FinancialTheoryandPractice.pdf

Financial Theory & Practice

OUBS002124

OPEN UNIVERSITYof MAURITIUS

Open University of Mauritius - Financial Theory & Practice i

Financial Theory & Practice

OUBS002124


ii Open University of Mauritius - Financial Theory & Practice

PROJECT COORDINATIONOpen University of Mauritiius

Open University of Muritius, May 2013First published 2013

All rights reserved. No part of this work may be reproduced in any form or by any means, without prior written permission from the Open University of Mauritius. Commercial use and distribution of this material is strictly prohibited.

Open University of Mauritius - Financial Theory & Practice 1

Financial Theory& Practice

OUBS002124

Table of Contents UNIT 1 - THE FINANCIAL SYSTEM 3

UNIT 2 - CAPITAL MARKETS 11

UNIT 3 - THE TIME VALUE OF MONEY 21

UNIT 4 - CAPITAL INVESTMENT APPRAISAL 33

UNIT 5 - SHARE VALUATION, RISK AND RETURN 45

UNIT 6 - FIXED INCOME SECURITIES 55

UNIT 7 - RISK, RETURN AND DIVERSIFICATION 69

ASSIgNMENT 83

SOLUTIONS 85


2 Open University of Mauritius - Financial Theory & Practice


THE FINANCIAL SYSTEMUNIT STRUCTURE

1.0 Overview

1.1 Learning Objectives

1.2 Introduction

1.3 Functions of the Financial System

1.4 Financial Intermediaries

1.5 Primary and secondary markets

1.6 The Relationship between Banks and Companies

1.7 Summary

1.8 Tutorial

1.9 Suggested Reading

UNIT1


1.0 OVERVIEW This unit lays out the foundation to the understanding of the importance of financial markets to the economy. The chapter will enable students to appreciate the various aspects and concepts of financial markets.

1.1 LEARNING OBJECTIVES By the end of this Unit, you should be able to:

1. Define a financial market and explain its importance to the economy.2. Explain the role of financial intermediaries.3. Discuss the differences between the primary and secondary markets.4. Describe the importance of the banking system to companies

1.2 INTRODUCTION A financial market helps transfer financial assets, real assets and financial risks in various forms from one entity to another, from one location to another and across time. The central figure to the whole world of finance is the management of cash as depicted in Figure 1.

Figure 1: Uses of Cash

The two main sources of cash are from equity capital and loan capital.

(a) Equity Capital Companies raise money by issuing equity (shares) that is turn bought by individual

and institutional investors. This capital is then invested in various projects that will bring added profitability to the company. When investors buy a share in a particular company, they become entitled to future dividends, paid out of profits by the firm. These investors are also entitled to participate in the management of the company through their votes in Annual General Meetings (AGMs).

(b) Loan Capital The public, companies and government very often need to spend money now, but do

not have sufficient funds. This loan capital can be obtained by contract a loan with their banks or other financial institution. The loan is then serviced by meeting interest payment and capital repayment within the time frame as agreed by both parties.

The Government can also borrow money from investors for various reasons. An example of the debt contracted by the Government of Mauritius, through the Bank of Mauritius, is depicted in Illustration 2. Such debts are referred to as Government Treasury Bills since they have a maturity of less than a year (182 days). Treasury Notes have a maturity that ranges from 1 year to 10 years. Treasury bonds have a maturity exceeding 10 years. The Government repays those debts through the taxes that they collect and from the projects funded by these debts. The following is an example of a treasury bill issued by Mauritius.

Equity Capital Shareholders

EmployeesLoan

Capital Lenders

GovernmentGovernment

CustomersSuppliers of Raw

Materials

Cash


Box 1: Notice of Tender for Government of Mauritius Treasury Bills

Government of Mauritius Treasury Bills (GMTB) with maturity of 182 days for a nominal amount of Rs800million will be sold through auction on Friday 08 March 2013, for same day settlement to:

(i) Primary Dealers, and(ii) Exceptionally and until further notice, to Non-Primary Dealer banks and

other eligible Financial Institutions, which have participated in the primary auction held by the Bank at least twice fortnightly.

The Bank will receive bids for this auction on Friday 08 March 2013 on a yield basis quoted to two decimal places, in multiples of Rs100,000, on tender forms which are obtainable at its seat or on its website.. Applications received after the prescribed time and date will not be considered.

Banks may submit bids through the Reuters Dealing System.

In the event of oversubscription of the GMTB, the Bank may issue Bank of Mauritius Bills of the same tenor to bidders who are willing to so accept at the weighted accepted yield for above maturity of GMTB.

Results of the auctions will be announced on the same day and successful bidders will be required to effect payment of the cost price of the GMTB/Bank of Mauritius Bills through the Mauritius Automated Clearing and Settlement System.

Adapted from the Bank of Mauritius

Source: Bank of Mauritius

Normally, a company in need of capital will use the services of a financial intermediary i.e. a bank to get access to the required funds. Alternatively, companies listed an exchange may opt to float their debt directly on the market. Through such an undertaking, companies lower their cost of debt by paying a lower rate of interest since they have omitted the use of the bank.

Consider the example of Omnicane in Box 2 where the company wished to contract debt directly from potential investors on the Stock Exchange of Mauritius. Box 2 showcases the Note issued by Omnicane. The company will pay interest semi-annually at the rate of 5.70% and the debt will be repaid on the 17th January 2016.


Box 2: Omnicane LimitedMulticurrency Medium Term Note Programme

(Aggregate Maximum amount: Up to MUR 3 Million)

Second Tranche of up to MUR 920Millions

Further to the communiqu dated 28 November 2012, Omnicane Limited hereby announces the results of the auction for the second issue of notes in respect of the above and held on 05 December 2012 as follows:

Issuer Omnicane Limited

Aggregate Nominal Amount Required MUR 920,000,000

Nominal Amount per Note MUR 100,000

Bids Received MUR 1,000,000,000

Bids Accepted MUR 920,000,000

Clearing Rate 5.70%

Fixed Interest Rate payable5.70% p.a. payable semi-annually in arrears on 18 July and on 18 January of each year until maturity

Settlement Date 18 January 2013

Issue Date 18 January 2013

Commencement of Trading 21 January 2013

Maturity Date and Redemption Date 17 January 2016

On the first day of trading of the second tranche of Notes issues, scheduled for the 31 Jnuary 2013, a minimum of 10 Notes will be made available for trading.

Source: Omnicane Limited

1.3 FUNCTIONS OF THE FINANCIAL SYSTEM The two main uses of the financial system are raising equity from stock markets and borrowing from the financial markets. The other uses of the financial system include:

(a) Saving money for future consumptionPeople always save a portion of their salaries for consumption in future periods. E.g. Workers who save for their retirement needs move some of their actual earnings into the future. At retirement, they then use these savings to cater for their needs. To move money across time, savers have a host of products in which to invest. Investors need a fair rate of return to compensate them for the use of their money and in the event that they lose the money. Therefore, a conservative investor will prefer to invest in Government Treasury Bonds as these as being risk free. A risk seeking investor will invest in other financial products such as mutual funds, stocks or even banks. Given the riskiness of these financial instruments, the return on each of them will differ, with the riskier asset offering more return.


Activity 1

Suppose you are a financial analyst working for a well-known bank. Currently, the market is offering the following rates:

Instrument Return

Banks savings rate 5%

Government Treasury Bond 4%

Mutual Fund (Expected) 7%

Stock A (Expected) 10%

Stock B (Expected) 12%

During the day, two potential investors take an appointment with you to discuss their financial situation and to identify suitable investment opportunities. Both investors have a capital of Rs 1million to invest.

The first investor is aged 30 and from his personality and subsequent discussion with him, you find that he is a risk seeking individual. The second investor has just retired from service and is looking for an investment that will allow him to have access to the funds at any point in time. Return is not of a major concern to him and you determine that he is a risk-averse investor.

What are the investments that you will recommend to each of the investors?

(b) To exchange assets for immediate and future deliveries Individuals and companies frequently trade one asset for another based on their

usefulness to them at a particular point in time. Investors may trade one currency for another one or use money to buy a commodity, etc. Consider the following example:

- A Mauritian hotel company e.g. LUX* Resorts pays its Mauritian workers in Rupees but invoices its services to tourists in Euros. Therefore, it will need to trade in the foreign exchange markets to exchange Euros for Rupees.

