Financial Modeling

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Financial Modeling - www.neteffect.in

Financial Modeling

Financial modeling is the task of building an abstract representation (a model) of a financial decision

making situation. This is a mathematical model, such as a computer simulation, designed to represent

(a simplified version of) the performance of a financial asset or a portfolio, of a business, a project, or

any other form of financial investment.

Financial modeling is a general term that means different things to different users. For some, it means

the development of a mathematical model to predict a fair equilibrium price for an asset. For others, it

means the development of a mathematical model and the associated computer implementation to

simulate scenarios of financial events, such as asset prices, market movements, portfolio returns and

the like. Or it might mean the development of optimization models for managing and controlling the

risk of a financial investment.

While there has been some debate in the industry as to the nature of financial modeling : whether it is

a tradecraft, such as welding, or a science, such as metallurgy, the task of financial modeling has

been gaining acceptance and rigor over the years. Several scholarly books have been written on the

topic, in addition to numerous scientific articles, and the definitive series Handbooks in Finance by

Elsevier contains several volumes dealing with financial modeling issues.

There are non-spreadsheet software platforms available on which to build financial models. However,

the vast proportion of the market is spreadsheet-based, and within this market Microsoft Excel now

has by far the dominant position, having overtaken Lotus 1-2-3 in the 1990s. From this it is easy to

see how the uninformed can equate Financial modeling competency with 'learning Excel'. However,

the fallacy in this contention is the one area on which professionals and experts in the financial

modeling industry agree.

Business valuation is a process and a set of procedures used to estimate the economic value of an

owner’s interest in a business. Valuation is used by financial market participants to determine the

price they are willing to pay or receive to consummate a sale of a business. In addition to estimating

the selling price of a business, the same valuation tools are often used by business appraisers to

resolve disputes related to estate and gift taxation, divorce litigation, allocate business purchase price

among business assets, establish a formula for estimating the value of partners' ownership interest

for buy-sell agreements, and many other business and legal purposes.

Standard and premise of value

Before the value of a business can be measured, the valuation assignment must specify the reason for

and circumstances surrounding the business valuation. These are formally known as the business

value standard and premise of value. The standard of value is the hypothetical conditions under which

the business will be valued. The premise of value relates to the assumptions, such as assuming that

the business will continue forever in its current form (going concern), or that the value of the business

lies in the proceeds from the sale of all of its assets minus the related debt (sum of the parts or

assemblage of business assets).

Business valuation results can vary considerably depending upon the choice of both the standard and

premise of value. In an actual business sale, it would be expected that the buyer and seller, each with

an incentive to achieve an optimal outcome, would determine the fair market value of a business

asset that would compete in the market for such an acquisition. If the synergies are specific to the

company being valued, they may not be considered. Fair value also does not incorporate discounts for

lack of control or marketability.

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Note, however, that it is possible to achieve the fair market value for a business asset that is being

liquidated in its secondary market. This underscores the difference between the standard and premise

of value.

These assumptions might not, and probably do not, reflect the actual conditions of the market in

which the subject business might be sold. However, these conditions are assumed because they yield

a uniform standard of value, after applying generally-accepted valuation techniques, which allows

meaningful comparison between businesses which are similarly situated.

Elements of business valuation

Economic conditions

A business valuation report generally begins with a description of national, regional and local

economic conditions existing as of the valuation date, as well as the conditions of the industry in

which the subject business operates. A common source of economic information for the first section of

the business valuation report is the Federal Reserve Board’s Beige Book, published eight times a year

by the Federal Reserve Bank. State governments and industry associations often publish useful

statistics describing regional and industry conditions.

In finance, valuation is the process of estimating the potential market value of a financial asset or

liability. Valuations can be done on assets (for example, investments in marketable securities such as

stocks, options, business enterprises, or intangible assets such as patents and trademarks) or on

liabilities (e.g., Bonds issued by a company). Valuations are required in many contexts including

investment analysis, capital budgeting, merger and acquisition transactions, financial reporting, taxable events to determine the proper tax liability, and in litigation.

Valuation overview

Valuation of financial assets is done using one or more of these types of models:

1. Relative value models determine the value based on the market prices of similar assets.

2. Absolute value models determine the value by estimating the expected future earnings from

owning the asset discounted to their present value.

3. Option pricing models are used for certain types of financial assets (e.g., warrants, put options,

call options, employee stock options, investments with embedded options such as a callable

bond) and are a complex present value model. The most common option pricing models are the Black-Scholes-Merton models and lattice models.

Common terms for the value of an asset or liability are fair market value, fair value, and intrinsic value.

The meanings of these terms differ. The most common sets market price. For instance, when an analyst

believes a stock's intrinsic value is greater than its market price, the analyst makes a "buy"

recommendation and vice versa. Moreover, an asset's intrinsic value may be subject to personal opinion

and vary among analysts.

For a comprehensive discussion on financial valuation see Aswath Damodaran, Investment Valuation,

(New York: John Wiley & Sons, 2002).

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Business valuation

Businesses or fractional interests in businesses may be valued for various purposes such as mergers

and acquisitions, sale of securities, and taxable events. An accurate valuation of privately owned

companies largely depends on the reliability of the firm's historic financial information. Public company

financial statements are audited by Certified Public Accountants (US), Chartered Certified Accountants

(ACCA) or Chartered Accountants (UK and Canada) and overseen by a government regulator.

Alternatively, private firms do not have government oversight--unless operating in a regulated industry-

-and are usually not required to have their financial statements audited. Moreover, managers of private

firms often prepare their financial statements to minimize profits and, therefore, taxes. Alternatively,

managers of public firms tend to want higher profits to increase their stock price. Therefore, a firm's

historic financial information may not be accurate and can lead to over- and undervaluation. In an acquisition, a buyer often performs due diligence to verify the seller's information.

Financial statements prepared in accordance with generally accepted accounting principles (GAAP) often

show the values of assets at their historic costs rather than at their current market values. For instance,

a firm's balance sheet will usually show the value of land it owns at what the firm paid for it rather than

at its current market value. But under GAAP requirements, a firm must show the values of some types

of assets--securities held for sale, for instance--at their market values rather than at cost. When a firm

is required to show some of its assets at market value, some call this process "mark-to-market." But

reporting asset values on financial statements at market values gives managers ample opportunity to

slant asset values upward--to artificially increase profits and stock prices. Managers may be motivated

to alter earnings upward so they can earn bonuses. Despite the risk of manager bias, investors and

creditors prefer to know the market values of a firm's assets--rather than their costs--because the

current values give them better information to make decisions.

Main business valuation methods

Discounted cash flows method

This method estimates the value of an asset based on its expected future cash flows, which are

discounted to the present (i.e., the present value). This concept of discounting future monies is

commonly known as the time value of money. For instance, an asset that matures and pays $1 in one

year is worth less than $1 today. The size of the discount is based on an opportunity cost of capital and

it is expressed as a percentage. Some people call this percentage a discount rate.

The idea of opportunity cost can be illustrated in an example. A person with only $100 to invest can

make just one $100 investment even when presented with two or more investment choices. If this

person is later offered an alternative investment choice, the investor has lost the opportunity to make

that second investment since the $100 is spent to buy the first opportunity. This example illustrates

that money is limited and people make choices in how to spend it. By making a choice, they give up

other opportunities.

In finance theory, the amount of the opportunity cost is based on a relation between the risk and return

of some sort of investment. Classic economic theory maintains that people are rational and adverse to

risk. They, therefore, need an incentive to accept risk. The incentive in finance comes in the form of

higher expected returns after buying a risky asset. In other words, the more risky the investment, the

more return investors want from that investment. Using the same example as above, assume the first

investment opportunity is a government bond that will pay interest of 5% per year and the principle

and interest payments are guaranteed by the government. Alternatively, the second investment

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opportunity is a bond issued by small company and that bond also pays annual interest of 5%. If given

a choice between the two bonds, virtually all investors would buy the government bond rather than the

small-firm bond because the first is less risky while paying the same interest rate as the riskier second

bond. In this case, an investor has no incentive to buy the riskier second bond. Furthermore, in order to

attract capital from investors, the small firm issuing the second bond must pay an interest rate higher

than 5% that the government bond pays. Otherwise, no investor is likely to buy that bond and,

therefore, the firm will be unable to raise capital. But by offering to pay an interest rate more than than

5%. the firm gives investors an incentive to buy a riskier bond.

For a valuation using the discounted cash flow method, one first estimates the future cash flows from

the investment and then estimates a reasonable discount rate after considering the riskiness of those

cash flows and interest rates in the capital markets. Next, one makes a calculation to compute the present value of the future cash flows.

