Chapter 1

Gitman defines finance as “The art and science of managing money’’. Financial management is therefore a subject that looks at the institutions, markets and instruments that deal with the transfer of money among and between individuals, businesses and governments. The following diagram shows this arrangement.

Individuals Individuals Corporations Financial intermediaries Corporations Governments Governments

Parties with Parties in need of Funds Funds (demanders of finance)

Buy financial Create attractive Instruments Financial instruments Thereby making that mobilize excess Finance available Funds To financial Intermediaries

Channel funds to individuals Corporations and governments In the form of loans and other Instruments.

To appreciate the scope of financial management one has to look at the functions performed by the financial manager in an organization. The functions performed by the financial manager can be best understood by focusing on the decisions that the financial manager makes in the organization.

The financial manager makes a number of important decisions but these have to be looked at in the context of the financial objectives that the firm would be striving to achieve. It is therefore important to look at the possible financial goals that can be pursued by an organization as this will help one to understand why a particular alternative (decision) would have been chosen by the decision maker.

Possible financial goals pursued by firms.There are a number of financial goals that can be pursued by firms either individually or collectively. These are summarized as follows:

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SurvivalSometimes severe economic or market shocks may necessitate survival to become the overriding objective. Should this be the case management focus on short-term issues to ensure survival of the concern, paying little attention to long-term survival of the organization. Should this be the case management can postpone the organization’s investment programme.

Maximizing sales This is alternatively known as maximizing market share. A firm may want to command a high market share. This is because a high market share can be seen as rewarding. The rewards may be in the form of improved profitability or increased survival chances. If this is the case decision like price reduction or relaxation of credit terms can be made.

Growth Growth, as an objective pursued by the firm is hardly admitted openly, but it is a financial goal that is sometimes pursued. Size is seen as an end in itself. This way managers can earn higher salaries, get huge expense accounts, cars and other perks. Growth can be achieved either internally or externally. Internal growth will generally take the form of expanded operations for a given concern while external growth is achieved through merging or take-over.

Maximizing shareholder wealthThis is the financial goal, which is assumed in financial management. A proxy, that is the firm’s current share price, can measure achievement of this goal. If the firm’s current share price is maximized then it can be argued that the goal of shareholder wealth maximization would have been achieved.

Maximization of profitThis is a much more popular financial objective that can be pursued by the firm. The firm will try to maximize its reported profits. This is a much more acceptable financial goal but others would want to argue that profit maximization should not be the firm’s purpose.

Although profit maximization is a popular objective, it is not the preferred financial objective from the financial management point of view. This is because the financial objective has a number of problems.

Problems with profit maximizationThe following problems associated with profit maximization should always be borne in mind should an organization be pursuing this objective.

Basis of computationProfit maximization is based on accrual or matching concepts unlike shareholder wealth maximization, which is based on cash flows. Profits can be padded through the use of cosmetic accounting. The following arrangements indicate how profits can be manipulated to give a picture, which may apparently be non-existent. An organization may under-provide for depreciation, adopt misleading stock valuations or carry dangerous stock levels, all in an attempt to manipulate reported profit.

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Objective’s orientationProfit maximization leads to the adoption of short-term objectives as it has a short-term orientation. The organization, in an attempt to improve reported profit, may cut discretionary spending like Research and Development expenditure. Wealth maximization favours long-term objectives, which is consistent with the assumed goal of wealth maximization.

Time value concernsProfit maximization places too much emphasis on the highest profit irrespective of the time value of money aspect. Wealth maximization takes into account the various times at which the benefits (cash flows) accrue and the eventual effect of the benefits on the firm’s share price.

RiskWealth maximization, unlike profit maximization, carefully weighs and adjusts for the risk inherent in projects since shareholders expect higher returns on investments with larger inherent risks.

Maintaining a balance between dividends and retention of earningsWealth maximization strikes a balance between regular dividend distribution and retained earnings since both decisions influence the share price, which in turn reflects the shareholder’s wealth.

Having looked at the possible financial goals of the firm, the functions performed by the financial manager can now be looked at. It is hoped that the decisions that are eventually made by the financial manager can be understood in their proper context if one has an appreciation of the financial objective that the firm would be striving to achieve.

Functions performed by a financial managerThere are a number of important generic functions that are performed by the financial manager and these are now discussed in the paragraphs that follow.

A. Financial analysis and planningIt is the responsibility of the financial manager to establish how well the firm would have performed. He will therefore examine the organization’s financial statements (Balance Sheet and Income Statement), to evaluate the performance of the organization. Following this evaluation a number of important planning decisions can then be made. These include the addition or reduction in planned capacity and the determination of additional funding or reduction of funding that may be necessary. The financial manager primarily uses financial ratio analysis and trend analysis to come up with an informed position on how well the firm would have performed.

B. Making investment decisionsThis particular function can also be looked at as managing the firm’s asset structure. It is the responsibility of the financial manager to decide on the

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mix and type of assets to be acquired by the firm. These are real assets like vehicles and plant or financial assets like shares. The financial manager must also make decisions relating to modification, replacement or liquidation of fixed assets. The financial manager uses appraisal techniques like net present value analysis, payback method, internal rate of return, accounting rate of return or profitability index to identify capital projects that can best enhance shareholder value.

C. Making financing decisionsFinancing decisions relate to the firm’s capital structure hence this decision is often referred to as managing the firm’s capital structure or financial structure. Having identified the assets to be acquired by the firm, an appropriate mode of finance has to be established. The financial manager must decide the best mix of financing that is both short-term and long-term for assets to be acquired by the firm or the financing needed for projects to be undertaken. There is a considerable body of knowledge that the financial manager can draw from to establish an optimal mix of financing that will maximize shareholder wealth. This will be looked at in detail under the capital structure decision.

D. Working capital managementThis is sometimes referred to as treasury management. All organizations need working capital. Working capital refers to the firm’s current assets and current liabilities. The financial manager must ensure that the firm has sufficient working capital to continue operations so as to avoid costly interruptions in the firm’s production operations.

E. Risk managementRisk is the probability that an outcome will not turn out as expected. Firms are more concerned with adverse outcomes (downside risk). It is the responsibility of the financial manager to manage or reduce the risk to which the organization is exposed. A notable type of risk that is worrisome to most organizations is exchange risk. This is a type of risk that organizations engaged in external trade have to face. With exchange risk the amount to be received in the home currency is not certain. It is the financial manager’s function to manage and reduce this exchange risk. The financial manager’s task is complicated if the organization he works for deals in primary commodities. In this case the prices of the primary commodities are not stable and in addition there will be exchange risk. All this requires the skills of the financial manager.

To summarize, the following diagram can capture the primary role of the financial manager:

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Capital Market Operating Assets - Equity - Non current assets - Debt - Current assets

Searching for Financial manager Searching for Financing Investment Opportunities Financial decisions opportunities

Money Market Financial Assets

The primary role of the financial manager

When discussing the investment decision it is important to appreciate the difference between Investment and speculation.

Investment Investment is the purchase by an individual or institutional investor of a financial or real asset that provides a return proportional to the risk assumed over some future investment period.

Primary differences between investment and speculationThere are basically four different approaches that can be adopted to differentiate investment from speculation.

1. Holding periodThe holding period is the period over which the investor intends to hold the investment. Usually speculation is for short periods of time for example one week to a few months. An investment is continuous for a series of a number of years for example 3 years over a long period of time. Emphasis in speculation because of the shorter holding period is on capital gains rather than dividend or interest income.

2. Expected returnReturn represents the total annual income and capital gains as a percentage of the beginning investment.

Return = P1 – P0 + D1 * 100 P0 1

Where P1 = Price at the end of period 1. P0 = Price at the beginning of period 1. D1 = Dividend received at end of period 1.

The expected return from a single speculative security purchase is much greater than the expected return from the purchase of an investment security.

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Investors earn a much lower annual return over a longer period of time than speculators.

3. Risk assumedSpeculators assume higher levels of risk than investors. This is because speculators expect higher returns and higher returns can only be expected if one is prepared to assume higher levels of risk.

4. Degree of information availableSpeculators look for opportunities where information available for analysis tends to be quite limited.

Investment approachesThere are three approaches that can be adopted when one is contemplating an investment transaction.

The fundamental approachThis approach assumes that a rigorous analysis of each company will result in the identification and selection of undervalued shares. These shares will be identified after an economic analysis, industry and company analysis would have been undertaken. The shares identified will be bought and held as long as they promise a high return. They are sold if the investor believes they have become overpriced. Usually the shares are held for relatively long periods of time. This is a buy and hold approach that is followed by the majority of institutional investors.

The technical approachThe approach emphasizes that the behaviour of the price of a share and the volume of trading determines the future price of the share. It centers on the plotting of the price movement of the share and drawing inferences from the price movement. The technician then selects a few shares and trades in them. The emphasis is on capital gains in the short term.

Modern portfolio theory (MPT)The approach assumes that the market is efficient and information is available about the market and individual shares. New information is quickly transferred to the market place and a new price established. Since the market is efficient and share prices of one moment are independent from prices in the next moment, it is impossible to predict future prices. Information is known to all, and no one on average can do much better than the market. Investors buy and hold on to their shares.

The financial environmentThe financial manager operates in an environment characterized by financial institutions and financial markets.

Financial institutions

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Financial institutions are intermediaries that channel the savings of individuals, businesses and governments into loans and investments. Examples of financial institutions in Zimbabwe include commercial banks like Kingdom bank, Standard Chartered or Barclays bank. There are also savings banks like the People’s Own Savings Bank (POSB), credit unions like the Zimta Co-operative Credit Union (ZCCU), life insurance companies like Zimnat and pension funds like the NRZ pension fund or the mining industry pension fund (MIFP).

Financial marketsFinancial markets provide a forum in which suppliers of funds and those in need of funds can transact business directly. Financial markets can take the following forms:

A. Primary marketThis is a financial market in which securities (shares) are initially issued. It is a financial market for new issues.

B. Secondary marketThis is a financial market in which pre-owned securities are subsequently traded.

C. The money marketThe money market is a financial market for short- term sources of finance and financial instruments. Short -term financial instruments are instruments having an original maturity of one year or less. The following are examples of short-term financial instruments.

- Treasury bills: These are government of Zimbabwe 90 day treasury bills. They are issued when the government wishes to raise short-term financing.

- Grain bills: These are issued on behalf of the Grain Marketing Board to raise finance to pay for the produce delivered to the GMB.

- RBZ financial bills: These are short- term bill issued by the RBZ to raise finance for central government or to achieve monetary objectives of the central bank.

- Agro bills: They are short-term financial instruments issued to raise short-term financing for the new farmers. This financing is used as seasonal finance to pay for land preparation, acquisition of inputs and other working capital requirements.

- Petrozim bills: These are issued on behalf of NOCZIM to raise finance to procure fuel.

- Megawatt bills: These are issued on behalf of the Zimbabwe electricity supply authority either to raise financing for the rural

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electrification programme or to retire ZESA debt and pay for electricity imports.

- Tobacco bills: They are bill issued on behalf of the Tobacco Marketing board to promote the production of tobacco.

- NCDS: Negotiable certificate of deposits are short-term financial instruments issued by banks. The certificates can be negotiated to other investors.

It is important to note that financial institutions participate in both the money market and the capital market as suppliers and demanders of finance.

Participants in the money marketThere are a number of institutions that participate in the money market either as suppliers or demanders of short-term finance. The following are examples of institutions that participate in the money market:

-Commercial banks: These are institutions that accept demand (cheque) and time (savings) deposits.

-Merchant banks: Merchant banks are bankers to corporations providing investment and short to medium term loans to corporations.

-Discount houses: They are financial institutions involved in buying and discounting money market instruments.

-Building societies: These are institutions involved in the mobilization of savings deposits to provide mortgage finance.

Functions of the money marketThe money market performs four main functions. These are explained in the paragraphs that follow.

1. Provision of short-term capitalThe money market provides short-term capital to companies, financial institutions, governments and other organizations requiring short-term finance.

2. Provision of a marketThe money market provides a market for short-term investors to invest funds in short-term financial instruments that are low risk and highly liquid.

3. Acting as a barometer of liquidityThe money market acts as a barometer of liquidity within the economy. The Reserve bank can increase or curb liquidity by adopting strategies that operate via the money market for example open market operations (OMO).

4. Determining interest ratesThe money market also acts as the main determinant of interest rates in the economy. The demand and supply of funds in the money market determines

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the interest rates in the economy for example APDS for ZIMRA. Interest rates firm because of excessive demand for cash. After the APDS the interest rates ease.

B. The capital marketThis is a financial market for long-term finance and financial instruments. These will be financial instruments having an original maturity of more than one year. Examples of these financial instruments include debentures, preference shares, ordinary shares and agro-bonds (instruments to provide finance for infrastructural development for the new farmers.

Functions of financial markets Financial markets perform five broad functions. These are explained below.

1. Allocation of financial resourcesFinancial markets provide a mechanism for transferring wealth between periods in a way that increases the individual’s total level of utility.

2. Transfer of risksFinancial markets enable investors to reduce or even eliminate some risks by shifting risk to those who are more willing to accept it (at a cost).

A invests in B`s debentures (a safe investment)

A B

(Risk averse) (Risk lover) Offers Debentures B buys equity in C B shoulders risk Inherent in C`s equity Plus probability of financial Distress (Debentures)

A has transferred risk to B C By virtue of holding relatively Safe debentures.

It is important to note that there is a cost involved with this arrangement. Equity pays more than debentures because of the risk element. The return differential represents the cost of transferring risk to B.

3. Liquidity/Marketability The availability of an active financial market provides the investor with liquidity or marketability that facilitates changing the level of investment as the situation dictates. If the investor requires cash he can readily sell part

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of his shareholding to get cash. If he has excess cash he can increase his shareholding by buying additional units of shares from the market.

4. Increasing divisibility of real capital The existence of financial markets reduces the effect of the indivisible nature of real capital (assets). Subject to meeting the minimum numbers required one can either increase or decrease his shareholding thereby altering (dividing) upwards or downwards their real capital.

5. Provision of financial information Financial markets provide information on the available returns of various investment opportunities. Financial publications for example, disclose the previous day or week’s price and give an indication of trading in given shares on the market.

The Zimbabwe Stock ExchangeThis is a physical market located in Harare. It provides two indices, the industrial and the mining indices and price quotations on a daily basis (Monday to Friday). The indices provide a measure of the overall performance of financial instruments traded on the stock exchange.

Characteristics of a well-run stock exchangeA well-run stock exchange is one in which:(a) Some investors and fundraisers are unable to benefit at the expense of

other participants.(b) Is well regulated to avoid abuses, negligence and fraud. This is

necessary because investors need to be reassured that their hard earned savings are safe.

(c) There are minimal transaction costs. It is desirable to transact cheaply.(d) There are a large number of buyers and sellers to ensure efficient

share price setting.(e) Investors can sell their shares at any time without materially altering

the share price.

Benefits accruing from a well-run stock exchangeSix benefits can be argued to accrue to any economy if the economy has well-run stock exchange in operation.1. Provision of funds to firmsInvestors with quoted financial securities are assured that they can sell their shares quickly and cheaply at a reasonably certain price. This induces them to supply funds at a lower cost than would be the case if selling of shares was slow and expensive or if the price was uncertain. Stock markets encourage investment by mobilizing savings.

2. Allocation of capitalAn efficient market assists in the direction or flow of investment capital. A poorly regulated and operated stock market can mis-price financial securities leading to the direction of scarce capital to sectors which are inappropriate given the assumed objective of profit maximization.

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3. Provision of a secondary market for shareholders Shareholders will benefit if there is a well-run stock market because they can speedily and cheaply sell their shares should they want to do so. They may also be able to establish the value of their investment even if they do not wish to sell their securities.

4. Status and publicity A stock exchange quotation enhances the public profile of a firm. Some firms have been referred to as blue chips, a status only accorded to quoted firms. The quotation also brings with it more confidence from banks and other financial institutions leading to the provision of funds at a lower cost. The detailed scrutiny of the firm brings about this confidence.

5. Facilitation of mergers A public quotation can facilitate a merger where the mode of acquisition is a share swap. Unquoted companies are difficult to value whereas quoted shares have a value that is defined by the market.

6. Improvement in corporate behaviour Directors of companies listed on the stock exchange are more inclined to behave in a manner likely to enhance shareholder’s interest. For example a quotation requires disclosure greater in range and depth than is required by accounting standards and the companies act. Because the information is disseminated widely it becomes the focus of the general public and press comment.

Efficient Capital MarketsAn efficient capital market is one in which security prices reflect available information.

Types of efficiencyThree types of market efficiencies can be identified and these are now explained.

(1) Operational efficiency: This refers to the cost of security transactions to buyers and sellers on the exchange. It is desirable that the cost is as low as possible and creating a lot of competition between market makers and brokers can bring this about.

(2) Allocation efficiency: This refers to the ability of the stock market to direct financial resources where they are most needed. Society’s financial resources are scarce so it is important that this scarce resource is allocated where it is most productive. Stock markets assist in the allocation of the scarce financial resources between competing real investments.

(3) Pricing efficiency: The market price of a share should reflect available information so that no investors can earn returns above those earned on average by the market. The ability of the market to

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correctly price a financial security is what is referred to as pricing efficiency. It is the efficiency to focus on when dealing with the efficient market hypothesis.

Importance of having an efficient marketIt is desirable that the stock market operating in an economy is efficient. There can be substantial benefits to be derived from this efficiency. These benefits are now discussed.

1. An efficient market encourages share buying: Accurate security pricing is important if investors are to invest in quoted companies. The investor wants an assurance that securities are correctly priced. He would not want to lose his hard earned financial resources. Inability to correctly price financial securities can lead to a shortage of funds to organizations.

2. An efficient market provides correct signals to corporate management: If companies are to pursue shareholder wealth maximization, sound financial decision-making will require that the market correctly price securities. The market will provide the necessary feedback on their efforts. Unreliable security prices can distort the investment decision. Share prices provide indication of the required rate of return. Projects can be wrongly accepted or rejected.

3. An efficient market assists in the allocation of resources: Allocation efficiency requires both operational and pricing efficiency. Assuming an inefficient company has highly priced shares it would be able to attract capital and the limited resources will be wasted.

Price behaviour in an efficient marketIn an efficient market the price reflects what is known about a company’s current operations, profitability and potential for future growth and profits.

Overreaction and correction Price ($) 220

180

140 Efficient market reaction 100 Delayed reaction

-4 -3 -2 -1 0 +1 +2 +3 +4 Time in days

Fig. Reaction of share price to new information in efficient and inefficient markets.

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Efficient market reaction: The share price instantaneously adjusts to and fully reflects new information. There is no tendency for subsequent increases and decreases to occur.

Delayed reaction: The share price partially adjusts to the new information. . Four days elapse before the share price completely reflects the new information.

Overreaction: The share price over-adjusts to the new information. It overshoots the new price and subsequently corrects.

Efficient Market Hypothesis (EMH)This is an investment theory that states that it is impossible to beat the market because prices already incorporate and reflect all relevant information. Proponents of this model believe that it is pointless to search for undervalued stocks or try to predict trends in the market through any technique from fundamental to technical analysis.

Eugene Farma formulated efficient market hypothesis in 1970. The hypothesis suggests that at any given time, prices fully reflect all available information on a particular stock and or market. No investor has an advantage in predicting a return on a particular stock price since no one in particular has access to information not already available to everyone else.

Degrees of market efficiencyThe following are three classifications of market efficiency. They reflect the degree to which efficiency can be applied to markets.

1. Strong efficiencyThis is the strongest version which states that all information in the market, whether public or private is accounted for in the stock price. Not even insider information could give an investor an advantage.

2. Semi-strong efficiencyAll PUBLIC information is calculated into a share’s current price. Neither fundamental nor technical analysis can be used to achieve superior gains.

3. Weak efficiencyThis type of efficient market hypothesis claims that all past prices of a stock are reflected in today’s stock price. Technical analysis cannot be used to predict and beat a market.

Challenges to Market efficiencyIn the real world there are some investors who have beaten the market. Warren Buffet’s investment strategy of focusing on undervalued stocks made millions and set an example that is now being followed by many.

There are also consistent patterns that are present in the market. There is the January effect, a pattern that shows that higher returns tend to be earned in

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the first four months of the year. There is also the “blue Monday on Wall street”. This is a term that discourages buying stock on Friday afternoon and Monday morning because of the “weekend effect”. This is a tendency for stock prices to be higher than the rest of the week.

Studies in behavioural finance (a study into the effects of investor psychology on stock prices) also reveal that there are some predictable patterns on the stock market. Investors buy undervalued stocks and sell overvalued stocks. Paul Krugman, MIT economics professor, suggests that because of mass mentality of the trendy, short-term shareholder, investors pull in and out of the latest and hottest stocks. This leads to stock price distortions and hence the market becomes inefficient. Prices in this case would be manipulated by profit-seekers.

Contributors to market efficiencyThe following can be noted as significant contributors to the improvement of market efficiency:

1. Investors must perceive that a market is inefficient and possible to beat. Investment strategies intended to manipulate inefficiencies will the actually be the fuel that keep a market efficient.

2. A market must be large and liquid.3. Information must be widely available (in terms of accessibility and

cost). It should also be released to investors more or less at the same time.

