nly about 15 percell! of the I Inns lil t elf samp "-budgeting simulations.

Real Options . [n Chapter 5 we st ressed the superiority of net present va lue (NPV) ana lYSIS over olher approa~hes when v<lluing capital budgeting projects. How~ve.~ bo~h sc~o:~r~ and ractitioners have pointed out problems with NPV. The bas~c I ea ere IS . • a NPl a nalysis, as well as all the other approaches in Chapter 5,. Ignores the adJ~I:; menls thal a firm can make after a project is accepted. These adjustments a rc ea

. I · dust" has pio"ce~tl app'ic-Jt;on~ of this methodo!· ' f',.lo re than perh:ap5 :any olher. the ph:armaceUL1C11 In . . .Ih ('FO Judy Oil.)'. For example. s« Nanc)' A. Nichols. "Sci~nlHk Mllna~mcnl OI l Mud:.: An jntervIC'W WI ~~n L·· J/uroord 8 .. si",SJ /w,.iroI· (Jalluar):I1·cbruarr t994 ).

'Sec figu re 2 of Gf"lIham lind H . .... "<!y. op. !;II.

Figure 7.5 Decision Tree fGr Ice HGtel

ChaptN" 7 Risk Anal),sii. Real Options. and c..p;tal Bud~el in! 219

real options. In this respect NPV underestimates the true va lue of a projec t. NPV's eonse rvati ~m is best expla ined thro ugh a series of examples.

The Option to Expand Conrad Willig, an en treprcneur, recently learned of a chemical treatment causing. water to rreeze at 100 degrees Fahrenheit ra ther than n degrees. Of all the many practical applica tions for this treatment. Mr. Willig li ked the idea of hotels made of ice more than anything else. Conrad estimated the annual c~lsh nows frool a si ngle ice hotel 10

be $2 million. based on an initia l inwstment o f 5 12 miUion. He felt that 20 percent was an appropria te discount rate. given the risk of this new venture. Believing that the cash nows would be perpetual, Mr. Willig determined the NPY of the project to be:

- $ 12,000,000 -+ $2,000,000/.20 = - S2 millio n

Most entrepreneurs would have rejected this venture. given its negative NPY. But Conrad was no t your typica l entrepreneur. He reasoned thai NPV analysis missed a hidden source o f va lue. While he was pretty sure that the initial investment would cost $12 millio n. there was some uncertaioty concerning annual cash nowS. His cash now estimate of 52 million per yea r actua lly renected his bel ief that there was a 50 percent probability that annual cash Ilows will be $3 million and a 50 percent probabili ty that annual cash nows will be 51 million .

The N PV calculations for the two forecas ts are given here:

Optimistic forecast: - S12 mjJlion + $) millionl.20 "" $3 million

Pessimistic forecasf : - S12 million + $1 millionl.20 = - 57 million

On the surface, lhis new calcula tion doesn·t seem to help Mr. Wi llig much. An average of the two forecas ts yields a n NPV for the projCCt of:

50'Vo x $3 million + 50% x (-$7 miJlion) = - $2 million

which is just the va lue he calcututed in the first place. However. if the optimistic forecas t IlIrns OUllO be correct , Mr. Willig wotdd Wa nt to

(':(pand. If he believes that there are, say, 10 lOCations in the country Ihal call sUpporl an ice hotel, the true N PV of the venture would be:

500/ ... X 10 X $3 mil/ion + 50% x ( - $7 million) "" $ 1 J.5 million

Figure 7.5. which reprcscnlS Mr. Willig's decision. is o f len ca lled u decision tree. The idea expressed in the fi gure is both basic and universa l. The entrepreneur has the option to expand if the pilot locat;on is succcssfu i. For example. think of all the people who start restaurants., most of them ultimately fa iling. These individuals are not

Build firsl iI:e Ilult!1

220 Pan 11 Valmllion 3ml Capillil Bud~ling

necess.'uily overly optimistic. The)' may realize the likel ihood of fai lure but go ahead any\vay because of the small chance of starting the next McDonald's or Burger King.

The Option to Abandon Manage rs a lso have the option \ 0 abandon existin g projccts. Abandonment n Ul)' seem cowdfd ly. but i1 ca n often save companies a great tlea l of money. Bct:ausc of this, the o ption to abandon increases the value of any potential project.

The example of icc hotels. which iUustr..t lL"!I the o ption to expand, can also illustrate the o ption 10 abandon. To sec this. imagine thl:ll Mr. Willig now believes that there is a 50 percent probability Ihut a nnual cash news will be S6 million and a 50 percent probability that nnnua l cash flows will be -$2 million . The NPV calculations under

the tWO forecas ts become:

Optimistic foret:lIst: - $ 12 millio n + S6 millionl.2 = S18 millio n

Pessimistic forecast: ~S l 2l1liJlion - S2 million/.2 = - $22 mi llion

yielding an NPV for the project o f:

50'1., x SIS million + SOC/., x (- £22 million) "" - $2 million (1.4)

Furthermore, now imagine that Mr. Willig wanls to own. at most. juSt one ice ho tel. im plying that there is no o ption to expand. Bec::ause thc NPV in EqU<Hion 7.4 is nega· live. it looks as if he will not build the hOlel.

But things change when we consider the abandonment opt ion, As of dille 1. the entrepreneur will know which forecas t has come tTue, If cash nows '--'qual those under the optimistic forecast. Con rad will keep the project alive. If, however, cash flo .... 'S equal those und~r the pessimist ic forecast. he will abandon the ho tel. If Mr, Willig knows these possibili ties ahead of time. the N PV of the project becomes:

SO'Y .. x SIS million + SO'v" x ( - S I2 million - S2 million/1.20) = S2, 17 million

Becausr: Mr. Willig abandons an er e:o;pe riencing the cash now of -$2 million a t date I, he does 110t have to endure this outflow in any of the later years. The N PV is now posi·

live. so Confl.ld will accept the project. The example here is clearly a stylized o ne. Whereas many years may p.1.SS bcforea proj­

ect is abandoned III the real world , our ice hotel was aba.ndoned "fler just o ne year. And , while sah'age vulues generally accompany abandonment, we assumed. no salvage value for the icc hotel. Nevertheless. aba ndonment options arc pervasive in the relll world,

For exam ple., consider the moviemak ing industry. As shown in Figure 7.6, movies begin with ei ther the purchase or development of a script . A completed script might cost a movie studio a few million dolll.lrs and polentially lead (0 aclua l production . However. the great majorit y of scripls (perhaps well in excess of 80 percent) are aban­doned . Why would studios aba ndon scripts that they commissioned in the first plucc? The studios know ahead of time that only a few scripts will be promising, and they don't know which ones.. Thus. they cast a wide net . commissioning many scriplS to get a few good ones. The studios mus t be ruthless wilh the bad scripts because the expeo­dilure here pales in comp<.l rison to the huge losses from producing a bad mo\·ie.

