Cost of Cap. & Cap. Structure

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MAFA-1 Cost Of Capital And And Capital Structure

Capital of a company consists of : 1. Equity ( equity share capital + reserves & surpluses ) 2. Preference share capital 3. Loan capital i.e. Debenture

EBIT-EPS Chart Falcon Limited plans to raise additional capital of Rs. 10 mln for financing an expansion project. In this context, it is evaluating two alternative financing plans: (i) issue of equity shares (1 mln equity shares at Rs. 10 per share), and (ii) issue of debentures carrying 14 per cent interest. What will be the EPS under the two alternative financing plans plans for two levels of EBIT, say Rs. 4 mln and Rs. 2 mln? Following table shows the value of EPS for these two levels of EBIT under the alternative financing plans.

Equity Financing

Debt Financing

EBIT: 2, 2,000,000 EBIT: 4, 4,000,000 EBIT: 2, 2,000,000

EBIT:

4,000,000

• Interest • Profit before taxes • Taxes • Profit after tax • Number of equity

— 2,000,000 1,000,000 1,000,000

— 4,000,000 2,000,000 2,000,000

1,400,000 600,000 300,000 300,000

1,400,000 2,600,000 1,300,000 1,300,000

Calculate the indiference EBIT.

In general, the relationship between EBIT and EPS is as follows : (EBIT - I) (1 – t) EPS = ———————— n The EBIT inifference point between two alternative plans can be obtained mathemetecally mathemetecally by solving the following equation

( EBIT – I1 ) ( 1 – t ) = ( EBIT – I2 ) ( 1 – t ) n1

n2

were

where where

EPS = EBIT EBIT = I = t = n =

earnings per share earn earnin ings gs bef befor ore e inte intere rest st and and tax taxes es interest burden tax rate number of equity shares

EBIT* EBIT* = indi indiffer fferenc ence e point point betwe between en the the two alter alterna nativ tive e financ financing ing plan plans s I1, I2 = interest expenses before taxes under financing plans 1 and 2 t = income-tax rate n1, n2 = number of equity shares outstanding after adopting financing plans 1 and 2.

Risk Considerations

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So far we looked at the impact of alternative financing plans on EPS. What is the effect of leverage on risk? A precise answer to this question is not possible with the help of EBIT-EPS analysis. However, a broad indication may be obtained with reference to it. The finance manager may do two things : (i) compare the expected value of EBIT with its indifference value, and (ii) assess the probability of EBIT falling below its indifference value. If the most likely value of  EBIT exceeds the indifference value of EBIT, the debt financing option, prima facie, may be advantageous. The larger the difference between the expected value of EBIT and its indifference value, the stronger the case for debt financing, other things being equal. Given the variability of EBIT, arising out of the business risk of the company, the probability of EBIT falling below the indifference level of EBIT may be assessed. If such probability is negligible, the debt financing option is advantageous. advantageous. On the other hand, if such probability is high, the debt financing alternative is risky. The notion may be illustrated illustrated graphically as shown in where two probability probability distributions of EBIT (A and B) are superimposed superimposed on the EBIT-EPS chart. Distribution A is relatively safe, as there is hardly any probability that EBIT will fall below its indifference level. With such a distribution, the debt alternative appears to be advantageous. Distribution B, on the other hand, is clearly risky because there is a significant probability that EBIT will decline below its indifference value. In this case, the debt alternative may not be regarded as desirable. ROI-ROE ANALYSIS In the preceding section we looked at the relationship between EBIT and EPS under alternative financing plans. Pursuing a similar line of analysis, we may look at the relationship between the return on investment (ROI) and the return on equity (ROE) for different levels of financing leverage. leverage. Suppose a firm, Korex Limited, which requires an investment outlay of Rs. 100 mln, is considering two capital structures.

Equity Debt

Capital Structure A 1 00 0

Capital Structure B 50 50

Equity Debt

While the average cost of debt is fixed at 12 per cent, the ROI (defined as EBIT divided by total assets) may vary widely. The tax rate of the firm is 50 per cent. Based on the above information, the relationship between ROI and ROE (defined as equity earnings divided by net worth) under the two capital structures, A and B, would be as shown in Table 13.2. Graphically the relationship is shown as below ROE