(c) To manage risks Investors face financial risks which include default risk, a change in foreign

exchange rates, a hike in raw materials, amongst others. These risks can be hedged by trading different contracts such as forward contracts, futures contracts, swaps, option contracts, etc. Consider the following:

- Arabica and a coffee manufacturer face different risks related to the price of coffee. Arabica fears that the price of coffee will increase while the coffee manufacturer believes that the price of coffee will fall. They can both eliminate their exposures by entering into a binding agreement referred to as a forward contract. In such a contract, the coffee manufacturer agrees to sell a fixed quantity of coffee to Arabica for a specified price and under the contract, Arabica is obligated to buy the coffee at that specified price. Such an undertaking therefore eliminates both parties exposure to changing coffee prices.

(c) Price discovery of assets at very low costs, thereby aiding liquidity of financial products trading in different markets

Stock prices and interest rate are valuable information used by different investors as to their pattern of consuming, saving or dividing their capital among different asset classes. However, research of these information is time-consuming and a costly one for an individual investor. However, when a financial institution researches the market price/rates, the cost is greatly reduced. The fact that such information is available at very low cost makes trading easier and hence increases the liquidity of different assets across different markets.


1.4 FINANCIAL INTERMEDIARIES Financial intermediaries have developed to bring lenders and borrowers together and help these entities to achieve their financial goals. These financial intermediaries include banks, credit unions, brokers, exchanges, dealers, mutual funds, hedge funds, insurance companies and various other finance corporations. Financial intermediaries are fundamental to the smooth running of the financial system.

Brokers are responsible for executing orders on behalf of their clients. Their mission is to identify traders who are willing to take the opposite side of their clients orders.

Investment banks provide advice to corporate clients and their expertise lies in structured finance, mergers and acquisitions, initial public offerings.

Exchanges are platforms where traders meet to arrange and execute their trades. Historically, exchanges used to be physical locations where buyers and sellers would meet. Over time, it has evolved to electronic exchanges whereby all transactions are executed over computer terminals. Examples of exchanges are NYSE-Euronext, Tokyo Stock Exchange, NASDAQ, Chicago Mercantile Exchange and London Stock Exchange.

Dealers, unlike brokers, fill their clients order by trading with them. After executing this initial transaction, dealers will then try to reverse such transactions by entering into an opposite trade with another client and making a profit. Such transaction enhance the liquidity of a particular market and hence, of financial products.

Mutual Funds or investment companies provide the added advantage of pooling and managing the money of various investors. Individual investors portfolios are not large enough to be able to buy the universe of securities compared to a mutual fund as this would tantamount to holding a number of individual stocks. On the other hand, the mutual fund offers the benefit of economies of scale since the transaction costs incurred whilst buying the stocks is dispersed over a much higher portfolio size.

Insurance companies help investors to minimize risks by creating insurance contracts (policies) against a payment in the even that some loss occurs. These contracts thus provide a hedge against potential losses. Examples of insurance contracts include, automobile, fire, life, medical, theft, etc.

1.5 PRIMARY AND SECONDARY MARKETSOnce a security has been issued, it lives a life of its own, in that it is sold from one investor to the other. The life of the security is connected to the fact that it can be bought or sold at any moment. For example, shares that were created when a company was incorporated can later be floated on an exchange. New issues of a security are floated on a primary market. Subsequent transactions, e.g. shares of the company being bought or sold, occur on a secondary market.

The main difference between the primary and secondary market is that the primary market is used for the issue of new financial products, from equity issues to bond issues. On the other hand, the secondary market is the market for used financial products. Instruments bought and sold on this market must have already been created and are simply exchanging hands, without any new security being issued.

In essence, the task of the secondary market is to ensure that the financial products are correctly priced and traded, thus increasing the liquidity of the product. The difference between the primary and secondary market is conceptual; they are not physically separated from each other.


Secondary markets play a vital role in valuing securities. Any investor buying a certain financial instrument does not wish to remain invested in that particular asset indefinitely. Consider the case of a share and a bond. An investor, who has bought a share at a price of Rs100, will want to realize a profit when the shares price increases to Rs150. Hence, the importance of a secondary market to provide liquidity (ability to buy or sell a product in a relatively short period of time and without incurring any loss of value) to sell the share at Rs150. Comparatively, a bond has a maturity date and a certain redemption value (price that will be repaid at the end of the maturity period). If an investor holding a bond wished to hold onto the bond until maturity, he may do so. In other cases, should he wish to sell the bond before the maturity date, he may do so if a liquid market for the product exists such that the market will value the security at a certain price at that particular date.

1.6 THE RELATIONSHIP BETWEEN BANKS AND COMPANIES Bank intermediation is provided mostly by commercial banks. The latter serve as intermediaries between those having a surplus of funds and those that in need of capital. The business of banking is such that these institutions collect capital from the former and lend to a wide range of borrowers that include individuals, companies and even the Government.

The risk of lending is borne by these banks and their balance sheet should be adequately funded and the portfolio of clients diversified enough to minimize the credit risk and hence, systemic risk on other banks and the economy should massive defaults arise in the economy.

Over the years, commercial banks have provided a wide range of value added services to their customers so as to provide them with funds in a more efficient and timely manner. Banks have further devolved and thus helped their corporate clients gain direct access to capital markets, leading to the rise of investment banking. The latter includes, but is not limited to, the following services: Access to Equity Markets: Investment bankers help companies to list their shares

on the stock market. They are responsible for preparing the initial public offering process such as supporting their client to prepare a prospectus. Later on, they advise the company on additional issues that the firm may require and on the type of instrument that is best suited for the issue.

Access to Bond Markets: Just like shares, investment banks can also help firms to list their debt on a bond market. Refer to Box 2 The case of Omnicane Limited.

Mergers and Acquisitions: Investment bankers are in contact with leading directors and are always on the lookout for potential mergers and acquisitions so as to help these firms to grow even further and accentuate their dominance on the market.

Asset Management: Banks use their deep knowledge of financial markets to provide this additional service to individuals, companies and other institutions. The products on offer comprise portfolios of listed and unlisted securities, bonds, commodities, real-estate. These portfolios are referred to as mutual funds.


1.7 SUMMARY The importance of the financial system to the economy has thoroughly been discussed in this unit. The key players in the form of financial intermediaries play an important role and are key to the effective transmission of services and capital. Lastly, we oversaw the differences between the primary and secondary markets and shedding light on the relationship between firms and the banking system.

The next unit shall be geared towards capital markets (Stock markets, bond markets, money markets, derivatives markets, futures markets, forward market, commodities market, real estate market) and the different financial products traded on those markets. Close attention shall be paid to the market existing on the Mauritian landscape.

1.8 TUTORIALS Question 1How can households, who need to invest their excess funds, reduce their risk?

Question 2Financial intermediaries can basically be split in two: brokers and market makers. (a) Discuss the differences between brokers and market makers(b) In your opinion, should the price earned by market makers be at a premium to the

commission earned by brokers?

Question 3The evolution of the financial system has contributed massively to the growth of various economies around the world. Discuss the ways in which the financial system has aided in this growth with the use of suitable examples.

Question 4With the use of relevant examples (i.e. recently issued stocks and already trading stocks), explain the differences existing between the primary and secondary markets?

Question 5Central Banks across the world have inferred that companies are increasingly dependent on banks to fund future growth and this relationship has since been under close supervision due its repercussion on the economy during times of crisis. Discuss the intricacies of the working relationship between firms and the banking system.

1.9 SUGGESTED READINGS Vernimmen, Pierre; Quiry, Pascal; Dallocchio, Maurizio; Le Fur, Yann; Salvi, Antonio, Corporate Finance, John Wiley & Sons, Ltd, Second Edition (Chapter 1)

Brealey, Richard A.; Myers, Stewart C., Principles of Corporate Finance, Latest Edition (Chapter 1)

Pike, Richard; Neale, Bill, Corporate and Finance Investment Decisions and Strategies, Second Edition (Chapters 1 and 2)

Bodie, Zvi; Kane, Alex; Marcus, Alan J., Investments, Eight Edition (Chapter 1)


UNIT STRUCTURE

2.0 Overview


2.2 Stock Markets

2.2.1 Initial Public Offering

2.2.2 International stock market indexes

2.2.3 The Stock Exchange of Mauritius and the Development Enterprise Market

2.2.4 Measuring the return of a stock

2.3 Bond Markets

2.4 Money Markets

2.5 Derivatives Markets

2.5.1 Futures Market

2.5.2 Forward Market

2.5.3 Swap Market

2.5.4 Options Market

2.6 Commodities Markets

2.7 Real Estate Market

2.8 Summary

2.9 Tutorial

CAPITAL MARKETSUNIT2


2.0 OVERVIEW After the brief introduction from the previous chapter, Unit 2 explores the world of equities in detail, spanning from the Mauritian Stock Exchanges to worldwide exchanges. Our attention to then shift to fixed income markets (bond and money markets). Derivatives markets (futures, forwards and swaps). An emerging investment trend in the form of commodities and real-estate is also introduced here.