The few lucky scripts then move into production, where costs might be budgeted in the tens of millions of d ollars.. if not much more. At this stage, the dreaded phrase is that o o.locution production gets "'bogged d own." crcutlng COSI o\·crruns.. But the stu­dios arc equlI Hy ruthless hcre, Shou ld these overruns become excessive, production is likely to be abandoned mid slreum. Interestingly, abandonment almost a lways occurs

Figure 7.6 The Abandonment Option In the Movie Industry

Chapt~r 7 Risk An3lrsis. R~lI l Oplions. tlnd Capi! 'li Bud~l'tin& , <

CO{l lin ission ~ript

COl't

Hit:.h 1xJ\ ofrJCc r~I'l'nue

r---,~"",~,";""~""m,---... }(elea."<: upon compi~li"n

Prviluce movie:

'--_--;-___ ~ Aoondon Lvgt prior IU

c .. ~ (wtmm C"QITlpklion

~1o\ ie studios lIavl: JD:nldomnent uplion. throughout IIII! pn",IU .. 1ion of 3 lIIe'l Ie.

~h"o: ad\'c "i ~ins

Nu furth!'r udl'mhing

dL~c lt O. h~£h co~ts. n Ol d ue 10 the fear that the mOllie won't be able 10 find an a ull III c tn . ormation on that sea ,' II be b ' . lence.

R I fl · , . re"1 0 Willed unlll the movie is actually released c ease a t le movie IS accompan ied by significant ' d .. , .

haps ill tbe mnge of 5 10 to $20 million , ',' u. vertl sl.ng expendl~ures. per­ticket sa les but it will J"k I be b ' Ad, enblOg WIll conl lnue followlOg strong r' l ey a andoned arter a few weeks of pON box office

pefio rmalK't, Movicmaking is one of the riskiest busine d' . d reds of miJljon f d Jl . sses a rolln ,with studiOS receivi ng hun-

, so 0 an III a maile r of weeks from II blockbuster wh'l .. pr<lcllca lly nOlhing duri ne: this riOO fr " " e recelvll~g cost~ t,ha t might otherwi~ ban~IPt the~~d'~~~:'- The abando nment options con tam

E 10 ~,Uslrate sOllie of.t hcsc ideas. consider thecasc of Euro Disney. The deal to open uro tsoey occurred m 1987. and the park opened its dr ' "

~~:I~'~~lbelilgg~meTnth thOugbeht EUrr~~a ll s wou ld go gOO; ~\'~~t;I:!en~~Vn~~k~9:1~~ cln . e num r 0 vlsll ors never met "

company priced ticke ts too high. Disnev also decided ~~ttat!on~ m pan ~'("a use the try, that was aCCustolll'--'"<i to wine with ~eals. French I' bo .0 ~t'ne a~c~hoI1ll a.coUl~-stnct d ress codes, and so on. a r Inspector:'> lought OISlle) S

Afler several years of oper.llio th k be . e red ticket prices. ' d . d ' I n'd' e par gan scrvlllg wine in its resta ura nts. low-. an ma COt ler a ~lJ stments.. In ot her words. m',n ' Jls optio n to rcformu1illC Ibe prOOuc!. The p'lrk beg. t k: ageml· ent exerclscd Ihe com n ' d e ' ,n a rna e a sma I profit. Then a nother ::e~ee::~~exlt~ ~PHO~,IO e,'<pand by addil)~ a "second gate," which WilS

, uro Isney named Walt Dlsnev Studios. The second " was Intended to ellcour~.ge visitors to e:o; tend their stays. But -the new park nopped ~;Ie rea sons ra.nged from htgh ticke t prices. amaelions seared toward H U 'W : le th:tUIl EU

1 ropean IiI mmaki ng. labor strikes in Paris.. a nd a summer heat ~';\"e ood rathcr

y t Ie summer of 1003 Euro Disn ' ' I b . discussed a ra nge of op-ti ~ Th .e} Wcl S C ose to an~ruptcy again . Executives

o n.... escOpllOtlS ranged from le1l1Og Ihe b (t.he oplion to aba nd on) to pulling lhe Disney name from the 'I rk.c~~i:SY ~o rok~ puny finall y agreed to a restruc turing with the help or the F_nP'ch . 11e com

TI h I 'd' f " ,.. !!OVernment .

overs:rwo; ~i~n~~'; th~~~~:~~:~ ~~~~nhse :~ s~,mO~e'dt h~IP a~I IYk by J~y Rasul.o. the , mg \\e now lo r sure IS tha t

m

Figure 7.7 Decision Tree for Vacanl Land

Pari II Valu:uioo and C;lpita.l Bu~getinl!'

you neve r get it 100 percent rig.ht the firs! time. We open everyone o f o ur pa rks with the nolion that .... 't're gOil11,: 10 add conlcnt."

A recent example of a company actua lly exercising the option to abandon occurred in 2005 when Sony Corporation aono unced that it was withdrawing fro m the hand· held computer, or PDA, market in Japa n. Whal was somewhat surprising. was Iha\ Ihe compa ny was the market leade r in sa les al the time, with about one-~ hl1'd of Ihe market. Howevcr. PDA sa les had been shrinking over the past three years., In large paTl due to increased competition from smarl phones thaI have PDA capabilities. So. Sony concluded that the future markel for stand-alone devices was limited and bailed oui.

Timing Options One often finds urban land that bas been vacanl for maoy years. YCt this land is bough t and sold from time to time. Why wou ld anyone pay a positive price for land that bas no source of revenuc? Cerlainly, one could not arrivc at a positive price thro ugh NPV analysis. However. the paradox can easily be explaincd in terms of real options.

Suppose Ihalthe land's highest and best use is as an olliee building. Total construc· lion costs for the building are estimated 10 be $, 1 milliOIl. C urrently. net rents (a fter all costs) are estimated to be $90.000 per year in perpetuity, and Ihe discount ra le is 10 percent. The NPV of thi s proposed building would be:

- $ 1 million + $90,000/.10 = - $100.000

Because this NPV is negative. one \\!Quld not currently want to build. However. sup­pose that the fed eral government is planning various urban revita l~tion progrums f~r Ihe city. Office rents u-ililikely increase if the programs succeed. to thlscasc.. the ~ropert~ S owner might want to ereet the office building afler all. Conversely. office rents WIU remalO the same, or even fall . if tbe progrilms fai l. The owner will n01 build in this case.