B

A

ROI

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MAFA-2

So far we looked at the impact of alternative financing plans on EPS. What is the effect of leverage on risk? A precise answer to this question is not possible with the help of EBIT-EPS analysis. However, a broad indication may be obtained with reference to it. The finance manager may do two things : (i) compare the expected value of EBIT with its indifference value, and (ii) assess the probability of EBIT falling below its indifference value. If the most likely value of  EBIT exceeds the indifference value of EBIT, the debt financing option, prima facie, may be advantageous. The larger the difference between the expected value of EBIT and its indifference value, the stronger the case for debt financing, other things being equal. Given the variability of EBIT, arising out of the business risk of the company, the probability of EBIT falling below the indifference level of EBIT may be assessed. If such probability is negligible, the debt financing option is advantageous. advantageous. On the other hand, if such probability is high, the debt financing alternative is risky. The notion may be illustrated illustrated graphically as shown in where two probability probability distributions of EBIT (A and B) are superimposed superimposed on the EBIT-EPS chart. Distribution A is relatively safe, as there is hardly any probability that EBIT will fall below its indifference level. With such a distribution, the debt alternative appears to be advantageous. Distribution B, on the other hand, is clearly risky because there is a significant probability that EBIT will decline below its indifference value. In this case, the debt alternative may not be regarded as desirable. ROI-ROE ANALYSIS In the preceding section we looked at the relationship between EBIT and EPS under alternative financing plans. Pursuing a similar line of analysis, we may look at the relationship between the return on investment (ROI) and the return on equity (ROE) for different levels of financing leverage. leverage. Suppose a firm, Korex Limited, which requires an investment outlay of Rs. 100 mln, is considering two capital structures.

Equity Debt

Capital Structure A 1 00 0

Capital Structure B 50 50

Equity Debt

While the average cost of debt is fixed at 12 per cent, the ROI (defined as EBIT divided by total assets) may vary widely. The tax rate of the firm is 50 per cent. Based on the above information, the relationship between ROI and ROE (defined as equity earnings divided by net worth) under the two capital structures, A and B, would be as shown in Table 13.2. Graphically the relationship is shown as below ROE

B

A

ROI

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Looking at the relationship between ROI and ROE it is observed that : 1.The ROE under capital structure A is higher than the ROE under capital structure B when ROI is less than the cost of  debt. 2.The ROE under the two capital structures is the same when ROI is equal to the cost of debt. Hence the indifference (or breakeven) value of ROI is equal to the cost of debt. 3.The ROE under capital structure B is higher than the ROE under capital structure A when ROI is more than the cost of debt. Mathematical Relationship

The influence of ROI and financial leverage on ROE is mathematically as follows :

Wher Wheree

ROE ROE ROI r D/E D/E t

ROE = [ROI + (ROI – r) D/E] (1 – t) = retu return rn on equi quity = return on investment =cost of debt = debt debt-e -eq quity uity rati ratio o = tax rate

ASSESMENT OF DEBT CAPACITY

Employment of debt capital entails two kind of burden: interest payment and principal repayment. To assess a firm’s debt capacity we look at its ability to meet these committed payments. This may be judged in terms of:

• • •

Coverage ratios Probability of cash insolvency Inventory of resources

Coverage Ratios

A coverage ratio shows the relationship between a committed payment and the source for that payment. The coverage ratios commonly used are: interest coverage ratio, cash flow coverage ratio, and debt service coverage ratio. This may be derived as follows: PAT ROE = ———  E (EBIT – I) (1 – t) ROE = ————————  E (TA × ROI – I) (1 – t) ROE = ———————————  E

[(E + D) ROI – rD] (1 – t) ROE = ————————————  E ROE = [ROI + (ROI – r) D/E] (1 – t) interest coverage ratio (also referred to as the times interest interest earned ratio) is simply Interest Coverage Ratio : The interest defined as:

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MAFA-4 Earnings before interest and taxes  ————————————————  Interest on debt

To illustrate, suppose the most recent earnings before interest and taxes (EBIT) for Vitrex Company were Rs. 120 million and the interest burden on all debt obligations were Rs. 20 million. The interest coverage ratio, therefore, would  be 120/20 = 6. What does it imply? It means that even if EBIT drops by 83 1/3 percent, the earnings of Vitrex Company cover its interest payment. Though somewhat commonly used, the interest coverage ratio has several deficiencies: (i) It concerns itself only with the interest burden, ignoring the principal repayment obligation. (ii) It is based on a measure of earnings, not a measure of cash flow. (iii) It is difficult to establish a norm for this ratio. How can we say that an interest coverage ratio of 2,3,4, or any other is adequate? Cash Flow Coverage Ratio This may be defined as:

EBIT + Depreciation + Other non-cash charges Loan repayment installment Interest on debt + —————————————-(1 – Tax rate) To illustrate, consider a firm : Depreciation EBIT Interest on debt Tax rate Loan repayment installment