2.1 LEARNING OBJECTIVES By the end of Unit 2, you should be able to:1. Appreciate how stocks are issued on the stock market and able to discuss about

major stock exchanges2. Differentiate between bond markets and money markets3. Assess the basic characteristics of futures contracts, forward contracts, swap

agreements and options markets.4. Discuss alternative investment forms commodities and real estate markets

2.2 STOCK MARKETS A stock exchange has two principal economic functions. These are to enable companies to raise new capital (via the primary market) and to facilitate the trading of existing shares (via the secondary market) through the negotiation of a price at which title to ownership of a company is transferred between investors. Table 1 presents some stock markets.

Country Exchange

Mauritius Stock Exchange of Mauritius

United Kingdom FTSE

France CAC 40

Germany Frankfurt Stock Exchange

U.S. New York Stock Exchange

India Bombay Stock Exchange

China Shanghai Stock Exchange

South Africa Johannesburg Stock Exchange

Table 1: Various Stock Exchanges around the World

Box 1: What is a Share?There exist basically two types of shares: Common shares and Preference shares.

Common Shares represent an ownership or stake in a company and are the leading type of equity security. On purchase of a common share in a company, the shareholder is entitled to participating in the governance of the firm through voting rights at Annual General Meetings (AGMs). These shareholders are also entitled to a claim on the companys assets in the case of liquidation. Companies may pay out all of their profits in the form of dividends to shareholders, but they are obligated to so.

On the other hand, holders of preference shares do not participate in the operating performance of the company nor do they have any voting rights. However, preference shares rank above common shares with respect to the payment of dividends and the distribution of the firms net assets in the event of liquidation. Dividends paid on preference shares are inherently fixed, similar to interest payments.


2.2.1 INITIAL PUBLIC OFFERINGThere are two types of primary market issues of common stock.

a) Initial public offerings or IPOs are stocks issued by a formerly privately owned company that is going public, that is, selling stock to the public for the first time.

b) Seasoned equity offerings are offered by companies that already have floated equity. For examples, a sale by IBM of new shares would constitute a seasoned new issue. (Bodie, Kane, & Marcus, 2009)

Investment bankers normally manage the issue of new securities to the investing community. Once the Financial and Services Commission has given its approval, the investment bankers can distribute a prospectus and organize road shows to market the stock and the company. These road shows are important in that it helps to generate interest about the company and provide financial and non-financial information about the firm to investors. The latter can also formulate the price at which they would like to purchase the stock of the company. These indications of interest are referred to as book and the process of polling potential investors is referred to as bookbuilding.

Box 2: Facebook IPO Facts, Fiction and Flops

Facebook Inc.s fiasco is still the talk of Wall Street. The newly public shares are losing an average of about $1 per trading day since their offering. If that lasts, the social-networking company would be worth nothing before the end of June, and Chief Executive Mark Zuckerbergs trips to McDonalds will seem less chic and more necessary.

Maybe the biggest miss is this: Facebook was a big bomb.

That might be true when measured against all the hype Facebook got leading up to its first day of trading. When it comes to the U.S. market for initial public offerings, though, Facebook was just a high-profile flop in a series of lesser-known flops.

Overlooked is that Facebook decided to make its entrance into an U.S. IPO market in the dumps and last year wasnt a blockbuster for U.S. IPOs. Even though IPOs world-wide are rising by 43% on the first day of trading, first-day gains arent as common in the U.S. Of the 53 U.S. deals priced in the last three months, the average price increase was 14% on the first day of trading. But through May 25, the average increase over the offering price was 8% for IPOs this year.

Like Facebook, many initial public offerings were overvalued by traditional measures. They simply have to come down to earth. Many of the companies that have seen sharp drops from their offering prices were trading at multiples that overestimated future growth: price-to-earnings ratios of 20, 30 or more.

Facebook trades at 60 times trailing 12-month earnings, 49 times prospective 12-month earnings, 43 times cash flow and 12 times book value. A report by Thomson Reuterss concluded that on a fundamental basis it is worth only about $10.22 a share.

So was Facebooks IPO a flop? Yes. But it was only a flop in a time when most offerings didnt bother to risk the embarrassment.

It is one thing to disappoint compared to other IPO newborns and quite another to compare to the stillborn public corporation.

By another measure, Facebook was far from a failure. The investors who cashed out at the top are hardly complaining. They maximized their take through the efforts of Morgan Stanley and the underwriters who marketed Facebook.

In the end, they paid for an IPO to make them rich. It was up to the rest of us to buy it.

Source: Wall Street Journal (31st May 2012)


2.2.2 INTERNATIONAL STOCK MARKET INDExESFor one particular country, there may exist various exchanges. Any exchange may possess one index or many indexes. A stock market index is a technique of measuring the value of a stock market or only a section of the stock market. An index is an important tool for investors and finance professionals alike in that it describes the evolution of the market over a certain time period.

Many stock exchanges exist in the U.S. for e.g. NYSE, NASDAQ, S&P500, etc. Different indices proposes various ways of following these markets e.g. the Wilshire 5000 index computes the market value of all NYSE and American Stock Exchange including actively traded NASDAQ stocks. On the other hand, the Dow Jones or DJIA includes 30 blue-chip companies. This index has been calculated since 1896.

2.2.3 STOCK ExCHANGE IN MAURITIUSThe stock exchange of Mauritius operates two markets: the Official Market and the Development and Enterprise Market. There are 42 companies listed on the SEM and 47 companies listed on the DEM. For a company to be able to list on the SEM or the DEM, it needs to satisfy the exchanges listing requirements. The Official Market of the SEM has three major indexes: SEMDEX, SEM-7 and SEMTRI. On the other hand, the indexes of the DEM include the DEMEX and the DEMTRI.

Activity 1Using the official website of the Stock Exchange of Mauritius, find the following information:

(a) Under which groupings has companies listed on the SEM and the DEM been categorized? http://www.stockexchangeofmauritius.com/officialmarket-listedcompanies

(b) What are the listing requirements for a company wishing to list on the SEM and the DEM? http://www.stockexchangeofmauritius.com/listingrules http://www.stockexchangeofmauritius.com/dem-listingrules

(c) What are the differences between the SEMDEX, SEM-7 and the SEMTRI? http://www.stockexchangeofmauritius.com/officialmarketindices/index/semdex/weekly#

(d) What are the difference between the DEMEX and the DEMTRI? http://www.stockexchangeofmauritius.com/officialmarketindices/index/semdex/weekly#

Note: The official website of the stock exchange of Mauritius is: http://www.stockexchangeofmauritius.com/

2.2.4 Measuring Return A stock market index is used to reflect changes in the average value of a list of companies which are traded on a particular market. For example, in France the CAC 40 provides such a means. The same goes for the Dow Jones in the U.S. and the SEMDEX in Mauritius.

The market capitalization is used to measure the size of a company or the size of the stock market or the size of part of the stock market.

Market Capitalisation of Company A = (Number of shares of Company A) X (Price of a share of Company at time t)


Consider the following example:An analyst gathers the following information for a market-capitalisation-weighted index comprised of securities A, B and C. The aim of this exercise is to find the total return of the index.

SecurityBeginning of Period Price/

MUR

End of Period Price/MUR

Dividends Per Share/ MUR

Shares Outstanding

A 2,500 2,700 100 5,000

B 3,500 2,500 150 7,500

C 1,500 1,600 100 10,000

The Beginning of Period Price column indicates the price of a share at the beginning of the period under investigation.

The End of Period Price column indicates the price of a share at the end of the period under investigation.

The Dividends Per Share column indicates the amount of dividends paid to the holder of one share.

The Shares Outstanding column shows the number of shares held by the company.