We say that the property owner has a liming 01";011. Ahhou~l she does n?t currently want to build , she wi ll want to build in the future should ren ts In tbe a rea nse substan­tially. This timing opLion ellplains why vacant land often has va~u~ There arc costs. su~h as taxes. from holding raw land. but the value of an office bUl ldmg aft er a substantial rise in rents may more than offset these holding cost$. Of course the exact value of the vaca nt land depends on both the probabil ity of success ill ihe revitalizatio n program and the extent of the rent increase. Figure 7.7 illustrates this timing option.

Mining operations almost a lways provide timing options as wel l. Suppose you own a eopper mine where the cost of mining eaeh ton o f eopper exceeds the sales revenue. It 's a no-brainer to say thai you would not want to mine the copper currently. And because there are costs of ownership slich as property taxes, insurance. and security. yo u might actually want to pay someone to take the mine off your hands. However,

00 001 build)'et bef:a11.<;e

rents:lnl '00 \Qw.

Rents rise substantially. Em,:, offICe building.

Rcnrs ei'ho.'t' stay lhe same Of filII. '--=-=='-""--. Do rIOt build yet.

Vacant tand rna)' ha\c n .luc today bcoI;:ausc (bt: o ... ·llCr can Cf'eCl a profi'ableofricc building if ron,s rist.

Chaplet' 7 Risk Anat)'$is. Real Op,lons.. and Cap;'al Bud8t l in~

we would caution you nOllO do so hastily. Coppe r prices in the future might increa se enough so tha t production is profitable. Given that possibi lity. you could li kely fi nd someone who would pay a positive price fo r Ibe property today.

7 .4 Decision Trees As sbown in the previolls section. managers adjust their decisions on the basis o f new information. For exa mple. a project may be expanded if early experience is prom is­ing. whereas the sa me project might be abandoned in t he wake of bad results. As we said earlier, the choices available to managers are cal led rcol oplions and all individual project can often be viewed as a series of real options, leading to v4l luation approaches. beyond the basic present value methodology of ea rljer chapters.

Earlier in this chapter. \ve considered Solar Eleetronks Corporation's (SEC's) solar­powered jet engine project . wi th cash Oows as shown in Table 7. 1. In then example. SEC planned to invest SI.5OO million at year I and expected to receive $900 million per year in each of the next five years. Our calculat ions showed an NPV of 51 ,5 J 7 million . so the firm would presumably wa nt to go ahead with the project. .

To illustrate decision trees in mo re detail. let's move back o ne yea r to year 0, when SEC's decision was more complicated . At thai time. the engineering group had devel­oped the technology for a solar·powered plane engine. but test marketing had not begun . The marketi ng depa rtment proposed that SEC develop some prototypes and conduct test marketing of the engine. A corporate planning group. including represen· tatives from production, marketing. and engineering. estimated that this preliminary phase wou ld take a year and cost $100 million . Furthermore. the group believed there was a 75 percent chance that the marketing test wou ld prove successful. After comple­tion of the marketing tests, SEC wou ld decide whet her to engage in fu ll·scale produc. lion. necessita ting the investment of S 1.500 m.iJl ion.

The marketing tests add a layer of complexity to the analysis. Our previo us work on the example assumed that the marketing tests had already proved successful. How do we ana lyze whether we want to go ahead with Ihe marketing tests in the fi rst place? This is where decision trees come in.

To recap, SEC faces two decisions. both of which are represen ted in Fi{ture 7.8. First the firm must decide whether to go ahead with the market in g tests. A~d if the tests are performed. Ihc firm mUSt decide whether the results of Ihe tests warrant full ­scale production. The important poi nt here. as we will see, is that decision trees answer the two questions in reverse order. So let's work backwa rd . lirst considering what to do with the results of the tesfS, which ca n be either successful or utl successful.

ASSIIII/c' tes/S "uI'e been .fllccess!1I1 ( 75 pert'e/1f probability). Table 7.1 tells us thai full-scale productio n will cost 51,500 mil lion and will generate an annual cash now of S900 miUion fOJ fi ve years, yielding an NPV of:

± $900 ;;:: - $1.500 + ,_l(TT5"')l

= -$1.500 + S900 X A~,

= 51.517

Because tbe NPV is posi tive. successful marketing tests should lead to (ull·scale production. (Note Ihat the NPV is calculated as of year I. the time a t which the im'CSlment of $1.500 million is made. Later we will discount this number baek to year 0, when the decision on test marketing is 10 be made.)

Figure 7.8 DeclslonTnHt tor SEC (5 millions)

Pan 11 Valuat ion ,Llltl Capit;l l Budgeting

No IcSI

______ ( T~t Tc.-uhs I I\"\'cakt.i

YCaT I

Initial inWSlnlc flt -51.500

(75% prub;lbi lit)' l

IJ\J 001 in"cst

Failure

(25'N probability)

Squares rqlI\:..'>('nl deci~ion poinl~. Circle ,....prcsc:nL~ n:a:ipt uf infonnatioo.

SEC InU)!. J\I~J;e 1"'0 d¢ci~ions: I. \Vhcttln' 10 de,'clop aoot':-1>1 til<! engine. 2, WhMhl..,.to i n\'l"~ fl'C" fun·",,':.l!! prodtll.'li')Il,

W ilh d<x l~ion IKCS, <k>.:ision~ ~ m:ode in rc\'cTh<' onkr.

NPV - 51517

Ni>V ... O

NPV", -53,611

NPY "' O

A fSllllle /t'.\·rs 1/(/1'£' /101 bet' ll sliccessflll (15 pt.' I'C(!1I1 probability) , Here. SEC's $ 1.500 n~illion investment would produ~ 311 NPV of - S3 .. 611 million. calculated as o r year I . (To save space, we will not provide Ihe r~w numbers leading: to this ca l~ul~. tio n.) Because the NPV here is negat ive, SEC Will not want rull·scale production Ir

the marketing te$tS ;tre unsuccessful.

D('risioll 011 marketing It'SIS. Now we kn ow what to do with the ,result s or Ihe mar· ket ing teSIs. Lct's usc these resuli s {Q move ba~~ o ne yea r. That IS. ~e ~ow w~nt. 10

ligure out whether SEC sho uld invest $ 100 mllhon for the test ma rketIng costs III

the li rst place.

Theexpccted payoff evaluated al date I (in millions) is:

Expected of x if + or x (

Probability Payon') ( prObabilil )'

payoff success successful railure

".. 1.75 x $1,5 171 + (.25

= SU J8

T he NPV or testing computed a t date 0 (in millions ) is:

i ) ,138 NPV = -S IOO +"Ti")

= 5890

x

Payon' ;r

railure

SO)

Beca use t he NPV is positive, the li nn should lest the market lo r solar-powe red jet

en~ines.