4. Transaction costs must be cheaper than the expected profits of an investment strategy.

5. Investors should have enough funds to take advantage of the inefficiencies until the inefficiencies disappear.

6. Investors must believe that they can outperform the market.

ConclusionEfficient market hypothesis supporters argue that profit seekers will exploit abnormalities that may exist until they disappear leaving the market to eventually correct itself. Large transaction costs are likely to outweigh the benefits of trying to take advantage of such a trend.

Markets cannot be absolutely efficient or wholly inefficient, they are a mixture of both. Daily decisions by market players cannot be reflected immediately into the market.

Electronic trading allows for prices to adjust more quickly to news entering the market.

Information technology is leading to greater market efficiency. It allows for a more effective, faster means to disseminate information widely. It however restricts the time for the verification of information used to make the trade. This may eventually result in less efficiency if the quality of the information no longer allows investors to make profit-generating decisions.

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Implications of the EMH for investors1. Public information cannot be used to earn abnormal profits.

Fundamental analysis is therefore a waste of money for as long as efficiency is maintained. The best an average investor can do is to select a diversified portfolio.

2. There is need for greater volume and timely information. Since semi-strong efficiency depends on the quality and quantity of publicly available information investors should pressure companies, accounting bodies, governments and stock market regulators to produce as much useful information as is possible without jeopardizing company operations to competitors.

Implications of the EMH for companies1. The timing of security issues does not have to be fine-tuned2. Large quantities of new shares can be sold without materially moving

the share price.

Factors contributing to developing stock market inefficiencies1. Lack of investment analysts. For the market to be efficient there must

be a large number of competing investment analysts. Competition among investment analysts ensures that information is instantly reflected in security prices. In emerging markets there are few analysts and this reduces market efficiency.

2. Few buyers and sellers. There are relatively few buyers and sellers on developing stock exchanges. Few institutional investors sometimes have a very large impact on the performance of some shares. This leads to less efficiency since price determination is only left to a few investors.

3. The Government. Poor or unrealistic government policies have effects on stock exchanges. In Zimbabwe for example, Socialist policies adopted at independence impacted on investor confidence leading to a slump in the operations of the exchange in the 1980s. This outside influence leads to increased inefficiency of the exchange. The position changed, however, following the adoption of more liberal policies and this so the exchange being voted as one of the best performing exchanges in the developing economies.

4. Limited number of traded firms (counters). In many developing states the number of firms listed on the stock exchange are few compared to the number of firms operating in those countries. This limited number means that all industries will not be represented on the exchange leading to problems in analyzing and incorporating information.

5. Limited information disclosure. There is limited disclosure of information by companies in developing economies. In Zimbabwe for example, financial reports only show the minimum information stipulated by legislation. This results in problems in the pricing of securities, as information is the basis of security pricing.

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Insider TradingInsider trading is the dealing in securities or financial instruments by a person knowingly in possession of inside information, relating to the financial instrument being dealt in.

Inside information is specific and precise information obtained by an insider, which is price sensitive and has not been made public.

Price-sensitive information is information that has a material effect on the price or value of an instrument if it is made public.

An insider is someone who has obtained inside information through being a director, employee or shareholder of the issuer of the financial instrument, or someone who has gained access to such information by virtue of his employment, office or profession.

Insiders can either be primary or secondary. Primary insiders obtain information directly. They include a director, employee, shareholder, legal advisor, auditor, corporate advisor or sponsoring stockbroker of the company. Secondary insiders are individuals who obtain inside information directly or indirectly from a primary insider.

NB. Insider trading undermines confidence in the stock market.

Approaches to deal with insider tradingTo avoid undermining the confidence in the stock market it is necessary to deal with insider dealing. The following approaches have been suggested as ways that could be used to deal with insider trading.

(a) Legislation and codes of conduct(b) Increasing the level of information disclosure (price sensitive

information).(c) Prohibiting certain individuals from dealing in the company’s shares at

crucial time periods. This is generally during the reporting season.

The Agency ProblemThe agency problem is the possibility of conflict of interest between the stockholders (owners) and management (agents of the stockholders) of the firm. The problem is created by absentee ownership.

Absentee ownership creates a number of problems for the firm. (1) Agents may consume excessive perquisites “Perks”. This is money or

goods given or regarded as a right in addition to one’s pay.(2) Agents may shirk. This refers to avoiding doing one’s duty or not

expending one’s best efforts.(3) Agents may act to their self-interest instead of that of the principal.

The problems highlighted above are of concern to shareholders. They would therefore want the firm to minimize cases of divergence of interest between

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shareholders and management. A number of possible solutions have been suggested.

Possible solutions to the agency problem1. Linking rewards to shareholder wealth improvementIt has been suggested that as motivation to management additional rewards should be offered to discourage them from diverging far from what is in the interest of shareholders. Those making this suggestion recommend that additional financial rewards like bonuses if the firm’s share price improves considerably can do the trick.

2. Share optionsDirectors and other senior managers are granted share options. These permit them to buy shares at some future date at a price that is fixed now. If the share price increases between the date of the option granting and share acquisition, the manager makes a profit. This gives the managers an interest in trying to improve the share price if they are to benefit. This brings congruence, which reduces the agency problem.

3. SackingsCompanies can also threaten to sack non-performing managers. These will be managers who will not be improving the firm’s share price. The humiliation and financial loss following sacking may encourage managers not to diverge too far from shareholder wealth maximization.

4. Selling shares and the take over threatFinancial institutions own the bulk of the shares quoted on the stock exchange. These are not prepared to fund the cost of monitoring directors in all firms in which they have shareholdings. If they perceive that directors are not acting in the institution’s best interests, they sell the shares rather than intervening. The downloading of a large volume of shares reduces the price creating a real threat of a take-over at such depressed prices. At such depressed prices the firm may also find it very difficult to raise financing, creating even more problems for the firm.

5. Corporate governance regulationsLegislation (companies act) and other regulatory pressures like the stock exchange guidelines are available and can be enforced to encourage directors to act in shareholders interests.

6. Increasing information flowThe accounting profession and the stock exchange should encourage firms to release accurate, timely and detailed information concerning their operations. To the extend that this is adhered to, this may help to monitor firms and identify wealth destroying actions of wayward managers early.

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Chapter 2

Valuation is the process that links risk and return to determine an asset’s worth. The value of an asset is the present value of all future cash flows expected from the asset over the relevant time period. The value is determined by discounting expected future cash flows to their present value using the discount rate, which is commensurate with the asset’s risk.

Determination of security prices

Security prices on the exchange are determined by supply and demand and this supply and demand depends on the information that investors have about the securities. This information can be obtained from the press, the company and other publications like magazines. The information obtained can be political, economic, industry or corporate information.

Political factors

Political events affect stock market prices. Included in political events will be things like political stability, government changes or statements by politicians. These events can cause a positive or negative movement in share prices.

Economic factors

Macro economic factors also affect security prices. Macro economic factors include variables like economic growth, rate of inflation or unemployment. These macro economic factors are influenced by government policies like fiscal and monetary policies. Ultimately these economic factors affect the financial performance of companies.

Interest rates

Interest rates play an important role in determining security prices in that the equity market is in competition for funds with the debt market. If the debt market has attractive interest rates debt instruments become attractive and more funds are attracted to the debt market at the expense of the equity market.

International factors

A recession in a country that is Zimbabwe’s major trading partner or higher returns in markets competing for foreign investors affects security prices as Foreign direct investment will be directed to those countries that offer higher returns.

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Corporate and industry information

The attractiveness of an individual company’s shares is largely determined by the attractiveness of the industry in which the firm operates and the performance of the company itself. If an industry is attractive the shares of the companies in that industry will be priced favourably. But the extend of the attractiveness of individual shares will be a function of each firm’s performance in that industry.

Level of financial and business risk of the firm

For risk averse investors the higher the level of risk the less the price the investors will be prepared to pay for the shares of such companies.

The valuation modelThe following is the basic model that can be used to value financial instruments.

V0 = CF1 + CF2 + ….CFn

(1+k)1 (1+k)2 (1+k)n

VALUATIONS

BONDS/ ORDINARY SHARES/ PREFERENCE DEBENTURES EQUITY SHARES

Redeemable Finite period Redeemable

Perpetual Perpetual Perpetual

A. VALUATION OF BONDS/DEBENTURESA bond is a long-term debt instrument used by organizations and governments to raise large sums of money. It carries a stated rate of interest also known as a coupon rate. The coupon rate is expressed as a percentage of the bond’s par value and it determines the periodic interest payments. The interest can be paid annually or semiannually.

A redeemable bond has a maturity date. This is the date on which the face value of the bond will be repaid. The last coupon payment is also paid when the bond matures.

Bonds have original maturity periods. The period refers to the time remaining until the bond matures from when the bond was issued. Remaining maturity refers to the time currently remaining until maturity date.

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Bonds redeemable by the issuer prior to maturity are called callable bonds. The call date is the date at which the bond can be called and the call price is the amount that the issuer pays to call a callable bond.

The value of the bond is equal to the present value of interest payments to be received over a defined period.

A1.Valuation of redeemable bonds/debenturesConsider the following example.

A Ltd. Issues a $50 000 10% 5 year bond. If the interest is paid annually and the required rate of return on similar bonds is 10%, what is the value of the bond if it is repayable at par?

Annual interest payment = 10/100*$50 000 = $5 000.

The following time line indicates the interest payments to be received by a holder of such a bond.

0 1 2 3 4 5 $Nil $5 000 $5 000 $5 000 $5 000 $5 000 + $50 000

During year 5 there is the principal that has to be repaid as well.

The present value of the cash flows can now be presented.

0 1 2 3 4 5 $Nil $5 000 $5 000 $5 000 $5 000 $5 000 + $50 000 $4 545 = 0.909 4 130 = 0.826 3 755 = 0.751 3 415 = 0.683 34 155 = 0.621 50 000 3.790

A tabular format can also be used to show how the present value can be arrived at. It is the method that will be used to illustrate the valuation of all financial securities.

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Present value computation Time Cash Flow Discount Present Interest Principal Factor Value 12345

$5 000 5 000 5 000 5 000 5 000

----$50 000

0.9090.8260.7510.6830.621

$4 5454 1303 7553 415

34 155 $50 000

As the interest payment is an annuity a shorter approach (annuity approach) can also be used to arrive at the same result.

Present value computation Time Cash Flow Discount Present Interest principal factor value

1-55

$5 000-

-$50 000

3.7900.621

$18 950 31 050 $50 000

The above table is a representation of the approach given below which is often indicated in the literature.

Bo = I (PVIFAkd,n) + RP (PVIFkd,n) Where Bo = Value of bond at time zero I = Interest in dollars PVIFA = Present value interest factor for an annuity PVIF = Present value interest factor kd = required rate of return on similar bonds n = number of years to maturity RP = redemption payment

Bo = $5 000(3.790) + $50 000(0.621) = $18 950 + $31 050 = $50 000

Whenever the required rate of return on similar bonds is EQUAL to the coupon rate of interest, the value of the bond will be EQUAL to the face value of the bond. The bond sells at par.

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Variations to the required rate of return

Whenever the required rate of return on similar bonds differs from the bond’s coupon rate, the value of the bond will differ from its par value. The required rate of return on a bond can differ from the coupon interest rate because of the following two reasons:

Economic conditions

Economic conditions change and this may result in a shift in the BASIC cost of long-term funds. An increase in the basic cost of long-term debt will increase the required rate of return on debt. A decrease in the basic cost of debt will lower the required rate of return.

Changes in the firm’s risk posture

If the risk posture that the firm is facing changes, this may change the rate of return required by suppliers of long-term debt finance. If risk increases, the required return increases, if risk decreases, the required rate of return decreases.

An increase in the required rate of return

The following example illustrates the effect of an increase in the required rate of return on the value of a bond.

B Ltd. Has a $50 000 10% 5 year bond outstanding. Interest is paid annually. Following an increase in the basic cost of long-term debt, the required rate of return is now 12%. What is the value of the bond if it is repayable at par?

Interest = 10/100 *$50 000 = $5 000, R P = $50 000

Present value computation Time Cash Flow Discount Present Interest Principal factor value

1-5 5

$5 000-

-$50 000

3.6050.567

$18 025 28 350

$46 375

When the required rate of return is greater than the coupon rate of interest the value of a bond will be less than its par value. The bond is said to sell at a discount. The discount is the amount by which the bond sells at a value that is less than its par/face value.

The discount = $50 000 - $46 375 = $3 675

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A decrease in the required rate of return

The example that follows shows the effect of a decrease in the required rate of return on the value of a bond.C Ltd. Has a $50 000 10% 5 year bond outstanding. Interest is paid annually. The risk posture of the firm lowers reducing the required rate of return to 8%. What is the value of the bond if it is repayable at par?

Time Cash Inflow Discount Present(Year) Interest Principal factor @8% value1-5 $5 000 0 3.993 19 9655 0 50 000 0.681 34 050

54 015

Whenever the required rate of return falls below the coupon rate of interest, the bond value will be greater than the par value. The premium is the amount by which a bond sells at a value that is greater than its par or face value. The premium in the example just presented will amount to:

Premium = $54 015 - $50 000 = $4 015

Valuation of redeemable bonds, redeemable at a discount

The following example illustrates how the valuation of a redeemable bond redeemable at a discount is valued. What is needed is to remove the discount from the redemption proceeds and apply the valuation model as already illustrated.

C Ltd. has a $100 000 10%, 5 year bond outstanding. Interest is paid annually and the required rate of return is 10%. What is the value of the bond if it is repayable at a discount of 10%?

The redemption payment = ($100 000 – (.10*$100 000)) = $90 000

Present value computationTime Cash inflow Discount Present(Years) factor @10% value1 -5 $10 000 0 3.791 $37 910 5 0 $90 000 0.621 55 890

93 800

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Valuation of redeemable bonds, redeemable at a premium

If a bond is redeemable at a premium, the premium should be incorporated into the redemption payment. The following example will illustrate how the bond that is redeemable at a premium will have to be valued.

D Ltd. has a $200 000 10%, 5 year bond outstanding. Interest is paid annually and the required rate of return is 10%. What is the value of the bond if it is repayable at a premium of 10%?

Redemption payment = ($200 000 +(.10*$200 000)) =$220 000

Present value computationTime Cash inflow Discount Present(Years) Interest Principal factor @10% value1 -5 $20 000 0 3.791 $75 820 5 0 $220 000 0.621 $136 620

$212 440

B. VALUATION OF IRREDEEMABLE/PERPETUAL BONDS

Perpetual bonds pay interest perpetually. This means that interest will be paid indefinitely.

Bo = I Kd

Where BO = value of a bond at time zero. I = annual interest in dollars. Kd = required rate of return on similar bonds.

An example on how a perpetual bond is valued is now presented under different scenarios.

E Ltd. has a $300 000 10% perpetual bond outstanding. Calculate the value of the bond if the required rate of return is:(a) 10%(b) 15%(c) 5%

(a) Bo = $30 000 0.10 = $300 000

(b) Bo = $30 000 0.15 = $200 000

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(c) Bo = $30 000 0.05 = $600 000

YIELD TO MATURITY

Sometimes investors pursue a buy and hold philosophy. They buy a financial asset and hold it until maturity. This type of investor is interested in knowing the annual rate of return on a financial asset that they hold until maturity. This return is what is known as yield to maturity.

Yield to maturity is a rate of return measuring the total performance of a bond (coupon payments and capital gain or loss) from the time of purchase until maturity. It is the market rate that equates a bond’s present value of interest payments and principal repayment with its price. It represents an annualized rate of return in percentage terms on a fixed income instrument such as a bond or debenture.

Mathematically yield to maturity is found by using the following formula:

C (1+r)-1 + C (1+r)-2 + - - - + C (1+r)-n + B (1+r)-n =P

Where C = annual coupon payment in dollars not percent n = number of years to maturity B = Par value P = Purchase price

Yield to maturity cannot be solved for directly and one has to use trial and error or some iterative technique. It is however, fairly ease to get yield to maturity if one uses a financial calculator.

An alternative would be to use some approximation using the approximation formula. The results obtained by this method are quite accurate for decision-making purposes. This approach is now presented.

Par Value – Current Value YTM » Annual Interest Payment + Years to Maturity

Par Value + Current Value 2

An illustration on how the approximation approach can be used to approximate yield to maturity can now be presented.

F Ltd. has a $400 000 10%, 5 year bond outstanding. Interest is paid annually. If the bond is redeemable at par, approximate its yield to maturity if the required rate of return is:

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(a) 10%(b) 12%(c) 8%

Before calculating the approximate yield to maturity, the bond current value has to be calculated first. So one has to calculate current value as the first step and then calculate approximate yield to maturity as the second step.

(a) Since the required rate of return is currently is 10%, the market value of the bond is $400 000.

Approximate yield to maturity = $40 000 + ($400 000 -$400 000/5) $400 000 + $400 000/2

= $40 000 $40 000

=0.10*100

= 10%

(b) When the required rate of return is 12% the value of the bond is as indicated below:

Present value computationTime Cash inflow Discount Present(Years) Interest Principal Factor @12% value1 - 5 $40 000 0 3.605 $144 2005 0 $400 000 0.567 $226 800

$371 000

Now that Bo is known the approximate yield to maturity can now be calculated.

Approximate yield to maturity = $40 000 + ($400 000 - $371 000/5) ( $400 000 + $371 000)/2

= $45 800 $385500

= 0.1188067*100

=12%

(c) When the required rate of return is 8%, the value of the bond is calculated as follows:

Present value computationTime Cash inflow Discount Present (Years) Interest Principal factor @8% value

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1 - 5 $40 000 0 3.993 $159 720 5 0 $400 000 0.681 $272 400

$432 120

The approximate yield to maturity can now be calculated.

Approximate yield to maturity = $40 000 +($400 000 - $432 120/5) ($400 000 + $432 120)/2

= $33 576 $416 060

= 0.0806998*100

= 8%

The above example has shown that the required rate of return is similar to the yield to maturity. This means that when computing the value of a bond one can use yield to maturity if the required rate of return is not given.

OTHER COMPOUNDING PERIODS

Occasionally interest is paid more than once annually. The valuation model has to be adjusted to incorporate the fact that interest is paid more than once annually. The table presented below summarizes the nature of the adjustments required to the variables in the valuation model. The adjustment to be made is generally a function of the number of times interest is paid annually.

Variable for model Frequency of interest payment and nature of adjustment to makeSemiannually Quarterly Monthly

Interest (I) 2/ (I/2) 4/ (I/4) 12/ (I/12)Years to maturity (n) 2/ n*2 4/ n*4 12/ n*12Required return (k) 2/ (kd/2) 4/ (kd/4) 12/ (kd/12)

VALUATION OF ORDINARY SHARES

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Equity-holders expect to be rewarded in the form of periodic payments (ordinary dividends) and an appreciation in the value of their shareholding. Equity holders need to value their shareholding because they need to make decisions l on whether to hold on to their investments or sell the equity. They choose to purchase stock when they believe the stock to be undervalued (its true value greater than the market value) and sell it when it is overvalued (its market value being greater than its true value). True value in this case is the intrinsic value. The summary below illustrates the positions just explained.

Share Intrinsic value Market value Valuation status Investor decisionA $100.00 $100.00 Correctly valued Hold shareB $100.00 $150.00 Overvalued Sell shareC $100.00 $80.00 Undervalued Buy share

Share A is correctly valued. It makes sense for an investor to hold on to this share. Share B is overvalued. The sooner the investor sells the better. The market self-corrects and the price will slide downwards to the intrinsic value so the sooner he sells the better, as his returns will be fairly substantial. Share C is undervalued. The market will self-correct and the market price will move upwards. If he buys early his rewards will be greater.

The situations highlighted for share B and share C are temporary states of disequilibria, which cannot be sustained. This is why one has to either buy or sell. The situation for share A is an equilibrium situation, which can be sustained so the investor need not do anything.

The valuation arrangements discussed in this chapter will show how one can get the intrinsic value of a share using the dividend valuation model.

VALUATION OF EQUITY WITH A FINITE HOLDING PERIOD

Sometimes investors wish to have an investment over a finite period. The valuation model to use should have a limited holding period. A limited holding period assumes a sale of the share at the end of an assumed holding period. The present value of the share in this case becomes the sum of the present values associated with the dividends received during the holding period, plus the present value of the sales price at the end of the holding period.

Valuation of equity with zero growth dividends over a finite holding period

A Ltd’s ordinary shares are currently paying a dividend per share of $20.00 per annum. The dividends are not expected to grow over the next 5 years because of stable economic activities obtaining. An investor currently holds 10 000 such shares. His intention is to sell them and earn a yield of 35% at the end of the 5 years. If the required rate of return is currently 15% what is the value of:

(i) each ordinary share(ii) the shareholder’s total shareholding?

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0 1 2 3 4 5 DO D1 D2 D3 D4 D5

DO = $20.00, therefore if g is zero DO = D1 =D5 = $20.00

In addition to the dividend in the final year, there are the sale proceeds of the share calculated using the yield approach.

Expected sale price computation

Yield = Dividendfinal year

Market pricefinal year

0.35 = $20.00 x 0.35x = $20.00

x = $20.00 0.35

= $57.14

Present value computationEnd of Cash Inflow Discount PresentPeriod Dividend Sale Price factor@ 15% value1-5 $20.00 0 3.352 $67.045 0 $57.14 0.497 $28.41

$95.45

Each ordinary share is worth $95.15

Value of shareholding = $95.45*10 000 = $954 500

Constant growth dividends over a finite period

Sometimes a shareholder may hold a share for a finite period but the share will be receiving a growing dividend. The valuation of such a share is illustrated by the following example.