(Explained again with examples later)

Guideline companies method

This method determines the value of a firm by observing the prices of similar companies (guideline

companies) that sold in the market. Those sales could be shares of stock or sales of entire firms. The

observed prices serve as valuation benchmarks. From the prices, one calculates price multiples such as

the price-to-earnings or price-to-book value ratios. Next, one or more price multiples are used to value

the firm. For example, the average price-to-earnings multiple of the guideline companies is applied to

the subject firm's earnings to estimate its value.

Many price multiples can be calculated. Most are based on a financial statement element such as a

firm's earnings (price-to-earnings) or book value (price-to-book value) but multiples can be based on other factors such as price-per-subscriber.

Usage

In finance, valuation analysis is required for many reasons including tax assessment, wills and estates,

divorce settlements, business analysis, and basic bookkeeping and accounting. Since the value of things

fluctuates over time, valuations are as of a specific date e.g., the end of the accounting quarter or year.

They may alternatively be mark-to-market estimates of the current value of assets or liabilities as of

this minute or this day for the purposes of managing portfolios and associated financial risk (for example, within large financial firms including investment banks and stockbrokers).

Some balance sheet items are much easier to value than others. Publicly traded stocks and bonds have

prices that are quoted frequently and readily available. Other assets are harder to value. For instance,

private firms that have no frequently quoted price. Additionally, financial instruments that have prices

that are partly dependent on theoretical models of one kind or another are difficult to value. For

example, options are generally valued using the Black-Scholes model while the liabilities of life

assurance firms are valued using the theory of present value. Intangible business assets, like goodwill and intellectual property, are open to a wide range of value interpretations.

It is possible and conventional for financial professionals to make their own estimates of the valuations

of assets or liabilities that they are interested in. Their calculations are of various kinds including

analyses of companies that focus on price-to-book, price-to-earnings, price-to-cashflow and present

value calculations, and analyses of bonds that focus on credit ratings, assessments of default risk, risk

premia and levels of real interest rates. All of these approaches may be thought of as creating

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estimates of value that compete for credibility with the prevailing share or bond prices, where

applicable, and may or may not result in buying or selling by market participants. Where the valuation

is for the purpose of a merger or acquisition the respective businesses make available further detailed financial information, usually on the completion of a Non-disclosure agreement.

It is very important to note that valuation is more an art than a science because it requires judgement:

1. There are very different situations and purposes in which you value an asset (e.g. company in

distress, tax purposes, mergers & acquisitions, quarterly reporting). In turn this requires different methods or a different interpretation of the same method each time.

2. All valuation models and methods have their limitations (e.g., mathematical, complexity,

simplicity, comparability) and could be widely criticized. As a general rule the valuation models

are most useful when you use the same valuation method as the "partner" you are interacting

with. Mostly the method used is industry or purpose specific;

3. The quality of some of the input data may vary widely

4. In all valuation models there are a great number of assumptions that need to be made and

things might not turn out the way you expect. Your best way out of that is to be able to explain and stand for each assumption you make;

When a valuation is prepared all assumptions should be clearly stated, especially the context. It is

improper, for example, to value a going concern, based on an assumption that it is going out of

business, since then only a salvage value remains.

Valuation of a distressed company

Additional adjustments to a valuation approach, whether it is market-, income- or asset-based, may be

necessary in some instances. These involve:

excess or restricted cash

other non-operating assets and liabilities

lack of marketability discount

control premium or lack of control discount

above or below market leases

excess salaries in the case of private companies.

There are other adjustments to the financial statements that have to be made when valuing a

distressed company. Andrew Miller identifies typical adjustments used to recast the financial statements that include:

working capital adjustment

deferred capital expeditures

cost of goods sold adjustment

non-recurring professional fees and costs

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certain non-operating income/expense items.

Valuation of intangible assets

Valuation models can be used to value intangible assets such as patents, copyrights, software, trade

secrets, and customer relationships. Since few sales of benchmark intangible assets can ever be

observed, one often values these sorts of assets using either a present value model or estimating the costs to recreate it. Regardless of the method, the process is often time consuming and costly.

Valuations of intangible assets are often necessary for financial reporting and intellectual property

transactions.

Stock markets give indirectly an estimate of a corporation's intangible asset value. It can be reckoned

as the difference between its market capitalisation and its book value (by including only hard assets in it).

There have been several new tools developed recently aiding in the valuation of intellectual property.

The 25% Rule, Monte Carlo Analysis, and Derivative Revenue Model (based on license revenue) are just

a few of these tools. Also, traditional methods such as Net Present Value, Internal Rate of Return, and

Discounted Cash Flow can also be used. However, these do not take into account the "book value", or

"pre-revenue" asset value of non income producing intellectual property. With the negotiability and

transferability of intellectual property being liberalized by court decisions in the 1990's, several

valuation specialists and merchant banking organizations have taken up valuation and market making

in intellecutual property. Essentially, treating intellectual property instruments as another asset class

for investor portfolios and treating them more like securities. Several firms are prevalent in this field,

Ocean Tomo of Chicago, Intellectual Ventures in Seattle, and Crais Management Group, LLC in New

Orleans. They have initiated auctions of intellectual property blocks. This some have done as a

percursor to their plans to create a "stock market" for intellectual property. Patents and trademarks

would be the dominant form of security traded on these exchanges. To have an open market for

intellectual property would create a more uniform and transparent form of IP valuation. The "Bid" and

"Ask" system, many believe, is the most efficient form of valuing an asset. A "stock exchange" for intellectual property would change the face of intellectual property valuation.

Valuation of mining projects

In mining, valuation is the process of determining the value or worth of a mining property.

Mining valuations are sometimes required for IPOs, fairness opinions, litigation, mergers & acquisitions

and shareholder related matters.

In valuation of a mining project or mining property, fair market value is the standard of value to be

used. The CIMVal Standards are a recognised standard for valuation of mining projects and is also

recognised by the Toronto Stock Exchange (Venture). The standards spearheaded by Spence & Roscoe,

stress the use of the cost approach, market approach and the income approach, depending on the stage of development of the mining property or project.

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Financial Analysis

The financial statement analysis generally involves common size analysis, ratio analysis (liquidity,

turnover, profitability, etc.), trend analysis and industry comparative analysis. This permits the

valuation analyst to compare the subject company to other businesses in the same or similar industry,

and to discover trends affecting the company and/or the industry over time. By comparing a

company’s financial statements in different time periods, the valuation expert can view growth or

decline in revenues or expenses, changes in capital structure, or other financial trends. How the

subject company compares to the industry will help with the risk assessment and ultimately help

determine the discount rate and the selection of market multiples.

Normalization of financial statements

The most common normalization adjustments fall into the following four categories:

* Comparability Adjustments. The valuer may adjust the subject company’s financial statements to

facilitate a comparison between the subject company and other businesses in the same industry or

geographic location. These adjustments are intended to eliminate differences between the way that

published industry data is presented and the way that the subject company’s data is presented in its

financial statements.

* Non-operating Adjustments. It is reasonable to assume that if a business were sold in a

hypothetical sales transaction (which is the underlying premise of the fair market value standard), the

seller would retain any assets which were not related to the production of earnings or price those non-

operating assets separately. For this reason, non-operating assets (such as excess cash) are usually

eliminated from the balance sheet.

* Non-recurring Adjustments. The subject company’s financial statements may be affected by

events that are not expected to recur, such as the purchase or sale of assets, a lawsuit, or an

unusually large revenue or expense. These non-recurring items are adjusted so that the financial

statements will better reflect the management’s expectations of future performance.

* Discretionary Adjustments. The owners of private companies may be paid at variance from the

market level of compensation that similar executives in the industry might command. In order to

determine fair market value, the owner’s compensation, benefits, perquisites and distributions must

be adjusted to industry standards. Similarly, the rent paid by the subject business for the use of

property owned by the company’s owners individually may be scrutinized.

Income, Asset and Market Approaches

Three different approaches are commonly used in business valuation: the income approach, the asset-

based approach, and the market approach[2]. Within each of these approaches, there are various

techniques for determining the value of a business using the definition of value appropriate for the

appraisal assignment. Generally, the income approaches determine value by calculating the net

present value of the benefit stream generated by the business (discounted cash flow); the asset-

based approaches determine value by adding the sum of the parts of the business (net asset value);

and the market approaches determine value by comparing the subject company to other companies in

the same industry, of the same size, and/or within the same region.

A number of business valuation models can be constructed that utilize various methods under the

three business valuation approaches. Venture Capitalists and Private Equity professionals have long

used the First chicago method which essentially combines the income approach with the market

approach.

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In determining which of these approaches to use, the valuation professional must exercise discretion.