Surruuary and Conclusions

Concept Questions

( lI:tpt ..... 7 Risk Allaly~is.. R~a! Or" ions. and Capillli Dud~c:(in2 125

Warning We have used a discount ra le o f 15 percent for both Ihe testing and Ihe investment decisions. Perhaps a higher discoun t ra te shou ld have been used ro r the initia l test marketing decision , whicb is li kely to be riskier than the investmen t decision..

Recap As mentio ned above. the analysis is graphed in Figure 7.8. As CRn be seen from the ligure. SEC must make the ro llowing two decisio ns:

I . Whether to develop and lest the sola r-powered jet engi ne.

1. Whether to invest for full-sca le production fo llowing the results of Ihe teSI.

Using a decision trec. we answered tile second question before we answered Ihe first one.

Decision trees represent the best approach 10 solving SEC's problem, given Ihe

informatio n presented so r<lr in the text. However, we will exam ine a more sophis ti ~ cated approach 10 va lui ng options ill a la ter chapter. Though this approach was lirst used to value fina nc ial options traded on organ ized o ption exchanges, it ca n be used to va lue real opti ons <IS wel l.

This chapter d iscussed a num~r of prtlctica l ltpplical ions or capil<ll budgeting.

I. Though NPV is the best capital budgeting approach conceprual1y .. il has lx-en criticized in pr.lctice ror giving managers i1 fal se sense or st:cu ri IY. Sensi tivity analysis shows NPV under \~.lryi ng assumptions. giving ma n;lgers 11 better feel lor the projcct's risks. Unfor­tunately. sensitivity an;llysis modHies only one variable at i1 time. but many vari;tblcs are likely 10 vary toget her in the real world . Scenario ana lysis e:<amincs a project's per­formance under d iO"eren t sccllarios (such as \\~dr breaking QU I or oil prices skyrocket­ing). Finally. managers want to know how bad forCCilsts must be berore.1 projl.'Ct 10St.'S

money. Bn::itk -evcn analysis calcu la les the sales figu~ ill which the project brca ks e\cn. Though break·even analysis is frcq uel11ly performed on itn account ing profi t bitsis.. we sugg("St Ih.1t a nel present vll luc basis is more appropriate.

2. Monte Cit rio simulation begins with a model of the firm's cash nowS. b;tscd on bot h Illl' inlera(.;tio l1s bel ween diOcrent v;l ri,tbles and Ihe m.,wem<tnl o r each indi"idual vari· able on~r time. Random slIlllpJing generates a dist ribution of Ihe~ cash Oow$. for each period, leading 10 a net pres.cnt va lue calculat ion.

3 .. We anillyzed the hidden oplions in (apit;t! budgeting. such as Ihe option to e .... p;md. Ihe optioll 10 abandon. and liming optioll:i.

4, Dl'Cision trees represenl ~n approach for va luin g projects wilh these hiddcll. or real. options.

I, Fort'C3sting Risk \Vhal is rorecast ing risk? In geneml. \\ould Ihe deg~c of forecast· ing risk be greater ror a new product o r 11 (';osl<u ll ing proposal'.' Why'.'

2, Scnsiri\'it)' Anal~'Sis and Scenario Anal~'sis WI:I.II is the essential d ilTeren~ belween ~nsiti \'ity analysis and scenario analysis','

J.. ~1arginal Cash Hows A coworker claims that looking at all this marginal this alld increment.al Ihat is just a bunch of nonsense. and Slates, "·listen. jJ our average

22'

Questions and Problems

connect BASIC (OuutJons 1- 10)

~

1'"ul II Valuation and Capital Budgeting

4.

5.

6.

7.

8.

9.

10.

I.

2.

revenue doesn' t exCt.'Cd ollr avcrag.! cost, then we will bave a negative cash now. imd we will go broke!"' How do you respond?

Brcak·Ewn Point As a shareho lder of a lirm Ih'lI is corllcmpla ling a new proj­ect. would \IOU be more concerned wilh the accounting break-even point. the cash brcak~\'cn poi III (Ihe point at which operating cash flow is zero), or the fin;1IH..'iul brea k-even point? Why?

8rcaJ.:-E\·clI Point Assume u finn is considering a new project thai requires an ini­tial tnvesuncnl and has equal 5.1les and costs over ils life. \ViII the project reach Ihe accounting. cash. or financial brca k..e\'cn point first ? Which will it reach next? L.lst? \Vjllthis order always ,'ppl),?

Real O ptions Wby does Irdditional NPV .malysis tend to underestimate the true \'alue or a capital budgeting project?

Real O ptions The Mango Republic has just libcr.tlizcd its mark7ts and is. no\~ per­mitting foreign investors. Tesla Ma nuracturing has al1:1lyzed star\lIlg a proJ~t III the country and has determined that the project has a ll.eg:l ~i\·c NP~ Why might tbe company go ahe,ld wilh Ihe project'! What Iype of opllon IS most likely to add value to this project?

Scn.'ii thity Analysis and Brcp ke,·en How does sensitivity analysis interael \\'i lh break-even ;malysis?

O ption to Wait An oplion can orten huvc more ~han onc source of ~alue. Cons.ider a logging company. The company can log the timber I~~Y or walt anOlher ~'ear (or more) to log the timber. What advantages would w;utlllg onc ye..1r potenually haw?

Proj«1 Analysis You ' U'e discussing a projoci analysis with a coworker. T he ~roject involvcs real options. such as c.'(p'lnding the proj(.'Ct .if suC(."CSsfu l. or ab~ndonmg. lh.e project if it fails. Your coworker makes Ihe follOWing sl~lcm.ent : "TillS ana lYSIS IS ridiculous. We looked at c,"(panding or abandoning the proJcct III two years. bu~ there are many olher options we should consider. ,",or examplc .. we could expand III one year. and expand further in two yeilrs. Or we coul~ exp.lI1d 11\ one yea.r. and abandon Ihe project in two yeilrs. There are too many opt ions for us to examine. Because ~f this. anything this analysis would give us is worthless. ... How w~uld you evaluate.thls statement? Considering that with any ca pital budgeung proJect. there a-: a.n . Infi­nite number of real options. when do you Stop the option analYSIS on an IIldl\'ldual project?

Sfnsirh·it)' Analysis arK! Break-E\'cn Point We <Ire evaluating a project Ihut CO~lS S724,000. has an eight-year li fe. lind has no sulvage va luc. Assume thai deprecm­tioll is strail!ht-line to zero over the life of the project. Sa les are projected at 75,000 uoils per ye7tr. Price per unit is S39, variable cost per unit ~s S23, and fh;ed costs are S85O.000 per year. The tax mte is 35 percent, and we reqUIre a 15 percenl return on this project. a. Calcul:ne the aecountiog break-e\·en point. b. Caleulate the base-casc cash flow and NPY. What is the sensitivity of ~PV I~

changes in the S-..1.les figure? Explain what your answer tells you about a 500-Ulllt decrease in projeclcd sales. .

c. What is the sensitivity of OCF to changes in the variable COSI figure·! Explain what your answer tells you about a SI decrease ill estimated variable costs.