EXAMPLEB Ltd.`s ordinary shares are currently paying a dividend of $30.00 per share per annum. The dividends are expected to grow at an annual rate of 8% over the next five years because of limited economic growth. An

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investor currently holds 100 000 such shares. His intention is to sell them to earn a yield of 40% at the end of 5 years. If the required rate of return on such shares is currently 15%, what is the value of each ordinary share?

Solution

D0 =$30.00D1 = 1.08($30.00) = $32.40D2 = 1.08($32.40) = $34.992D3 = 1.08($34.992) = $37.7914D4 = 1.08($37.7914) = $40.8147D5 = 1.08($40.8147) = $44.0798

Sale price = 0.40 = $44.0798 X 0.40x = $44.0798

x = $44.0798 0.40

= $110.20

Present value computationEnd of Cash Inflow Discount PresentPeriod Dividend Sale price factor@ 15% value1 32.4 0 0.87 28.1882 34.992 0 0.756 26.4543 37.7914 0 0.658 24.86674 40.8147 0 0.572 23.3465 44.0798 100 0.497 76.6769

179.5315

The value of each share is $179.53

EARNINGS PER SHARE

Sometimes one is given earnings per share and no dividends. The model being illustrated uses dividends and not earnings per share. It is necessary to calculate how much of the earnings are paid as dividends and then use the dividends as illustrated in the following illustration.

EXAMPLEA share is bought at the end of year 0 at $95.00. Earnings per share at the time of purchase were $9.50 and are expected to grow at a compound annual rate of 6 per cent. The company pays out 55 per cent of earnings in the form of dividends each year. The share will be sold at the end of the third year and a price earnings ratio of 15 is expected to apply to the share at the time of sale. If a rate of 8 per cent is available in alternative investment opportunities felt to be of equivalent risk, what is the present value of the share?

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Solution

Year EPS DIVIDEND0 $9.501 1.06($9.50) = $10.07 0.55($10.07) = $5.538502 1.06($10.07) = $10.6742 0.55($10.67420) = $5.870813 1.06($10.6742)=$11.31465 0.55($11.31465) = $6.22306

Computation of sale priceThe sale price can be estimated by using the price earnings ratio that the investor wishes to realize.

Price earnings ratio = Market priceend of period

EPSend of period

15 = X/$11.31465 = $169.7197

The following table shows the computation of the present value of the share.

End of Cash Inflow Discount Present Period Dividend Sale price factor@8% value1 5.5385 0 0.926 5.128652 5.8708 0 0.857 5.031283 6.2231 169.71975 0.794 139.69859

149.85852

Variable growth dividends over a finite periodThe following example shows how an ordinary share that pays dividends with variable growth will be valued.

EXAMPLEC Ltd`s ordinary shares are currently paying an annual dividend per share of $20.00. The dividends are expected to grow at a supernormal growth rate of 15% for the next three years. Thereafter the growth rate is expected to stabilize at 10% annually for the next two years. A shareholder intends to sell her shareholding at the end of year 5. What is the value of each share if her intention is to realize a yield of 25% and the required rate of return is currently 20%?

SolutionD0 = $20.00D1 = 1.15($20.00) = $23.00D2 = 1.15($23.00) = $26.4500

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D3 = 1.15($26.4500) = $30.41750D4 = 1.10($30.41750) = $33.45925D5 = 1.10($33.45925) = $36.80518

Sale price = $36.80518/x =0.25

= $147.22070

Present value computationEnd of Cash Inflow Discount PresentPeriod Dividend Sale price factor @20% value1 23,0000 0 0.833 19.1592 26.4500 0 0.694 18.35633 30.4175 0 0.579 17.611734 33.45925 0 0.482 16.127365 36.80518 147.2207 0.402 73.9784

145.23279

The value of each share is $145.23

VALUATION OF PERPETUAL EQUITYThe value of perpetual equity is the present value of all future dividends expected to be provided by the share over an infinite horizon.

Dividends vs. earningsEarnings not paid out as dividends are retained. The retained earnings invested in profitable projects add earnings to produce opportunities for higher future dividends. The present value approach considers the earnings potential that result from the reinvested earnings by taking account of future dividends generated. It would be double counting to discount both present earnings and future dividends that result from earnings retention.

Zero growth dividends with infinite horizonThe approach assumes that a constant non-growing dividend stream will be paid. Thus D0 = D1 = D2 = D¥

P0 = D1

ke

Where D1 = dividend expected at end of year 1. Ke = required rate of return on equity. P0 = price of share now.

EXAMPLED Ltd. Currently pay $20.00 per share as dividend annually. This dividend is to remain at this level indefinitely. If the required rate of return is currently 16%, calculate the value of the ordinary share.

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SolutionD0 = $20.00D1 = D0 = $20.00

P0 = $20.00/0.16

= $125.00

Constant growth rate model (Gordon model) with infinite holding period

The model assumes that the dividends will grow at a constant rate perpetually at a rate that is less than the required rate of return.

The value of such a share is obtained by using the following approach:

P0 = D1 Ke -g

EXAMPLEE Ltd. has the following dividend history:

Year DPS ($)2003 14.002002 12.902001 12.002000 11.201999 10.501998 10.00

Calculate the value of E Ltd`s shares assuming that the required rate of return on equity is currently 30%.

It is necessary to first of all calculate the growth rate of dividends (g). g = $10.00(1+g)5 = $14.00 (1+g)5 = $14.00/$10.00

1 +g = 5Ö $14.00/$10.00

1 + g = 1.0696104

g = 1.0696104 -1

= 0.0696*100

= » 7%

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Next D1 (D2004), next dividend must be calculated.

= 1.07($14.00)

=$14.98

By applying the constant growth model the value of the share can now be found.

P0 = $14.9800 0.30 – 0.07

= $65.13

Variable growth rate with infinite holding period

This model allows for a change in the dividend growth rate. This appears to be a more realistic assumption in that the arrangement allows for shifts in growth rate due to changing expectations.

EXAMPLEF Ltd. Has introduced a highly competitive and attractive electric gadget. It is expected to experience a supernormal growth rate of 15% for the first 4 years. This will then be followed by a fairly above normal growth rate of 10%…. For the following 5 years. The anticipated new competition after the ninth year will see a 2% decline in dividend for each of the following three years. After this period a normal growth rate of dividends of 3% is expected to prevail indefinitely. If the current annual dividend is $20.00 per share and the required rate of return on equity is 25%, what is the value of each ordinary share?

Solution

D0 = $20.00D1 =1.15($20.00) = $23.00D2 = 1.15($23.00) = $26.45D3 =1.15($26.45) = $30.41750D4 = 1.15($30.41750) = $34.98013D5 = 1.10($34.98013) = $38.47814D6 = 1.10($38.47814) = $42.32595D7 = 1.10($42.32595) = $46.55855D8 = 1.10($46.55855) = $51.21440D9 = 1.10($51.21440) = $56.33584D10 = 1.08(456.33584) = $60.84271D11 = 1.06($60.84271 = $64.49327D12 = 1.04($64.49327) = $67.07300D13 = 1.03($67.07300) = $69.08519

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Priceend of year 12 = $69.08519/(0.25 – 0.03) = $314.02359

Present value computationEnd of Cash Inflow Discount PresentPeriod Dividends Sale price Factor @25% value1 23 0 0.800 18.42 26.45 0 0.640 16.9283 30.4175 0 0.512 15.573764 34.98013 0 0.410 14.341855 38.47814 0 0.328 12.620836 42.32595 0 0.262 11.08947 46.55855 0 0.210 9.77738 51.2144 0 0.168 8.604029 56.33584 0 0.134 7.54910 60.84271 0 0.107 6.5101711 64.49327 0 0.086 5.5464212 67.073 314.02359 0.069 26.29566

153.2364

The value of each ordinary share is $153.24

VALUATION OF PREFERENCE SHARES

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The reward for holding preference shares is the preference dividend that is paid after all the other expenses are paid. Unless otherwise stated a preference share is cumulative and non-redeemable.

REDEEMABLE PREFERENCE SHARES WITH NO ARREAR DIVIDENDS

P Ltd. would like to sell 1 000 000, 15%, $100.00, 5 year redeemable preference shares that it has as an investment. Similar shares available on the stock exchange yield 20%. How much can P Ltd. expect to get from the disposal of the investment? Assume that the preference shares are redeemable at par.

Preference dividend per share = 15/100*$100.00 = $15.00

$15.00 $15.00 $15.00 $15.00 $15.00 + $100.00

Present value computationEnd of Cash Inflow Discount PresentPeriod Dividend Principal factor @20% value1 -5 $15.00 0 2.991 $44.8655 0 $100.00 0.402 $40.200

$85.065

Proceeds expected from disposal of investment = 1 000 000 *$85.065 = $85 065 000.00

REDEEMABLE CUMULATIVE PREFERENCE SHARES WITH ARREAR DIVIDENDS

Where the preference dividends are in arrears these have to be brought into account in the valuation because the current dividend cannot be paid before the arrears are cleared. An estimation of when the arrear dividends will be paid is needed for valuation purposes.

EXAMPLEA company in which Q owns 10 000 Preference shares of $100.00 each has just made an announcement of financial difficulties ahead. It is expected that the dividends for the next three years will be passed; thereafter normal dividend payments will then be expected to resume. If the preference dividend is 15% and the shares are redeemable at the end of 5 years, what is the value of each preference share if the required rate of return is currently 25%?

Preference dividend = 15/100*$100.00 = $15.00

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0 1 2 3 4 5 $0 $0 $0 $15 +$45 $15 +$100

Present value computationEnd of Cash Inflow Discount PresentPeriod Dividend Principal factor @25% value1 0 0 0.800 02 0 0 0.640 03 0 0 0.512 04 $60.00 0 0.410 $24.605 $15.00 $100.00 0.328 $37.72

$62.32

Each preference share is worth $62.32.

REDEEMABLE NON-CUMULATIVE PREFERENCE SHARES WITH ARREAR DIVIDENDS

If dividends are passed, non-cumulative preference shareholders lose out, as the passed dividends are lost. From a valuation point of view only the current dividends will be relevant as these are the ones that will be paid only.

The example just illustrated will now be re-visited with the assumption that the preference shares are non-cumulative.

Present value computationEnd of Cash Inflow Discount PresentPeriod Dividend Principal factor @25% value1 0 0 0.8 02 0 0 0.64 03 0 0 0.512 04 $15.00 0 0.41 $6.155 $15.00 $100.00 0.328 $37.72

$43.87

Each preference share is worth $43.87

PERPETUAL PREFERENCE SHARESThe value of a perpetual preference share is the present value of the preference dividend received in perpetuity.

PO = Preference dividend Required return (kp)

EXAMPLE

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Find the value of perpetual preference shares that have a par value of $5.00 each and carry a dividend of 10%. Similar shares available on the stock exchange yield 20%.

Preference dividend = 10/100*$5.00 = $0.50

Po =$0.50 0.20

= $2.50

PERPETUAL CUMULATIVE PREFERENCE SHARES WITH ARREAR DIVIDENDS

A Ltd. has in issue 100 000, 15% $100.00, cumulative perpetual preference shares. It has made an announcement of financial difficulties ahead. It expects that the dividends for the next four years will be passed. Thereafter normal dividend payments will then be expected to resume with no further passing of dividends. If the required rate of return is 25% what is the value of each preference share?

Present value computationEnd of Cash Inflow Discount PresentPeriod Dividend Share value factor @ 25% value1 0 0 0.8 $02 0 0 0.64 03 0 0 0.512 04 0 0 0.41 05 $75.00 $60.00 0.328 44.28

Pend of year 5 = $15.00 0.25

= $60.00

PERPETUAL NON-CUMULATIVE PREFERENCE SHARES WITH ARREAR DIVIDENDS

It was indicated earlier on that if dividends are passed, then the arrear dividends are lost. The example just illustrated will now be re-visited with the assumption that the shares are non-cumulative.

Present value computationEnd of Cash Inflow Discount Present

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Period Dividend Share value factor @25% value1 0 0 0.800 02 0 0 0.640 03 0 0 0.512 04 0 0 0.410 05 $15.00 $60.00 0.328 $24.60

The value of each preference share is $24.60

LIMITATIONS OF THE DIVIDEND VALUATION MODEL

The model that was used to value ordinary shares and preference shares, the dividend valuation model, has a number of limitations and these are now highlighted.

Estimation of earnings and dividends

The tendency is to assume that earnings grow at a constant rate and that dividends also grow at a constant rate or that the dividend payout ratio is constant. Experience suggests that earnings growth rates can vary markedly over time and that firms do change their dividends policies.

Constant required rate of return

The discount rate is held constant for the time period covered by the model. Required market rates change over time and the risk class of the firm may also change. This invalidates the assumption of a constant required rate of return.

Time horizon covered by the model

The model assumes earnings growth into perpetuity or a terminal value representing the expected sales price of the stock at some pre-determined time. The difficulty lies in imagining how accurate estimates can be made over such long horizons. When a finite holding period is assumed the question arises as to how one determines that holding period in advance. Even if the holding period could be estimated accurately, one still faces the difficult problem of estimating the market value of the stock at the end of the holding period.

Taxation

After tax cash flows are estimated by assuming the tax bracket applicable to the investment income for each annual holding period. Estimating applicable rates into perpetuity or long holding periods is not an easy task. Where a finite holding period is assumed the applicable capital gains tax on the estimated market value of shares is also required.

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PRICE EARNINGS RATIO (PER) MODEL

The model estimates the intrinsic value of a share by multiplying normalized earnings per share by an adjusted price earnings ratio, which reflects the analyst’s subjective judgment about future growth prospects for the firm and dividend policy.

The model is useful when a company’s share is not traded publicly and no market price exists. The model is applied as follows:

a. Determine the P/E ratio for the industry.b. Calculate the EPS of the company.c. Multiply the P/E for the industry with the EPS of the company.

Price = Sustainable P/E ratio * EPS

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PRACTICE PROBLEMS ON VALUATIONSPROBLEM 1Complex Systems has an issue of $1 000 par value bonds with a 12 percent coupon interest rate outstanding. The issue pays interest annually and has 16 years remaining to its maturity date.

a. If bonds of similar risk are currently earning a 10 percent rate of return, how much will the Complex Systems bond sell for today?

b. Describe the two possible reasons that similar-risk bonds are currently earning a return below the coupon interest rate on the Complex Systems bond?

c. If the required return were at 12 percent instead of 10 percent, what would the current value of Complex Systems’ bond be? Contrast this finding with (a) and discuss.

(b) Jones Designs wishes to estimate the value of its outstanding preferred stock. The preferred issue has an $80 par value and pays an annual dividend of $6,40 per share. Similar-risk preferred stocks are currently earning a 10 percent annual rate of return.

a. What is the market value of the outstanding preferred stock? b. If an investor purchases the preferred stock at the value calculated in

a, how much would she gain or lose per share if she sells the stock when the required rate of return on similar-risk preferred stock has risen to 12 percent? Explain.

(c) Lawrence Industries’ most recent annual dividend was $1,80 per share, and the firm’s required return is 10 percent. Find the market value of Lawrence’s shares when:

a. Dividends are expected to grow at 8 percent annually for three years followed by a 5 percent constant annual growth rate from year 4 to infinity.

b. Dividends are expected to grow at 8 percent annually for each of three years followed by zero percent annual growth in years 4 to infinity.

c. Dividends are expected to grow at 8 percent annually for three years followed by a 10 percent constant annual growth rate in years 4 to infinity.

PROBLEM 2(a) B Limited has an outstanding issue of $100 par value debentures with

a 12% coupon interest rate. Interest on the debentures is paid annually and 16 years still remain to their maturity. If debentures of similar risk are currently earning a 10% rate of return, how much will the B Limited debenture sell for today?

(b) Find the value of a debenture maturing in six years with a $100 par value and a coupon interest rate of 10 percent per annum (interest paid

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semi annually) if the required rate of return on similar risk debentures is 14 percent per annum (interest paid semi annually).

(c) You are requested to advise a potential investor who is considering making an investment in a small business currently generating $85 000 of after tax cash flow. A review of similar risk investment opportunities reveals that the fair rate of return for the proposed investment is 18 percent. You decide to estimate the firm’s value using several possible cash flow growth rate assumptions.

i. Estimate the value of the firm assuming that cash flows grow at an annual rate of zero percent to infinity

ii. Estimate the value of the firm assuming that cash flows are expected to grow at a constant annual rate of 7 percent to infinity

(d) TDA Limited has a better of 1,20. The risk – free rate of return is 10 percent and the required return on the market portfolio is 14 percent. The company plans to pay a dividend of $5,20 per share in the next year. The anticipated future dividend growth rate is expected to be consistent with that experienced over the last 7 years.

Year Dividend per share ($)2004200320022001200019991998

4,904,564,203,803,643,603,46

You are required:i. To determine the required return on TDA Limited’s equity using the

capital asset pricing model ii. Ii Estimate the value of TDA Limited using the Gordon constant

dividend valuation model

PROBLEM 3(a) Suppose a debenture has the following characteristics:

Face value of $1 000 Coupon rate of 20% A yield to maturity of 20% A maturity of 10 years

i. What is the value of the debenture? ii. When the coupon rate is increased to 30%, everything else

remaining constant, what is the new value of the debenture? iii. Everything else remaining the same, when the coupon rate is

reduced to 10%, what is the value of the debenture?

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(b) Identify from parts (i) to (iii) when the debenture is selling at a premium, discount or par. Explain why?

(c) Given that the debenture with a nominal value of $1000, with a yield to maturity of 20% a maturity of 10 years is now paying interest semi-annually. The coupon rate is 10%, what is the value of the debenture?

(d) An irredeemable debenture has a face value of $1000, coupon rate of 20% and a yield to maturity of 30%, what is the value of the debenture?

(e) Preference shares are to be issued with a nominal value of $1,00. The coupon dividend rate is 25% per annum. Assuming the required rate of return is 30%, what is the value of the Preference share?

A firm has just paid a preference stock dividend and it plans to pass the next 3-year dividend and resume regular dividend thereafter. Given that the par value is $1,00, coupon dividend rate is 24% per annum and the required rate of return is 30%, what is the value of the preference share if preference shares are cumulative?

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Chapter 3

RISK AND ITS MEASUREMENT

Risk is the probability that an outcome will not be as expected. The outcome may be favourable in which case we talk of upside risk. The outcome may turn out to be unfavourable. This is what is known as downside risk. Normally when people talk of risk they focus more on downside risk largely because of the negative effect it has on organizational operations. But this should not be the case as the upside risk should be looked at as well.

TYPES OF RISK

Business risk. Business risk refers to the variability in organizational earnings, which is function of the firm’s normal operations. It can be regarded as risk that is intrinsic to the firm’s operations.

Investment risk. This variability in earnings due to variations in cash inflows and outflows of capital investment projects undertaken. It is a function of the ability of a decision maker to make accurate cash flow forecasts that are used in the evaluation of potential investment projects.

Portfolio risk. This can be looked at as variability in earnings that is a function of the degree of efficient diversification that the firm has achieved in its operations and its overall portfolio of assets. If a firm identifies assets whose returns are negatively correlated then its diversification can be argued to be efficient and its variability of portfolio returns will be fairly minimal, minimizing portfolio risk.

Cataclysmic risk. Cataclysmic risk refers to variability in earnings that is function of events beyond managerial control and anticipation. Examples of these events include expropriation, erratic changes to consumer preferences or energy shortages. Management should not have anticipated the events and management should not be in a position to control the events if they are to qualify as events under cataclysmic risk.

Financial risk. This variability in earnings that is a function of the financial structure of an organization and the need to meet obligations of fixed-income securities. When an organization brings debt into its capital structure, it creates a fixed obligation, which will have to be serviced whether the organization makes a profit, or not. The variability in earnings that this arrangement brings constitutes financial risk.

Political risk. Political risk is the probability of selective interference in a company’s operations by host governments. This is a type of risk, which is faced by transnational corporations.

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CATEGORIES OF RISKRisk can be categorized into two broad categories, diversifiable and non-diversifiable risk.

Diversifiable risk, unique risk, unsystematic risk, firm specific riskThis is that risk that can be diversified away through the selection of other risky assets that are lowly or negatively correlated with the asset in question. It is risk that is unique to a particular firm hence it can be diversified away.

Non-diversifiable risk, systematic risk, market riskThere will always be an element of risk, which cannot be diversified away despite all efforts to diversify risk on the pert of a firm. This risk is what is referred to as non-diversifiable risk. It is risk that obtains in the market that a firm will have chose to operate.

The total risk of a project (j) = Systematic risk + Unsystematic risk.

The following diagram shows the two categories of risk just explained.

Risk (standard Total risk deviation)

Unique, company specific, unsystematic, diversifiable risk

Systematic risk, market risk, non – diversifiable risk

0 No of securities in portfolio

Fig. Diversifiable and non – diversifiable risk

MEASURES OF RISKFor the decision maker to make an informed decision, there is need to quantify the level of risk that will be associated with the potential investment being evaluated. There are statistical approaches that quantify the level of risk associated with a potential investment. These are now going to be explained and illustrated.

THE RANGEThis is a measure of an asset’s risk arrived at by subtracting the pessimistic (worst) outcome from the optimistic (best) outcome. The greater the range for the asset, the greater the variability (risk) associated with the asset.