Each technique has advantages and drawbacks, which must be considered when applying those

techniques to a particular subject company. Most treatises and court decisions encourage the valuator

to consider more than one technique, which must be reconciled with each other to arrive at a value

conclusion. A measure of common sense and a good grasp of mathematics is helpful.

Income approaches

The income approaches determine fair market value by multiplying the benefit stream generated by

the subject or target company times a discount or capitalization rate. The discount or capitalization

rate converts the stream of benefits into present value. There are several different income

approaches, including capitalization of earnings or cash flows, discounted future cash flows (―DCF‖),

and the excess earnings method (which is a hybrid of asset and income approaches). Most of the

income approaches look to the company’s adjusted historical financial data for a single period; only

DCF requires data for multiple future periods. The discount or capitalization rate must be matched to

the type of benefit stream to which it is applied. The result of a value calculation under the income

approach is generally the fair market value of a controlling, marketable interest in the subject

company, since the entire benefit stream of the subject company is most often valued, and the

capitalization and discount rates are derived from statistics concerning public companies.

Discount or capitalization rates

A discount rate or capitalization rate is used to determine the present value of the expected returns of

a business. The discount rate and capitalization rate are closely related to each other, but

distinguishable. Generally speaking, the discount rate or capitalization rate may be defined as the

yield necessary to attract investors to a particular investment, given the risks associated with that

investment.

* In DCF valuations, the discount rate, often an estimate of the cost of capital for the business are

used to calculate the net present value of a series of projected cash flows.

* On the other hand, a capitalization rate is applied in methods of business valuation that are

based on business data for a single period of time. For example, in real estate valuations for

properties that generate cash flows, a capitalization rate may be applied to the net operating income

(NOI) (i.e., income before depreciation and interest expenses) of the property for the trailing twelve

months.

There are several different methods of determining the appropriate discount rates. The discount rate

is composed of two elements: (1) the risk-free rate, which is the return that an investor would expect

from a secure, practically risk-free investment, such as a high quality government bond; plus (2) a

risk premium that compensates an investor for the relative level of risk associated with a particular

investment in excess of the risk-free rate. Most importantly, the selected discount or capitalization

rate must be consistent with stream of benefits to which it is to be applied.

Capital Asset Pricing Model (―CAPM‖)

The Capital Asset Pricing Model ( CAPM) is one method of determining the appropriate discount rate in

business valuations. The CAPM method originated from the Nobel Prize winning studies of Harry

Markowitz, James Tobin and William Sharpe. The CAPM method derives the discount rate by adding a

risk premium to the risk-free rate. In this instance, however, the risk premium is derived by

multiplying the equity risk premium times ―beta,‖ which is a measure of stock price volatility. Beta is

published by various sources for particular industries and companies. Beta is associated with the

systematic risks of an investment.

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One of the criticisms of the CAPM method is that beta is derived from the volatility of prices of

publicly-traded companies, which are likely to differ from private companies in their capital structures,

diversification of products and markets, access to credit markets, size, management depth, and many

other respects. Where private companies can be shown to be sufficiently similar to public companies,

however, the CAPM method may be appropriate.

Weighted Average Cost of Capital (―WACC‖)

The weighted average cost of capital is an approach to determining a discount rate. The WACC

method determines the subject company’s actual cost of capital by calculating the weighted average

of the company’s cost of debt and cost of equity. The WACC must be applied to the subject company’s

net cash flow to total invested capital.

One of the problems with this method is that the valuator may elect to calculate WACC according to

the subject company’s existing capital structure, the average industry capital structure, or the optimal

capital structure. Such discretion detracts from the objectivity of this approach, in the minds of some

critics.

Indeed, since the WACC captures the risk of the subject business itself, the existing or contemplated

capital structures, rather than industry averages, are the appropriate choices for business valuation.

Once the capitalization rate or discount rate is determined, it must be applied to an appropriate

economic income streams: pretax cash flow, aftertax cash flow, pretax net income, after tax net

income, excess earnings, projected cash flow, etc. The result of this formula is the indicated value

before discounts. Before moving on to calculate discounts, however, the valuation professional must

consider the indicated value under the asset and market approaches.

Careful matching of the discount rate to the appropriate measure of economic income is critical to the

accuracy of the business valuation results. Net cash flow is a frequent choice in professionally

conducted business appraisals. The rationale behind this choice is that this earnings basis corresponds

to the equity discount rate derived from the Build-Up or CAPM models: the returns obtained from

investments in publicly traded companies can easily be represented in terms of net cash flows. At the

same time, the discount rates are generally also derived from the public capital markets data.

Build-Up Method

The Build-Up Method is a widely-recognized method of determining the after-tax net cash flow

discount rate, which in turn yields the capitalization rate. The figures used in the Build-Up Method are

derived from various sources. This method is called a ―build-up‖ method because it is the sum of risks

associated with various classes of assets. It is based on the principle that investors would require a

greater return on classes of assets that are more risky. The first element of a Build-Up capitalization

rate is the risk-free rate, which is the rate of return for long-term government bonds. Investors who

buy large-cap equity stocks, which are inherently more risky than long-term government bonds,

require a greater return, so the next element of the Build-Up method is the equity risk premium. In

determining a company’s value, the long-horizon equity risk premium is used because the Company’s

life is assumed to be infinite. The sum of the risk-free rate and the equity risk premium yields the

long-term average market rate of return on large public company stocks.

Similarly, investors who invest in small cap stocks, which are riskier than blue-chip stocks, require a

greater return, called the ―size premium.‖ Size premium data is generally available from two sources:

Morningstars' (formerly Ibbotson & Associates') Stocks, Bonds, Bills & Inflation and Duff & Phelps'

Risk Premium Report.

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By adding the first three elements of a Build-Up discount rate, we can determine the rate of return

that investors would require on their investments in small public company stocks. These three

elements of the Build-Up discount rate are known collectively as the ―systematic risks.‖

In addition to systematic risks, the discount rate must include ―unsystematic risks,‖ which fall into two

categories. One of those categories is the ―industry risk premium.‖ Morningstar’s yearbooks contain

empirical data to quantify the risks associated with various industries, grouped by SIC industry code.

The other category of unsystematic risk is referred to as ―specific company risk.‖ Historically, no

published data has been available to quantify specific company risks. However as of late 2006, new

ground-breaking research has been able to quantify, or isolate, this risk for publicly-traded stocks

through the use of Total Beta calculations. P. Butler and K. Pinkerton have outlined a procedure,

known as the Butler Pinkerton Model (BPM), using a modified Capital Asset Pricing Model ( CAPM) to

calculate the company specific risk premium. The model uses an equality between the standard CAPM

which relies on the total beta on one side of the equation; and the firm's beta, size premium and

company specific risk premium on the other. The equality is then solved for the company specific risk

premium as the only unknown. The BPM is a relatively new concept and is gaining acceptance in the

business valuation community.

It is important to understand why this capitalization rate for small, privately-held companies is

significantly higher than the return that an investor might expect to receive from other common types

of investments, such as money market accounts, mutual funds, or even real estate. Those

investments involve substantially lower levels of risk than an investment in a closely-held company.

Depository accounts are insured by the federal government (up to certain limits); mutual funds are

composed of publicly-traded stocks, for which risk can be substantially minimized through portfolio

diversification.

Closely-held companies, on the other hand, frequently fail for a variety of reasons too numerous to

name. Examples of the risk can be witnessed in the storefronts on every Main Street in America.

There are no federal guarantees. The risk of investing in a private company cannot be reduced

through diversification, and most businesses do not own the type of hard assets that can ensure

capital appreciation over time. This is why investors demand a much higher return on their

investment in closely-held businesses; such investments are inherently much more risky.

Asset-based approaches

The value of asset-based analysis of a business is equal to the sum of its parts. That is the theory

underlying the asset-based approaches to business valuation. The asset approach to business

valuation is based on the principle of substitution: no rational investor will pay more for the business

assets than the cost of procuring assets of similar economic utility. In contrast to the income-based

approaches, which require the valuation professional to make subjective judgments about

capitalization or discount rates, the adjusted net book value method is relatively objective. Pursuant

to accounting convention, most assets are reported on the books of the subject company at their

acquisition value, net of depreciation where applicable. These values must be adjusted to fair market

value wherever possible. The value of a company’s intangible assets, such as goodwill, is generally

impossible to determine apart from the company’s overall enterprise value. For this reason, the asset-

based approach is not the most probative method of determining the value of going business

concerns. In these cases, the asset-based approach yields a result that is probably lesser than the fair

market value of the business. In considering an asset-based approach, the valuation professional

must consider whether the shareholder whose interest is being valued would have any authority to

access the value of the assets directly. Shareholders own shares in a corporation, but not its assets,

which are owned by the corporation. A controlling shareholder may have the authority to direct the

corporation to sell all or part of the assets it owns and to distribute the proceeds to the

shareholder(s). The non-controlling shareholder, however, lacks this authority and cannot access the

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value of the assets. As a result, the value of a corporation's assets is rarely the most relevant

indicator of value to a shareholder who cannot avail himself of that value. Adjusted net book value

may be the most relevant standard of value where liquidation is imminent or ongoing; where a

company earnings or cash flow are nominal, negative or worth less than its assets; or where net book

value is standard in the industry in which the company operates. None of these situations applies to

the Company which is the subject of this valuation report. However, the adjusted net book value may

be used as a ―sanity check‖ when compared to other methods of valuation, such as the income and

market approaches.