Scenario AnalYsis In the previous problem. suppose tbe projcctions given for price. quantity. variable costs. ilnd fi xed costs are all accurate to within .=: 10 percer1l. Cal­culate the besl-case and worst-case NPV figures.

Ch.plfr 7 Risk Analysis. Rt'~ 1 Oplions. and C:lpirill Budgt ling 227

3.

4.

5.

6.

Calculating 8rcakc\'tn In each of lhe following cases. fi nd the unknown \'ariable. Ignore taxes.

Accounting Umt Vanablc

Brcakcvcn Unit Price Cost Fixed Costs Depreciation

110.500

143.806

7.8]5

. ., lOS

,,0

" $ 820.000

].200.000

160.000

$1.1 50.000

105,000

Financia.l Break(,'·en LJ. ·s Toys Inc. just purchased a S250,000 machine to proouce toy cars. The machine will be fully depredated by the st raight-l ine method over its fi ve-year economic life. Elich toy sells for $25. The variuble COSI per toy is $6. ~tnd the fir m incurs fixed costs of S360,000 each year. The (.'Orpora te tax ra te for Ihe COOl­

p.my is 34 percent. The 'lppropriate discount rate is 12 percent. What is Ihe financial break-e\"en point for the project'~

O ption 10 Wail Your company is deciding whet her to invCSI in a ncw mach ine. Tbe new machine .... ill incrcasecash flow by S340.000 per year. You believe the technology used in the machine has a 10-year life: in other words. no mailer when you purchase the machine, it will be obsolete 10 years from today. The machine is currently priced at $ 1.800.000. The COSt of the machinc will decline by $ 130.000 per year until 11 reaches 5 1, 150.000. where il will remain. If your required return is 12 percclli. should you purchase the machine? Lf so. when should you purchase it?

Decision Trccs Ang Electronics. Inc .. has developed a new DVDR. If the DVDR is successful, the present value of the payoff (when the product is brought 10 markcl) is 522 million. If the DVDR f:tils. the present value of the payoff is $9 million . If the prodUCI goes direct ly to market. there is a 50 percent chance of success. Alternatively. AnS can delay the launch by one year and spend SI.5 million to test market the DVDR. Test marke ting would allow the firm to improvc the product and increase the probability of success to 80 percent. The appropriale discount rolte is I I percent . Should the firm conduct test marketing?

7. Decision Trees The manager for it growing firm is considering the launch of a new product. If the prodUCI goes directly 10 market. there is a 50 percent chance of .suc­cess. For SI35_000 Ihe manager can conduct a focus group tlull will increase the product's chance of success 10 65 percent. Ahernmively. the manager has the option to pay a consulting firm S400.ooo to research the market and refine the product. The consulting firm successfully launches new products 85 percent of the lime. If tue (irm successfully launches l'he product. the payoff will be SI.5 mi ll ion. If Ihe product is a failure. the NPV is zel0. Which action will result in the highcsi expected payoff to the firm?

8. Decision Trees 8&8 has a new baby powder ready to market. If the firm goes directly 10 the market with the producI, there is on ly it 55 percell! chance of success. However. the firm can conduct customer segment research. which will lake a year aod cost S 1.8 million. 8y going through research. B&1l will be able to better target potentia l customers and will increase the probability of success to 70 percent. I f suc­cessful. the baby powder will bring II present value profi t (at time of ini tial selling) of S28 million. If unsuccessful. the present va lue payon' is only $4 million_ Should the firm conduct customcr segment research or go directly to market? The appropriate discount rate is 15 percent.

228

INTERMEOIA.TE (a uesl ions 11-25)

P:arl II V;aluation and Capital Budgering

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Financial Break-EH:n Anal~'s is You om! considering investing in a comp;any Ihm (" uh ivates abalone for sale \0 Joe:11 rcs!Uur;tnls.. Usc the following info rmatio n:

Sales price p!r abalone = $90

Variable cosu per abalone = $5040

Fixed costs per year = $750.000

Depredation per year = $5 1.·H9

Tu rate :=: ]5%

The discount rale for Ihe company is 15 percenL lhe initial investment in equipmcllI is $360,000. and tbe projcct"s economic life is seven years.. Assume the ("'qlupmcnl is dcprechtled on a stntigh t-linc basis over the project's life. a. What is the accou nting break-even level for the projccl? b. What is the IIn an,,!:! i brcak-evcn level for the projecf?

Financial Breakel"cn Niko has purcilaSc.--d a br.l.nd new machine \0 produce its High Flight line of shO\.'S. The machine has an economic life of five ycars. The deprecia­tion schedule for the machine is straight-line with no salvage va lue. The machine costs $390.000. The sales price per pair of shO\."'S is $60. wh ile the va riable cost is S1 4. 5185.000 of lixcd c:osts per )'car a re att ributed to the l11achinc. Assume thatthc corpo rate tax rate is 34 pen.-cnt and the appropriate discount mtl! is 8 percellt. What is the financial break-even point?

Brc!l k-En~n Intuition Consider a projttt with a rcquil\."'d return of R percent that costs SI and will last for N years. The project uses st raight-line depredat ion 10 zero over the ,v.year life: there are neither ~11v:.ISe val ue nor lIet working C".Ipital requiremen ts, &. Atthe accounting brC'.tk·cven level of output. what is thc IRR of this project? The

payback period? The NPV? b. At the cash break-even level of output. what is Ihe IRR of this projttt"! The pay­

back period? The NPV? c. At thc filllln(.'ial break-even level of output. what is the IRR of this projcct'!The

payback period'! The N PV,? Sensith'ily Amtlysis Consider a four-ycar project with Ih..: follo\\~n£ information: Initiillli:'(ed ;lSset investment = S380.000: straight-line depreciat ion 10 zero o\'Cr the fou r-year life: zero salvagc val ue: price = S54: v:..riilblc costs:::: S42: fixed costs = SI85.000: qmllllit)' sold = 90.000 units: lax rate = 34 pen.'I."llt. How sensitive is OCF to chan~es in quantity sold'~

Project Ana l ~'sis You an: considering a new product l:nmch. The proj~"Ct will cost S960.0CH:l. havc a four-year life. and have 110 sa lvage \~dlue: deprecialion is slr.lishl­line 10 zero. Sales .m: projected at 240 uni ts pe r year: price per unil will be S25.(}()O: variable cost per unit will be SI9,500: and lixed costs will bc S83O.000 per ye:Jr. The required return on the projt."Ct is 15 pcn.-cnt. ilnd Ihe relevant tax mte is 35 IJCrcCIII. it. Based on your expt!riellcc. you think the unit sa les. \'ariable COSI. and fi;l(cd cost

projections givcn here arc probably accurate 10 within ~ 10 percen\. Whilt ilre the upper ilnd lower bounds for these projcctions1 What is the basc-<:asc NPV"? What are the best-case and worst-case scenarios"?

b. Evaluate the sensitivit), of your basc-casc NPV to ch'lIlges in fixed costs. e. What is the ilccomning break -even le\'el of output for this projccl?