The range (Rg) = Rh-Rl

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Where Rg = range of the distribution Rh = highest value in the distribution Rl = lowest value in the distribution

EXAMPLEThe following information is given for assets A and B. Asset A Asset BInitial Investment $10 000 $10 000Annual rate of returnPessimistic 13% 7%Most likely 15 15Optimist 17 23

If the investor is risk averse, which asset will he select?

SolutionThe range can be used to answer this question.

RangeA =17% - 13% = 4%

RangeB = 23% - 7% = 16%

A risk averse investor will select asset A because it offers the same most likely return (15%) but with a lower risk (range) of 4%.

STANDARD DEVIATIONAlthough the range as explained above can be used to quantify the risk of an asset, it is not very useful as outliers affect it. A much more useful measure of risk is the standard deviation. The standard deviation (dk) is a measure of the dispersion of returns around the expected value (mean). Expected value of a return (k) is the most likely return on a given asset. The basic idea is that the standard deviation is a measure of volatility: the more a share’s returns vary from the share’s average return, the more volatile the share. STANDARD DEVIATION: NON-PROBABILISTIC DATAWhen evaluating the risk of an asset given non-probabilistic data, the following should be the procedure to adopt. Start by calculating the expected value and then establish the dispersion around the expected value (mean).

Step 1. Expected value computationThis is the simple average of the return figures given. The following is the applicable formula.

k = i

n

Where ki = return for the ith outcome

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n = number of observations

Step 2. Standard deviation computationEstablish the dispersion around the expected value (mean) by using the following formula:

dk = Ö (ki - k)2

n – 1

The greater the standard deviation, the greater the risk.

EXAMPLEThe example earlier presented will now be re-visited to illustrate the determination of standard deviation with non-probabilistic data.

Asset A Computation of mean (expected value):

Expected return for asset: A = 13%+15%+17 3

= 15%

Computation of standard deviation: (Asset A)

Possible state Potential Mean Squaredreturn return Deviation deviation

Pessimistic 13 15 -2 4Most likely 15 15 0 0Optimistic 17 15 2 4

Ö8/(3-1) = Ö4 =2%

ASSET BComputation of expected value:

Expected return for asset: B = 7%+15%+23% 3

= 15%

Computation of standard deviation:

Possible state Potential Mean Squared

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return return Deviation deviationPessimistic 7 15 -8 64Most likely 15 15 0 0Optimistic 23 15 8 64

Ö128/3-1 =Ö64 = 8%

Asset B is more risky as it has a higher dispersion around the mean (a higher standard deviation).

STANDARD DEVIATION: PROBABILISTIC DATA

The computation of the standard deviation of an investment whose probable returns are given as a probability distribution also requires the two-step approach already illustrated. First one has to calculate the expected value and then establish the dispersion around the expected value (mean).

Expected value computationFor a probabilistic distribution, the expected value is the weighted value of possible return multiplied by the probability of occurrence. It is obtained by using the following formula:

k = (ki = Pri)

Where ki = return for the Ith outcome Pri = Probability of occurrence of the Ith outcome

Standard deviation computationTo get the standard deviation of a probabilistic distribution use the following formula:

dk = Ö (ki - k)2 * Pri

EXAMPLEThe following information is given for two assets:

Returns

Possible outcome Probability Asset C Asset DPessimistic 0.25 23% 17Most likely 0.50 25 25Optimistic 0.25 27 33

Which asset is riskier and why?

Step 1. Start by calculating the expected value for the asset. As indicated earlier this is the weighted value of the possible returns. One can use one of the following two approaches.

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APPROACH ONE

Expected value computation: Asset CPossible outcome Probability Return Weighted valuePessimistic 0.25 23 5.7500Most likely 0.5 25 12.5000Optimistic 0.25 27 6.7500

25.0000% APPROACH TWOExpected value: Asset C =(0.25*23%)+(0.50*25%)+(0.25*27%) =25.000%

After obtaining the expected value (mean) one must then calculate the standard deviation of returns for the asset being evaluated.

Standard deviation computation: Asset CPossible Potential Mean Squared Squared deviation*outcome return return Deviation deviation Probability probabilityPessimistic 23 25 -2 4 0.25 1.000Most likely 25 25 0 0 0.50 0Optimistic 27 25 2 4 0.25 1.000

Ö2.000 =1.41%

Expected value computation: Asset D

Possible WeightedPossible outcome Probability return valuePessimistic 0.25 17 4.25000Most likely 0.50 25 12.50000Optimistic 0.25 33 8.25000

25.0000

Alternatively: Expected value: Asset D = (0.25*17%)+(0.50*25%)+(0.25*33%) = 25.000%

Now the standard deviation of return for asset D can now be calculated.

Standard deviation computation: Asset D

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Possible Mean Squared Squared dev*Possible outcome return return Deviation deviation Probability probabilityPessimistic 17 25 -8.000 64.000 0.25 16.000Most likely 25 25 0 0 0.50 0Optimistic 33 25 8.000 64.000 0.25 16.000

Ö32.000 = 5.66%

Asset D is riskier as it has a higher standard deviation.

COEFFICIENT OF VARIATION (CV)The coefficient of variation is a measure of relative dispersion used when comparing assets with different expected returns. The following approach is used to compute the coefficient of variation

CV = Standard deviation Expected returnAn example now follows to show how the coefficient of variation is used to decide on an asset having a lower degree of relative risk.

EXAMPLEM Ltd. has identified four alternatives that meet its need for increased production capacity. The data gathered relative to each of these alternatives is summarised in the following table.

Expected Standard deviation Alternative return (%) of returns (%)

A 20 7.00B 22 9.50C 19 6.00D 16 5.50

(a) Calculate the coefficient of variation for each alternative.(b) If the firm wishes to minimize risk, which alternative would you

recommend and why?

Solution(a) CVA = 7.0

20

=0.35

CVB = 9.5 22

= 0.43

CVC = 6.0 19

50

=0.32

CVD = 5.5 16

=0.34

(c) Alternative C is chosen as it has the least risk as measured by coefficient of variation.

TWO ASSET PORTFOLIO RISK ANALYSES

A portfolio is a group of assets from which returns are expected. Portfolios are created because individuals do not usually want to hold shares in isolation. They prefer instead to hold a portfolio of selected shares. The motivation is the reduction in risk brought about by diversification.

Portfolio returnA portfolio’s return is the weighted average returns on the individual assets constituting the portfolio. The weights reflect the proportion of the portfolio invested in the shares.

PORTFOLIO ANALYSIS: NON-PROBABILISTIC DATA

The analysis of a given portfolio requires one to look at the expected return from the portfolio in relation to the risk associated with the asset. This section looks at how a portfolio expected return is calculated. It also looks at the calculation of portfolio risk, which is then related to portfolio expected return for decision-making purposes.

EXAMPLEPortfolio AB comprises 50% of securities A and 50% securities B. Expected returns for A and B for the next five years are as follows:

Year Share A Share B1 12 282 16 243 20 204 24 165 28 12

Compute portfolio AB`s expected return and the portfolio’s standard deviation of returns.

a) Expected return on portfolio AB computation.Expected Return Computation of Portfolio

ReturnExpected Portfolio Return

Year Share A Share B

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1 12 28 (0.50*12%)+(0.50*28%) 202 16 24 (0.50*16%)+(0.50*24%) 203 20 20 (0.50*20%)+(0.50*20%) 204 24 16 (0.50*24%)+(0.50*16%) 205 28 12 (0.50*28%)+(0.50*12%) 20

b) Mean value of portfolio returns (mean) = 20%+20%+20%+20%+20% 5

=20%

c) Computation of standard deviation of expected portfolio returnsPortfolio Mean Squared

Year Return Return Deviation Deviation1 20 20 0 02 20 20 0 03 20 20 0 04 20 20 0 05 20 20 0 0

Ö0/4 =0%

There is no variability in expected earnings from this portfolio. It is a perfect portfolio.

DIRECT FORMULA FOR PORTFOLIO STANDARD DEVIATION

dk = Öw d + w d + 2. w1 .w2. Covariance1, 2

The use of this method requires computation of covariance.

Covariance Covariance is a measure of association of two variables. It is measured mathematically by finding the average of the products of the deviations of each of the paired variables from the overall mean of the relevant variable.

Covariance xy = Correlation xy * standard deviation x*standard deviation y

Computation of r – correlation coefficient

Year A (x) A2 (x2) B (y) B2(y2) AB (xy)1 12 144 28 784 3362 16 256 24 576 384

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3 20 400 20 400 4004 24 576 16 256 3845 28 784 12 144 336

åA = 100 åA2 = 2160 åB =100 åB

2 = 2160 åAB =1840

Correlation (r) = n å xy - å x å y Önåx2 – (åx)2 * Önåy2 – (åy)2

r =5(1840) – (100)(100) Ö5(2160) – (100)2 * Ö5(2160) – (100)2

= 9 200 –10 000 Ö10 800 – 10 000 * Ö10 800 – 10 000

= -800 Ö800 * Ö800

= -800 28.28437 * 28.28427

= -800 799.99996

= -1.0000

Standard deviation of returns: Asset A

Mean return = 12% + 16% + 20% + 24% + 28% 5

= 20%

Ö160/(5-1)

=Ö40 = 6.325%

Standard deviation for asset B = 6.325%

Covariance = --1.000 * 6.325 * 6.325

= -40.00563

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AB = Ö(0.50)2(6.325)2 + (0.50)2(6.325)2 + 2(0.50)(0.50)(-40.00563)

= Ö(0.2500)(40.00563) + (0.2500)(40.00563) + 0.50(-40.00563)

= Ö10.00141 + 10.00141 +(-20.00280)

= Ö20.00282 – 20.00280

= 0%

PORTFOLIO ANALYSIS: PROBABILISTIC DATAThe following example will be used to illustrate how the risk – return computations for a portfolio with probabilistic data is handled.

EXAMPLE

There is an investor who has $20 000 to invest in total. He wishes to invest $15 000 in share D and the remainder in share E. What is the expected return and standard deviation on the portfolio?

ALTERNATIVE ONEComputation of portfolio mean return

=0.2650 = 26.50%

Standard deviation of portfolio returns

= Ö0.04662

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= 21.59%

ALTERNATIVE TWO (2)

Computation of expected portfolio returnExpected return Share D = (0.20*-0.15) + (0.50*0.20) + (0.30*0.60) = 0.25 or 25%

Expected return Share E = (0.20*0.20) + (0.50*0.30) + (0.30*0.40) = 0.31 or 31%

Proportions of investment: Share D = 15/20 =0.75 Share E = 5/20 = 0.25

Expected portfolio return = (0.75*25%) + (0.25*31%) = 26.50%

Standard deviation of returns: Share D

= Ö0.070 = 26.46%

Standard deviation of returns: Share E

= Ö0.0049 =7%

Covariance: DE

Standard deviation computationDE = Ö(0.75)2(0.26458)2 + (0.25)2(0.070)2 = 2(0.75)(0.25)(0.01850)

= Ö(0.56250)(0.070) + (0.06250)(0.00490) + 2(0.00347)

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= Ö0.03938 + 0.00031 + 0.00694

= Ö0.04663

= 21.59%

Capital asset pricing model (CAPM)Investors can eliminate diversifiable risk through diversification. The only relevant risk, which the investor should be concerned about, is non-diversifiable risk. Measurement of non-diversifiable risk becomes important in selecting assets to build up a portfolio. The capital asset pricing model links together non-diversifiable risk and return for all assets (return on a portfolio). CAPM can therefore be looked at as a measure of a security’s systematic risk.

The CAPM provides an expression relating the expected return on an asset to its systematic risk (Rock Mathis). This relationship is referred to as the Security Market Line (SML). The measure of the systematic risk in the CAPM is known as Beta ().

The security market lineThe following is an expression of the SML equation:

E[Ri] = Rf + (E[Rm] – Rf)I

Where E[Ri] = the expected return on asset I, Rf = the risk-free rate, E[Rm] = the expected return on the market portfolio, I = the Beta on asset I, [Rm] – Rf = the market risk premium.

The following graph shows the security market line (SML)

E[Ri] SML

E[Rm]

Rf

1 i

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The slope of the SML is equal to (E[Rm] – Rf) which is the market risk premium. The SML intercepts the y-axis at the risk free rate. When the capital market is in equilibrium, the required rate of return on an asset should equal its expected return. This is why the SML equation can also be used to determine an asset’s required rate of return if its Beta is given.

The above SML equation, (CAPM) can be presented in a more simplified arrangement as follows:

Re = Rf + Beta (Rm – Rf)

Risk free rate (Rf): This is the amount obtained from investing in financial securities considered free fro credit risk such as government bonds. The interest rate of interest on government treasury bill is generally used as a proxy for the risk-free rate.

Beta (): This is a measure of how a company’s share price reacts against the market as a whole. A beta of one indicates that the company moves in line with the market. A beta in excess one indicates that the share exaggerates the market’s movements and a beta less than one means that the share is more stable. Occasionally a company may have a negative beta meaning that the share price moves in the opposite direction to the broader market.

There are basically two main approaches that can be used to compute beta.

Approach one: The regression approach

EXAMPLE.The following historical data on the return of security X and market returns M has been collected for the past five years.

Computation of beta

The slope of the regression line, which defines beta, is given by:

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= å x(X) å x(M) - n å x(X-) å x(M-) åx(M)2 - nåx(M-)

Where åx(X) = excess of security returns over risk free rate of return, åx(M) = excess of market returns over risk free rate of return, åx(X-) = average of excess security returns over risk free returns, åx(M-) = average of excess of market returns over risk free returns.

= 0.0449 – 5(0.062)(0.082)0.0499 – 5(0.082)2

= 0.0449 – 0.025420.0499 – 0.03362

= 0.019480.01628

=1.20

Approach two (2): Graphical approachA graph is prepared with the x-axis (horizontal) axis measuring excess market returns and the y-axis (vertical axis) measuring the excess individual asset returns. Coordinates for the excess market returns and excess asset returns at various points in time are plotted. A characteristic line or line of best fit is developed. The slope of this line is the beta of a given asset.

A higher beta (steeper line of best fit) indicates that its return is more responsive to changing market returns and is therefore more risky.

The following table summarizes the excess returns from the earlier example. A graph is prepared from these excess returns.

Excess returns, Asset X 0.15 0.10 slope = 0.05 Excess returns, market portfolio

-0.06 -0.04 -0.02 -0.05 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18

-0.10

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Equity market risk premium (Rm – Rf): This represents the returns investers expect to compensate them for taking extra risk by investing in the stock market and above the risk-free rate.

PRACTICE PROBLEMS ON RISK MEASUREMENT AND RETURN

PROBLEM 1Two assets have the following returns:

Possible state Probability X YA 0.18 10% 12%B 0.22 12% 15%C 0.31 15% 20%D 0.08 -8% 25%E 0,21 2% 15%

i. What is the expected return for each of these assets? ii. Calculate the standard deviation of each of the two assets iii. Which asset is preferable if the investor is risk averse?

(b) You have collected the following information on security M and N. The information is a reflection of your projections for a six-year period.

Year M N1 18% 20%2 20% 15%3 22% 21%4 15% 18%5 10% 15%6 20% 18%

i. Calculate the expected rate of return for each security ii. Calculate the variance of each security

iii. Calculate the standard deviation of each security

PROBLEM 2Three F, G, and H assets are currently being considered by Perth Industries. The following probability distributions of expected returns for these assets have been developed.

Asset F Asset G Asset Hi Pri Return, ki Pri Return, ki Pri Return, ki1 0.10 40% 0.40 35% 0.10 40%2 0.20 10 0.30 10 0.20 203 0.40 0 0.30 - 20 0.40 104 0.20 - 5 0.20 0

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5 0.10 - 10 0.10 - 20

a. Calculate the expected value of return, for each of the three assets. Which provides the largest expected return?

b. Calculate the standard deviation, for each of the three asset’s returns. Which appears to have the greatest risk?

c. Calculate the coefficient of variation for each of the three assets. Which appears to have the largest relative risk?

PROBLEM 3a) Explain your understanding of the following types of risk:

i. Business riskii. Investment riskiii. Portfolio riskiv. Cataclysmic riskv. Financial risk

b) You are given the following expected return data on three assets:- X, Y and Z over the period 2001 – 2004.

Expected return %

Year2004200320022001

Asset X16171819

Asset Y17161514

Asset Z14151617

Using these assets you have isolated three Investment alternatives:

Alternative Investment123

100% of Asset X50% of Assets X and 50% of assets Y50% of Assets X and 50% of Asset Z

Requireda) Calculate the expected return over the four – year period for each of

the three alternatives b) Calculate the standard deviation of returns over the four- year period

for each of the three alternatives c) Use your findings in (a) and (b) to calculate the coefficient of variation

for each of the three alternatives On the basis of your findings above which of the three alternatives would you recommend? Why?

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Chapter 4

Weighted average cost of capital

Cost of capital is the rate of return that a firm must earn on its project investments to maintain its market value. It represents the investors` opportunity cost of taking on the risk of putting money into a company.

Importance of weighted average cost of capitalIt is important to correctly compute an organization’s weighted average cost of capital since the weighted average cost of capital affects a number of important decisions that will be made by the organization’s management.

1. Weighted average cost of capital and security valuationSecurity analysts employ the weighted average cost of capital when valuing financial securities. In the valuation of financial securities the

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weighted average cost of capital is used as a discount rate, which is applied to future cash flows to be generated by the financial instrument being valued. In this case the weighted average cost of capital will be used as a hurdle rate. If the weighted average cost of capital is wrongly calculated then the intrinsic value of the financial instrument as calculated will be wrong.

2. Weighted average cost of capital and the investment decisionOrganizations also use the weighted average cost of capital when evaluating capital projects. The weighted average cost of capital is used as a hurdle rate when evaluating project cash flows using the net present value analysis. If the weighted average cost of capital is wrongly calculated then capital projects will either be wrongly accepted or rejected.

3. Weighted average cost of capital and economic value added (EVA)

In financial management economic value added (EVA) is the determination of value created for the shareholders of the company. The approach used is as follows:

EVA = NPAT – (NOA * WACC) Where NPAT = Net profit after taxes NOA = Net operating assets WACC = Weighted average cost of capital

Shareholders will receive a positive value added when the return from the equity employed in the business operations is greater than the cost of capital.

Schmalenbach, first introduced this concept, but the EVA as used today has been developed by Stern Stewart and Company.

It can be noted that if the computation of weighted average cost of capital were wrongly carried out then the value added would be wrong. Any decisions that are eventually made on the basis of the economic value added as calculated will be misleading.

4. Weighted average cost of capital and the individual investorWeighted average cost of capital serves as a useful reality check for investors. The average investor may not bother to calculate weighted average cost of capital because it is a complicated measure that requires much detailed information but it helps investors to know the meaning of weighted average cost of capital when they encounter it in brokerage analysts` reports.

Assumptions underlying the computation of weighted average cost of capital 1. Business risk is assumed to remain constant.2. Financial risk is also assumed to remain constant.

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3. Component costs used in the computation of weighted average cost of capital are after tax costs. This assumption is consistent with the framework of making capital decisions.

Cost of capital is estimated at a given point in time and it represents the expected average future cost of funds over the long run based on the best information available.

Cost of capital is obtained by first obtaining the component costs of individual sources of finance comprising the capital structure of the organization and then multiplying this by the weight of each component. The weight of each component is usually determined by the firm’s target capital structure. This is the desired optimal mix of debt and equity financing the firm tries to achieve and maintain.

Computation of component costsA. Cost of debt: Investors who subscribe to debentures anticipate future

interest payments. This means that the present value of a debenture is equal to the investor’s future expected receipts discounted at the investors required rate of return.

Component cost of irredeemable debenturesThese debentures give a return to the investor in the form of a constant interest payment, which is paid in perpetuity. Debentures are usually denominated in units of $1 000 or $100 nominal value and companies are entitled to tax relief on the interest payable on debenture capital.

Cost of debt (ki) = Interest charge (1 – t) Market value of debt (ex – interest)

Where ki = after tax cost of debt T = marginal tax rate of corporation tax payable

EXAMPLEA Ltd. has in issue 6% debentures quoted at $980 cum interest. Calculate the cost of debt, assuming a tax rate of 35%. Ki = $60 (1 – 0.35) * 100 $980 - $60

= $39 * 100 $920

= 4.24%

Assumption: Interest is payable annually.

Component cost of redeemable long- term debtThe starting point is to establish the before-tax cost of debt (kd) and then provide the tax adjustment since interest payment is tax deductible.

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Methods of obtaining before tax cost on debt (kd)1. Quotations: A common method is to quote the coupon interest rate on

the bond as the before tax cost of debt if the bond is selling at par on a net basis. A variation would be to quote YTM on similar risk bonds as before tax cost on debt.

2. Approximating the cost of debt using YTM: This approach relies on the use of the approximate yield to maturity on similar risk bonds. This approximate YTM will then be used as the before tax cost of debt (kd). For a bond with a $1 000 par value the approximate YTM (kd) is obtained by the following equation:

Kd = I + ($1 000 – Nd) n Nd + $1 000 2

Where I = annual interest in dollars Nd = net proceeds from the sale of bond N = number of years to the bond’s maturity.

After tax cost of debt (ki): Since interest on debt is tax deductible a tax adjustment is required because the real cost of debt should be lower.