Market approaches

The market approach to business valuation is rooted in the economic principle of competition: that in

a free market the supply and demand forces will drive the price of business assets to a certain

equilibrium. Buyers would not pay more for the business, and the sellers will not accept less, than the

price of a comparable business enterprise. It is similar in many respects to the ―comparable sales‖

method that is commonly used in real estate appraisal. The market price of the stocks of publicly

traded companies engaged in the same or a similar line of business, whose shares are actively traded

in a free and open market, can be a valid indicator of value when the transactions in which stocks are

traded are sufficiently similar to permit meaningful comparison.

The difficulty lies in identifying public companies that are sufficiently comparable to the subject

company for this purpose. Also, as for a private company, the equity is less liquid (in other words its

stocks are less easy to buy or sell) than for a public company, its value is considered to be slightly

lower than such a market-based valuation would give.

Guideline Public Company method

The Guideline Public Company method entails a comparison of the subject company to publicly traded

companies. The comparison is generally based on published data regarding the public companies’

stock price and earnings, sales, or revenues, which is expressed as a fraction known as a ―multiple.‖

If the guideline public companies are sufficiently similar to each other and the subject company to

permit a meaningful comparison, then their multiples should be similar. The public companies

identified for comparison purposes should be similar to the subject company in terms of industry,

product lines, market, growth, margins and risk.

Transaction Method or Direct Market Data Method

Using this method, the valuation analyst may determine market multiples by reviewing published data

regarding actual transactions involving either minority or controlling interests in either publicly traded

or closely held companies. In judging whether a reasonable basis for comparison exists, the valuation

analysis must consider: (1) the similarity of qualitative and quantitative investment and investor

characteristics; (2) the extent to which reliable data is known about the transactions in which

interests in the guideline companies were bought and sold; and (3) whether or not the price paid for

the guideline companies was in an arms-length transaction, or a forced or distressed sale.

Discounts and premiums

The valuation approaches yield the fair market value of the Company as a whole. In valuing a

minority, non-controlling interest in a business, however, the valuation professional must consider the

applicability of discounts that affect such interests. Discussions of discounts and premiums frequently

begin with a review of the ―levels of value.‖ There are three common levels of value: controlling

interest, marketable minority, and non-marketable minority. The intermediate level, marketable

minority interest, is lesser than the controlling interest level and higher than the non-marketable

minority interest level. The marketable minority interest level represents the perceived value of equity

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interests that are freely traded without any restrictions. These interests are generally traded on the

New York Stock Exchange, AMEX, NASDAQ, and other exchanges where there is a ready market for

equity securities. These values represent a minority interest in the subject companies – small blocks

of stock that represent less than 50% of the company’s equity, and usually much less than 50%.

Controlling interest level is the value that an investor would be willing to pay to acquire more than

50% of a company’s stock, thereby gaining the attendant prerogatives of control. Some of the

prerogatives of control include: electing directors, hiring and firing the company’s management and

determining their compensation; declaring dividends and distributions, determining the company’s

strategy and line of business, and acquiring, selling or liquidating the business. This level of value

generally contains a control premium over the intermediate level of value, which typically ranges from

25% to 50%. An additional premium may be paid by strategic investors who are motivated by

synergistic motives. Non-marketable, minority level is the lowest level on the chart, representing the

level at which non-controlling equity interests in private companies are generally valued or traded.

This level of value is discounted because no ready market exists in which to purchase or sell interests.

Private companies are less ―liquid‖ than publicly-traded companies, and transactions in private

companies take longer and are more uncertain. Between the intermediate and lowest levels of the

chart, there are restricted shares of publicly-traded companies. Despite a growing inclination of the

IRS and Tax Courts to challenge valuation discounts , Shannon Pratt suggested in a scholarly

presentation recently that valuation discounts are actually increasing as the differences between

public and private companies is widening . Publicly-traded stocks have grown more liquid in the past

decade due to rapid electronic trading, reduced commissions, and governmental deregulation. These

developments have not improved the liquidity of interests in private companies, however. Valuation

discounts are multiplicative, so they must be considered in order. Control premiums and their inverse,

minority interest discounts, are considered before marketability discounts are applied.

Discount for lack of control

The first discount that must be considered is the discount for lack of control, which in this instance is

also a minority interest discount. Minority interest discounts are the inverse of control premiums, to

which the following mathematical relationship exists: MID = 1 – [1 / (1 + CP)] The most common

source of data regarding control premiums is the Control Premium Study, published annually by

Mergerstat since 1972. Mergerstat compiles data regarding publicly announced mergers, acquisitions

and divestitures involving 10% or more of the equity interests in public companies, where the

purchase price is $1 million or more and at least one of the parties to the transaction is a U.S. entity.

Mergerstat defines the ―control premium‖ as the percentage difference between the acquisition price

and the share price of the freely-traded public shares five days prior to the announcement of the M&A

transaction. While it is not without valid criticism, Mergerstat control premium data (and the minority

interest discount derived therefrom) is widely accepted within the valuation profession.

Discount for lack of marketability

Another factor to be considered in valuing closely held companies is the marketability of an interest in

such businesses. Marketability is defined as the ability to convert the business interest into cash

quickly, with minimum transaction and administrative costs, and with a high degree of certainty as to

the amount of net proceeds. There is usually a cost and a time lag associated with locating interested

and capable buyers of interests in privately-held companies, because there is no established market

of readily-available buyers and sellers. All other factors being equal, an interest in a publicly traded

company is worth more because it is readily marketable. Conversely, an interest in a private-held

company is worth less because no established market exists. The IRS Valuation Guide for Income,

Estate and Gift Taxes, Valuation Training for Appeals Officers acknowledges the relationship between

value and marketability, stating: ―Investors prefer an asset which is easy to sell, that is, liquid.‖ The

discount for lack of control is separate and distinguishable from the discount for lack of marketability.

It is the valuation professional’s task to quantify the lack of marketability of an interest in a privately-

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held company. Because, in this case, the subject interest is not a controlling interest in the Company,

and the owner of that interest cannot compel liquidation to convert the subject interest to cash

quickly, and no established market exists on which that interest could be sold, the discount for lack of

marketability is appropriate. Several empirical studies have been published that attempt to quantify

the discount for lack of marketability. These studies include the restricted stock studies and the pre-

IPO studies. The aggregate of these studies indicate average discounts of 35% and 50%, respectively.

Some experts believe the Lack of Control and Marketability discounts can aggregate discounts for as

much as ninety percent of a Company's fair market value, specifically with family owned companies.

Restricted stock studies

Restricted stocks are equity securities of public companies that are similar in all respects to the freely

traded stocks of those companies except that they carry a restriction that prevents them from being

traded on the open market for a certain period of time, which is usually one year (two years prior to

1990). This restriction from active trading, which amounts to a lack of marketability, is the only

distinction between the restricted stock and its freely-traded counterpart. Restricted stock can be

traded in private transactions and usually do so at a discount. The restricted stock studies attempt to

verify the difference in price at which the restricted shares trade versus the price at which the same

unrestricted securities trade in the open market as of the same date. The underlying data by which

these studies arrived at their conclusions has not been made public. Consequently, it is not possible

when valuing a particular company to compare the characteristics of that company to the study data.

Still, the existence of a marketability discount has been recognized by valuation professionals and the

Courts, and the restricted stock studies are frequently cited as empirical evidence. Notably, the lowest

average discount reported by these studies was 26% and the highest average discount was 45%.