Project Ana lysis McGilla G ol f has decided to sell :t new line of gol f dubs. The dubs wi ll sell for S750 per sel and have a \'ilriable cost of S390 per SCI. The com­p<lIly has spen t SI50.000 for a marketing study that detennined Ihc company will sell 55.000 sets per year for scven years. The nmrketiog study also determined that the compauy will lose sa les of 12,000 SCIS of its high-priced clubs. The high-priced cl ubs sell at $1. 100 and have v:lriable costs of S620. The company will also inctellSC S<lles of its cheap clubs by 15.000 sets. Tho: cheap clubs sell fo r 5400 and have variable

Ch~pl<'r 7 Risk Anulysis. Real Oplions. and Olpitlll Bmlgcling

IS.

16.

17.

18.

19.

20.

21.

costs of S2 10 per set. The IIxed (.'Osts each yea r will be $8. 100.000. The comp'lny h' . also. spent 5 1.00?'000 ~n resclm:h lind development for the new clubs. The p l ~tn t a~~ eqU!PLllcnt r~ulred \\:~II cost SI8,?<X!,OI?O and w.ill be depreciated on;\ straight-line baSIS- ~he ne\\ clubs \\ III also require an Inc rease III nel working capilal of S 1,400.000 that w~ll ~ returned :11 the end of the project . The tax nlle is 40 pcl\.'CnL and the COSI

of capJta l ls 14 percent. Caleulllle the payback period. the NPV. and the IRR ~n.ario Ana lYSis lnlhc previous problem. you fee l thUlthc values arc accll'rate to wl~hLll on ly ~ 10 percent. What are lhe best-case and WOrs\<;ISC NPVs? (Him: The pnce ilUd vanab~e costs for the two existing sets of cl ubs 1m: known with ccrta int . only Ihe solles gamed or lost arc ulK:ertain.) y.

SeDsit i \' i~~' Anal)"~is MeGil!;1 Golf would like to know the sensi livity of Nfl\, to ~~l:! I~~~ III the pnce of the new clubs and the quantity of new clubs sold . Whm is the )c nslllvity of the NPV to each of these V"Miablcs'!

Abandonment Value We are examining a new projcct. We expect to scll 9 000 IInit' per ~e.~r at $50 net ~dsh O?W apiece fo r the nex t 10 years. In o ther words. tile lInnua~ Opcnlllllg cash now IS projected to be $50 x 9 000 = 5450 000 Th I d' . . . . . . .. e rc evaJit ISCOU nl rate IS 16.pcrcent. and the II1l11al mV('stment req uired is SI.900.000. 3. What IS the base-case NPV? b. After the first year. I~e projecl ca n be dismantled and sold for SI.300.OOO. If

e.xpccted sa les arc reVIsed based on the 11rs! year's perfonmlllcc. when would it ~ake sense ~o abandon the investment'? In other WOrdS-lit what le\"el of ex!"-'Cted solles ~ould It make sense to aba.ndon the projl.'Ct?

e. Explal.n how the $1,300.000 abandonment v:.l luccil n be viewed as the opportunity cost 01 keeping the project in one year.

~band~nmcnl }n the pre\'iolls problem. ~u~pose you think it is likely thai eXJ)I.'Ctcd sollcs \\ 111 be re\' lscd upward 10 11 .000 Units If thc IIrst year is a success and revised down\\~.Ird to 4.000 units if the first y~il r is not a success. ' A. If success lind fai lure are equally likely, what is the: NPV of the p-' ,'/ C 'd

'h 'b' I' f b '''JCC. onSI cr e po.SSI I tly 0 a ilndonment in ansv.'ering. b. What IS the value of the option to abandon?

Ab~lIdonmenl and Exp~nsion In the previous problem. suppose the scale of the project. can be dOl:bled III one yeilr. in the sense that twke as mao)' unit s ca n be pro. duced .lI1d ~o~d. ~:lI l1rall~. expansJ~n \\'?uld be desirable only if the project were it s~ccess. ThiS mlpites Ihot If the prOJCCI IS a success. projected sa les 'Ifter expo •. WI ]] be 2' 000 A' . h • .II1Slon

-. . ga.11.I ~ssumrng t at success and railure are equally likclv, what is th~ NPV of 11.le proJect! Note that ab;mdonment is still an option if the p~jcct is a fmlurc. What IS the va lue of the option to c.'tpa nd?

B~a"-E\"('I) Analysis Your buddy comes to you wi th II sure-fire W:t" to ma ke some qUick mOlle~.a nd help pay ofr your student loans. His idea is to sell T-shirts "jlh Ih' wor~s .. , get a ll them. "You get iI1" Hc SOtys. "You sec all those bumper stickers an~ T.s~lns that say '~ot milk' or 'gol surf.' So Ihis says. ., get.' It 's funny! All we have to do IS buy a used Silk ~reet1 press for $3.200 and we are in business!" Assume there a re no fi:'(oo ~ts. and yo\! ~eprcc ia le the $3.200 in the first period. Taxes are 30 percent. n. What IS the aocoontmg b~ak·e\"en point if each shirl costs 57 to make 'lIld \OU

can sell them for S I 0 ilpiece? ' .

No~v assume one yea r h:~s passed and you have sold 5.000 shins! You lind oUlthat the D"lry Farmers of Amenca have copyrighted the "gOt milk" slogan .. nd are requiring you to pay $ 12.000 to cont inue oper.u ions. You expt:\:t this craze will last lor anothe~ th ree ye:trs and that your discoun t rate is 12 percent .

b. Wll"t is the linancial break-even poi nt for your enterprisc now':'

~ion Trees Young st'reell\l'riter Carl Dmper hllsjustllnishcd his firslstTipt . It has action. dr~ma, : Uld hum~r. ~nd he thinks it will be n blockbuster. He t:tkes thc SCriPI to e~'Crymollon ptcturestu~lo III to\V1'I and tries to sell it bulto nOll\'ail. Finally. ACME stu­dlOS alTers 10 buy the scn pt fo r either ta) 5 12,000 or (b) I percent of the movie's profits.