Return of Stock A over the period considered

= (Price at end Price at beginning / Price at beginning) = (2700-2500 / 2500) * 100%

= 8%

Total Return of Stock A over the period considered

= Price at end + Dividends Paid Price at Beginning Price at Beginning = (2700 + 100 2500) / 2500 = 12%

Carrying out the same calculation for stock B and C will yield:Stocks Simple Return Total ReturnB -28.6% -24.3%C 6.7% 13.3%

Total Market Capitalisation of Stock A

= No. of Shares of A X Price of Share of A

= 5,000 X 2,700

= MUR 13,500,000

Total Market Capitalisation of Stock B

= No. of Shares of B X Price of Share of B

= 7,500 X 2,500

= MUR 18,750,000


Total Market Capitalisation of Stock C = No. of Shares of C X Price of Share of C = 10,000 X 1,600 = MUR 16,000,000

Total Market Capitalisation of the Index = Total Market Capitalisation of Stock A + Total Market Capitalisation of Stock B + Total Market Capitalisation of Stock C = 13,500,000 + 18,750,000 + 16,000,000 = MUR 48,250,000

Weight of a stock in the index = Market Capitalisation of the stock / Market Capitalisation of Index

WeightMarket

Capitalisation of the stock / MUR

Total Market Capitalisation of

Index/ MURWeight / %

A 13,500,000 48,250,000 27.98B 18,750,000 48,250,000 38.86C 16,000,000 48,250,000 33.16

Return of Index = Weight of a particular Stock X Total Return of the Stock

Weight / % Return of the Stock / % Weighted Return

A 27.98 12% 3.4%B 38.86 -24.3% -9.4%C 33.16 13.3% 4.4%Return of Index 100% - -1.7%

Hence, the return of the index is -1.7%

2.3 BOND MARKETS The bond market comprises longer term debt instruments other than those that trade on the money market. This market includes Treasury notes and bonds, corporate bonds, municipal bonds, amongst others. Most of these instruments promise either a fixed stream of income or a stream of income that is determined according to a specific formula. It is common practice to refer to these instruments as debt instruments or bonds.

Treasury notes and bonds are issued by the Government and are virtually considered as being risk free i.e. there is no risk that the Government will default on repayment. Treasury notes have a maturity of up to 10 years while Treasury bonds have a maturity greater than 10 years. These debt instruments pay annual or semi-annual coupons over the life of the bond, with final repayment at maturity. (Refer to Chapter 1 Box 1)

Corporate bonds are issued when firms borrow money directly from the public. These bonds are listed on an exchange and are typically similar to Treasury notes and bonds in that they pay annual or semi-annual coupons over the life of the bond and return the face value to the holder of the bond at maturity. (Refer to Chapter 1 Box 2)

Municipal bonds are issued by state and local governments. They are similar to treasury securities exempt that their interest income is exempt from tax. The interest income is also exempt from state and local taxation in the issuing state. Capital gains tax is however payable when the bonds mature or are sold prior to their maturity dates.


Convertible Bonds give the bondholder a guaranteed coupon as well as the option to exchange the bond into a predetermined number of common stocks of the issuing company. While this feature allows investors to take advantage of favourable movements in the price of the issuing companys common stocks, it also enables issuers to offer a lower coupon rate and thereby reducing their cost of financing. However, in the event of a default by the issuing company, both the bond and the conversion option may become worthless. Furthermore, the company can also force conversion by calling the bond.

Eurobonds are international bonds which can be issued by both corporations and governments with the main aim of tapping secured and long-term financing across a geographical diverse investment clientele. It is generally underwritten by an international syndicate and sold simultaneously in many countries different from the country of the currency in which the issue is denominated. Thus, a dollar-denominated Eurobond would be sold outside the United States only. As an example, a Greek corporation issuing dollar-denominated bonds through a consortium of Japanese, Greek and UK investment banks.

2.4 MONEY MARKETS The money market is a sub-sector of the fixed income market. It consists of very short term debt securities that usually are highly liquid. These securities trade in large denominations and are out of reach of individual investors. Examples of instruments traded on money markets include Treasury Bills, Certificates of Deposits, Commercial Paper, amongst others.

Treasury Bills are most liquid and marketable of all money market instruments. Investors buy bills at a discount from the stated maturity value. At the bills maturity, the holder receives from the government a payment equal to the face value of the bill. The difference constitutes the investors gain. T-Bills are issued with initial maturities of 28, 91, 182 days. Individuals and institutional investors can purchase T-Bills directly at auction or on the secondary market from a government securities dealer.

A certificate of deposit or CD is a time deposit with the bank. Time deposits may not be withdrawn on demand. The bank pays interest and principal to the depositor only at the end of the fixed of the CD.

Commercial papers are short-term unsecured debt notes that are issued by large and well-known companies. Commercial paper maturities range up to 270 days and are considered to be fairly safe assets since a firms condition presumably can be monitored and predicted over a term as short as 1 month.

2.5 DERIVATIVE MARKETS One of the most significant developments in financial markets in recent years has been the growth of futures, options and related derivatives markets. These instruments provide payoffs that depend on the values of other assets such as commodity prices, bond and stock prices or market index values.

2.5.1 Futures MarketsA Futures contract calls for delivery of an asset at a specified delivery or maturity date for an agreed-upon price, called the futures price, to be paid at contract maturity. The long position is held by the trader who commits to purchasing the asset on the delivery date. The trader who takes the short position commits to delivering the asset at contract maturity. The long position, which commits to purchasing, gains if the asset value increases while the short position, which commits to selling, loses.


Unlike a forward contract, however, a futures contract is not a private and customized transaction but rather a public transaction that takes place on an organised exchange. In addition, a futures contract is standardised the exchange, rather than the parties, sets the terms and conditions, with the exception of price. Also, parties to futures contracts are guaranteed against credit losses resulting from the counterpartys inability to pay. A clearing house ensures that credit risk is eliminated.

2.5.2 Forward MarketsA forward contract is an agreement between two parties in which one party, the buyer agrees to buy from the other party, the seller, an underlying asset or other derivative, at a future at a price established at the start of the contract. The global market for forward contracts is part of a vast network of financial institutions that make markets in these instruments. Transactions in forward contracts typically are conducted over the phone.

2.5.3 Swap MarketsAlthough swaps were the last of the main types of derivatives to be invented, they are clearly not the least important. In fact, judging by the size of the swap market, they are probably the most important. The Bank of International Settlements had estimated the notional principal of the global over-the-counter derivatives market as of 30th June 2001 at $100 trillion. Of that amount, interest rate and currency swaps accounted for about $61 trillion. Swaps are widely used by corporations, financial institutions and Governments.

Swaps are multi-period extensions of forwards contracts. For example, rather than agreeing to exchange British Pounds for U.S. dollars at an agreed-upon forward price at one single date, a foreign exchange swap would call for an exchange of currencies on several future dates. Similarly, interest rate swaps calls for the exchange of a series of cash flows proportional to a given interest rate corresponding series of cash flows proportional to a floating interest rate.

2.5.4 Option MarketsA call option gives its holder the right to purchase an asset for a specified price, called the exercise price or strike price, on or before a specified expiration date. For example, a December call option on a MCB share with an exercise price of MUR 35 entitles its owner to purchase the MCB stock for a price of MUR 35 at any time up to and including the expiration date in December. The holder of the call need not exercise the option; it will be profitable to exercise only if the market value of the asset that may be purchased exceeds the exercise price. On the other hand, a put option is the right to sell an asset at some exercise price. Calls increase in value while puts decrease in value as the price of the underlying asset increases.

2.6 COMMODITIES MARKETS Commodities are different in that they are the oldest trading instruments and need to be physically delivered, with custom settlement terms. Participants need to pay storage and maintenance costs. Their forward prices are determined by the laws of demand and supply and these are closely correlated with environmental factors.

Most commodities markets are exchange-screen based. OTC markets in commodities is generally larger than the corresponding exchange market. Instruments traded on commodities markets include the following:

- Energy: Crude Oil, Natural Gas, Coal; Refined Products: Fuel Oil, Jet Fuel, Gasoline, Diesel Fuel, Naphtha

- Base Metals: Copper, Aluminium, Lead, Nickel, Tin, Zinc

- Precious Metals: Gold, Silver

- Agricultural Products: Corn, Sugar, Coffee, Wheat, Cotton


2.7 REAL ESTATE MARKETS Real estate is usually considered to be buildings and buildable land, including offices, industrial warehouses and retail space. Real estate is a form of tangible assets, one that can be touched and seen, as opposed to financial claims that are recorded as pieces of paper. Real estate is an important investment category. In many countries, domestic real estate is a common investment vehicle for pension funds and life insurance companies. In various countries, pooled funds have been created with the specific purpose of real estate investment.