Option pricing

In addition to the restricted stock studies, U.S. publicly traded companies are able to sell stock to

offshore investors (SEC Regulation S, enacted in 1990) without registering the shares with the

Securities and Exchange Commission. The offshore buyers may resell these shares in the United

States, still without having to register the shares, after holding them for just 40 days. Typically, these

shares are sold for 20% to 30% below the publicly traded share price. Some of these transactions

have been reported with discounts of more than 30%, resulting from the lack of marketability. These

discounts are similar to the marketability discounts inferred from the restricted and pre-IPO studies,

despite the holding period being just 40 days. Studies based on the prices paid for options have also

confirmed similar discounts. If one holds restricted stock and purchases an option to sell that stock at

the market price (a put), the holder has, in effect, purchased marketability for the shares. The price of

the put is equal to the marketability discount. The range of marketability discounts derived by this

study was 32% to 49%.

Pre-IPO studies

Another approach to measure the marketability discount is to compare the prices of stock offered in

initial public offerings (IPOs) to transactions in the same company’s stocks prior to the IPO.

Companies that are going public are required to disclose all transactions in their stocks for a period of

three years prior to the IPO. The pre-IPO studies are the leading alternative to the restricted stock

stocks in quantifying the marketability discount. The pre-IPO studies are sometimes criticized because

the sample size is relatively small, the pre-IPO transactions may not be arm’s length, and the financial

structure and product lines of the studied companies may have changed during the three year pre-IPO

window.

Applying the studies

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The studies confirm what the marketplace knows intuitively: Investors covet liquidity and loathe

obstacles that impair liquidity. Prudent investors buy illiquid investments only when there is a

sufficient discount in the price to increase the rate of return to a level which brings risk-reward back

into balance. The referenced studies establish a reasonable range of valuation discounts from the mid-

30%s to the low 50%s. The more recent studies appeared to yield a more conservative range of

discounts than older studies, which may have suffered from smaller sample sizes. Another method of

quantifying the lack of marketability discount is the Quantifying Marketability Discounts Model

(QMDM).

In finance, the discounted cash flow (or DCF) approach describes a method of valuing a project,

company, or asset using the concepts of the time value of money. All future cash flows are estimated

and discounted to give their present values. The discount rate used is generally the appropriate

WACC, that reflects the risk of the cashflows. The discount rate reflects two things:

1. the time value of money (risk rate) - investors would rather have cash immediately than having to

wait and must therefore be compensated by paying for the delay.

2. a risk premium (risk premium rate) - reflects the extra return investors demand because they want

to be compensated for the risk that the cash flow might not materialize after all.

Discounted cash flow analysis is widely used in investment finance, real estate development, and

corporate financial management.

Very similar is the net present value.

Thus the discounted present value (for one cash flow in one future period) is expressed as:

where

DPV is the discounted present value of the future cash flow (FV), or FV adjusted for the delay in

receipt;

FV is the nominal value of a cash flow amount in a future period;

i is the interest rate, which reflects the cost of tying up capital and may also allow for the risk

that the payment may not be received in full;

d is the discount rate, which is i/(1+i), ie the interest rate expressed as a deduction at the

beginning of the year instead of an addition at the end of the year;

n is the time in years before the future cash flow occurs.

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Where multiple cash flows in multiple time periods are discounted, it is necessary to sum them as

follows:

for each future cash flow (FV) at any time period (t) in years from the present time, summed over all

time periods. The sum can then be used as a net present value figure. If the amount to be paid at time

0 (now) for all the future cash flows is known, then that amount can be substituted for DPV and the equation can be solved for i, that is the internal rate of return.

All the above assumes that the interest rate remains constant throughout the whole period.

(1+i)^(-t) can of course also be expressed as exp(-it).

Continuous cash flows

With continuous cash flows, the summation in the above formula is replaced by an integration - nothing

else changes:

where FV(t) is now the rate of cash flow.

Example DCF

To show how discounted cash flow analysis is performed, consider the following simplified example.

John Doe buys a house for $100,000. Three years later, he expects to be able to sell this house

for $150,000.

Simple subtraction suggests that the value of his profit on such a transaction would be $150,000 −

$100,000 = $50,000, or 50%. If that $50,000 is amortized over the three years, his implied annual

return (known as the internal rate of return) would be about 14.5%. Looking at those figures, he might

be justified in thinking that the purchase looked like a good idea.

1.1453 x 100000 = 150000 approximately.

However, since three years have passed between the purchase and the sale, any cash flow from the

sale must be discounted accordingly. At the time John Doe buys the house, the 3-year US Treasury

Note rate is 5% per annum. Treasury Notes are generally considered to be inherently less risky than

real estate, since the value of the Note is guaranteed by the US Government and there is a liquid

market for the purchase and sale of T-Notes. If he hadn't put his money into buying the house, he

could have invested it in the relatively safe T-Notes instead. This 5% per annum can therefore be

regarded as the risk-free interest rate for the relevant period (3 years).

Using the DPV formula above, that means that the value of $150,000 received in three years actually

has a present value of $129,576 (rounded off). Those future dollars aren't worth the same as the dollars we have now.

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Subtracting the purchase price of the house ($100,000) from the present value results in the net

present value of the whole transaction, which would be $29,576 or a little more than 29% of the purchase price.

Another way of looking at the deal as the excess return achieved (over the risk-free rate) is (14.5%-

5.0%)/(100%+5%) or approximately 9.0% (still very respectable). (As a check, 1.050 x 1.090 = 1.145 approximately.)

But what about risk?

We assume that the $150,000 is John's best estimate of the sale price that he will be able to achieve in

3 years time (after deducting all expenses, of course). There is of course a lot of uncertainty about house prices, and the outturn may end up higher or lower than this estimate.

(The house John is buying is in a "good neighborhood", but market values have been rising quite a lot

lately and the real estate market analysts in the media are talking about a slow-down and higher

interest rates. There is a probability that John might not be able to get the full $150,000 he is expecting

in three years due to a slowing of price appreciation, or that loss of liquidity in the real estate market might make it very hard for him to sell at all.)

Under normal circumstances, people entering into such transactions are risk-averse, that is to say that

they are prepared to accept a lower expected return for the sake of avoiding risk. See Capital asset

pricing model for a further discussion of this. For the sake of the example (and this is a gross

simplification), let's assume that he values this particular risk at 5% per annum (we could perform a

more precise probabilistic analysis of the risk, but that is beyond the scope of this article). Therefore,

allowing for this risk, his expected return is now 9.0% per annum (the arithmetic is the same as above).

And the excess return over the risk-free rate is now (9.0%-5.0%)/(100% + 5%) which comes to

approximately 3.8% per annum.

That return rate may seem low, but it is still positive after all of our discounting, suggesting that the

investment decision is probably a good one: it produces enough profit to compensate for tying up

capital and incurring risk with a little extra left over. When investors and managers perform DCF

analysis, the important thing is that the net present value of the decision after discounting all future

cash flows at least be positive (more than zero). If it is negative, that means that the investment

decision would actually lose money even if it appears to generate a nominal profit. For instance, if the

expected sale price of John Doe's house in the example above was not $150,000 in three years, but

$130,000 in three years or $150,000 in five years, then on the above assumptions buying the house

would actually cause John to lose money in present-value terms (about $3,000 in the first case, and

about $8,000 in the second). Similarly, if the house was located in an undesirable neighborhood and

the Federal Reserve Bank was about to raise interest rates by five percentage points, then the risk

factor would be a lot higher than 5%: it might not be possible for him to make a profit in discounted terms even if he could sell the house for $200,000 in three years.

In this example, only one future cash flow was considered. For a decision which generates multiple cash

flows in multiple time periods, all the cash flows must be discounted and then summed into a single net present value.

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Methods of appraisal of a company or project

This is necessarily a simple treatment of a complex subject: more detail is beyond the scope of this

article.

For these valuation purposes, a number of different DCF methods are distinguished today, some of

which are outlined below. The details are likely to vary depending on the capital structure of the

company. However the assumptions used in the appraisal (especially the equity discount rate and the

projection of the cash flows to be achieved) are likely to be at least as important as the precise model used.

Both the income stream selected and the associated cost of capital model determine the valuation

result obtained with each method. This is one reason these valuation methods are formally referred to

as the Discounted Future Economic Income methods.

Equity-Approach

o Flows to equity approach (FTE)

Discount the cash flows available to the holders of equity capital, after allowing for cost of servicing

debt capital

Advantages: Makes explicit allowance for the cost of debt capital

Disadvantages: Requires judgement on choice of discount rate

Entity-Approach:

o Adjusted present value approach (APV)

Discount the cash flows before allowing for the debt capital (but allowing for the tax relief obtained on

the debt capital)

Advantages: Simpler to apply if a specific project is being valued which does not have earmarked debt

capital finance

Disadvantages: Requires judgement on choice of discount rate; no explicit allowance for cost of debt

capital, which may be much higher than a "risk-free" rate

o Weighted average cost of capital approach (WACC)

Derive a weighted cost of the capital obtained from the various sources and use that discount rate to

discount the cash flows from the project

Advantages: Overcomes the requirement for debt capital finance to be earmarked to particular projects

Disadvantages: Care must be exercised in the selection of the appropriate income stream. The net cash

flow to total invested capital is the generally accepted choice.

o Total cash flow approach (TCF)

This distinction illustrates that the Discounted Cash Flow method can be used to determine the value of

various business ownership interests. These can include equity or debt holders.