Pari II Valuation and Clipital lJudgcting

Then: are twodccisions the studio will have to make. First is to dccide if the script is good or b.1d. Clnd second if the movie is good or lxtd . First. there is a 90 percent chance that the script is b.1d. If it is b.1d. the studio does nothing more lind throws the script OUi. If the st:ript is good. they will shoot tbe movie. Aficr the movie is shot, the studio will review it. and there isa 70 perrent chance that the movie is b.1d. if the mov;c is b.1d. the movie wiU not be promoted and ,~;II not tum a profit . If the movle is good. the studio will promote heavily: the lwcrage profit for this type of movie is S20 million. Carl rejects the SI2.000 a nd says be \\~dnts the I percent o f profits. Was this a good decision by Carl?

22. Option to Wait Hickock Mining is evalu.1ting when to open a gold mine. The mine has 60,000 ounces o f gold left that elln be mined. and mining opcnuions \\111 produce 1.500 ounces per year. The requir<XI return on the gold mine is 12 percen!. and it \\111 COSt $ 14 m.illion to open Ihemine. When the mine isopened. thecompan), will sign a contrdCt that \\; 11 guarantee the price of gold for the remaini ng life of the mine. If the mine is opened today. each ounce of gold will generate an aflf!rta~ C'dsh !low of S450 per ounce If the company waits one year. there is a 60 percellt probability Ihal I.he contrdct price will gencrate an aftertax cash now of S500 per ounce and a 40 percent probability Ihal the ;lnerta~ cash flow wi ll be $4 1 0 per ounce. What is the value o f the optio n to , ..... .til?

23. Abandonmcnt ~ecisions Allied Products, loc .. is considering a new product launch. The firm expects to have an annual operating cash now of $22 million for Ihe next 10 years. Allied P roducts uses a discount nile of 19 pen.."Cnt for new product launches.. The initial invest lilent is $84 million. Assume tha t the project hus no salvage value at the end of its e<:ono mic life. a. What is the N PV of the new prod uct? b. Aft er the first year, the project ca n be dismanlled and sold for S30 miUion. If the

estimates of remaining cash nows are revised oosc.:d on the first year's e;\perienee. at whatle"el o f e:q>l:ctoo eash nows does it make scn~ 10 abandon the project?

24. Expansion Decis.ions Applied Nanotech is thinking about introducing a new sur­face cleaning machine. The marketing depilrtment has come up with the estimate thilt Applied N:lIIotech can sell 15 units per year i1 t S410.000 net cash now per unit for the ne~t live years. The engineering depilrtment has come up with the estimate thilt developing the machine wi ll take a $17 million initia l investment. The fina ncc depanment has estimated that a 25 percent discount ra tt: should be used. a. Whal is the oosc-c:a sc N PV! b. If unsuccessful. after the fi rst ye:tr the project C,II1 be dismantled and will have an

aftertax salvage V'"diue of SII million. Also. after the first year. expecled cash nows will be revised up to 20 units per year o r \0 0 un its. wit h equal probability. Wh:tt is the revised N PV?

25. Sct'nario Anal)'sis You arc the financial ana lyst fo r a tennis racket manuf:tcturer. The company is considcriog usi ng a gr,lphitelike material in its tennis r.tckets. The compmly has estimated the info rmm ion in the following table about the market for a rackct wit h the new m.lIerial. -n e company expects 10 sell the racket fo r six years. 11le equipment req uired for the project hlls 110 salvage va lue. The required return for projects of this type is 13 percent . lind the company h:ls a 40 percent ta~ rate. Should you recommend the project:

Pessimistic Expected Optimistic

Market sile 1)0.000 150.000 165.000

Market share 21 % 2'" 2"" Selling price $ 1.0 $ 1<5 S ISO Vari.;Jble cosu per unit $ 102 $ .. • " FiKed cosu pu year 51 .015.000 $ 950.000 $ 900.'" Initial invesrment $2.200.000 $2.100.000 $2.000.000

QjALLENGE (Que.tlon.26-30)

Chapter 7 Risk Anal~·sis. ReH l Options. and Cllpi tal Rudgt ting 231

26. Scenario Analys.is Consider .. projl.'Ct losupply Detroit with 55.000 tons of ll111chi l1e screws ann ually for automobile production. You will need an ini tial S I. 7OO.000 investment in threading. equipment to get the project started: tht: projL'Ct will la st for five years. The accounting depilrtmen! estimates tha t a nnual fixL-d costs will be S5·20.000 and that varillble costs should be S220 per tOil : accounting will depreciate the initial fixed asset in .... estmeot straight· line to zero over the fi,"c-year project life. It also estimates a s,1lvage value o f $300.000 after d ismantling costs. The market­ing department estimates that the :tutolllakers will let the contract at ,I scll ing price o f S245 per ton . Tht: engineering department estimates you '\111 net.-d an initial net working capi tal investmen t of S600.000. You require a 13 percent return and face II marginal tax r.lte of ]8 percent on th is project. a. What is the est imated OCF for th is project? The N PV? Should you pursue this

project? b. Suppose you believe that the accoullling deparlment 's initial cost and salmge

value projcct ions lire accurate only to wi thin .:!: 15 percen!; the marketing dCI);'lrl' menl's price estim:tte is :tccurate o n ly to wi lhin .:!: 10 percent; and the cngineering department 's net workin g capita l est im:tte is accurate only to within ~5 percent. What is you r wo rst-case scenario fo r this projcct? Your best<asc scenario? Do you st ill want to pursue the project?

27. Se.nsitiyity Analysis In Problcm 26. suppose you're confiden t about your own pro­jectio ns. but you 're a li ttle unsure abou t Detroit's actual machine screw req uiremen ts. What is thc sensit ivi ty of the projcct OCF to changes in the quanti ty suppui!d'! What about the sensitivity of N PV to chllnges in quanti t), supplied? Given the sensitivity numbe~ you calcu lilted , is there some minimum level of outpu t below which you wouldn t wa nt to opcmte? Why?

28. Abandonment Decisions Consider the fo llowi ng project for Hand C lapper. Inc. The company is considering a four-yea r p roject to manufacture dap-c:ommilnd g:t mge door openers. This project requires an initial investment of SIO Olillion tbat wiJl be depreciated straight-line to 7..ero over the projc."'Ct's life. An initial investment in net working capital o r S I.3 million is required 10 support spare parts inventory: this cost is rully rccO\'Cfablc whenever the project ends. The company believes it can gener.lIc $1.35 million in preta~ revcnues with $2.4l11illio n in total pretax operating costs. The tax rate is 38 percent. and the discount ra te is 16 perceut. nle market value of the equiproelll over the Hfc o f the project is as follows:

29.