2.8 SUMMARY In this unit, you explored various types of markets and products while appreciating the financial products on offer on the Stock Exchange of Mauritius and its scope for development. The attention is now turned onto one of the most important concept in finance: The Time Value of Money. Going forward in time, the present value and future value of money is not the same. Unit Three offers further clarification.

2.9 TUTORIALS Question 1With the help of an example, discuss how stocks are issued on the market

Question 2Differentiate between futures, forwards, swaps and options

Question 3Money markets and bond markets are believed to be the same and are used interchangeably. Discuss.


THE TIME VALUE OF MONEYUN

IT3UNIT STRUCTURE

3.0 Overview


3.2 Time Value of Money

3.3 Factors Influencing the Time Value of Money

3.4 Simple and Compound Interest

3.5 Present Value of Future Cash Flows

3.6 Introduction - Annuity

3.7 Future Value of an Annuity

3.8 Summary

3.9 Tutorial

3.10 Suggested Readings


3.0 OVERVIEW This unit focuses on the time value of money. This chapter is of particular importance in that cash that is received in the future has a different value from the cash that is received presently. Future cash flows are subject to inflation and risk across time and these variables need to be factored in the value of any future cash flows arising. Additionally, this unit will introduce the concept of simple and compound interest.

3.1 LEARNING OBJECTIVES By the end of this Unit, you should be able to do the following: 1. Understand the rationale behind the time value of money and the need to take into

consideration the concept of discounting future cash flows and bring them back to the present value.

2. Work out the differences between simple and compound interest theory and perform calculations thereon.

3. Calculate the present value and future value of annuities arising.

3.2 TIME VALUE OF MONEY We start with the case of an individual who is offered a choice: Receive Rs 1,000 now or in a years time. It is assumed that there is no inflation and no risk affecting the receipt of the money in a years time.

A rational investor will normally elect to receive the money now. To the investor, this choice implies that Rs 1,000 that is received now is more valuable received one year later.

Hence, the value of the cash flow depends on when the cash flow is to occur. The further the timing of the cash flow, the lower will be its value now. The essence of this statement is that going forward, we expect the inflation rate and further risks to affect the receipt of any cash inflow. Since the inflation rate and risks can only at best be forecasted, the cash inflow will be discounted in such a way that it has a lower value.

An individual will normally want to use his money for present consumption or save for future consumption. If he foregoes his current consumption and saves the money for latter use i.e. he is willing to receive the Rs 1,000 in one years time, he must be given some sort of compensation and this is called interest or can also be referred to as his opportunity cost of capital. In effect, Interest is the price for foregoing present consumption to increase future consumption.

Time value of money: simple illustrationSuppose an investor requires Rs180 in 1 years time and decides to invest Rs100 now. The investor thus requires compensation of 80 cents for every Rs1 of consumption he foregoes today. The investors time value of money or required rate of return is therefore:

FVPV

180100-1 = -1 = 0.080 or 80%

Hence, the investors return over the period of 1 year is equal to 80%.


3.3 FACTORS INFLUENCING THE TIME VALUE OF MONEY (a) The real risk-free rate of return

Given that there is no future inflation and no uncertainty in the receipt of the future cash flows, an investor will require some return for giving up his or her present consumption in order to increase future consumption. This return is the real risk free rate of return. Such a return is attainable by investing in Government issued financial instruments such as Government Treasury Bonds which are assumed to be risk-free, i.e. there is no risk of default from the Government.

(b) Inflation

If inflation and hence prices do increase, the purchasing power of money declines over time. Investors will therefore demand compensation in terms of an inflation premium.

Real risk-free rate + inflation premium = Nominal risk free return

(c) Risk

If there are uncertainties over the promised future cash flows, the investor will require a risk premium. The level of risk and uncertainty (on which the investment is subject to) will influence the amount of the risk premium.

Nominal risk adjusted return = Nominal risk-free return + risk premium.

3.4 SIMPLE AND COMPOUND INTEREST Simple interest

Note: interest earned is fixed to the principal amount invested (i.e. the initial amount invested) only

Suppose you want to invest Rs20,000 for 2 years @ 13% simple interest per annum.

Future value (FV) = 20,000 + (20,000 x 0.13) + (20,000 x 0.13) = 20,000 [1 + (1 x 0.13) + 1 x 0.13) ] = 20,000 [1 + (0.13 x 2) ] = 25,200

Generalizing on the above results yields the following formula:

FV = PV [1 + r x n ] Where:FV = Future valuePV = Present valuer = Proportional rate of interest per periodn = Number of periods

Compound interestNote: Interest earned is not fixed to the principal amount invested (i.e. the initial amount invested) only; subsequent interest payments depend on previous interest payments as well.


Illustration 1:

Suppose you want to invest Rs20,000 for 2 years @ 13% compound interest per annum.

FV = 20,000 + (20,000 x 0.13) + [20,000 + (20,000 x 0.13)] x 0.13 = 20,000 (1 + 0.13) + 20,000 (1 + 0.13) x 0.13 = 20,000 (1 + 0.13) [1 + 0.13] = 20,000 (1 + 0.13)2 = 25,538

Generalising from the above:

FV = PV (1 + r)n

Illustration 2:

You borrow $4,000 from the MCB to further invest in your business. The contract terms states that you need to pay 10% interest compounded annually. How much will you owe in 5 years if you return the banks $4,000 plus interest?

FV = PV (1 + r)n = 4,000 (1.10)5 = $6,442.04

Illustration 3:

How much money must be invested today earning an 11% interest rate compounded annually to have $500,000 in 5 years?

Note: You know that you want to earn $500,000 in 5 years time. Therefore, future value = $500,000 and n = 5 years since interest is being compounded annually (alternatively, it could have been said that the money is being compounded monthly, in which case n would have equaled to [5x12 = 60] and the interest rate would have been [0.11/12]%) PV = FV [1/(1+r)]t = 500,000 [1/(1.11)5] = $296,725.7

Illustration 4:

Shares in a sugar plant sell for $4,000 today and will be worth $5,500 in 6 years. What is the rate of return expressed as an annually compounded interest rate?

r = (FV/PV)(1/n) - 1 = (5,500/4,000)1/6 - 1 = 5.45%

Discrete Compounding

In this section, we examine investments paying interest more than once a year. For instance, many banks offer a monthly interest rate that compounds 12 times a year. In such an arrangement, they pay interest on interest every month. Financial institutions often quote an annual interest rate that we refer to as the stated annual interest rate or quoted interest rate and is denoted by rs.


With more than one compounding period per year, the future value formula can be expressed as :

FVN = PV [ 1+ (rs/m)mN

Where :

rs the stated annual interest rate

m the number of compounding periods per year

N stands for the number of years

Illustration 5

Suppose your bank offers you a certificate of deposit with a two-year maturity and a stated annual interest rate of 8 percent compounded quarterly. You decide to invest $10,000. What will the Certificate of Deposit be worth at maturity ?

PV = 10,000rs = 8%N = 2 yearsm = 4FVN = PV [ 1+ (rs/m)

mN

FV2 = 10000 [ 1+ (8%/4)4x2 = $11,716.59

Continuous Compounding

The predecing discussion on compounding periods illustrates discrete compounding, which credits interest after a discrete amount of time has elapsed. If the number of compounding periods per year becomes infinite, the interest is said to compound continuously. The expression for the future value of a sum in N years with continuous compounding is :

FVN = PVersN

The termersN is the transcendental number e = 2.7182818 raised to the power rsN.

Illustration 6Suppose a $10,000 investment will earn 8 percent compounded continuously for two years. Calculate the future value of the investment.

PV = $10,000

rs = 8%

N = 2

FVN = PVersN

FVN = 10000e0.08(2) = $11,735.11

With the same interest rate but using continuous compounding, the $10,000 investment will grow to $11,735.11 in two years, compared with $11,716.59 using quarterly compounding, as shown in the previous example.


3.5 PRESENT VALUE OF FUTURE CASH FLOWS The future value of an investment of Rs1,000 @ 10% compounded annually will be:After 1 year: 1,000 x 1.10 = Rs1,100

After 2 years: 1,000 x 1.102 = Rs1,210

We have simply applied the following formula:

FV = PV (1 + r )n

Now, lets turn the question around! Given that interest is 10% compounded annually how much we need to invest now to obtain:

Rs1,100 after one year?