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Alternatively, the method can be used to value the company based on the value of total invested

capital. In each case, the differences lie in the choice of the income stream and discount rate. For

example, the net cash flow to total invested capital and WACC are appropriate when valuing a company based on the market value of all invested capital.

History

Discounted cash flow calculations have been used in some form since money was first lent at interest in

ancient times. As a method of asset valuation it has often been opposed to accounting book value,

which is based on the amount paid for the asset. Following the stock market crash of 1929, discounted

cash flow analysis gained popularity as a valuation method for stocks. Irving Fisher in his 1930 book

"The Theory of Interest" and John Burr Williams's 1938 text 'The Theory of Investment Value' first

formally expressed the DCF method in modern economic terms.

Financial analysis refers to an assessment of the viability, stability and profitability of a business, sub-business or project.

It is performed by professionals who prepare reports using ratios that make use of information taken

from financial statements and other reports. These reports are usually presented to top management as

one of their bases in making business decisions. Based on these reports, management may:

Continue or discontinue its main operation or part of its business;

Make or purchase certain materials in the manufacture of its product;

Acquire or rent/lease certain machineries and equipment in the production of its goods;

Issue stocks or negotiate for a bank loan to increase its working capital;

Make decisions regarding investing or lending capital;

Other decisions that allow management to make an informed selection on various alternatives in

the conduct of its business.

Goals

Financial analysts often assess the firm's:

1. Profitability - its ability to earn income and sustain growth in both short-term and long-term. A

company's degree of profitability is usually based on the income statement, which reports on the

company's results of operations;

2. Solvency - its ability to pay its obligation to creditors and other third parties in the long-term; 3. Liquidity - its ability to maintain positive cash flow, while satisfying immediate obligations;

Both 2 and 3 are based on the company's balance sheet, which indicates the financial condition of a

business as of a given point in time.

Assessing a company's stability requires the use of both the income statement and the balance sheet,

as well as other financial and non-financial indicators.

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Ratios

Liquidity Analysis

a Current ratio

Current Assets/Current Liabilities

b Quick ratio Quick Assets/Current Liabilities

c Net Working Captial Ratio

Net Working Capital/Total Assets

Profitability Analysis

a Return On Assets (ROA)

Net Income/Average Total Assets

b Return On Equity (ROE)

Net Income/Average Stock Holders Equity

c Return On Common Equity (ROE)

Net Income/Average Common Stock Holders Equity

d Profit Margin

Net Income/sales

e Earnings/share

Net Income/Number of common shares outstanding

Activity Analysis

a Asset Turnover

Ratio Sales/Average Total Assets

b Accounts Receivables Turnover Ratio

Sales/Average Accounts Recievables

c Inventory Turnover Ratio

Cost of Goods Sold/Average Inventories

Capital Structure Analysis

a Debt to Equity Ratio

Total Liabilities/Total Stockholders Equity

b Interest Coverage Ratio

Income before Interest and Tax/Total Interest

Capital Market Analysis

a Price Earnings (PE) Ratio

Market Price of Common Stock per share/Earnings per share OR ((Net Income - Dividend)/Average

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Outstanding Shares)

b Market to Book Ratio

Market Price of Common Stock per share/Book value of equity per share

c Dividend Yield

Annual Dividends per common share/Market Price of Common Stock per share

d Dividend Payout Ratio Cash Dividends/Net Income

Methods

Financial analysts often compare financial ratios (of solvency, profitability, growth, etc.):

Past Performance - Across historical time periods for the same firm (the last 5 years for

example),

Future Performance - Using historical figures and certain mathematical and statistical

techniques, including present and future values, This extrapolation method is the main source of errors in financial analysis as past statistics can be poor predictors of future prospects.

Comparative Performance - Comparison between similar firms.

These ratios are calculated by dividing a (group of) account balance(s), taken from the balance sheet

and / or the income statement, by another, for example :

n / equity = return on equity

Net income / total assets = return on assets

Stock price / earnings per share = P/E-ratio

Comparing financial ratios are merely one way of conducting financial analysis. Financial ratios face

several theoretical challenges:

They say little about the firm's prospects in an absolute sense. Their insights about relative

performance require a reference point from other time periods or similar firms.

One ratio holds little meaning. As indicators, ratios can be logically interpreted in at least two

ways. One can partially overcome this problem by combining several related ratios to paint a more comprehensive picture of the firm's performance.

Seasonal factors may prevent year-end values from being representative. A ratio's values may

be distorted as account balances change from the beginning to the end of an accounting period. Use average values for such accounts whenever possible.

Financial ratios are no more objective than the accounting methods employed. Changes in

accounting policies or choices can yield drastically different ratio values.

They fail to account for exogenous factors like investor behavior that are not based upon

economic fundamentals of the firm or the general economy (fundamental analysis)

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In corporate finance, free cash flow (FCF) is cash flow available for distribution among all the

securities holders of an organization. They include equity holders, debt holders, preferred stock

holders, convertible security holders, and so on.

Element Data Source

Net Income Current Income Statement

+ Depreciation/Amortization Current Income Statement

– Changes in Working

Capital Prior & Current Balance Sheets: Current Assets and Liability accounts

– Capital Expenditure Prior & Current Balance Sheets: Property, Plant and Equipment

accounts

= Free Cash Flow

Note that the first three lines above are calculated for you on the standard Statement of Cash Flows.

Element Data Source

Net Income Current Income Statement

+ Depreciation/Amortization Current Income Statement

– Changes in Working Capital Prior & Current Balance Sheets: Current Assets and Liability accounts

= Cash Flows – Operations same as Statement of Cash Flows: section 1, from Operations

Therefore,

Element Data Source

Cash Flows – Operations Statement of Cash Flows: section 1, from Operations

– Capital Expenditure Statement of Cash Flows: section 2, from Investment

= Free Cash Flow

There are two differences between Net Income and Free Cash Flow that should be noted. The first is the

accounting for the consumption of capital goods. The Net Income measure uses depreciation, while the Free Cash Flow measure uses last period's net capital purchases.

Measurement

Type Component Advantage Disadvantage

Free Cash Flow Prior period net Spending is in Capital investments are at the discretion of

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investment

spending

current dollars management, so spending may be sporadic.

Net Income Depreciation

charge

Charges are

smoothed, related

to cumulative

prior purchases

Allowing for typical 2% inflation per year,

equipment purchased 10 years ago for $100 would

now cost about $122. With 10 year straight line

depreciation the old machine would have an annual

depreciation of $10, but the new, identical machine

would have depreciation of $12.2, or 22% more.

The second difference is that the Free Cash Flow measurement deducts increases in net working capital,

where the net income approach does not. Typically, in a growing company with a 30 day collection

period for receivables, a 30 day payment period for purchases, and a weekly payroll, it will require

more and more working capital to finance the labor and profit components embedded in the growing

receivables balance. The net income measure essentially says, "You can take that cash home" because

you would still have the same productive capacity as you started with. The Free Cash Flow

measurement however would say, "You can't take that home" because you would cramp the enterprise

from operating itself forward from there.

Likewise when a company has negative sales growth it's likely to diminish its capital spending

dramatically. Receivables, provided they are being timely collected, will also ratchet down. All this

"deceleration" will show up as additions to Free Cash Flow. However, over the longer term, decelerating sales trends will eventually catch up.

Net Free Cash Flow definition should also allow for cash available to pay off the company's short term

debt. It should also take into account any dividends that the company means to pay.

Net Free Cash Flow = Operation Cash flow – Capital Expenses to keep current level of

operation – dividends – Current Portion of long term debt – Depreciation

Here Capex Definition should not include additional investment on new equipment. However

maintenance cost can be added.

Dividends - This will be base dividend that the company intends to distribute to its share holders.

Current portion of LTD - This will be minimum Debt that the company needs to pay in order to not

create defaults.

Depreciation - This should be taken out since this will account for future investment for replacing the

current PPE.

If the Net Income category includes the income from Discontinued operation and extraordinary income

make sure it is not be part of Free Cash Flow.

Net of all the above give Free Cash available to be reinvested on operation without having to take more

debt.

Alternative Mathematical formula

FCF measures

operating cash flow (OCF) (this includes the reduction for interest),

less expenditures necessary to maintain assets (capital expenditures or "capex").