Ki = kd (1 – t) Where kd = before tax cost of debt t = tax rate

SUMMARY ON COST OF DEBTComputation of component cost of debt

Computation of component cost of perpetual debtBegin by computing the before tax cost of debt. This is obtained by using the following formula:

kd = I SV

Where kd = before – tax cost of debt I = Annual interest payment SV = Sale proceeds of the bond/debenture

ki = I (1 – t) SV

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Where ki = Tax – adjusted cost of debt t = tax rate

Computation of component cost of redeemable debtAn accurate result can be obtained by trial and error.

EXAMPLEA company issues new 15% debentures of $1 000 face value to be redeemed after 10 years. The debenture is expected to be sold at 5% discount. It will also involve floatation costs of 5%. The company’s tax rate is 50%. What would the cost of debt be?

SOLUTIONThe cash flow pattern of the debenture would be as follows:

Years Cash flow0

1 – 1010

+ $900 ($1 000 - $100 i.e. par value less floatation cost less discount.

- $150 (interest payment)- $1 000 (repayment of principal at maturity)

Tax adjusted cost of debt, kd = $900 = $75 + $1 000

(1 + ki )t (1 + ki )10

The value of kd is obtained by trial and error. But there is a short cut approach that can be used to obtain the after tax cost of debt.

Short – cut Method for the Determination of After – tax Cost of Debt

The formula for approximating the effective cost of debt can, as a short – cut, be shown as follows:

ki = I (1 – t) + ( f + d + pr – pi)/ Nm (RV + SV)/2

Where I = Annual interest payment RV = Redeemable value of debentures/debt SV = Net sale proceeds from the issue of debenture/debt (face value of debt minus expenses) Nm = Term of debt f = Floatation cost d = Discount on issue of debentures pi = Premium on issue of debentures

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pr = Premium on redemption of debentures t = Tax rate

Application of the short – cut method on the previous example

ki = $150 (1 – 0.50) + ($50 + $50)/10 ($900 + $1 000)/2

= $75 + $10 $950

= 8.947%

» 9%

Follow up problem

Nomzamo Holdings has debentures outstanding with 5 years left before maturity. The debentures are currently selling for $90 (the face value is $100). The debentures are to be redeemed at 5% premium. The interest is paid annually at a rate of 12%. The firm tax rate is 50%. Calculate the after tax cost of debt using the short – cut method.

B. Cost of preference sharesAs with debentures, the cost of preference shares is calculated on the assumption that the market value of the share is equal to all expected future receipts (dividends) discounted at the investor’s required rate of return.

Cost of irredeemable preference shares

Cost of preference shares (kps) = Preference dividend payable Market value of share ex div

If floatation costs are incurred these have to be incorporated in the calculation of cost of preference shares.

Kpn = Dp Np

Where kpn = before tax cost of preference shares Dp = annual preference dividend payable Np = Net proceeds from sale of preference shares.

EXAMPLE

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D Ltd. is considering issuing 10% preference shares that are expected to sell for $87 per share par value. Floatation costs are expected to be $5.00 per share. Calculate kpn.

Dp = 10/100 *$87 = $8.70 Np = $87 - $5 = $82

Kpn = $8.70 * 100 $82.00

= 10.61%

Tax adjustmentNo tax adjustment to before tax cost of preference shares is necessary since preferred share dividends are paid out from the firm’s after tax cash flows.

Cost of redeemable preference sharesThe method is identical to that used for redeemable debentures ignoring corporate tax.

C. Cost of equity Cost of equity is the rate at which investors discount the expected dividends of the share to determine its intrinsic value.

Determination of cost of equity depends with the assumption made regarding the dividends to be paid by the equity being looked at.

Cost of equity with a constant dividend If the rate of ordinary dividend is assumed to be fixed, cost of equity (ke) is obtained as follows:

Cost of equity (ke) = Ordinary dividend payable * 100 Market price ex dividend

EXAMPLE. A $1.00 share is quoted at $2.32 and is about to receive a $0.20 dividend. Calculate the cost of equity.

Ke = $0.20 * 100 $2.32 -$0.20

= 9.43%

Cost of equity with constant growth dividendsThe model assumes that the value of a share equals the present value of all future dividends (assumed to grow at a constant rate) that it is expected to provide over an infinite time horizon. The following equation is used:

Ke = D1 + g Po ex dividend

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Where Po = Value of equity now. D1 = per share dividend expected at the end of year 1 Ke = required return on equity (cost of equity) g = constant growth rate of ordinary dividends.

EXAMPLE. A $0.50 share is quoted at $1.80 and is about to receive a $0.10 dividend. Dividends are expected to increase at the rate of 4% per annum. Calculate the cost of equity.

Ke = $0.10(1.04) + 0.04 $1.80 - $0.10

= $0.104 + 0.04 $1.70

= 0.0612+0.04

= 0.1011764 * 100 = 10.12%

Limitations to computation of cost of equity1. The computational assumption is that the dividend valuation model is

valid. This may not be the case.2. The computational assumption is that dividends are payable at annual

intervals. In practice this is not usually the case as there are interim dividends.

3. An accurate knowledge of the shareholder’s expected required rate of return is also assumed. If what the shareholder requires, for some reason changes, and this is unknown to the organization, then the valuation becomes wrong. This problem is usually brought about by growth in dividends.

Capital asset pricing modelThe capital asset pricing model can also be used to approximate the cost of equity.

The model calculates the risk-adjusted cost of equity capital. It describes the relationship between the required rate of return (cost of equity) and the non-diversifiable risk of the firm as measured by the beta coefficient, b.

Ke = Rf + [b * (Km – Rf)]

Advantage of the CAPM approach: While the constant growth model does not look at risk and uses the market price to reflect the expected risk – return preferences of investors the CAPM directly considers the firm’s risk as reflected by beta.

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Disadvantage of the CAPM approach: It is not easy to adjust for floatation costs when using CAPM, as is the case with the Gordon model.

NB. The preferred approach is to use the Gordon model.

Cost of new ordinary sharesThis is the cost of new ordinary shares being issued after considering the amount of under pricing and floatation costs. Under pricing is the selling of shares at a price below its current market price. It is necessary in order to make an issue attractive.

Ken = D1 + g Nn

Where ken = cost of new ordinary shares D1 = dividend payable at the end of year 1 Nn = net proceeds from issue of new ordinary shares.

EXAMPLE: F Ltd. uses a constant growth model. Its expected dividend at the end of the coming year is $4.00. Its current market price is $50.00 and the expected growth rate of dividends is 5%. If a $3.00 under pricing is necessary because of the competitive nature of the market and an underwriting fee of $2,50 per share is required, what is the cost of new ordinary shares?

Nn = $50.00 – ($3.00 + $2.50) =$50.00 - $5.50 = $44.50

ken = $4.00 + 0.05 $44.50

= 0.1398876 * 100 = 13.99%

Tax adjustmentNo tax adjustment is necessary as ordinary dividends are paid out of after tax cash flows.

Cost of retained earningsCost of retained earnings (kr) is the cost of an equivalent fully subscribed issue of ordinary shares. Thus kr = ke.

Weighting schemesWeights can be calculated as book value, market value or target weights.

Book value weightsAccounting book values are used to measure the proportion of each type of capital in the financial structure when calculating the weighted average cost of capital.

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The advantage of this approach is that the accounting information is readily available. The disadvantage is that book values do not usually indicate the approximate value that could be realized on the sale of the assets.

Market value weightsThe market values of each type of capital in the firm’s capital structure are used to establish the weights to use when calculating the weighted average cost of capital.

The advantage of using market values is that the market values closely approximate actual dollar amounts to be realized should assets be sold. The problem, however, is the fact that market values are generally not readily available.

Target weightsTarget weights can also be used. The target weights can either be book values or market values based on desired capital structure proportions. These will then be used when calculating weighted average cost of capital.

The preferred weighting scheme is to use target market values.

Calculating the weighted average cost of capitalOnce the component cost is established and the appropriate weighting scheme chosen, the weighted average cost of capital can then be calculated. There are two computational approaches that can be used.

Method 1The weighted average cost of capital can be obtained by using the following approach:

WACC = (wi * ki) + (wp * kp) + (we * ke)

Where Wi = proportion of long-term debt in the capital structure, Ki = after tax component cost of debt, Wp = proportion of preference shares in the capital structure, Kp = component cost of preference shares, We = proportion of ordinary shares in the capital structure, Ke = component cost of ordinary shares.

Wi + wp + we = 1.0.

For computational convenience one can convert the weights to decimal form and leave component costs in percentage terms.

Method 2A tabular format can also be used to compute weighted average cost of capital. The structure of the table to be used can now be presented.

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Weighted marginal cost of capital (WMCC)This is the firm’s weighted average cost of capital associated with its next dollar of total financing. WMCC is an increasing function of the level of total new financing. As new financing increases, risk increases, increasing the cost associated with the new financing. This ultimately increases weighted average cost of capital. Computing weighted marginal cost of capital will require knowledge of the breaking point for each type of financing. This is the point at which the component cost of a particular type of financing increases.Breaking pointThis is the level of total new financing at which the cost of the financing component increases creating an upward shift in the weighted marginal cost of capital. The breaking point is obtained by using the following equation:

Breaking point = Amount of financing available from a given financing source Capital structure weight stated in decimal form

Once the breaking points are established, the different weighted average cost of capital at given levels of financing can be calculated. From this, the marginal increments, which define the weighted marginal cost of capital, can be deduced. It is also necessary to have knowledge of the investment opportunities schedule. This can then be used in conjunction with the weighted marginal cost of capital to indicate the various investments that will be acceptable.

The investment opportunities scheduleThis is the ranking of investment possibilities from the one with the highest returns (best) to the one with the lowest returns (worst). As the cumulative amount of money invested in a firm’s investment projects increases, the returns from the projects as measured by IRR decreases. The return on investments decreases as the firm accepts additional projects.

EXAMPLE.Nice Time Ltd is a leading company with an optimal capital structure made up of 30% debt, 20% preference shares and 50% equity. The cost of debt is 20%, cost of preference shares is 18% and cost of equity is 24%. The company can borrow up to $2.4 million in debentures and $3 million in preference shares without a change in the cost of debt and preference shares respectively. The expected retained earnings for the firm are $5 million after which the cost of equity would increase because of floatation costs. If additional debt finance over $2.4 million is required the cost will

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increase by 15%, additional preference shares over $3 million will increase the cost of preference shares to 24% and a new issue of ordinary shares will increase the cost of equity to 28%.(a) What is the breaking point for each source of financing?(b) What is the marginal cost of capital for each range of capital raised? (c) Suppose that the firm had the following capital projects under

consideration?

Project IRR Initial Investment ($)

A 22% 2 000 000

B 25% 4 000 000

C 23% 6 000 000

D 24% 5 000 000

E 20% 7 000 000

F 18% 4 000 000

Construct a graph showing the marginal cost of capital and the investment opportunity schedule and show which projects will be implemented.

Solution

Breaking point (Equity) = $5 000 000

0.50

= $10 000 000

Breaking point (Debt) = $2 400 000

0.30

= $8 000 000

Breaking point (Preference shares) = $3 000 000

0.20

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= $15 000 000

Amount raised Source of capital Weight Cost Weighted cost

0 -<$8 000 000 Ordinary shares 0.50 24% 12%

Debt 0.30 20% 06%

Preference shares 0.20 18% 03.6%

1.00 21.60%

$8m - <$10 000 000 Ordinary shares 0.50 24% 12%

Debt 0.30 35% 10.50%

Preference shares 0.20 18% 03.60%

1.00 26.10%

$10m - <$15 000 000 Ordinary shares 0.50 28% 14%

Debt 0.30 35% 10.50%

Preference shares 0.20 18% 03.60%

1.00 28.10%

$15m + Ordinary shares 0.50 28% 14%

Debt 0.30 35% 10.50%

Preference shares 0.20 24% 04.80%

1.00 29.30%

The weighted marginal cost of capital schedule can now be prepared from the results obtained in the table above. This schedule will, however be, presented in conjunction with the investment opportunity schedule. It is therefore necessary to illustrate the preliminary requirements before one can prepare the investment opportunity schedule.

The first step is to prepare a table of cumulative investments. The schedule shows the ranking of the available opportunities starting with the most preferred in terms of the internal rate of return to the lest preferred. The schedule also shows the cumulative amount of investment financing needed as each successive project is considered. The investment opportunity schedule now follows.

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F 18% 4 000 000 28 000 000

From the above schedule it can be noted that the graph to be prepared should be able to accommodate on one axis a 25% return and on the other axis total new financing amounting to $28 000 000. From the weighted marginal cost of capital table it can also be noted that the graph to be prepared should be able to accommodate on one axis a maximum of 29.30% cost while on the other axis the ceiling is not defined but it should be above $15 000 000. Since the vertical axis will record both weighted average cost of capital and the internal rate of return this axis should be able to accommodate a highest rate of 29.30%, which is the highest weighted average cost of capital. The horizontal axis will record new financing and investment so provision should be made to accommodate a cumulative investment of $28 000 000.

The weighted marginal cost of capital and the investment opportunities schedule can now be presented on a single graph to show which investment opportunities are acceptable and those that are not acceptable.

IRR,WACC% 29.30% 30 28.10% WMCC 26.10% 25 B

D C 21.60% A 20 E F IOS 15

10

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5

5 10 15 20 25 30 New financing or investment $m

Only those projects whose internal rate of return is above the weighted marginal cost of capital are acceptable as they generate a positive return for the shareholders.

From the previous graph it can be noted that project B is acceptable. Project D can be problematic as part of it lies below the cost function. If it is a divisible project then a substantial part of it can be implemented. If it is not divisible then the whole project should not be considered at all.

PRACTICE PROBLEMS ON WEIGHTED AVERAGE COST OF CAPITAL

PROBLEM 1Assuming the corporate tax rate of 55%, compute the after tax cost of capital in the following situations:

(i) A perpetual 12% debenture of $1 000, sold at the premium of 10% with no flotation costs.

(ii) A fifteen – year 10% debenture of $2 000, redeemable at par, with 3.75% floatation costs.

(iii) A ten – year 11% Preference share of $100, redeemable at a premium of 5%, with 5% floatation costs.

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(iv) An equity share selling at $50 and paying a dividend of $6 per share, which is expected to be continued indefinitely.

(v) The same equity share (in iv above), if dividends are expected to grow at the rate of (a) 5%, (b) –5%.

(vi) An equity share, selling at $120 per share, of a company that engages only in equity financing. The earnings per share amounts to $20 of which 50% is paid in dividends. The shareholders expect the company to earn a constant after – tax rate of 10% on its investment of retained earnings.

(vii) The cost of equity capital of the company is 12%. The company wishes to finance its new investment project by retained earnings.

PROBLEM 2From the following information supplied, determine the appropriate weighted average cost of capital, relevant for evaluating long – term investment projects of the company:

Cost of equity 12%After – tax cost of long – term debt 7%After – tax cost of short – term loans 4%

Source of capital Book value Market value

EquityLong – term debtShort – term debt

$500 000400 000100 000

1 000 000

$750 000375 000100 000

1 225 000

PROBLEM 3An electricity equipment manufacturing company wishes to determine the weighted average cost of capital for evaluating capital projects. You have been supplied with the following information to calculate the value of the weighted average cost of capital:

Balance sheet at 31 March 2006AssetsSundry assets

Liabilities and equityEquity sharesPreference sharesRetained earningsDebenturesCurrent liabilities

$3 900 000

1 200 000 450 000 450 000 900 000 900 000 3 900 000

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Anticipated external financing information:

i. 20 year, 8% debentures of $2 500 face value, redeemable at 5% premium sold at par, 2% floatation costs.

ii. 10% preference shares: sale price $100 per share, 2% floatation costs.iii. Equity shares: sale price $115 per share floatation costs would be $5

per share.

The corporate tax rate is 55% and expected equity dividend growth is 5% per year. The expected dividend at the end of the current financial year is $11 per share. Assume that the company is satisfied with its present capital structure and intends to maintain it.

PROBLEM 4Zamndela Investments is interested in measuring its cost of specific types of capital as well as its overall capital cost. The finance department of the company indicates that the following costs would be associated with the sale of debentures, preference shares and equity shares. The corporate tax rate is 55%.

Debentures: The company can sell 15 – year 10% debentures of the face value of $1 000 for $970. In addition, an underwriting fee of 1.5% of the face value would be incurred in this process.

Preference shares: 12% preference shares having a face value of $100 can be sold at a premium of 10%. An underwriting fee of $2 per share is to be paid to the underwriters.Equity shares: The Company’s equity shares are currently selling for $125 per share. The firm expects to pay $15 per share at the end of the coming year. Its dividend payments over the past 6 years per share are given below:

Year Dividend ($)123456

10.6011.2411.9112.6213.3814.19

It is expected that the new equity shares can be sold at $123 per share. The company must also pay $3 per share as underwriting fee.

Market and book values for each type of capital are as follows:

Book value ($) Market value ($)Long – term debtPreference sharesEquity sharesRetained earnings

1 800 000 450 0006 000 0001 500 0009 750 000

1 930 000 520 000

1 000 000 12 450 000

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Requirement(a) Calculate the specific cost of each source of financing. (b) Determine the weighted average cost of capital using

(i) book value weights and (ii) market value weights.

PROBLEM 5A company has the following specific cost of capital along with the indicated book and market value weights.

Type of capital Cost Book valueweights

Market valueweights

Long – term debtPreference sharesEquity sharesRetained earnings

%5101212

%30204010100

%25174612100

(a) Calculate the weighted average cost of capital using book value and market value weights. Which of them do you consider better and why?

(b) Calculate the weighted average cost of capital using marginal weights if the company intends to raise the needed funds using 50% long – term debts, 35% preference shares and 15% retained earnings.

PROBLEM 5

Moroka Investments has compiled the following data relating to the current costs of its sources of capital for various ranges of financing:

Source of capital Range of new financing After- tax costLong-term debt $0 to $200 000

$200 000 to $300 000$300 000 and above

6%7%9%

Preference shares $0 to $100 000$100 000 and above

17%19%

Ordinary shares $0 to $220 000$220 000 to $320 000$320 000 and above

22%24%26%

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The company’s current earnings, of which 40 per cent will be retained, amount to $200 000. The cost of retained earnings has been estimated to be 20 per cent. The company’s target capital structure is as follows:

Source of capital Target capital structuresLong-term debtPreference sharesOrdinary shares

40%20%40%

100%

1) Determine the breaking points and ranges of total new financing associated with each source of capital.

2) Using the data developed in 1 above, determine the levels of total new financing at which the company’s weighted average cost of capital will change.

3) Calculate the weighted average cost of capital for each range of total new financing found in 2 above.

4) Using the results obtained in 3 above along with the following information on the investment opportunities of Moroka Investments, determine the optimal capital budget of Moroka Investments.

Investmentopportunity

Initialinvestment

Internal rate of return(IRR)

ProjectABCDEFGHI

$200 000300 000100 000600 000200 000100 000300 000100 000400 000

%191522142313211716

Chapter 5The capital budgeting decision

Capital budgetingCapital budgeting is the decision area in financial management that establishes the decision area of financial management that establishes criteria for investing resources in long-term projects (Clark, Hinderlang and Pritchard: 1989). This decision area is very important for the organization because of the following reasons:

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(a) The cost of assets to be acquired normally represents relatively large expenditures.

(b) The funds will generally be committed for lengthy periods of time. In addition, capital investment decisions are difficult or very costly to reverse.

(c) The ability of the firm to attain most of its important financial objectives is significantly impacted upon by its capital investment decisions.

(d) The capital decision also determines the company’s future course of development.

(e) The decision is also important because working capital requirements closely relate to the size and utilization of fixed assets.

Basic assumptions of capital budgeting The following assumptions underlie the capital budgeting decision:

1. Management’s primary function is to increase the value of the firm as reflected by the price of its ordinary shares.

2. Shareholders have a preference for current cash flows as opposed to future cash flows. Investors must be compensated for postponing the recovery of their investments and returns on investment. Since the benefits of a capital asset acquisition are received over a future period, the time value of money becomes the core of capital budgeting.

3. Shareholders are risk averse. Because of this risk aversion, present dollars have greater value than future dollars. Should an investment fail, the value of funds lost would be greater than the value of the funds gained should the project have succeeded. For this reason rational investors require higher returns for perceived higher risks.

4. When evaluating capital budgeting projects the analysis should be based on after tax incremental cash flows directly attributable to the project. These should be the cash flows that would otherwise not exist if the project were rejected. Sunk costs are not relevant to the analysis.

MAKING THE CAPITAL BUDGETING DECISION IN A CERTAIN ENVIRONMENTMaking a choice between a number of alternative capital projects should be systematic. The following diagram illustrates the usual procedure to follow when making such a decision.

A. Compute relevant cash flows

B. Systematically evaluate the cash flows

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C. Select the best project

CAPITAL BUDGETING UNDER CONDITIONS OF CERTAINTY

Computation of the initial investmentThe initial investment is the relevant cash outflow that has to be paid now to implement the selected capital project. The format presented below illustrates how the initial investment is arrived at.

1. Cost of new asset: This is the total net cash outflow required to acquire a new asset.

2. Installation cost: These are additional costs that will be incurred to place the asset being acquired into production.

3. Installed cost of new asset: This is the combination of cost of new asset and installation costs incurred. It is also known as the depreciable cost of the asset as it is the amount to be used when calculating depreciation on the new machine.