Rs. 20 mln Rs. 120 mln Rs. 20 mln 50% Rs. 20 mln

Calculate the cash flow coverage ratio for this firm . Debt Service Coverage Ratio Financial institutions which provide the bulk of long-term debt finance judge the debt capacity of a firm in terms of its debt service coverage ratio. This is defined as:

PATi + DEPi + INTi DSCR = ∑  —————————— t INTi + LRIi n

where

DSCR PATi DEPi INTi LRIi n

n

= debt service coverage ratio = profit after tax for year I = depreciation for year I = interest on long-term loan for year I = loan repayment instalment for year I = period of loan

In determination of best capital structure , share- holder prefers higher E.P.S. ( i.e. earning per share ) or

EPS volatility EPS volatility refers to the magnitude or the extent of fluctuation of earnings per share of a company in various years as compared to the mean or average earnings per share. In other  words, EPS volatility shows whether a company enjoys a stable income or not. It is obvious that higher the EPS volatility, greater would be the risk attached to the company. A major cause of  EPS volatility would be the fluctuations in the sales volume and the operating levarage. It is obvious that the net profits of a company would greatly fluctuate with small fluctuations in the sales figures specially if the fixed cost content is very high. Hence, EPS will fluctuate in such a situation. This effect may be heightened by the financial leverage. E.P.S. = =

Profits available to equity. Share holders number of equity shares Earning per share or EPS = [ (PBIT - I ) (1-t) - Pref Dividend ]

No. of Equity Share.

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Where, PBIT = Profit before tax. ; I = Interest.; t = Tax rate of the firm. At point of Indifference : (EPS)1 = (EPS ) 2

SEBI Guidelines Uptil early 1992, matters like a company’s capital structure, its pricing of capital issues, dividend and interest rates, capitalisation reserves, etc. were governed by the Capital Calculation of costs forofeach Elements issues (Control) Act, 1947. The system had certain drawbacks like the under pricing of  equity issues, delays in getting clearances, etc. So the Act was abolished and companies are now required to conform to the disclosure and investor protection guidelines issued by the Securities and Exchange Board of India (SEBI). The important guidelines are : 1.

A new company set up by existing companies with a five-year track record of consistent profitability can freely price its capital issues, provided the promoting companies’ participation is at least 50 percent. Other new companies must price their issues at par.

2.

Closely held companies and private companies going public can price their issues of capital freely provided they have been profitable for at least three years.

Costs of Capitals are of two types 1. One Time Cost Or Flotation Cost 2. Annual Costs e.g. Interest, Dividend Cost of Debt (Cd) a) When date of redemption is not given in the problem. Cost of Debt. (after tax ) or C d = ( 1-t ) x I Where, i = Effective rate of Interest . T = Tax rate . Effective rate of interest = Interest amount p.a. x 100 Net Proceeds Net proceeds = Face value – discount + premium –flotation cost . You can calculate on per debenture basis . b) Cost of redeemable debt : When Redemption is made at the end of its life or project . Cost of debt (after tax ) I + RV - NP Cd= , n , (1 - t )

Where, I = RV = NP = n =

RV + NP 0 2 Fixed Interest charges p.a. or interest per debenture. Redeemable value i.e. face value + premium Net proceeds or Cash Inflow. Life of the debt.

c) When DEBENTURES are redeemed during its life: Apply the principle of EXPLICIT COST i.e. the rate of return at which the initial cash inflow equates the discounted future cash outflows . This method is opposite to I.R.R.

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Cost of Preference Share Capital (Cp ) a) Cost of irredeemable preference Share . Cp = Preference Dividend 100 NOTE : Tax on Dividend may be charged Net Proceeds (NP ) or Market Value( MP ) b) Cost of redeemable preference Share i. Redemption at the end

Cp

=

D

+

RV - NP n ,

D= preference dividend

RV + NP 2 Pref. sh. Redeemed intermittently --

ii.

Apply Explicit Cost principle as before.