Simply make PV become subject of the above formula

FV(1+r)n

= 1,000PV = = 1,100(1+0.10)1

Rs1,210 after 2 years

FV(1+r)n

= 1,000PV = = 1,100(1+0.10)2

The future cash flows have been discounted. Discounting is therefore a process, which inverts the compounding process to provide the present value of the future cash flows.

Example:Given that an investment will produce Rs1,050 at the end of year 1, Rs1,102.50 at the end of year 2 and Rs1,157.63 at the end of year 3, Calculate the present value of the investment if the investor requires a rate of return of 5% compounded annually.

1,0501,051

= 1,000PV = + 1,102.501,052

1,157.631,053

+

By discounting each of the future cash flows occurring at the end of year 1, 2 and 3, what we are doing is bringing back all future cash flows to the present value so that they may be compared. Note that the discounting factor in year three (1/1.053 = 0.864) is greater than the discounting factor in year one (1/1.05 = 0.952). This shows that future cash flows that are more distant in the future have a greater discounting factor since they are more uncertain than those arising at the present value or the first few years.

Therefore, if the present worth of this investment taking into consideration the investors time value of money (5%) is Rs3,000. In effect, Rs3,000 represents the maximum sum the investor is prepared to pay now for undertaking the investment. The return on the investment will be exactly 5% if the investor pays Rs3,000 for the investment; if the investor pays less than Rs3,000, he will be earning a return of more than 5%. However, if the investor pays more that Rs3,000, a return of less than 5% will be earned.

In conclusion, we can say that the worth of any asset is currently the present value of the assets future income stream.


3.6 INTRODUCTION - ANNUITY An annuity is a succession of predetermined identical payments or receipts made over consistent time intervals. Examples of annuities are weekly rent, monthly wages, monthly insurance premiums, and monthly loan repayments amongst others.

In an ordinary annuity, the set of equivalent payments/receipts take place at the last part of the time interval e.g. rent paid at the end of each month.

In a due annuity, the set of equivalent payments/receipts take place at the beginning of the time interval e.g. rent paid at the beginning of each month.

A perpetual annuity, whether ordinary or due, is one which carries on forever.

Present value of an ordinary annuity A Let P denote present value, A being the annuity value and let n denote the number of terms

A(1+r)1

P = + +A

(1+r)2A

(1+r)3A

(1+r)n+ .................. + [1]

Multiply [1] by 1(1+r)

gives:

A(1+r)2

P(1+r)1

= + +A

(1+r)3A

(1+r)4A

(1+r)nA

(1+r)n+1+ .................. + + [2]

Taking [1] - [2] gives:

P(1+r)1

P - = -A

(1+r)1A

(1+r)n+1 [3]

Multiplying [3] by (1+r) gives:

(1+r)-PP = A - A(1+r)n

P + Pr - P = A - A(1+r)n

Pr = A 1 - A(1+r)n

P = Ar

1 - A(1+r)n

[4]


Present value of an ordinary annuity A to infinity

From equation [4] above as n tends to infinity Ar

P = [5]

Present value of a due annuity A

A(1+r)1

P = A + + +A

(1+r)2A

(1+r)3A

(1+r)n-1+ .................. + [6]

P = A + Ar

1 - A(1+r)n-1

[7]

Illustration 1:Calculate the present value of an ordinary annuity of Rs20,000 per year for five years if the interest rate is 12% per year.

P = 20,000 x = Rs 72,0960.12

1 - 1(1+0.12)5

Illustration 2:Calculate the present value of a due annuity of Rs20,000 per year for five years if the interest rate is 12% per year.

P = 20,000 + 20,000 x = Rs 80,7470.12

1 - 1(1+0.12)5-1

3.7 FUTURE VALUE OF AN ANNUITY Future value of an ordinary annuity The future value (F) of an annuity invested each period (at interest per period r) beginning one period from now for n periods is:

F = A + A (1+r)1 + A (1+r)2 + A (1+r)3 + ........................ A (1+r)n-2 + A (1+r)n-1 [1]

Last annuity 2nd Annuity 1St Annuity

Multiply throughout by (1 + r )

F (1+ r) = A (1+r)1 + A (1+r)2 + A (1+r)3 + ................... + A (1+r)n-1 + A (1+r)n [2]


Take 2 1

F (1+ r) F = A (1+r)n A

F + Fr F = A (1+r)n A

F = A (1+r)n - 1

r

Illustration 1What is the future value of a 5 year ordinary annuity, if the annual interest is 10%, and the annual payment is $3,000?

F= 3000{(1+0.1)5-1/0.1} = $ 18,315.3

Illustration 2Assume that an individual plans to retire at the age of 50, with the life expectancy of 30 years. He expects to spend Rs 50,000 at the end of each year during your retirement. How much money does he need to save by the age of 50 (lump sum) to support his post retirement consumption expenditure? Assume an interest rate 7%.

Lump sum at P50 = 50,000 + 50,000 + 50,000 + ......... + 50,000 = (1 + 0.07) (1 + 0.07)2 (1 + 0.07)3 (1 + 0.07)30

= 50,000 0.07

1 - 1(1.07)30

= Rs 620,452.1

Future value of a due annuityThe future value (F) of an annuity invested each period (at interest per period r) starting now for n periods is:

F = A (1+ r) = A (1+r)2 + A (1+r)3 + ................... + A (1+r)n [1]

Multiply throughout by (1 + r )

F(1+r) = A (1+r)2 + A (1+r)3 + A (1+r)4 +................... + A (1+r)n + A (1+r)n+1 [2]

Term before last term


Take 2 1

F (1+ r) F = A (1+r)n+1 A (1+r)

F + Fr F = A (1+r)n+1 A (1+r)

F = A(1+ r) (1+r)n - 1

r

Illustration 1What is the future value of a 5 year due annuity, if the annual interest is 10%, and the annual payment is $3,000?

F= 3000 (1+0.1) {(1+0.1)5-1/0.1} = $ 20,146.83

3.8 SUMMARY

For economic progress to be possible, there must be a universally applicable time value of money, even in a risk-free environment. This fundamental concept introduced in this chapter gives rise to the techniques of capitalization, discounting and net present value, described in Unit 4.

3.9 TUTORIALS Question 1On 1 January 2012, Rs400, 000 was borrowed by Mr Nuri from a bank for a period of 10 years at a fixed annual rate of interest of 15%. Mr Nuri will reimburse interest and principal by equal annual payments. Calculate the annual payment if:

The first annual payment is effected on 31 December 2012. The first annual payment is effected on 1 January 2012.

Question 2Compute the size of the fund at the end of the period if a company decides to set up a fund for its employees with an initial payment of Rs30,000 compounded six-monthly over a five year period at a six-monthly interest of 5%. Also, calculate the effective annual interest rate.

Question 3On January 1, 2013, you will deposit $2,000 into a savings account that carries a 10% interest per annum. (i) If the bank compounds interest annually, how much will you have in your

account on Jan 1,2017?

(ii) What would your Jan 1,2017 balance be if the bank compounds interest on a semi annual basis?

(iii) Calculate the effective annual rate of interest if the bank compounds interest on

a quarterly basis.


3.10 SUGGESTED READINGS Fabozzi, F.J., Modigliani, F., Jones, F.J., and Ferri, M.J., Foundations of Financial Markets and Institutions. Third or Latest Edition

Zvi Bodie, Alan Marcus and Alex Kane Investments, 6th or Latest Edition by McGraw-Hill Higher Ed.

Wilmott, P., Quantitative Finance, Vol 1 & 2, John Wiley & Sons, Reprinted, 2003.


UNIT STRUCTURE

4.0 Overview


4.2 Introduction

4.3 Identifying the Projects Cash Flows

4.4 What Does it Mean to Discount a Sum?

4.5 Methods of Investment Appraisal

4.5.1 The Net Present Value (NPV)

4.5.2 The Internal Rate of Return (IRR)

4.5.3 The Payback Period

4.5.4 The Accounting Rate of Return (ARR)

4.6 Summary

4.7 Tutorial

4.8 Suggested Readings

CAPITAL INVESTMENT APPRAISAL UN

IT4


4.0 OVERVIEW Capital Budgeting is the process that companies use for decision making on capital projects those projects with a life of a year or more. This is a fundamental area of knowledge for financial analysts for many reasons. Capital Budgeting undergirds the most critical investments for many corporations their investment in long term assets.