4. Proceeds from sale of old asset: The amount received from the sale of the asset being replaced, net of removal or clean up costs, is the proceed from sale of old asset.

5. Change in net working capital: This will represent the difference between a change in current assets and a change in current liabilities attributable to the new machine being evaluated.

Computation of change in net working capitalThe following computation may prove to be very useful when there are a number of changes to current assets and current liabilities associated with the new capital asset.

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Computation of terminal cash flowTerminal cash flow is the relevant cash flow attributable to the liquidation of a long -term investment at the end of its useful life. It can be computed with the aid of the following schematic diagram.

Incremental after tax operating cash flowsThese are relevant cash inflows resulting from the use of a proposed long- term capital project. The after tax operating cash inflows are calculated using the following format.

Computing incremental after tax operating cash inflows where depreciation is involved and has an assumed tax shield effect

Computing after tax operating cash inflows where capital allowances are available and are claimed

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It is important to note that the relevant flow required for capital budgeting purposes is after tax cash inflows rather than after tax net income. This is why depreciation and the capital allowances are added back since their effect on after tax cash flows would have been adjusted for.

When a replacement project is being evaluated an additional computation will be required. The purpose of this computation would be to obtain differential cash inflows. The following working arrangement can prove to be useful.

1. Compute the relevant cash flows on an after tax basis for the existing project using the suggested format above.

2. Compute the relevant cash flows on an after tax basis for the new project using the format already suggested above.

3. Compute incremental cash flows using the following format.

After computing the relevant cash flows discount the cash flows when the evaluation is done using discounted cash flow methods.

Even when the evaluation is done using non discounted cash flow techniques, the cash flows to be evaluated will still be the incremental cash flows as calculated from the above schedules.

CAPITAL PROJECT APPRAISAL TECHNIQUESAn example now follows to illustrate how project cash flows are computed and evaluated before one can recommend which project to invest in.

EXAMPLEMusharukwa Investments Ltd. Currently uses an injection-moulding machine that was purchased two years ago. This machine is being depreciated on a straight-line basis towards a $500 000 salvage value, and it has six years of remaining life. Its current book value is $2 600 000, and it can be sold at $3 000 000 at this point in time.

The company is offered a replacement machine which has a cost of $8 000 000, an estimated useful life of six years, and an estimated salvage value of $800 000.The replacement machine would permit an output expansion, so

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sales would rise by $1 000 000 per year. The new machine’s much greater efficiency would cause operating expenses to decline by $1 500 000 per year. The new machine would require that inventories be increased by $2 000 000, but accounts payable would simultaneously increase by $500 000.

The company’s effective rate is 46 percent and its cost of capital is 15 percent.

Requirement

Using the net present value technique determine whether the company should replace the old machine.

SolutionComputation of initial investment

Note 1.

Note 2.

Computation of operating cash inflows

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Computation of terminal cash flow

Summary of cash flows for the period

THE NET PRESENT VALUE TECHNIQUE The net present value criterion for evaluating proposed capital projects involves summing the present values of cash outflows required to support an investment with the present value of the cash inflows resulting from operations of the project. The inflows and outflows are discounted to present value using the firm’s required rate of return for the project. The NPV is the difference in the resent value of the inflows and outflows.

Decision rules1. If the NPV is positive, the project is expected to yield a return in excess

of the required rate of return. The project will be acceptable.2. If the NPV is zero, the yield is expected to exactly equal the required

rate of return. The decision maker would be indifferent.3. If the NPV is negative, the yield is expected to be less than the

required rate of return. Projects of this nature do not meet the criterion for acceptance. They are only acceptable in unusual circumstances.

The example earlier presented can now be worked through using the net present value method. Two methods of computation will be illustrated: the annual discounting method and the annuity method (since the cash flows are an annuity).

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Method 1: The annual discounting approach

Method 2: Annuity method

Time01 – 66

Cash flow(6 684 000)1 902 0002 300 000

Discount factorAt 15%

1.000003.784490.43233

NPV

PresentValue

(6 684 000)7 198 100

994 3591 508 459

Since the NPV of the project is positive, the replacement project can be undertaken.

Advantages of the NPV approacha. The approach takes into account the time value of money. For

this reason it can be regarded as a sophisticated evaluation technique.

b. The approach uses cash flows and cash flows are less subjective than profits.

c. The NPV of a project reveals the amount by which the productive value (present value of cash inflows) exceeds or is less than the project cost.

d. The method also identifies those projects that meet the minimum desired rate of return. These are projects having a zero or positive NPV.

Disadvantages of the NPV approach1. Uncertainty introduced by cost of capital

computation To discount cash flows to their present value, one has to calculate the weighted average cost of capital. This is extremely difficult to calculate and forecast. As a result, any decision made depends on the accuracy of the calculations and forecasts.

2. Shareholders may not necessarily require high cash flows The basic assumption in financial management is shareholder wealth maximization. This is achieved by dividends paid to shareholders from profits made. If this is the case, then the objective should be to maximize profits and not achieve high cash flows.

3. The concept is not easily understood Discounted cash flow as a concept is difficult to grasp (for the layman). It would be beneficial for the person on whose behalf the

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calculations are performed (the layman investor) to have a grasp of the basic concept underlying the technique.

4. Determination of the hurdle rate There are problems in deciding the appropriate hurdle rate to use when discounting the cash flows. The firm’s cost of capital is sometimes used as the discount rate.

UNDISCOUNTED PAYBACKThe payback period is the time required to recover the investment in a project. It is the period during which the cumulative net cash inflows generated by the project just equal the net cash outflow necessary for the project.

PAYBACK WITH EQUAL ANNUAL CASH INFLOWS (ANNUITY)The payback period is equal to the net cash outlay divided by the annual net cash inflow. Payback period = Net cash outlay Annual net cash inflow

EXAMPLE A company is evaluating a project that requires $60 000 cash outlay, and it is expected to generate annual net cash inflows of $8 000 over its 15 year useful life. Determine the payback period for the project.

Payback period = $60 000 $8 000 = 7.5 yearsThis indicates that after 7.5 years the firm’s $60 000 cash outlay will have been recovered.

PAYBACK WITH UNEQUAL ANNUAL CASH INFLOWS-When net cash inflows are not equal from year to year, the payback period is found by cumulating the cash inflows until they equal the net cash outlay.

EXAMPLEB. Ltd. is evaluating a capital project that requires a $38 000 net cash outlay and will generate net cash inflows of $10 000 for each of the first two years, $8 000 each for years 3 and 4, and $6 000 for each of years 5 through 7. Determine the payback period.

SolutionTable of annual and cumulative expected cash inflows

Year Net Cash Inflow ($) Cumulative Cash Inflow ($)1234567

10 00010 000 8 000 8 000 6 000 6 000 6 000

10 00020 00028 00036 00042 00048 00054 000

The payback period lies between year 4 and 5. The exact payback period can be obtained as follows:

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Either 4 + 2 000/6 000 = 41/3 years

Or 4 + [ 2 000/6 000 * 12 ] = 4 years and 4 months.

Decision rules1. If calculated payback is less than the cut off payback period for the

firm, accept project.2. If calculated payback is equal to the cut off payback period for the firm,

the decision maker can be indifferent.3. If the calculated payback is greater than the cut off payback period for

the firm, the project is rejected.

Advantages of the Payback Period as a capital project evaluation technique

1. Simplicity The payback period approach is simple in terms of computation and comprehension.

2. Uncertainty Many managers have reservations about the estimates of expected cash flows to be received in future and feel that if they were to recover their investment early, they will make a profit. The payback method assists them in identifying projects of this nature.

3. Liquidity Many firms have liquidity problems and are very concerned about how rapidly invested funds will be recovered. The payback method assists in identifying projects that rapidly repay invested funds.

4. Cost of external financing Some firms have high costs of external financing and have to look for internally generated funds to support their ventures. These firms become interested in the rate at which their investment will be recovered. Again the payback method helps in identifying projects with high capital recovery rates.

5. Compensation for risk It is simple to compensate for the differences in risk associated with alternative projects. Projects that have higher degrees of risk are evaluated using shorter payback periods compared to the payback period associated with the projects usually undertaken by the firm.

6. Technological changes and competition Some firms may be involved in areas where the risk of obsolescence as a result of technological changes and severe competition may be great so they may be anxious to recover funds rapidly. The payback method assists in cases like these.

7. Model changes There are firms that manufacture products that are subject to model changes and therefore must recover their investment within the model life. They need to use an evaluation technique that can indicate a high rate of capital recovery. The payback method is quite useful in this regard.

Disadvantages of the payback period

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1. Limited period of consideration The period to be considered when using the payback technique is limited to the payback period. Expected cash flows beyond the payback period established by the firm are not considered.

2. Time value of money The undiscounted payback period fails to consider the time value of money. Because of this limitation it is sometimes referred to as a naïve technique (an unsophisticated technique) of appraising capital projects.

3. Magnitude of investment The payback method does not differentiate between projects requiring different cash investments. If the decision maker is not careful they may end up selecting fairly smaller projects at the expense of larger capital projects.

4. Liquidity While the payback method does measure a project’s rate of capital recovery (liquidity) it does not consider the firm’s liquidity position as a whole which is a much more important consideration.

5. Cost of funds The undiscounted payback method ignores the cost of funds used to support the investment even during the payback period. By ignoring the coast of funds a very important cost is overlooked.

Recommended situations when to use the payback periodThe payback period method of appraising capital projects can a be recommended appraisal technique for the following cases:

1. As a measure of a project’s liquidity if such liquidity is of particular importance to the firm.

2. For projects involving uncertain returns, especially when those returns become increasingly more uncertain in future time periods.

3. During periods of very high external financing costs, which make capital recovery very important.

4. For projects involving a high degree of cataclysmic risk.5. For projects subject to model-year changes or obsolescence resulting

from technological changes or changing consumer preferences.

RETURN ON INVESTMENT (ROI) - ACCOUNTING RATE OF RETURN (ARR)

The return on investment (ROI) method of appraising capital projects compares the yearly after-tax (or pre-tax) income with the investment in the asset. The underlying idea is to compare the return expected to be received from a project with some pre-established requirement. The following are some of the different methods that can be used.

EXAMPLEThe following information is provided concerning a potential capital project.

InvestmentEstimated useful life (5 Years)Income: Year 1 – Year 5

$1 000

300

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Compute the return on investment by various methods

SolutionMethod 1: Average annual return on Investment

ROI = [Average annual income/ Original Investment * 100] = [300/1 000 * 100] = 30%

Method 2. Average annual return on average investment

ROI = [Average annual income/(Original Investment/2) * 100] = [ 300/ (1000/2) * 100] = 60%

Method 3: Average return on average investment

ROI = [(Total Income – Original Investment/ useful life)/(Original Investment/2] = [(1 500 – 1 000/5)/ (1 000/2)] * 100 = 20%

Decision rulesIf calculated ROI is greater than the established ROI the project is acceptable.If calculated ROI is equal to the established ROI the decision maker is indifferent and should the calculated ROI be less than the established ROI then the project is unacceptable.

Return on investment calculationsA firm is evaluating a project which has an original investment of $24 000 and a projected salvage value of $4 000 at the end of its 6-year life. The net income before taxes generated by the project each year is as follows:

Year Net income before tax ($)123456

2 0003 5004 0002 4002 0001 000

The firm’s marginal tax rate is 40%. Determine:a) ROI before tax on original Investment.b) ROI before tax on average Investmentc) ROI after tax on original Investment.d) ROI after tax on average Investment.

SolutionAverage net income before tax = $[(2 000 + 3 500 + 4 000 + 2 400 + 2 000 + 1 000)/6]= $2 483.33

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a) ROI before tax on original investment = $2 483.33/24 000 * 100 = 10.35%b) ROI before tax on Average Investment = $[(2 483.33/(24 000 + 4 000)/2] * 100 = 17.74%

If the firm’s marginal tax rate is assumed to remain at 40% over the six years then the average annual net income after tax is computed as follows:

Average net income after tax = (Average net income before tax)(1-tax rate) = ($2 483.33)(1 –0.40) = ($2 483.33)(0.60) =$1 490.00c) ROI after tax on original investment = $1 490.00/$24 000 * 100 = 6.21%d) ROI after tax on average investment

= [$1 490.00/($24 000 + 4 000)/2] * 100=10.64%

Advantages of Return on Investment1. Simplicity The method gives a simple measure of anticipated

profitability from the project. It is also easy to understand.2. Understandability The decision to undertake a project is made by

managers who have to convince shareholders on the gains to be realized from such a project. Not all managers and shareholders are skilled in financial management techniques and ROI is much easier to understand.

3. Profitability If it is the maximization of profits that is hoped to be achieved, then the ROI technique will ensure that profits are maximized, by identifying a project with maximum profit.

4. The needed information is usually readily available.

Disadvantages of Return on Investment1. Timing of the expected profits The ROI does not consider the timing

of the expected profits. Thus a project with a low initial profitability and a high future profitability would have the same average rate of return as a project with a higher initial profitability and a lower future profitability. The former project would have much less value to the firm than the latter. The following example illustrates the argument just presented.

Project 1 Expected Profits ($) Project 2 Expected Profits ($)Year 1

2345

5 0004 0003 0002 0001 000

Year 12345

1 0002 0003 0004 0005 000

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If both projects cost $20 000, then the ROI for both projects would be identical creating a situation of indifference, which should clearly not be the case for these two projects.

2. Problems associated with asset valuation The real value of an asset to the firm is a function if management `s ability to employ the asset in a productive manner. The firm’s balance sheet only lists the investments that the firm has made and the sources of capital used to obtain and maintain those investments. The listed amounts reflect accounting values, which may differ substantially from the market and productive values. Since the balance sheet values neither reflect the value of the assets in terms of their earning ability nor their market value, the return on investment method may be extremely misleading. It is the fair market value or the productive value of the asset to the firm, not the book value, which must be considered.

3. Time value of money The Return on Investment is a naïve appraisal technique in that it ignores the time value of money.

4. Use of accounting profits The Return on Investment uses accounting flows (profits) rather than cash flows. Accounting flows can be manipulated (“doctored”) unlike cash flows.

5. Lack of benchmark for project selection Usually there is no benchmark for project acceptance. Because of this the cost of capital is sometimes used as a surrogate benchmark. The use of cost of capital as a surrogate benchmark has inherent problems:

a. The cost of capital is based on the after-tax cost of funds used for financing. Comparing pre-tax ROI with the cost of capital is erroneous.

b. Even for cases where ROI is computed on an after-tax basis, the fact that the time value of money is ignored renders the cost of capital invalid as a benchmark.

PROFITABILITY INDEX (PI)The profitability index is the ratio of the present value of the after-tax cash inflows to the outflows. A ratio of 1 or greater indicates that the project has an expected yield equal to or greater than the discount rate. The PI is a measure of a project’s profitability per dollar of investment. Being a ratio it can be used to rank projects of varying costs and expected economic lives in order of their profitability.

Profitability Index = Present value of cash Inflows/ Present value of cash Outflows

EXAMPLEThree projects have been suggested to a company. The after-tax cash flows for each are tabulated below. If the firm’s coast of capital is 12% rank the projects in order of profitability.

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After tax cash flowsTime

01234

Project A($10 000) 2 800 3 000 4 000 4 000

Project B($30 000) 6 000 10 000 12 000 16 000

Project C($18 000) 6 500 6 500 6 500 6 500

Step 1. Calculate the present value of cash inflows for each projectPresent value of cash inflows: Project A

Time1234

Cash Flow ($)2 8003 0004 0004 000

Discount factor @ 12%0.8930.7970.7120.636

Present value ($)2 5002 3912 8482 54410 283

Present value of cash inflows: Project B.Time

1234

Cash Flow ($) 6 00010 00012 00016 000

Discount factor @ 12%0.8930.7970.7120.636

Present value ($) 5 358 7 970 8 54410 17632 048

Present value of cash inflows: Project CTime1 - 4

Cash Flow ($)6 500

Discount factor @ 12%3.037

Present value ($)19 741

Step 2. Compute the Profitability Indices

Present value of outflows ($)Present value of inflows ($)

Project A($10 000) 10 283

Project B($30 000) 32 048

Project C($18 000) 19 741

PIA = $(10 283/10 000) = 1.028

PIB = $(32 048/30 000) = 1.068

PIC = $(19 741/18 000) = 1.097

Project ranking 1. C 2. B 3. A

The profitability index measures the return per dollar of investment. From the above results it can be seen that while project B has the highest NPV it is not the most profitable investment.

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Advantages of Profitability Index1. It takes into account the time value of money.2. It is computed using cash flows3. As it measures a project’s profitability per dollar of investment it can be

used to rank projects of varying outlays and expected economic lives.

Disadvantage of the Profitability IndexIt ignores the size of a project. As a result an investment in a small project might appear better than one in a huge project.

INTERNAL RATE OF RETURN (IRR)The internal rate of return (IRR) is that rate of return, which exactly equates the present value of expected after-tax cash inflows with the present value of the after-tax cash outflows. It is that rate of return, which gives a zero NPV zero.

The IRR of a project is arrived at by trial and error but the following approach can be helpful to establish the rate at which trials can commence.

EXAMPLEA new project has an after-tax cost of $10 000 and will result in after-tax cash inflows of $3 000 in year 1, $5 000 in year 2 and $6 000 in year 3. Determine the internal rate of return of the project.

SolutionSet up a solution table

Time Cash flow ($) Discount Factor @ ?% Present value ($)0123

($10 000)3 0005 0006 000

1.000UnknownUnknownUnknown

($10 000)UnknownUnknownUnknown

NIL

The present value of the three cash inflows is $10 000. Reconstruct the problem using an average cash inflow each year rather than the exact amount given.

[$(3 000 + 5 000 + 6 000)/3] = $4 667

After obtaining the average cash inflow reconstruct the solution table.Time Cash Flow ($) Discount Factor @ ?% Present Value ($)

01 – 3

(10 000)4 667

1.000Unknown

(10 000)10 000)

NIL

Since now only one unknown remains, it can be obtained as follows:

$4 667 * discount factor (x) = $10 000discount factor = $10 000/ $4 667 = 2.143

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The discount factor is 2.143. Determine the corresponding IRR from the tables. The closest factor is 2.1399, which corresponds with 19%. 19% is the estimate to be used to solve the problem. Refer to the original solution table and replace the unknown discount factors with discount factors corresponding to 19% to get the NPV.

Time Cash Flow ($) Discount Factor @ 19%

PresentValue ($)

0123

($10 000)3 0005 0006 000

1.0000.8400.7060.593NPV =

($10 000)2 5653 6553 744($392)

The NPV is negative therefore the rate applied is too high. Trying a lower rate, say 17%, the NPV is obtained as follows:

Time Cash Flow ($) Discount Factor @ 17%

Present Value ($)

0123

($10 000) 3 000 5 000 6 000

1.0000.8550.7310.624

($10 000) 2 565 3 655 3 744 ($36)

The NPV is close to zero but still positive so the rate is still high. Trying 16% the NPV is going to be as follows:

Time Cash Flow ($) Discount Factor @16%

Present Value ($)

0123

($10 000) 3 000 5 000 6 000

1.0000.8620.7430.641NPV

($10 000) 2 586 3 715 3 846 $147

The IRR lies between 16% and 17%. By interpolation the exact IRR can now be computed.

Interpolation

Decision rulesOnce the IRR of a project has been determined, it is compared with the required rate of return to decide whether or not a project is acceptable. If the IRR equals or exceeds the required rate of return, the project is acceptable. If the IRR is less than the required rate of return the project is not acceptable.

Advantages of the IRR1. It takes into account the time value of money so it is a sophisticated

capital appraisal technique.

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2. Understandability Although IRR is not truly a rate of return it provides a basis for a decision that is readily acceptable by a layman with no understanding of the NPV concept. To say a project has a positive NPV at 10% has little meaning to the layman than to say while money is costing 10% this project is generating a return of 15%.

3. Provision of margin of error If IRR is calculated and found to be say 15%, then it can be argued with certainty that as long as the cost of money is less than 15% then the NPV of the project will be positive. This cannot be the case with the NPV analysis. If the actual cost of money exceeds the cost used to evaluate the project, then to check whether the project is still acceptable one would have to recalculate the NPV. With IRR this recalculation is not necessary.

Disadvantage of IRRIf a project has non-conventional cash flows, multiple IRRS will be arrived at. It will therefore be problematic to indicate which of the rates would be the correct IRR.

Superiority of the Net Present Value techniqueDCF methods are more superior appraisal techniques to non- DCF techniques because DCF methods take into account the time value of money. Of the DCF methods the NPV method is the unique evaluation technique that consistently helps firms to maximize ordinary shareholders` wealth positions.

Whenever mutually exclusive projects are being evaluated, only the NPV model will consistently show the firm the project or set of projects that will maximize the value of the firm. This is true for the following reasons:

1. The NPV model results in an absolute measure of the projects` worth, while both PI and IRR are relative measures of project viability. The NPV shows the dollar amount by which the project’s discounted cash inflows (DCI) exceeds its discounted cash outflow (DCO). The PI computes the ratio of DCI to DCO and the IRR determines a percentage return figure. If three projects have NPVS OF $10 000, $14 000 and $16 000 these figures show the magnitude of the increase in shareholders` wealth if the respective projects are accepted. On the other hand if the same projects have IRRS OF 40%, 30% and 25% and PIS of 1.68, 1.22 and 1.53 respectively, there is no indication which of the three will lead to the greatest increase in shareholders` wealth by looking at the IRRS and PIs.