Cost of Equity Share Capital

(Ce)

a. Dividend Price Approach ( D/P ) with growth model Ce =

Dividend

100 + g

Net Proceeds or Market value. Where, g = growth rate or expected growth in dividend from coming year. b) Earning/ Price Approach ( E / P ): Ce =

Current Earning per Share

100

Current Market Price per share c) Realised yield Approach :- It is that rate of return where investor’s initial investment = Total discounted cash Inflow in form of dividend and sales realisation at the end of the period. d) Earning growth Model Ce =

EPS x 100 + g

NP e)

Estimating growth rate (g ) 1) Dn = Do ( 1+ g ) n ;

Dn = div / share in current year ; n = no of years Do = div / share in first year ; g = growth rate

2) GORDON’S MODEL : g = br ; g = growth rate ; b = constant proportion of net profit retained each year ; r = average return of the firm . where ,

b = Net profit - dividends Net profit r=

Right share:

net profits Book value of capital employed

THIS METHOD IS ONLY APPLICABLE TO FIRMS WHICH HAVE ALL EQUITY CAPITAL STRUCTURE

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Theoretical Post Right Price = { market price no. of old share + no. of right share price } total no. of shares Theoretical value of rights = Post right price – subscription price

subscription

Bond Yield Plus Risk Premium Approach

According to this approach the rate of return required by the equity investors of a firm is equal to Yield on the long-term bonds of the firm + Risk premium The logic of this approach is simple. Equity investors bear a higher degree of risk than bond investors and, hence, their required rate of return should include a premium for this higher risk. The problem with this approach is how to determine the risk premium. Should it be 1 percent, 2 percent, or n percent ? There is no theoretical basis for estimating the risk premium. Most analysts look at the operating risk and financial risk characterising the business and arrive at a subjectively determined risk premium figure which varies normally between 2 percent and 6 percent. This is added to the yield on the firm’s long-term bonds to estimate the rate of return required by equity investors.

THE CAPITAL ASET PRICING MODEL (CAPM)

The previous chapter on portfolio theory dealt with how to measure the risk and expected return of a portfolio or  collection of assets; so far we have not attempted to bring the two together, that is to specifically link risk with return. In the chronological development of modern financial management, portfolio theory came first with Markowitz in 1952. It was not until 1964 that William Sharpe derived the capital Asset Pricing Model (CAPM)1 based on Markowitz’s portfolio theory. For example, a key assumption of the CAPM is that investors hold highly diversified  portfolios and thus can eliminate a significant proportion of total risk. The CAPM was a breakthrough in modern finance because for the first time a model became available which enable academic, financiers and investors to link the risk and return for an asset together, and which explained the underlying mechanism of asset pricing in capital markets. TYPES OF INVESTMENT RISK 

In the preceding chapter we have seen how the total risk (as represented by the standard deviation, σ) of a two-security  portfolio can be significantly reduced by combining securities whose returns are negatively correlated, or at least have low positive correlation – the principle of diversification. According to the CAMP, the total risk of a security or portfolio of securities can be split into two specific types, systematic risk and unsystematic risk . This is sometimes referred to as risk partitioning , as follows : Total risk = Systematic risk + Unsystematic risk   Systematic (or market) risk  cannot be diversified away : it is the risk which arises from market factors and is also frequently referred to as undiversifiable risk. It is due to factors which systematically impact on most firms, such as general or macroeconomic conditions (e.g. balance of payments, inflation and interest rates). It may help you remember which type is which if you think of systematic risk as arising from risk factors associated with the general economic and financial system. Unsystematic (or specific) risk  can be diversified away by creating a large enough portfolio of securities : it is also often called diversifiable risk or  company-unique risk. It is the risk which relates, or is unique, to a  particular firm. Factors such as winning a new contract, an industrial dispute, or the discovery of a new technology or product would contribute to unsystematic risk.

The relationship btween total portfolio  below . Notice that total risk diminshes as the that unsystematic risk does not disappear size.

Systematic Risk 

risk, σ p, and portfolio size can be bshon diagramatically as in Figure number of assets or securities in the portfolio increases, but also observe completely and that systematic risk remains unaffected by portfolio

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Total risk 

Portfolio risk

Unsystematic risk 

σ p

1

5

10 15 Number of securities in portfolio

20

THE CAPM MODEL We have previously described the CAPM as a method of expressing the risk-return relationship for a security or portfolio of  securities: it brings together systematic (undiversifiable) risk and return. After all, for any rational, risk-averse investor it is only systematic risk which is relevant, because if the investor creates a sufficiently large portfolio of securities, unsystematic or  company-specific risk can be virtually eliminated through diversification.

It is therefore the measurement of systematic risk which is of primary importance for rational investors in identifying those securities which possess the most desired risk-return characteristics. It is the measurement of systematic risk which becomes critical in the CAPM because the model relies on the assumption that investors will only hold well diversified portfolios, so only systematic risk matters. The CAPM is quite a complex concept so if you find it difficult to grasp at first do not become disillusioned, stick with it. For reasons of presentation and ease of understanding we will approach our study of the CAPM by breaking it down into five key components as follows: 1. The beta coefficient, ( ); 2. The CAPM equation; 3. the CAPM graph—the security market line (SML); 4. Shifts in the SML—inflationary expectations and risk aversion; 5. Comments and criticisms of the CAPM.