Year Market Value ($ millions)

I

1 )

•

$6.8

6.2 3 .•

0.0

Ill. Assuming Hand ~appcr opemtes this project for four years. what is the N PV? b. Now compute the project NJ>Vs assuming the: project is lIbandoned lifter only one

year. after two ycars. lind after three yea rs.. What economic lire for this project maximizes its valuc to the finn? What docs this p ro blem tell you abou t oot con­sidering abandonment possibilities whcn evaluating projccls?

Ab:ilndonmenl Oec:: isions M.Y.P. a:tmcs. Inc .. has hired you to perfoml a feasibil­ity study of a nC\\· vidco game that requires a S5 million initilll investmen t. M.V.P. expects a tolal annual opcrdting cash now of S880.000 for the next 10 yea N.. T he relevan t discount mte is 10 percellt. Cash Hows occur <It yea r-end. a. What is the PV o f thc new video game? b. After one yellr. the cstim:ne of remaining allnual cash nows will be revised either

upward to S I.75 million o r downward to $290.000. Each revision has an equal

ParI II V:lluatiou aud Capital Dl,lu~"1:ling

probability of occurring. At th,lI lime. Ih~ video game projeet ca n be sold for SI.300.000. Whm is the revised NPV given th"t the finn can abandon the project ufter one year?

30. Finanda.1 Breaken'n The Cornchoppcr Company is considering the purchase of a ocw hilrvester. Cornchopper has hired you 10 determine the break-even purchase price in terms of present val ue of the har .... ester. This brcak·evcn purchase price is the p~ at which the projec( s NPV is zero. nOIse your analysis on the follo\\;ng facts:

The new harvester is not expected to alTeet revenues. but pretax oper.lling expenses will be reduced by SI2.000 per year for 10 years. The old harvester is now 5 yC<lrs old. with 10 years of ilS scheduled life remain­ing. II was originally pun:h:tsed for S50.000 and has bt.-cn depI\.'Ciated by the str.t illht-]jne method. The ~Id han'ester can be sold for S IS.OOO tooay. T he new han'ester will be depredated by the straight-line method over its lO·year life. The ... 'Orporate tax. rate is 34 percent. Tbe ftJm's required rate of return is 15 pert·en\. The initial investment. the prDC\.~s from selling the old harvesler. ;t nd any resulting t:!x cnCcls occur immediiltdy. All other ca.sh flows occur a t year-cnd. The market value of each harvester al the end of ils economic life is zero.

BUNYAN LUMBER. LLC Bunynn Lumber. LLC. harvests timber and deliver.; logs to timber mills for sale. The COIll­

pany was founded 70 ye,lrs ago by Pete Buny.lIl. The current CEO is Pl.Iula Bunyan. the gmnddaughter of the founder. The comp;.lIly is currently eWl luating a 5.000-acre forest it owns in Oregon. Paula has asked Steve Roles.. the company's finance officer. to evaluate the project. Paula's concern is when the company should harvest the timber.

Lumber is sold by the company for its "pond value." Pond value is thc amount a mill will p:ly for a log delivered to Ihe mi1llocation. The pricc paid for logs ddivcred to a mill is quoted in dol1ars per thousands of board reet (MBF). and the price depends 011 the gl1lde of the logs. The forest Bunyan Lumber is evaiullting was planted by the company 20 years :lgo and is made up entirely of Douglas fir trees. The table hcre shows Ihe current price per M SF for the th~ grades of timber the comJXIIlY feels will cOllle from the stand:

Timber Grade Price per MBF

IP

2P

lP

$660 630 620

Sieve believes that the pond value of luulber will increase at the inflation rdte. The com­pany is planning to thin the fo rest too;'!)" and it expects to realize a posi tive cash flow of SI,OOO per acre from thinning. The thivning is done 10 increase the growth roue or the remaining trees, aDd it is ahV'.lYs done 20 years following" planting.

The major decision the company races is when to log the forest. When the company logs the forest. it will immediately repl •• nt saplings. which will allow for a future han·cst. The longer the fores t is allowed to grow. Ihe larger the har"esl becomes per acre. Additionally, lin old..:r fores t has a higher gmde of timber. Steve has compiled the fo llowing table witb

Ol:lpll'r 7 Risk An:llysis. Rc;1I Options. ,lIld O lp;I:'I1 Hudgeling 2JJ

the expt.'Ctcd han·est per acre in thousands of board fce t, .. long with the breakdown of lhe timber gr.tdes:

Years from Today Harvest (MBF) Timber Grade to Begin Harvest per Acre I P 2P lP

20 2S JO

JS

104.1 t 6.4

17.3 lal

"" 20 22 ,.

,,% <0 ., 15

• • %

.0 JS ]I

The company e;\peets to lose 5 percent of the timber it cuts due to defeels and breakage. Tbe fores l will be clear-cut when thc compa ny hal"\'csls the timber. This melhod of

han·csting allows for fasler growth of replanted trees. All of the harvesting. processing, replanting. and Ir.tnsporlation ' II\: lO be handled by SU bcOnlr.lctors hired by Bunyan Lumber. The cost of Ihe loggi ng is cxpt.'Cted to be $140 per MBE A road system has to be eonstTllcted and is cxpcc:lcd to cost $50 per MDF on average. Sa les preparation and admin· istrati\'e costs. cxcluding onl ce ovcrhead cost& are expected to be SIS per M BF.

As soon :IS the harvcsli ng is complete. the company will reforest the IlUld. RcloTCStiog costs include Ihe rollowing:

Exuv.lltor piling

Broadcast burning

Site pre~r.lltion

Planting COSts

Cost per Acre

$150

lOO 115

ns

All costs arc expected 10 increase at the in fl ation rate. Assume all cash nows occur at the year of han1!S\. For example. if the company begins

har\'csling the timber 20 yea rs from toda)'. the co'lsh now from the harvest \\;11 be recei\'ed 20 ycars from today. When the company logs the land. i1 will immediately replant the land with new saplings. The han·est period chosen will be repeated for the foreseeable fut ure. The company's nomimll required tetum is 10 pcn .. :ent. and the innation nile is expected 10 oc 3.7 percent per yeur. Bu ny;m Lumber ha s :1 35 pe rLx""nt U!X r.lIe.

Clear-cutting i ~ a contro\'ersial method of lorest manag..:ment. To oblilin the nccessar) lX·rmits. Bunyan Lumber has agr~ed 10 con tribute 10 a consen'ation fund evcry time it harvests the lumber. If t he company han'cs t ... -d the fo rcst today, the required contribution would be 5250,000. The com pany h:!s agreed that the req uired contribution will gro\\ by 3.2 percent per year. When should the compa ny harvest the fores !"!

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