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In symbols:

where

OCBt is the firm's net operating profit after taxes (Also known as NOPAT)during period t

It is the firm's investment during period t including variation of working capital

Investment is simply the net increase (decrease) in the firm's capital, from the end of one period to the

end of the next period:

where Kt represents the firm's invested capital at the end of period t. Increases in non-cash current

assets may, or may not be deducted, depending on whether they are considered to be maintaining the status quo, or to be investments for growth.

Unlevered Free Cash Flow (i.e., cash flows before interest payments) is defined as EBITDA - capex -

changes in net working capital. This is the generally accepted definition. If there are mandatory

repayments of debt, then some analysts utilize levered free cash flow, which is the same formula above, but less interest and mandatory principal repayments.

Investment bankers compute Free Cash Flow using the following formula:

FCFF = Net income + Noncash charges (such d&A) - Capex - Working capital expenditures = Free Cash

Flows to the Firm (FCFF)

FCFE = Net income + Noncash charges (such d&A) - Capex - Working capital expenditures + Net

borrowing - Net debt repayment = Free Cash Flows to the equity (FCFE)

Or simply:

FCFE = FCFF + Net borrowing - Net debt repayment

Uses of the metric

Free cash flow measures the ease with which businesses can grow and pay dividends to shareholders.

Even profitable businesses may have negative cash flows. Their requirement for increased financing will result in increased financing cost reducing future income.

According to the discounted cash flow valuation model, the intrinsic value of a company is the present

value of all future free cash flows, plus the cash proceeds from its eventual sale. The presumption is

that the cash flows are used to pay dividends to the shareholders. Bear in mind the lumpiness discussed below.

Some investors prefer using free cash flow instead of net income to measure a company's financial

performance, because free cash flow is more difficult to manipulate than net income. The problems with this presumption are itemized at cash flow and return of capital.

24


The payout ratio is a metric used to evaluate the sustainability of distributions from REITs, Oil and Gas

Royalty Trusts, and Income Trust. The distributions are divided by the free cash flow. Distributions may include any of income, flowed-through capital gains or return of capital.

Problems with capital expenditures

The expenditures for maintenances of assets is only part of the capex reported on the Statement of

Cash Flows. It must be separated from the expenditures for growth purposes. This split is not a

requirement under GAAP, and is not audited. Management is free to disclose maintenance capex or not.

Therefore this input to the calculation of free cash flow may be subject to manipulation, or require

estimation. Since it may be a large number, maintenance capex's uncertainty is the basis for some people's dismissal of 'free cash flow'.

A second problem with the maintenance capex measurement is its intrinsic 'lumpiness'. By their nature,

expenditures for capital assets that will last decades may be infrequent, but costly when they occur.

'Free cash flow', in turn, will be very different from year to year. No particular year will be a 'norm' that

can be expected to be repeated. For companies that have stable capital expenditures, free cash flow will (over the long term) be roughly equal to earnings

Agency costs of free cash flow

In a 1986 paper in the American Economic Review, Michael Jensen noted that free cash flows allowed

firms' managers to finance projects earning low returns which therefore might not be funded by the

equity or bond markets. Examining the US oil industry, which had earned substantial free cash flows in

the 1970s and the early 1980s, he wrote that

[the] 1984 cash flows of the ten largest oil companies were $48.5 billion, 28 percent of the total cash

flows of the top 200 firms in Dun's Business Month survey. Consistent with the agency costs of free

cash flow, management did not pay out the excess resources to shareholders. Instead, the industry

continued to spend heavily on [exploration and development] activity even though average returns were below the cost of capital.

Jensen also noted a negative correlation between exploration announcements and the market valuation

of these firms - the opposite effect to research announcements in other industries.

Modeling and analysis of financial markets

Much effort has gone into the study of financial markets and how prices vary with time. Charles Dow,

one of the founders of Dow Jones & Company and The Wall Street Journal, enunciated a set of ideas on

the subject which are now called Dow Theory. This is the basis of the so-called technical analysis

method of attempting to predict future changes. One of the tenets of "technical analysis" is that market

trends give an indication of the future, at least in the short term. The claims of the technical analysts

are disputed by many academics, who claim that the evidence points rather to the random walk

hypothesis, which states that the next change is not correlated to the last change.

The scale of changes in price over some unit of time is called the volatility. In 1900, Louis Bachelier

modeled the time series of changes in the logarithm of stock prices as a random walk in which the

short-term changes had a finite variance. This causes longer-term changes to follow a Gaussian distribution.

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Modeling the changes by distributions with finite variance is now known to be inappropriate. In the

1960s it was discovered by Benoît Mandelbrot that changes in prices do not follow a Gaussian

distribution, but are rather modeled better by Lévy stable distributions. The scale of change, or

volatility, depends on the length of the time interval to a power a bit more than 1/2. Large changes up

or down are more likely than what one would calculate using a Gaussian distribution with an estimated standard deviation.

Project finance is the financing of long-term infrastructure and industrial projects based upon a

complex financial structure where project debt and equity are used to finance the project, rather than

the balance sheets of project sponsors. Usually, a project financing structure involves a number of

equity investors, known as sponsors, as well as a syndicate of banks that provide loans to the

operation. The loans are most commonly non-recourse loans, which are secured by the project assets

and paid entirely from project cash flow, rather than from the general assets or creditworthiness of the

project sponsors, a decision in part supported by financial modeling. The financing is typically secured

by all of the project assets, including the revenue-producing contracts. Project lenders are given a lien

on all of these assets, and are able to assume control of a project if the project company has difficulties complying with the loan terms.

Generally, a special purpose entity is created for each project, thereby shielding other assets owned by

a project sponsor from the detrimental effects of a project failure. As a special purpose entity, the

project company has no assets other than the project. Capital contribution commitments by the owners

of the project company are sometimes necessary to ensure that the project is financially sound. Project

finance is often more complicated than alternative financing methods. Traditionally, project financing

has been most commonly used in the mining, transportation, telecommunication and public utility

industries. More recently, particularly in Europe, project financing principles have been applied to public

infrastructure under public-private partnerships (PPP) or, in the UK, Private Finance Initiative (PFI) transactions.

Risk identification and allocation is a key component of project finance. A project may be subject to a

number of technical, environmental, economic and political risks, particularly in developing countries

and emerging markets. Financial institutions and project sponsors may conclude that the risks inherent

in project development and operation are unacceptable (unfinanceable). To cope with these risks,

project sponsors in these industries (such as power plants or railway lines) are generally completed by

a number of specialist companies operating in a contractual network with each other that allocates risk

in a way that allows financing to take place. The various patterns of implementation are sometimes

referred to as "project delivery methods." The financing of these projects must also be distributed

among multiple parties, so as to distribute the risk associated with the project while simultaneously ensuring profits for each party involved.

A riskier or more expensive project may require limited recourse financing secured by a surety from

sponsors. A complex project finance structure may incorporate corporate finance, securitization, options, insurance provisions or other types of collateral enhancement to mitigate unallocated risk.

Project finance shares many characteristics with maritime finance and aircraft finance; however, the

latter two are more specialized fields.

Islamic project finance

Increasing attention is now focusing on Islamic project finance solutions (Shariah compliant) as a

catalyst for revitalising growth.World Islamic Infrastructure Conference is an annual unique platform for industry leaders seeking to tap into the potential of Islamic project finance.

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A basic project finance scheme

Hypothetical project finance scheme

Acme Coal Co. imports coal. Energen Inc. supplies energy to consumers. The two companies agree to

build a power plant to accomplish their respective goals. Typically, the first step would be to sign a

memorandum of understanding to set out the intentions of the two parties. This would be followed by an agreement to form a joint venture.

Acme Coal and Energen form an SPC (Special Purpose Corporation) called Power Holdings Inc. and

divide the shares between them according to their contributions. Acme Coal, being more established,

contributes more capital and takes 70% of the shares. Energen is a smaller company and takes the remaining 30%. The new company has no assets.

Power Holdings then signs a construction contract with Acme Construction to build a power plant. Acme

Construction is an affiliate of Acme Coal and the only company with the know-how to construct a power plant in accordance with Acme's delivery specification.

A power plant can cost hundreds of millions of dollars. To pay Acme Construction, Power Holdings

receives financing from a development bank and a commercial bank. These banks provide a guarantee

to Acme Construction's financier that the company can pay for the completion of construction. Payment

for construction is generally paid as such: 10% up front, 10% midway through construction, 10%

shortly before completion, and 70% upon transfer of title to Power Holdings, which becomes the owner of the power plant.