2. The IRR expresses the return as a percentage and is therefore inappropriate for evaluating projects of different sizes.

Concluding remarkSince firms try to maximize shareholders` wealth it is recommended that the NPV criterion be used because it is the only model capable of helping the firm achieve this goal.

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CAPITAL BUDGETING UNDER CONDITIONS OF RISKThe nature of the environment in which firms operate is one, which can best be described as risky or highly uncertain. It is important to highlight how firms make the important decision of investing in long-term capital projects.

Project selection under conditions of riskThere are basically two methods of incorporating risk into the capital budgeting process - The certainty equivalent method of risk adjustment and the risk adjusted discount rate.

THE CERTAINTY EQUIVALENT METHODThe method permits adjustment for risk by incorporating the manager’s utility preference for risk versus return directly into the capital investment process. The method is useful when management perceives different levels of risk associated with the estimated annual cash flows over the life of the project. Given the limitations of economic forecasting it is reasonable to assume that the estimates of cash flows during early periods in a project’s life are likely to be more accurate than those corresponding to the latter years.

When the certainty equivalent method is used, the estimated annual cash flows (which represent the expected value of a probability distribution of returns) are multiplied by a certainty equivalent coefficient (CEC) .

The CEC reflects management’s perception of the degree of risk associated with the estimated cash distribution as well as management’s degree of aversion to perceived risk. The product of the expected cash flow and the CEC represents the amount that management would be willing to accept for certain in each year of the project’s life as opposed to accepting the cash flow distribution and its associated risk.

The CECS range in value from zero to 1. The higher values indicate a lower penalty assigned by management to that cash flow distribution. A value of 1 indicates that management does not associate any risk with the estimated cash flow and therefore is willing to accept the expected value of the cash flow estimates as certain. The certainty equivalent adjusted cash flows are then discounted at the risk free rate of return as opposed to the firm’s cost of capital (to accommodate time value of money)

EXAMPLEA firm is evaluating two projects – project A and project B. The following details are provided:

PROJECT A PROJECT B Initial InvestmentCash Inflow – Year 1 2 3 4 5

Cash Flow ($)(42 000)14 00014 00014 00014 00014 000

CEC1.000.900.900.800.700.60

Cash Flow ($)(45 000)28 00012 00010 00010 00010 000

CEC1.001.000.900.900.800.70

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Which project do you recommend using the certainty equivalent method assuming a risk free rate of return of 6%.

SolutionPROJECT A

Time

Cash Inflow

($)

Certainty equivalentCoefficient

CertainCash

Inflows ($)

DiscountFactor @

6%PresentValue ($)

012345

(42 000)14 00014 00014 00014 00014 000

1.000.900.900.800.700.60

(42 000)12 60012 60011 2009 8008 400

1.0000.9430.8900.8400.7920.747

(42 000)11 88211 214 9 408 7 762 6 2754 541

PROJECT B

Time

CashInflow

($)

CertaintyEquivalentCoefficient

CertainCash

Inflow ($)

DiscountFactor @

6%Present

Value ($)012345

(45 000)28 00012 00010 00010 00010 000

1.001.000.900.900.800.70

(45 000)28 00010 8009 0008 0007 000

1.0000.9430.8900.8400.7920.747

(45 000)26 404 9 612 7 560 6 336 5 22910 141

The project with a higher NPV is acceptable so in this case project B would be recommended for acceptance.

Advantages of the certainty equivalent method1. The method requires individual examination of projects in each time

period since the risk associated with a given project may change over its life.

2. While the NPV methods lump together the discounting for time and the adjustment for risk, the CE method disaggregates the two by adjusting for risk with a CEC and discounting for time value of money at the risk free-rate.

Disadvantage of the certainty equivalent methodThe CECS used to convert uncertain cash flows to certain cash flows are subjective estimates provided by managers.

THE RISK ADJUSTED DISCOUNT RATE (RADR) APPROACHThis is the rate of return that must be earned on a given project to compensate the firm’s owners adequately, thereby resulting in the maintenance or improvement of the share price.

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The rationale underlying the use of the risk adjusted discount rate (RADR) technique is that projects which have a greater variability in the probability distributions of their returns should have these returns discounted at a higher rate than projects having less variability or risk.

A project that has no risk associated with it would be discounted at the risk free rate, since this is the appropriate rate just to account for the time value of money. Any project that has risk associated with it has to be discounted at a rate in excess of the risk free rate to discount both for futurity (the time value of money) and for the risk associated with the project (risk premium).

r1 = i+ u + a

Where r1 = risk adjusted discount rate i = risk free rate u = adjustment for the firm’s normal risk a = adjustment for above (or below) the firm’s normal risk.

EXAMPLEM Ltd. is considering a replacement project. This type of project requires a return of risk free rate plus 4%.

Cash InflowsOriginal Cost Years 1 - 5 Years 6 - 10

Probability Amount Probability Amount Probability Amount0.300.400.30

13 00014 00015 000

0.200.400.300.10

2 0002 4002 8003 400

0.200.600.100.10

2 6003 2003 4003 600

If the risk free rate is 10% determine the risk adjusted NPV.

Cost = (0.30 * 13 000) + (0.40 * 14 000) + (0.30 * 15 000) = $3 900 + $5 600 + $4 500 = $14 000Cash inflow Years 1-5 = (0.20 * 2 000) = (0.40 * 2 400) + (0.30 * 2 800) + (0.10 * 3 400) = $400 + $960 + $40 + $340 = $2 540

Cash inflows Year 6 – 10 = (0.20 * 2 600) + (0.60 * 3 200) + (0.10 * 3 400) + (0.10 * 3 600) = $520 + $1 920 + $340 + $360 = $3 140

Present value computationTime Cash Flow ($) Discount Factor @14% Present Value

01 – 56 - 10

(14 000)2 5403 140

1.0003.4331.783

(14 000)8 7205 599 319

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Since the present value of this project is positive, the project is a candidate for acceptance.

Advantages of Risk Adjusted Discount Rate1. Project risk is dealt with explicitly through the determination of risk

premia (for a project’s cash flows).2. Calculation of risk premia can be more straightforward than CE

analysis.

Disadvantages of Risk Adjusted Discount Rate1. Decision on the risk premium for a given project class is problematic. It

is an intuitive analysis that is undertaken by the decision maker.2. It is difficult to incorporate differences in risk for different periods as

compared the CE method.3. It is based on risk – averse investors. This is not necessarily the case

with some investors.

SENSITIVITY ANALYSISThis is a method of risk analysis. It is an analysis of the effect on a project NPV of changes in the assumed values of key variables for example sales level or labour costs. It is also known as “a what if” analysis foe example what if raw material costs were to rise by 30%.

Advantages of the analysis1. It is a practical method of risk analysis.2. The results of a sensitivity analysis can be easily appreciated and used

in decision-making.

Disadvantages of the analysis1. The method deals with one variable at a time while in capital budgeting

a change in one variable causes changes in other variables, for example a change in unit sales changes both revenue and variable costs.

2. Sensitivity analysis does not really measure risk but only looks at the sensitivity of the expected NPV to different input factors.

General application of Risk Adjusted Discount Rate Required SML Rate of Return (%) C D k A B RF

Project riskSML = Security Market Line. This is a graphic depiction of the CAPM k = Single firm wide discount rate (SFDR)

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It is generally not recommended to use a single hurdle rate (k) for all projects as this fails to account for risk associated with the projects. If a single firm wide discount rate is used the general assumption is that all the projects are of equivalent risk. The graph shows the risk – return characteristics of the projects. Using a single firm wide rate A and B would be rejected because they fall below k. C and D will be accepted as they are above k.

If a simultaneous adjustment is made is made for risk and return using CAPM projects C and A would now be acceptable while B and D would be rejected. A, which was previously rejected is now acceptable. D, which was previously acceptable is now rejected.

PRACTICE PROBLEMS ON THE INVESTMENT DECISION

PROBLEM 1Moroka Investments has compiled the following data relating to the current costs of its sources of capital for various ranges of financing:

Source of capital Range of new financing After- tax costLong-term debt $0 to $200 000

$200 000 to $300 000$300 000 and above

6%7%9%

Preference shares $0 to $100 000$100 000 and above

17%19%

Ordinary shares $0 to $220 000$220 000 to $320 000$320 000 and above

22%24%26%

The company’s current earnings, of which 40 per cent will be retained, amount to $200 000. The cost of retained earnings has been estimated to be 20 per cent. The company’s target capital structure is as follows:

Source of capital Target capital structuresLong-term debtPreference sharesOrdinary shares

40%20%40%100%

Determine the breaking points and ranges of total new financing associated with each source of capital.

Using the data developed in 1 above, determine the levels of total new financing at which the company’s weighted average cost of capital will change.

Calculate the weighted average cost of capital for each range of total new financing found in 2 above.

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Using the results obtained in 3 above along with the following information on the investment opportunities of Moroka Investments, determine the optimal capital budget of Moroka Investments.

Investmentopportunity

Initialinvestment

Internal rate of return(IRR)

ProjectABCDEFGHI

$200 000300 000100 000600 000200 000100 000300 000100 000400 000

%191522142313211716

PROBLEM 2Chakalaka Investments (Pvt) Ltd employs the certainty – equivalent approach in the evaluation of risky investments. The capital budgeting department of the company has developed the following information regarding the new project.

Year Expected CFATCertainty – equivalent

quotient

012345

$(200 000)160 000140 000130 000120 000 80 000

1.00.80.70.60.40.3

The firm’s cost of equity capital is 18%; its cost of debt is 9% and the risk less Rate interest in the market on government securities is 6%. Should the project be accepted?

PROBLEM 3Changamukai Investments is considering a proposal to replace an automatic press in one of its plants with a newer model that is expected to reduce labour and raw material costs by $150 000 per year. Due to its greater capacity and increased output, net income before taxes will increase by $50 000 per year.

The new press will cost $550 000 plus an additional $50 000 for installation. It will be depreciated on a straight – line basis over its 5-year depreciable life to a zero book value. However, at the end of five years it is still expected to have a market value of $100 000, for which it is expected to be sold. The increased

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output will require an immediate, one – time increase of $50 000 in net working capital.

The old press can be sold today for $120 000. It was purchased 5 years ago for $300 000, and is being depreciated over its 10 – year life to a book value of zero.

RequirementGiven a tax rate of 40%, and a required rate of return of 12%, should the company replace the old machine now? No initial or investment allowance applies and inflation should be ignored.

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Chapter 6

Leverage can be defined as the employment of an assets or sources of funds for which the firm has to pay a fixed cost or return. The employment of an asset resulting in the payment of a fixed cost creates operating leverage while the employment of sources of funds for which the firm has to pay a fixed return generates financial leverage. There are therefore two types of leverage, operating leverage, which is a result of the investment decision of the firm and financial leverage, which is a result of the financial decision of the firm.

The financing decision is concerned with financial leverage but a working knowledge of operating leverage is necessary as the two types of leverage are closely related. Operating leverage highlights the relationship between the firm’s sales revenues and its earnings before interest and taxes (EBIT). These earnings are also known as operating profits. Financial leverage on the other hand highlights the relationship between the firm’s earnings available to ordinary shareholders. It can be noted that EBIT is central in explaining both operating and financial leverage.

Operating leverageOperating leverage results from the existence of fixed operating expenses in the firm’s income stream. It shows the firm’s ability to use fixed operating expenses to magnify the effects of changes in sales on its earnings before interest and taxes. Operating leverage occurs whenever a firm has fixed costs that have to be met regardless of the volume of production. Firms employ assets with fixed costs hoping that the volumes produced will generate sales revenues that will cover all costs.

Degree of operating leverage (DOL)This is a measure in quantitative terms, of the extent of operating leverage. It exists when a proportionate change EBIT resulting from a change in sales is more than a proportionate change in sales.

DOL = Percentage change in EBIT 1 Percentage change in SalesEXAMPLEA firm produces and sells a single product with the following revenue and cost patterns: (Per unit)

Annual fixed costs $ 1 000 000,00.Show comparative income statements for the following annual productions:

1. 10 000 units2. 20 000 units and3. 30 000 units

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SolutionIncome statementsSales (units)

Sales revenueVariable costContribution marginFixed costEBIT

10 000$

2 000 0001 000 0001 000 0001 000 000

NIL-100%

20 000$

4 000 0002 000 0002 000 0001 000 0001 000 000

30 000$

6 000 0003 000 0003 000 0001 000 0002 000 000

+100%

It can be argued that since the firm’s normal level of production is 20 000 units then the point of reference is 20 000 units.

If production decreases to 10 000 units:DOL1 = (1 000 000 – 0/1 000 000 * 100) (4 000 000 – 2 000 000/2 000 000 * 100)

= 100 100 = 1

DOL2 = 100 100

= 1

In both cases the quotient is 1 so there is no operating leverage.

Operating leverage can be favourable as well as unfavourable. The degree of operating leverage depends on fixed operating costs. The higher the fixed operating costs, the higher the firm’s operating leverage and operating risk and vice versa. Operating risk refers to the firm’s inability to cover its fixed operating costs. High operating leverage is a good working arrangement when revenues are increasing but a disaster when revenues are falling.

In conclusion, the higher the firm’s fixed operating cost, the higher the degree of operating cost, the higher the degree of operating leverage and the higher the break-even volume and vice versa.

Financial leverageFinancial leverage is the ability of a firm to use fixed financial charges to magnify the effects of changes in EBIT on the firm’s EPS. It involves the use of funds obtained at a fixed cost in the hope of increasing the return to the ordinary shareholders. Financial leverage results from the presence of fixed financial charges in the firm’s income stream. The fixed charges do not vary with the earnings before interest and taxes or operating profits. They have to be paid regardless of the amount of EBIT available to pay them.

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Financial leverage is also called trading on equity.

Degree of financial leverageFinancial leverage exists whenever a firm has fixed cost in its capital structure. The greater the amount of fixed-interest sources of funds, (larger financial cost), the higher the financial leverage. The degree of financial leverage can be measured quantitatively as follows:

CAPITAL STRUCTURE AND VALUATIONFirms should strive to achieve an optimal capital structure. An optimal capital structure is the combination of debt and equity that results in the maximization of the value of the firm. Alternatively, capital structure can be argued to be the combination of debt and equity that results in the minimization of the firm’s cost of capital.

There is no consensus as to whether the capital structure decision affects value. Some writers believe that the capital structure decision of a firm affects the value of the firm while others argue that the capital structure decision does not affect the value of the firm.

Four theories on capital structure decision will be looked at. They are:a. The Net Income Approach (NI),b. The Net Operating Income Approach (NOI),c. The Modigliani-Miller Approach (MM) andd. The Traditional Approach.

Before the capital structure theories can be looked at, it is important to look at the assumptions that underlie these theories.

The following are the assumptions underlying the capital structure theories:1. The organization has two sources of financing namely perpetual debt

(assumed to be risk less) and ordinary share capital.2. The organization’s net income is not subject to corporate tax.3. The firm has a 100% dividend payout ratio. This means that the

organization does not retain any earnings.4. The organization’s total assets are given and will not change.5. The operating profits of the firm are not expected to grow.6. The firm’s business risk will be constant over time. The business risk

will be independent of the firm’s capital structure and financial risk.7. The organization’s total financing will remain constant. If the firm’s

financial leverage increases, the proceeds are used to reduce equity. If additional equity is issued, the proceeds will be used to retire debt.

8. The organization has perpetual life.

Formulae and symbols used in the evaluationE = total market value of equityB = total market value of debtV = total market value of the firm i.e. V = (E + B)I = interest payments.

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Cost of debt (ki) = I/BValue of debt = I/kiCost of equity capital = D1/P0 + gOR ke = Net Income attributable to equity holders Total market value of equity shares

Weighted average cost of capital (WACC) (ko) = (wi *ki) + (we *ke)Or k0 = [B/(E + B)]*ki + [E/(E + B)]*keOr ko = EBIT/V

The Net Income (NI) ApproachDurand suggested the Net Income approach. Durand argues that the capital structure decision of a firm is relevant to the valuation of the firm. A change in financial leverage would affect the firm’s cost of capital and total value. An increase in financial leverage, (as measured by the ratio of debt to equity), reduces the weighted average cost of capital and increase the value of the firm. A decrease in financial leverage increases the weighted average cost of capital and reduces the value of the firm.

The argument behind the approachAn increase in financial leverage increases the proportion of inexpensive financing in the organization’s capital structure and this reduces the weighted average cost of capital, which results in an increase in the total value of the concern. Since the cost of debt and equity would be constant, an increase in financial leverage magnifies shareholders` earnings resulting in an increase in the market value of equity.

Conclusion on the approachAccording to the Net Income approach financial leverage is an important variable in the firm’s capital structure decision. A judicious mix of debt and equity financing, results in an optimal capital structure, which maximizes the value of the firm. This optimal capital structure reduces the overall cost of capital to its lowest possible position.

IllustrationA Ltd.`s expected annual net operating income (EBIT) is $500 000,00 and these are not expected to grow. The company has $2 000 000,00 10% debentures outstanding. The company also has 24 000 ordinary shares outstanding. The equity capitalization rate of the company is 12.5%.

Using the Net Income Approach: 1. (a) Calculate the total value of the firm

(b) Calculate the cost of equity capital(c) Calculate the value of each ordinary share(d) Calculate the weighted average cost of capital.

2.Assume that A Ltd. raises its financial leverage by bringing in $1 000 000more worth of debentures using the proceeds to retire equity.

a. Calculate the total value of the firm b. Calculate the cost of equity capital

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c. Calculate the value of each ordinary shared. Calculate the weighted average cost of capital.

3.Assume that A Ltd. issues $1 000 000,00 worth of equity, using the proceeds to retire debt:

a. Calculate the total value of the firmb. Calculate the cost of equity capitalc. Calculate the value of each ordinary shared. Calculate the weighted average cost of capital.

SolutionThe basic approach to follow when calculating the total value of the firm when using the Net Income approach is as follows:

1) Compute earnings attributable to equity holders.2) Capitalize these earnings using the equity capitalization rate (ke). This

gives the total value of equity (E).3) Bring in the market value of debt (B).4) Add the market value of equity (E) and the market value of debt (B) to

get the total value of the firm.

1 (a) Value of the firm computation

EBITDebenture interest (0.10 * $2 000 000,00)Income before taxTaxationIncome after taxationPreference dividendAttributable earningsEquity capitalization rate (ke)Market value of equity (E)Market value of debt (B)Total value of the firm (V) = (E) + (B)

$500 000

(200 000)300 000

NIL300 000

NIL300 000

0.1252 400 0002 000 0004 400 000

(b) Cost of equity capital (ke) = $300 000/$2 400 000,00 * 100 = 12.5%(c) Cost of each ordinary share = $2 400 000,00/24 000 = $100,00.(d) Computation of weighted average cost of capital (WACC)

= 12.5%($2 400 000,00/$4 400 000) + 10%($2 000 000/4 400 000)= 0.0681818 + 0.0454545= 11.36%

OR WACC = $500 000,00/$4 400 000,00 * 100 = 11.36%

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2(a) Value of the firm computation

EBITDebenture interest (0.10 * $3 000 000,00)Income before taxTaxationIncome after taxPreference dividendAttributable earningsEquity Capitalization rate (ke)Market value of equity (E)Market value of debt (B)Total value of the firm (V) = (E) + (B)

$500 000

(300 000)200 000

NIL200 000

NIL200 000

0.1251 600 0003 000 0004 600 000

(b) Cost of equity capital (ke) = $200 000/$1 600 000 * 100 = 12.5%(c) Cost of each equity share

= $1 600 000/[$2 400 000 – ($1 000 000/$100)]= $1 600 000/14 000= $114.29

(e) Computation of weighted average cost of capital= 12.5%($1 600 000/$4 600 000) + 10%($3 000 000/$4 600 000)= 0.0434782 + 0.0652173= 10.87%

OR weighted average cost of capital = $500 000/$4 600 000 * 100 = 10.87%

EvaluationIncreasing financial leverage to $3 000 000 increases the total value of the firm to $4 600 000 ($114.29 on a per share basis), lowering the weighted average cost of capital to 10.87% compared to the original position of $100,00 and 11.36% respectively. This is precisely what Durand indicated in his argument. Increasing financial leverage increases the value of the firm reducing the weighted average cost of capital for the firm.

3. (a) Value of the firm computation

EBITDebenture interest (0.10 * $1 000 000)Income before taxTaxationIncome after taxPreference dividendAttributable earningsEquity capitalization rate (ke)Market value of equity (E)Market value of debt (B)Total value of the firm (V) = (E) + (B)

$500 000

(100 000)400 000

NIL400 000

NIL400 000

0.1253 200 0001 000 0004 200 000

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(b) Cost of equity capital (ke) = $400 000/$3 200 000 *100 = 12.50%

(d) Cost of each ordinary share = $3 200 000/[24 000 + ($1 000 000/$100,00)]= $3 200 000/34 000= $94,12

OR weighted average cost of capital = $500 000/$4 200 000 * 100 =11.90%

EvaluationReducing financial leverage to $1 000 000 reduces the total value of the firm to $4 200 000 ($94.12 on a per share basis), increasing cost of capital to 11.90% compared to the original position of $100,00 and 11.36% respectively. Again this is what Durand indicated would happen if financial leverage is reduced. Reducing financial leverage reduces the value of the firm increasing the weighted average cost of capital for the firm.