The process of evaluating long-term investment decision is referred to as Investment Appraisal. The decision whether or not to select a project will usually depend on the stream of cash flows which are generated over a given time period. These cash flows will undergo rigorous transformations under different investment appraisal techniques, namely: the Net Present Value (NPV) method, the Internal Rate of Return (IRR) method, the Payback method and Accounting Rate of Return (ARR).

4.1 LEARNING OBJECTIVES By the end of this Unit, you should be able to do the following:1. Explain the importance of the capital budgeting process2. Assess the issues in relation to the identification of a projects relevant cash flows.3. Assess the difference between discounting (net present value and internal rate

of return) and non-discounting cash flow techniques (payback and accounting rate of return).

4. Assess the feasibility of a particular project using different investment appraisal techniques

5. Examine the comparative advantages and disadvantages of the investment appraisal techniques.

4.2 INTRODUCTION The specific capital budgeting procedures that a manager uses depend on the managers level in the organization, the size and complexity of the project being evaluated, and the size of the organization.

The typical steps in the capital budgeting process are as follows:

Step One: Generating Ideas - Investment ideas can come from anywhere, from the top or the bottom of the organization, from any department or functional area, or from outside the company. Generating good investment ideas to consider is the most important step in the process.

Step Two:Analysing Individual Proposals This step involves gathering the information to forecast cash flows for each project and then evaluating the projects profitability.

Step Three:Planning the capital budget The company must organize the profitable proposals into a coordinated whole that fits within the companys overall strategies, and it must also consider the projects timing. Some projects that look good when considered in isolation may be undesirable strategically. Because of financial and real resource issues, the scheduling and prioritizing of projects is important.

Step Four:Monitoring and Post-Auditing In a post-audit, actual results are compared to planned or predicted results, and any differences must be explained. For example, how do the revenues, expenses, and cash flows realized from an investment compare to the predictions?


Post-auditing capital projects is important for several reasons.

First, it helps to monitor the forecasts and analysis that underlie the capital budgeting process. Systematic errors, such as overly optimistic forecasts, become apparent.

Second, it helps improve business operations. If sales or costs are out of line, it will focus attention on bringing performance closer to expectations if at all possible.

Finally, monitoring and post-auditing recent capital investments will produce concrete ideas for future investments. Managers can decide to invest more heavily in profitable areas and scale down or cancel investments in areas that are disappointing.

Capital budgeting is a cost-benefit exercise. At the margin, the benefits from the improved decision making should exceed the costs of the capital budgeting efforts. The aim of the capital budgeting process is thus to identify projects that support the goal of maximizing the market value of the firm.

4.3 IDENTIFYING THE PROJECTS CASH FLOWS One of the key priorities in the capital budgeting process is to identify the relevant cash flows accruing to the project under consideration. These relevant cash flows should be satisfying the following criteria.

Accounting profits are irrelevant and only cash flows ought to be consideredProfit is an accounting concept to report performance of a firm by accountants in each accounting year. Basically, accounting profit takes both cash sales and credit sales in its computation of sales. However, credit sales are not cash flows as they have not yet been converted into cash. Hence, we disregard all non-cash flows for the purpose of investment appraisal.

Incremental cash flows are the relevant cash flows All sunk costs, committed future costs, non-incremental fixed costs and overheads should not be taken into account when evaluating the feasibility of the project. Only incremental cash flows are relevant (i.e. those cash flows that will change as a direct result of undertaking the project).

All financing cash flows should be disregardedThe present value of the financing cash flows is represented by the projects initial outlay. To avoid double counting, we must not include interest and principal repayments over and above the initial capital outlay.

A company wishes to replace a machine which will cost Rs150, 000 and has a three year life. The company decides to finance the purchase of this machine by undertaking a loan from the bank. The bank charges an interest rate of 12% per annum with the principal being paid at the end of the third year.

Year 0 1 2 3

Initial Outlay (150,000)

Interest (18,000) (18,000) (18,000)Principal Repayment

(150,000)

The above representation is wrong since the present value of the loans cash flows is the machine initial outlay. The interest and principal are financing cash flows and should be ignored.


In fact, the following calculation shows:

PV of loan cash flows: 18,0001.121

+ +18,0001.122

18,000 + 18,0001.123 = Rs 150,000

Working capital adjustment needs to be incorporated in the calculation of relevant cash flows

Changes in the level of working capital represent changes in cash flows. Basically, cash outflows are represented by increases in the working capital requirement such as increase in debtors or stocks. In fact, the increase in debtors represents an investment in working capital as payment of sales is not made immediately. Also, increases in stock are due to lower stock turnover. On the other hand, cash inflows are represented by decreases in the working capital requirement. For instance, reduction in stocks may be due to greater stock turnover or reduction in debtors due to earlier settlement of debt by debtors

Take into account all opportunity costs that may arise from undertaking the project

An opportunity cost is what resource is worth in its next-best use. For example, if a company uses some idle property, what should it record as the investment outlay: the purchase price several years ago, the current market price or nothing? If you replace an old machine with a new one, what is the opportunity cost? If you invest Rs 10million, what is the opportunity cost? The answers to these questions are respectively: the current market value, the cash flows the old machine would generate, and Rs 10million (which you could invest elsewhere)

Taxation

In the appraisal of an investment project, focus is on the cash flows that will be generated by the project and that which are available for shareholders. As such, we want to assess the after tax cash flows of the project. It is important to note that the taxation charge is levied on the taxable profits of the business and not on the net cash flows.

4.4 WHAT DOES IT MEAN TO DISCOUNT A SUM? To discount means to calculate the present value of a future cash flow.

Discounting into todays rupees helps us to compare a sum that will not be produced until later. Technically speaking, to discount is to depreciate the future. It is to be more rigorous with future cash flows than present cash flows, because future cash flows cannot be spent or invested immediately.

First, take tomorrows cash flow and then apply to it a multiplier coefficient below 1, which is called a discounting factor. The discounting factor is used to express a future value as a present value, thus reflecting the depreciation brought on by time.

Consider an offer whereby someone will you Rs1,000 in 5 years. As you will not receive this sum for another 5 years, you can apply a discounting factor to it, for example, 0.6. The present, or todays value of this future sum is then 600. Having discounted the future value to a present value, we can then compare it to other values. For example, it is preferable to receive 650 today than 1000 in 5 years, as the present value of 1000 5 years from now is 600, and that is below 650.


Discounting make is possible to compare sums received or paid out at different dates.

Discounting is based on the time value of money. After all, time is money. Any sum received later is worth less than the same sum received today. Remember that investors discount they demand a certain rate of return. If a stock pays you Rs110 in one year and you wish to see a return of 10% on your investment, the most you would pay today for the security (i.e. the present value) is 100.

Discounting is calculated with the required return of the investor. If the investment does not meet or exceed the investors expectations, he will forego it and seek a better opportunity elsewhere.

4.5 METHODS OF INVESTMENT APPRAISAL The investment appraisal techniques can be classified into two main categories, discounting and non-discounting techniques.

Discounted Cash Flow Techniques: Takes into account the time value of money Net present value Internal Rate of Return. Discounted payback

Non-Discounting Techniques : Ignores the time value of money Payback period Accounting rate of return

We will now explore these four investment appraisal techniques with the help of the following example:

Glass Company is a manufacturer of plates for the hospitality sector. Currently, the firm is considering whether to invest in one of the two proposed machines, Machine A and Machine B. The Management of Glass Company wishes to revamp its existing operations and firmly believes that such securing such a machine will automate its processes and contribute to further savings on its production line. The following information is provided:

Investment Case: Glass Company

Machine A (MUR)

Machine B (MUR)

Investment outlay (payable immediately) 250,000 325,000Annual cost saving:

Year 1 80,000 90,000Year 2 90,000 91,000Year 3 100,000 92,000Year 4 1100,000 93,000

The rate of return that is expected on projects with similar risk is 7%.Note: The annual cost savings imply that the company will receive these cash flows and as such are relevant cash flows for the company

Which one of the above machines should be purchased, should the company decide to move forward with its investment decision?