Acme Coal and Energen form Power Manage Inc., another SPC, to manage the facility. The ultimate

purpose of the two SPCs (Power Holding and Power Manage) is primarily to protect Acme Coal and

Energen. If a disaster happens at the plant, prospective plaintiffs cannot sue Acme Coal or Energen and target their assets because neither company owns or operates the plant.

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A Sale and Purchase Agreement (SPA) between Power Manage and Acme Coal supplies raw materials to

the power plant. Electricity is then delivered to Energen using a wholesale delivery contract. The cashflow of both Acme Coal and Energen from this transaction will be used to repay the financiers.

Complicating factors

The above is a simple explanation which does not cover the mining, shipping, and delivery contracts

involved in importing the coal (which in itself could be more complex than the financing scheme), nor

the contracts for delivering the power to consumers. In developing countries, it is not unusual for one

or more government entities to be the primary consumers of the project, undertaking the "last mile

distribution" to the consuming population. The relevant purchase agreements between the government

agencies and the project may contain clauses guaranteeing a mimimum offtake and thereby guarantee

a certain level of revenues. In other sectors including road transportation, the government may toll the

roads and collect the revenues, while providing a guaranteed annual sum (along with clearly specified

upside and downside conditions) to the project. This serves to minimise or eliminate the risks associated with traffic demand for the project investors and the lenders.

Minority owners of a project may wish to use "off-balance-sheet" financing, in which they disclose their

participation in the project as an investment, and excludes the debt from financial statements by

disclosing it as a footnote related to the investment. In the United States, this eligibility is determined

by the Financial Accounting Standards Board. Many projects in developing countries must also be

covered with war risk insurance, which covers acts of hostile attack, derelict mines and torpedoes, and

civil unrest which are not generally included in "standard" insurance policies. Today, some altered

policies that include terrorism are called Terrorism Insurance or Political Risk Insurance. In many cases,

an outside insurer will issue a performance bond to guarantee timely completion of the project by the contractor.

Publicly-funded projects may also use additional financing methods such as tax increment financing or

Private Finance Initiative (PFI). Such projects are often governed by a Capital Improvement Plan which adds certain auditing capabilities and restrictions to the process.

History

Limited recourse lending was used to finance maritime voyages in ancient Greece and Rome. Its use in

infrastructure projects dates to the development of the Panama Canal, and was widespread in the US

oil and gas industry during the early 20th century. However, project finance for high-risk infrastructure

schemes originated with the development of the North Sea oil fields in the 1970s and 1980s. For such

investments, newly created Special Purpose Corporations (SPCs) were created for each project, with

multiple owners and complex schemes distributing insurance, loans, management, and project

operations. Such projects were previously accomplished through utility or government bond issuances, or other traditional corporate finance structures.

Project financing in the developing world peaked around the time of the Asian financial crisis, but the

subsequent downturn in industrializing countries was offset by growth in the OECD countries, causing

worldwide project financing to peak around 2000. The need for project financing remains high

throughout the world as more countries require increasing supplies of public utilities and infrastructure.

In recent years, project finance schemes have become increasingly common in the Middle East, some incorporating Islamic finance.

The new project finance structures emerged primarily in response to the opportunity presented by long

term power purchase contracts available from utilities and government entities. These long term

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revenue streams were required by rules implementing PURPA, the Public Utilities Regulatory

Policies Act of 1978. Originally envisioned as an energy initiative designed to encourage domestic

renewable resources and conservation, the Act and the industry it created lead to further deregulation

of electric generation and, significantly, international privatization following amendments to the Public

Utilities Holding Company Act in 1994. The structure has evolved and forms the basis for energy and other projects throughout the world.

In corporate finance, real options analysis or ROA applies put option and call option valuation

techniques to capital budgeting decisions. A real option itself, is the right—but not the obligation—to

undertake some business decision; typically the option to make, or abandon, a capital investment. For

example, the opportunity to invest in the expansion of a firm's factory, or alternatively to sell the

factory, is a real option.

ROA is often contrasted with more standard techniques of capital budgeting (such as NPV), where only

the most likely or representative outcomes are modelled, and "flexibility" of this type is thus "ignored";

see Valuing flexibility under Corporate finance. ROA is therefore additionally useful in that it forces

decision makers to be explicit about the assumptions underlying their projections, and is increasingly employed as a tool in business strategy formulation.

Considerations

In contrast to financial options, a real option is not often tradeable — e.g. the factory owner cannot sell

the right to extend his factory to another party, only he can make this decision; however, some real

options can be sold, e.g., ownership of a vacant lot of land is a real option to develop that land in the

future. Some real options are proprietary (owned or exercisable by a single individual or a company);

others are shared (can be exercised by many parties). Therefore, a project may have a portfolio of

embedded real options; some of them can be mutually exclusive.

With real option analysis, uncertainty inherent in investment projects is usually accounted for by risk-

adjusting probabilities (a technique known as the equivalent martingale approach). Cash flows can then

be discounted at the risk-free rate. With regular DCF analysis, on the other hand, this uncertainty is

accounted for by adjusting the discount rate, (using e.g. the cost of capital) or the cash flows (using

certainty equivalents). These methods normally do not properly account for changes in risk over a

project's lifecycle and fail to appropriately adapt the risk adjustment.

The valuation methods generally employed are Closed form solutions - often modifications to Black

Scholes - and binomial lattices. The latter are probably the most widely used. Specialised Monte Carlo

Methods have also been developed and are increasingly applied particularly to high dimensional

problems. When the Real Option can be modelled as a partial differential equation, then the related

finite difference scheme is sometimes applied, although this is uncommon due to its mathematical

sophistication.

In general, all of these methods are limited either as regards dimensionality, or as regards early

exercise, or both; in selecting a model, analysts must usually tradeoff between these considerations.

Sometimes, the stochastic nature of such projections can make analysis using the Monte Carlo method

infeasible, necessitating more traditional investigatory methods, such as Robinson differentials. Other

new methods have recently been introduced to simplify the calculation of the real option value and thus

make the numerical use of the methods easier for practitioners; these include the Datar-Mathews method (2004,2007) and the Fuzzy Pay-Off Method for Real Option Valuation (2008).

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History

Whereas business operators have been making capital investment decisions for centuries, the term

"real option" is relatively new, and was coined by Professor Stewart Myers at the MIT Sloan School of

Management in 1977. It is interesting to note though, that in 1930, Irving Fisher wrote explicitly of the

"options" available to a business owner (The Theory of Interest, II.VIII). The description of such

opportunities as "real options", however, followed on the development of analytical techniques for

financial options, such as Black–Scholes in 1973. As such, the term "real option" itself is closely tied to these new methods.

Real options are today an active field of academic research. Professor Lenos Trigeorgis (University of

Cyprus) has been a leading name in academic real options for many years, publishing several influential

books and academic articles in the field. He has also broadened exposure to real options through

layman articles in publications such as The Wall Street Journal. An academic conference on real options is organized yearly (Annual International Conference on Real Options).

Amongst others, the concept was "popularized" by Michael J. Mauboussin, the chief U.S. investment

strategist for Credit Suisse First Boston and an adjunct professor of finance at the Columbia Business

School. Mauboussin uses real options in part to explain the gap between how the stock market prices

some businesses and the "intrinsic value" for those businesses as calculated by traditional financial

analysis, specifically using discounted cash flows. This popularization is such that ROA is now a

standard offering in postgraduate finance degrees, and often, even in MBA curricula at many Business Schools.

Recently, in business strategy, real options have been deployed in the construction of an "option

space", where volatility is compared with value-to-cost.

Books

Amram, Martha; Kulatilaka,Nalin (1999). Real Options: Managing Strategic Investment in an

Uncertain World. Boston: Harvard Business School Press. ISBN 0-87584-845-1.

Copeland, Thomas E.; Vladimir Antikarov (2001). Real Options: A Practitioner's Guide. New

York: Texere. ISBN 1-587-99028-8.

Dixit, A.; R. Pindyck (1994). Investment Under Uncertainty. Princeton: Princeton University

Press. ISBN 0-691-03410-9.

Moore, William T. (2001). Real Options and Option-embedded Securities. New York: John Wiley

& Sons. ISBN 0-471-21659-3.

Müller, Jürgen (2000). Real Option Valuation in Service Industries. Wiesbaden: Deutscher

Universitäts-Verlag. ISBN 3-824-47138-8.

Smit, T.J.; Trigeorgis, Lenos (2004). Strategic Investment: Real Options and Games. Princeton:

Princeton University Press. ISBN 0-691-01039-0.

Trigeorgis, Lenos (1996). Real Options: Managerial Flexibility and Strategy in Resource

Allocation. Cambridge: The MIT Press. ISBN 0-262-20102-X.