Diagrammatical presentation of the Net Income Approach Ke, ki, ko (%)20

15 ke ko 10 ki

5

0.5 1.00Degree of leverage

Theoretically the above diagram shows that according to the Net Income Approach, the firm can employ 100% debt to maximize its value. In practice this is not possible.

NET OPERATING INCOME (NOI) APPROACHDurand also suggests this theory. In this theory he presents an argument, which is diametrically opposed to the argument he presented for the Net Income Approach to capital structure.

The argumentIn this theory Durand argues that the capital structure decision of the firm is irrelevant to the valuation of the firm. Changing the degree of financial leverage of the firm will not affect the total value of the firm as the weighted

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average cost of capital is taken to be independent of the degree of financial leverage.

The following arguments relating to the cost of equity and debt are worth noting when discussing the Net Operating Income approach.

The cost of equity capital (equity capitalization rate) is an increasing function of financial leverage. Increasing financial leverage increases financial risk to equity holders who in turn require compensation for this higher financial risk in the form of a higher required rate of return.

The cost of debt consists of two parts: an explicit cost and an implicit cost (hidden cost). The explicit cost is represented by the interest rate. From the assumptions it was indicated that the firm could borrow at a fixed rate of interest as financial leverage is assumed not to affect financial risk. The implicit cost (hidden cost), relates to the change to cost of equity capital. This is the increase in the required rate of return by equity holders brought about by increasing financial leverage.

The advantage of using debt (supposedly cheaper), in terms of explicit cost is EXACTLY NEUTRALIZED by the implicit cost (the increase in the required rate of return by equity holders).

Conclusion on Net Operating IncomeThe total value of the firm is not a function of the firm’s capital structure decision. Regardless of the degree of financial leverage, the total value of the firm remains constant. Since the market value of the shares will not change with financial leverage, there cannot be an optimal capital structure.

IllustrationB Ltd.`s expected net operating income (EBIT) is $500 000 and these earnings are not expected to change. The company has $2 000 000,00 10% debentures outstanding. The company also has 20 000 ordinary shares outstanding. The overall capitalization rate (overall cost of capital – weighted average cost of capital) is 12.5%.

Using the Net Operating Income Approach:1. (a) Calculate the total value of the firm (b) Calculate the cost of equity capital (c) Calculate the value of each ordinary share (d) Calculate the weighted average cost of capital.

2.Assume that B Ltd. raises its financial leverage by bringing in $1 000 000,00 additional debentures, using the proceeds to retire equity shares.

a. Calculate the total value of the firmb. Calculate the cost of equity capitalc. Calculate the value of each ordinary shared. Calculate the weighted average cost of capital.

3. Now assume that B Ltd raises $1 000 000,00 additional equity the proceeds to retire debt.

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a. Calculate the total value of the firmb. Calculate the cost of equity capitalc. Calculate the value of each ordinary shared. Calculate the weighted average cost of capital.

SolutionThe basic approach to follow when calculating the total value of the firm when using the Net Operating Income approach is as follows:

i. Since the overall capitalization rate of the firm remains the same for all degrees of financial leverage, capitalize the given level of EBIT using the overall capitalization rate (ko). This gives the total value of the firm i.e. V = EBIT/ko.

ii. Subtract the value of debt from the total value of the firm to get the value of equity (which is a residual value) i.e. V – B = E.

1 (a) Value of the firm computation

EBITOverall capitalization rate (ko)Total value of the firm (V)Total value of debt (B)Total market value of equity (E)

$500 000

0.1254 000 000

(2 000 000)2 000 000

(b) Cost of equity = Attributable earnings * 100 Total market value of equity

= ($500 000 - $200 000)/$2 000 000 * 100 = 15%

(c) Value of each ordinary share = $2 000 000/20 000 = $100,00

(d) Weighted average cost of capital = 10%($2 000 000/$4 000 000) + 15%($2 000 000/$4 000 000) = 0.05 + 0.075 = 12.5%

OR Weighted average cost of capital = ($500 000/$4 000 000) * 100 = 12.50%

2.Value of the firm computation

EBITOverall capitalization rate (ko)Total value of the firm (V)Total value of debt (B)Total value of equity (E)

$500 000

0.1254 000 000

(3 000 000)1 000 000

(b) Cost of equity capital =($500 000 - $300 000)/$1 000 000 * 100 =20%

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(c) Value of each ordinary share = $1 000 000/[20 000 – ($1 000 000/$100,00) = $1 000 000/10 000 = $100,00

(d) Weighted average cost of capital = 20%($1 000 000/$4 000 000) + 10%($3 000 000/$4 000 000) = 0.05 + 0.075 = 12.50%

OR Weighted average cost of capital = $500 000/$4 000 000 * 100 = 12.50%

EvaluationThe above analysis shows that an increase in financial leverage has no effect on the total value of the firm. The value of ordinary shares remains the same and the cost of capital is also not affected by the increase in financial leverage.

3. (a) Value of the firm computation

EBITOverall capitalization rate (ko)Total value of the firm (V)Total value of debt (B)Total value of equity (E)

$500 000

0.1254 000 000

(3 000 000)1 000 000

(b) Cost of equity capital = $500 000 - $100 000/$3 000 000 * 100 =13.33%

(c) Value of each ordinary share = $3 000 000/[$2 000 000 + ($1 000 000/$100,00)] = $3 000 000/30 000 = $100,00

(d) Weighted average cost of capital = 13.33%($3 000 000/$4 000 000) + 10%($1 000 000/$4 000 000) = 0.099975 + 0.025 = 12.50%

OR Weighted average cost of capital = $500 000/$4 000 000 * 100 =12.50%

EvaluationThis analysis shows that decreasing financial leverage does not affect the total value of the firm. The value of the ordinary shares remains the same

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and the cost of capital is also not affected by the reduction in the degree of financial leverage.

Diagrammatical illustration of the net operating income approach

Ke, ki Ko (%) ke

20.0

15.0 ke

10.0 ki

5.5

0.5 1.0 Degree of leverage

The diagram shows that the cost of debt and overall cost of capital are independent of the degree of financial leverage but the cost of equity is an increasing function of the degree of financial leverage.

MODIGLIANI – MILLER (MM) APPROACHFranco Modigliani and Morton Miller in their thesis relating to the relationship between capital structure, cost of capital and valuation, presented a proposition that is similar to the net operating income approach. They support the argument put forward in the net operating income approach regarding the independence of the cost of capital to the degree of financial leverage. Their approach maintains that the weighted average cost of capital does not change with the degree of financial leverage.

Ko(%) V ($)

V

Ko

Degree of leverage (B/V)

Assumptions behind the approachThe proposition by MM is based on the following assumptions:

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1. Perfect capital markets: This is a market in which:a. Securities are infinitely divisible.b. Investors are free to buy and sell securities c. Investors can borrow without restrictions on the same terms and

conditions as firms.d. There are no transaction costs.e. There is perfect information i.e. each investor has the same information

which is readily available at no cost.f. Investors are rational and behave accordingly.

2. Business risk is equal among firms operating in a similar environment. (The firms are assumed to have the same risk characteristics).

3. The firm’s dividend payout ratio is 100%.

4. There are no taxes (assumption relaxed latter when proposition ii was highlighted).

Proposition IMM argue that the value of a firm remains constant regardless of the degree of financial leverage. Since value does not change with financial leverage, the weighted average cost of capital and the firm’s market price of shares remains the same regardless of the degree of financial leverage.

Operational justification of propositionMM provide an operational justification of their proposition by highlighting the arbitrage process.

The Arbitrage processThis is the act of buying a financial asset in one market at a lower price and selling it in another market at a higher price to bring about equilibrium in the market price of the financial asset in different markets. Arbitragers take advantage of temporary disequilibria and buy undervalued financial assets in one market and sell overvalued financial assets in related markets. Arbitrage is a balancing operation and implies that a financial security cannot sell at different prices.

MM argue that firms similar in all respects except for leverage cannot command different values. According to MM such firms are perfect substitutes. Should differences in value occur, investors of the firm whose value is higher would sell their shares and buy shares of the firm whose value is lower. This way, MM argue, investors will be able to earn the same return at a lower outlay with the same perceived risk or even lower risk. This leaves the investors better off. This behaviour by investors will increase the share price (value) of the firm whose shares would be purchased while lowering the share price (value) of the firm whose shares would be sold. This will continue till the market prices of the two identical firms become identical.

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MM also argue that investors are able to use “home-made” leverage or “personal” leverage to substitute corporate leverage to finance the arbitrage transaction.

Illustration of the arbitrage processAssume that there are two firms, L Ltd. (Levered) and U Ltd. (Unlevered), which are identical in all respects except that L Ltd. has 7.5% $4 million debentures. The earnings before interest and taxes (EBIT) of both companies are equal ($900 000). The equity capitalization rate for both companies is 10%.

L Ltd. U Ltd.

7.5% $4 million debenturesEBIT $900 000Ke 10%

All equity financedEBIT $900 000Ke 10%

U Ltd. L Ltd.

EBITDebenture interest (0.075 * $4m)Attributable earningsEquity capitalization rateMarket value of equity (E)Market value of debt (B)(Note)Total value of the firm (V)

$900 000

-900 000

0.109 000 000

-9 000 000

$900 000

(300 000)600 000

0.106 000 0004 000 00010 000 000

Note (B) = $300 000/0.075 = $4 000 000

According to MM an investor in L Ltd. can increase his return without incurring any additional financial risk. He will achieve this through the arbitrage process.

Assuming the investor in L Ltd. owns 10% total equity, he will have 10% of $6 000 000 i.e. $600 000 worth of shares in L Ltd. Assume that this investor wishes to dispose of this 10% shareholding to purchase a 10% shareholding in U Ltd.

This equity brings in $600 000. Assuming he can borrow an amount equal to 10% holding in L Ltd.`s debts, this brings in $400 000 (0.10 * $4m).

He then purchases 10% shareholding in U Ltd. for $900 000 (0.10 * $9 000 000). This leaves him with a surplus of $100 000 of uncommitted funs.

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The investor’s income position

Old income – Dividend (.10% of L Ltd.) (1.10 * $6 000 000)New income – Dividend (10% of U ltd.) (0.10 * $9 000 000)Debenture interest (0.075 * $4 m)

$60 00090 000

(30 000)60 000

Real income remains the same although the cash flow position has changed (+$100 000). If the investor can invest this $100 000, elsewhere, he can then have a return on this investment on top of the shareholding in U Ltd.

According to MM homemade leverage is a perfect substitute for corporate leverage and the arbitrage process operates because of this alleged substitutability.

Limitation of the MM hypothesisThe MM hypothesis does not provide a valid framework to explain the relationship between capital structure, weighted average cost of capital and the total value of the firm.

Perfect substitutability of homemade and corporate leverageMM argue that homemade leverage and corporate leverage are perfect substitutes. This would imply that the risk perception of personal and corporate leverage would be the same. If this were true then the risk to which the investor is exposed to would be identical irrespective of whether it is the firm that has borrowed (corporate leverage) or the investor himself has borrowed (homemade leverage). The risk exposure to the investor is greater with personal leverage (because of unlimited liability) than with corporate leverage (corporations have limited liability). As a result, since homemade leverage and corporate leverage are not perfect substitutes, the arbitrage process cannot be effective.

InconvenienceIn addition to higher risk exposure, personal leverage can be very inconvenient. This is because with personal leverage, the formalities and procedures involved in borrowing will have to be done by the individual himself whereas with corporate leverage these formalities and procedures are undertaken by the corporation itself. Because of this inconvenience, some investors may prefer that the borrowing be done by the firm, rather than by investors themselves. This will, in turn constraint the arbitrage process.

High borrowing costsHomemade leverage is more costly in that the cost of borrowing to an individual is higher than the cost of borrowing by a firm. If homemade leverage and corporate leverage are perfect substitutes as argued by MM, then the cost of borrowing ought to be the same. Since it is more costly to borrow personally (because of limited credit standing), the two cannot be perfect substitutes and this limits the effectiveness of the arbitrage process.

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Institutional restrictionsInstitutional restrictions could also limit the arbitrage process. Institutions cannot engage in personal leverage. This means that the switching option from the unlevered to the levered firm may not apply to all investors. To the extent that this is the case, personal leverage and corporate leverage cannot be argued to be perfect substitutes.

Double leverageSome times homemade leverage does not work. A typical case is where an investor has already borrowed to invest in the shares of the unlevered firm. For an investor in this category arbitrage will entail double leverage, leverage in the personal portfolio and leverage in the firm’s portfolio.

Transaction costsSince transaction costs are inevitable, the investor will receive net proceeds from the sale of shares, which will be lower than his investment holding. He will have to invest a large amount in shares than his present investment to earn the same return. This arrangement will limit the operation of the arbitrage process.

ConclusionThe foregoing discussion showed that personal leverage and corporate leverage are not perfect substitutes. The arbitrage process will therefore be hampered and will not be effective. The MM argument cannot be valid. A firm may increase its total value and lower its weighted average cost of capital with an appropriate degree of financial leverage. The capital structure decision of the firm is relevant to its valuation. Imperfections in the capital market retard the perfect functioning of the arbitrage process. The MM approach does not provide a valid framework for the theoretical relationship between capital structure, weighted average cost of capital and the valuation of the firm.

THE TRADITIONAL APPROACHThe traditional view holds that through a judicious use of financial leverage, a firm can increase its total value and reduce its weighted average cost of capital. Using debt in its capital structure causes a decline in the weighted average cost of capital (debt is a relatively cheaper source of funds). The advantage of using modest levels of debt will outweigh the increased financial risk to equity holders as reflected by a higher required rate of return (ke).

Going beyond modest levels of debt will however have the effect of raising the weighted average cost of capital and adversely affecting the total value of the firm. Thus, up to a point financial leverage favourably affects the value of the firm, beyond that point financial leverage adversely affects the total value of the firm. This is the optimal capital structure.

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Ke

Ko, ki ko

Ke, (%) ki

Degree of leverage (B/V)

A variation of the traditional approach suggests that there is no single capital structure but a range of capital structures where the weighted average cost of capital will be at its minimum and total value of the firm at its maximum. Changes to financial leverage in this range will have little effect on the total value of the firm.

FACTORS AFFECTING THE CAPITAL STRUCTURE DECISIONThe combination of debt and equity that a firm chooses to use is affected by a number of factors.

ControlThe attitude of management towards control has a bearing on the capital structure decision. Lenders are not directly involved in the management of a company as long as there is no default in the payment of interest and principal. If management wishes to maintain control on organizational operations they will bring in more debt than equity. With this arrangement management sacrifices little or no control. But this arrangement can be costly if the company borrows more than it will have the ability to service, as management will lose ALL control.

Industrial standardsSome firms wish to maintain capital structures that are in tandem with those companies having similar risk complexions. The argument in this case will be that what is good for the other companies would be good for the firm. Adopting a capital structure not in line with the other players would make the firm look conspicuous in the market place.

Nature of industryIf a firm is operating in an industry whose sales are subject to wide fluctuations over the business cycle, it should adopt a low degree of financial leverage. If a high degree of financial leverage is adopted the firm runs the

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risk of not being able to meet required payments during lean years and this can lead to financial distress. On the other hand firms that deal in products having inelastic demand can adopt modest levels debt if their capital structures as the sales expected will generally not fluctuate much.

Stage of the life cycle of the industryWhen the industry is in its infancy, the mortality rate would be high. Firms cannot afford to adopt high levels of financial leverage. Emphasis will be on the use of equity capital. When maturity is reached the firm should strive for manoeuvrability to ensure that growth is financed and the needed funds are obtained under acceptable terms. During the decline phase the firm should aim to adopt financing strategies that allow for early contraction of financing used.

Expert opinionThe opinion of investment analysts and institutional investors also influences the capital structure decision of the firm. It is argued that these experts are in a better position to assess a given financial plan. The recommendation would be to seriously consider the experts` opinion.Financial flexibilityIt is necessary to maintain flexibility when creating an organization’s capital structure. Flexibility is the firm’s ability to adjust its sources of funds either upwards or downwards in response to changes in need for funds. If a firm were to adopt an aggressive debt policy it may forced to issue equity on unfavourable terms later on because of heavy indebtedness. It is therefore important for the firm to maintain unused debt capacity for future needs if the firm is to be able to maintain operating flexibility.

TimingSometimes the firm can make substantial savings by properly timing when to issue financial securities. A public offering should be made when the state of the economy and capital market is ideal to provide funds. When management feels that debt finance will become costly or scarce they may chose to benefit from financial leverage immediately. The organization will immediately use high levels of financial leverage. If management expect interest rates to decline, a choice may be made to postpone becoming highly financially levered in order to remain flexible in order to take advantage of the lower rates expected to prevail in the future.

Credit standingOrganizations that enjoy a high credit standing with investors or lenders in the capital markets are usually in a better position to obtain funds from sources of their choice. Those firms that have a poor credit standing usually find that their choice of obtaining funds is limited.

RiskSmall firms have limited sources of financing and rely on the owner’s funds for their financing. Providers of long-term debt see them as risky propositions. Large companies on the other hand use funds from different sources as no single source of financing can cater for their total financial requirements.

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PRACTICE PROBLEMS ON CAPITAL STRUCTURE

PROBLEM 1Mojo Ltd has to make a choice between debt issue and equity issue for its expansion programme. Its current position is as follows:

5% DebtEquity capital ($10 per share)SurplusesTotal capitalization

SalesTotal costsIncome before interest and taxesInterest

Taxation at 50%Income after taxation

$20 00050 00030 000

100 000

300 000(269 000) 31 000

(1 000) 30 000

(15 000) 15 000

The expansion programme is estimated to cost $50 000. If this is financed through debt, the rate on new debt will be 7% and the price – earnings ratio will be 6 times. If the expansion programme is financed through equity, new shares can be sold netting $25 per share; and the price – earnings ratio will be 7 times. The expansion will generate additional sales of $150 000 with a return of 10% on sales before interest and taxes.

If the company is to follow a policy of maximizing the market value of its shares, which form of financing should it choose?

PROBLEM 2Mapepa Ltd is a plastic manufacturing company that is planning to expand its assets by 50%. All financing for this expansion will come from external sources. The expansion will generate additional sales of $300 000 with a return of 25% on sales before interest and taxes. The finance department of the company has submitted the following plans for the consideration of the Board.

Plan 1: Issue 10% debenturesPlan 2: Issue 10% debentures of half the required amount and the

balance in equity shares to be issued at 25% premium.Plan 3: Issue equity shares at 25% premium.

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Balance sheet of the company on 31 December

AssetsTotal assets

Equity and liabilitiesEquity capital ($10 per share)8% debenturesRetained earningsCurrent liabilities

$

1 200 000

400 000 300 000 200 000 300 0001 200 000

Income statement for the year ending 31 December

SalesOperating costsEBITInterestEarnings after interestTaxation at 50%EATEPS

$1 900 000

(1 600 000) 300 000

(24 000) 276 000

(138 000) 138 000 3.45

(i) Determine the number of equity shares that will be issued if financial plan 3 is adopted?

(ii) Determine the indifference point between (a) plans 1 and 2, (b) plans 1 and 3, and (c) plans 2 and 3.

(iii) Assume that the price – earnings ratio is expected to remain unchanged at the figure of 8 if plan 3 is adopted, but is likely to drop to 6 if either plan 1 or 2 is used to finance the expansion. Determine the market price of the shares in each of the situations.

PROBLEM 3Company X and company Y are in the same risk class, and are identical in every fashion except that company X uses debt while company Y does not. The levered firm has $900 000 debentures, carrying 10% rate of interest. Both the firms earn 20% before interest and taxes on their total assets of $1 500 000. Assume perfect capital markets, rational investors and so on: a tax rate of 50% and capitalization rate of 15% for an all – equity company.

(i) Compute the value of firms X and Y using the net income approach.(ii) Compute the value of each firm using the net operating income

approach.(iii) Using the NOI approach, calculate the over – all cost of capital for

firms X and Y.(iv) Which of these two firms has an optimal capital structure according

to the NOI approach? Why?

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PROBLEM 4The financial manager of Zamani (Pvt) Ltd. has formulated various financial plans to finance $3 000 000 required to implement various capital budgeting projects.

(a) Determine the indifference point for each financial plan assuming a 55% corporate tax rate and a par value of equity shares as $100:

(i) Either equity capital of $3 000 000 or $1 500 000 10% debentures and $1 500 000 equity,

(ii) Either equity capital of $3 000 000 or 12% preference shares of $1 000 000 and $2 000 000 equity,

(iii) Either equity capital of $3 000 000 or 12% preference capital of $1 000 000, $1 000 000 10% debentures and $1 000 000 equity,

(iv) Either equity share capital of $2 000 000 and 10% debentures of $1 000 000 or 12% preference share capital of $1 000 000, 10% debentures of $800 000 and $1 200 000 equity.

(b) Indicate and briefly describe various considerations to be looked at before a company comes up with an ideal capital structure.

PROBLEM 5In considering the most desirable capital structure of a company, the following estimates of the cost of debt and equity capital (after tax) have been made at various levels of debt – equity mix:

Debt as percentage of total capital employed

Cost of debt%

Cost of equity%

0102030405060

5.05.05.05.56.06.57.0

12.012.012.513.014.016.020.0

Determine the optimal debt – equity mix for the company by calculating the weighted average cost of capital.

- End of module -Good luck with your studies

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