4.5.1 THE NET PRESENT VALUE (NPV) Calculating the NPV of a project is conceptually easy. There are basically two steps to be followed:1. Write down the net cash flows that the investment will generate over its life2. Discount these cash flows at an interest rate that reflects the degree of risk inherent

in the project

The resulting sum of discounted cash flows equals the projects net present value. The NPV Decision Rule says to invest in projects when the net present value is positive (greater than zero): NPV > 0 Invest NPV < 0 Do Not Invest

The NPV Rule implies that firms should invest when the present value of future cash inflow exceeds the initial cost of the project. The firms primary goal is to maximize shareholder wealth. The discount rate r represents the highest rate of return (opportunity cost) that investors could obtain in the marketplace in an investment with equal risk. When the NPV of cash flow equals zero, the rate of return provided by the investment is exactly equal to investors required return. Therefore, when a firm finds a project with a positive NPV, that project will offer a return exceeding investors expectations

NPV of Machine A project

250,000 + 80,0001.07+ +

90,0001.072

100,0001.073

110,0001.074 = Rs 68,924.10+

NPV of Machine B project

325,000 + 90,0001.07+ +91,0001.072

92,0001.073

93,0001.074 = Rs 15,356.27+

What does an NPV of Rs 68,924.10 for Machine A project stands for?

NPV shows how much more or how much less in money terms the project is earning in comparison with an alternative project that have similar risk levels. A positive NPV of Rs 68,924.10 indicates that the shareholders wealth will increase by this amount should they decide to go forward with the project. Hence, this implies that the project has a higher return than on other similar risk level investments.

Basically, if Rs 250,000 were invested on a similar risk level project, a return of 7% will be obtained. However, it is noted that the NPV of Machine B project is negative, which shows that this project is earning a return less than 7%. This implies that the company should not invest in that project.

Advantages of NPV: Takes into account the risk levels of the projects- Basically, the risk is reflected in

the discount rate as it is the return that is obtained on projects having similar risks; Decision to reject or accept a project is a relative one not an absolute one- in fact, it

is relative to what the foregone alternative will earn; Considers the time value of money concept; Take into consideration all cash flows arising; It is an absolute measure of return; Leads to maximization of shareholder wealth


Disadvantages of NPV It is difficult to explain to managers. To understand the meaning of the NPV

calculated requires an understanding of discounting. The method is not intuitive as techniques such as payback;

It requires the knowledge of the cost of capital; It is relatively complex.

4.5.2 THE INTERNAL RATE OF RETURN (IRR)

If net present value (NPV) is inversely proportional to the discounting rate, then there must exist a discounting rate that makes NPV equal to zero. The discounting rate that makes NPV equal to zero is called the internal rate of return or IRR. The IRR is the actual rate of return of the project.

The decision making rule is very simple: if an investments internal rate of return is higher than the investors required return, he will make the investment. Otherwise, he will abandon the investment.

The IRR of Machine A project is calculated as follows:

250,000 + 80,000(1+IRR)+ +

90,000(1+IRR)2

100,000(1+IRR)3

110,0001.074 = Rs 68,924.10+

A variety of computer software can be used to solve the above equation. Alternatively, linear interpolation, a mathematical technique can be used to estimate the IRR. This consists of determining two discount rates such that one of them produces a positive NPV and the other produces a negative NPV.

For Machine As project, a discount rate of 15% produces a positive NPV of Rs 16,262.63 whilst a discount rate of 20% produces a negative NPV of Rs 9,915.12. By linear interpolation, we apply the following formula to estimate IRR:

IRR= LDR + HDR - LDR

NPVLDR

- NPVHDR x NPV

LDR

=15% + 20 - 15

16,262.63 + 9,915.12 x 16,262.63 = 18%

Where:

HDR = Higher discount rate

LDR = Lower discount rate

NPVLDR

= NPV corresponding to the LDR

NPVHDR = NPV corresponding to the HDR

The IRR for the Machine B project is approximately equal to 4.90%. (Calculate it!)


IRRs and NPVsThe IRR only compares the project yield with that of the capital market. In other words, it answers the question can the project produce a higher return than the capital market. However, it does not give an indication to judge between alternative projects like the NPV i.e how much more or less the project is earning relative to the risk equivalent capital investment alternative.

Another problem arising with the IRR is that this method gives rise to multiple IRRs when uneven cash flows are considered. Out of these two investment appraisal techniques, NPV always prevail over IRR.

Advantages of IRR Considers the time value of money Is a percentage and is readily understood Uses cash flows and not profits Consider the whole life of the project Means a firm selecting projects where the IRR exceeds the cost of capital, should

increase shareholders wealth

Disadvantages It is not a measure of absolute profitability Interpolation only provides an estimate and an accurate estimate requires the use

of spreadsheet program It is fairly complicated to calculate Non-conventional cash flows may give rise to multiple IRRs which means the

interpolation method cannot be used.

4.5.3 THE PAYBACK PERIOD The payback period measures the number of years it takes to recover the initial cash outlay on a real asset. A company can also define a cut-off date i.e. set the number of years over which it wants to recuperate the initial amount invested. E.g. If a certain company sets its cut-off date to 2 years, it implies that the company wants to recuperate its investment within two years. In the event that a project offers a payback period of 3 years, the company will refuse the investment since the payback period (3 years) is greater than the cut-off date of 2 years. In practice, the faster a firm recoups the initial capital outlay, the less risky are the projects.

The advantages of the payback period method include the following: Easy to understand and simple to compute

When capital is scarce or in short supply, it could be argued that projects that returned the expenditure rapidly are the best ones.

It is useful in certain situations (rapidly changing technology and improving investment conditions)

It favours quick return, which in turn help company growth, minimizes risk and maximizes liquidity

It uses cash flows, not accounting profits

The drawbacks of this method are: Ignore the time value of money.

It does not assess the impact of cash inflows arising after the payback period, which could greatly affect the projects profitability.

It is subjective no definitive investment signal

It ignores project profitability


Consider the following table where the payback period for Machine A is considered:

Year Cash FlowCumulative Cash

FlowPayback Period

0 (250,000) (250,000) 0

1 80,000 (170,000) 1

2 90,000 (80,000) 2

3 100,000 20,000(80,000/100,000) x

(1 year or 12 months)= 0.8 years or 9.6 months

4 110,000

Payback period for Machine project A is 2.8 years or 2 years and 10 months.

Payback period for Machine project B is 3.6 years or 3 years and 7 months. (Calculate it!)

Machine A project has the shortest payback period as it recoups initial capital expenditure earlier that the Machine B project. Hence, management will consider going forward with the Machine A project under the payback period method.

The Discounted Payback Period method

The Discounted payback period method has been introduced to cater for the time value disadvantage borne by the payback period. By discounting the future cash flows arising from the project, you will have taken into consideration the time value of money. Consider the following example:

Year Cash FlowDiscounted Cash Flow

(at 7%)

Cumulative Cash Flow

Payback Period

0 (250,000) (250,000) (250,000) 0

1 80,000 74,766 (175,234) 1

2 90,000 78,609 (96,625) 2

3 100,000 81,629 (14,996) 3

4 110,000 83,918 68,92214,996/83,918x 12 Months

= 3 years and 3 Months

Hence, using the discounted payback period, as opposed to the normal payback period, the payback period has increased from 2 years and 10 months to 3 years and 3 months. This new method has taken into consideration the riskiness of the cash flows and has accounted for the risk by applying the time value of money to it. This would reflect a more conservative approach by management as regards to the payback period method.


4.5.4 THE ACCOUNTING RATE OF RETURN (ARR)

The ARR measure the projects profitability over the entire asset life. It compares the average accounting profit of the project with the initial or average amount of capital invested. The ARR can be calculated as follows:

ARR = Average annual profitInitial (or average) capital invested

x 100

We assume that straight line depreciation method is used in each case.

The average accounting profit and the ARR (based on initial capital invested) for Machine A and Machine B projects are as follows:

Machine Project A Year 1RsYear 2

RsYear 3

RsYear 4

Rs

Cash flow 80,000 90,000 100,000 110,000

Depreciation (62,500) (62,500) (62,500) (62,500)

Profit 17,500 27,500 37,500 47,500

The average profit over the years is: (17,500 + 27,500 + 37,500 + 47,500) / 4 = Rs 32,500

Hence, the accounting rate of return for Machine project A is given by:

(32,500/250,000) x 100 = 13%

Calculate the accounting rate of return for Machine Project B.

The advantages of this method are: easy to understand and simple to compute It takes into account the importance of profitability.

The drawback of this method: It ignore the time value of money It makes use of accounting data instead of cash flow data

4.6 SUMMARY Unit 4 presented various techniques for appraising a project, followed by a discussion of the strengths and weaknesses of each method. Unit 5 will now build further on the concept of discounting, with a different application. The methodology will now be applied to the valuation of shares.


4.7 TUTORIALS Question 1

Rose Company Ltd is considering investment in either project A or project B. The management of the company has entrusted you the responsibility to determine the feas

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