Let us examine each component in turn, beginning with the key concept of beta, β, The beta coefficient ( ) Recall that the standard deviation, σ, is used to measure an asset or share’s total risk, while the beta coefficient, β, in contrast is used to measure only part of a share or portfolio’s risk, namely the part that cannot be reduced by diversification, that is the systematic or market risk of an individual share or portfolio of shares.

Systematic risk can be further subdivided into business risk and financial risk. Business risk arises from the nature of  the firm’s business environment and the particular characteristics of the type of business or industry in which it operates. For  example the competitive structure of the industry, its sensitivity to changes in macroeconomic variables such as interest rates and inflation and the stability of industrial relations all combine to determine a firm’s business risk. The level of business risk  in some industries, for example catering and construction, is higher than in others and is a variable which lies largely outside management’s control. Categories of beta

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Shares or securities can be broadly classified as aggressive, average or defensive according to their betas. Shares with a beta>1.0 are described as aggressive; they are more risky than the market average, although they will tend to perform well in a rising or bull market. Consequently investors would require a rate of return from the share which is greater than the market average. Shares with a beta = 1.0 are described as average or neutral as their rate of return moves in exact harmony with movements in the stock market average return; they are of average risk and yield average returns. In contrast, shares with a beta < 1.0 are classed as defensive. A defensive share does not perform well in a bulk market but conversely it does not fall as much as the average share in a falling or bear market. How are betas determined? A share’s beta is determined from the historical values of the share’s return relative to market returns. It is important to appreciate therefore that beta is a relative, not an absolute, measure of risk. As each individual beta is derived from a common base, that is, the return on the market portfolio or a suitable stock index substitute, then beta is a standardised risk  measure, i.e. this makes the beta of one share directly comparable with the beta of another.

One way of determining the beta for a share is to plot on a graph the historic (ex post) relationship between the movement in the share’s returns and the market (or stock index) returns over a defined period of time. For example, if a stock  market analyst considers that the share’s actual performance over the past five years also gives a fair indication of the share’s likely future performance, then deriving its beta is a matter of: 1.

2.

Computing both the average individual share’s return and the average market return (utilising an appropriate stock market index) for each month of the five-year period. Sometimes betas are also computed using daily averages. Plotting on a graph the co-ordinates for each monthly set of returns. Conventionally the market’s or index’s returns are platted on the horizontal (x) axis and the individual share’s returns on the vertical (y) axis. The results will probably appear in the form of a scattergram and the statistical technique called regression analysis can then  be used to derive the regression or characteristic line of the data. Derivation of beta 

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Return on Share

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Market Return The characteristic line is the straight line that best represents or fits the relationship between the share’s return and the return from the market over the period. Beta is the slope of this characteristic line for the share as illustrated in Figure above. Shares with high betas will have steeper the slope of t he line the more volatile (risky) are the returns from the sahre in relation to the returns from the market. Figure below illustrates the respective characteristic line for two different risk securities, A and B. Security A has a  beta of 1.5 and is represented by the steeper sloped line, compared with Security B which has a beta of 0.7. Security A’s higher   beta suggests that its returnreturn is more( sensitive to changes in the market return: it is thus a more risky investment than Security B. Security %)

A

Figure below Characteristic lines for two different risk securities, A and B

B

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Market return ( % ) Alternative derivation of beta

Using past data on individual share and market returns over a sufficiently lengthy period, say, the most recent four to five years, betas can also be calculated statistically. For example the beta ( β)of a share (S) is equal to the covariance between the share’s returns and the market’s returns (COV sm) divided by the variance of the market’s returns (Var m)—which in turn is the standard deviation of the market’s returns squared, that is:

Beta, βs

Covariancesm COVsm = ——————— = ———— = ————  Variancem Var m

COVsm

σ2m

The returns on a suitable stock market index can be used as a proxy for the market returns. For example, substituting the FTSE 100 Share Index, the beta ( β) of a share (S) would be calculated as: COVs,FTSE100 COVs,FRSE100 Beta,βs = —————— = ——————  Var FRSE100 σ2FTSE100 As the covariance of each individual share is divided by a common denominator, the variance of the market (Var m) or  a suitable surrogate market index, we end up with a standardised measure of risk, that is, the share’s beta. Being a standardised measure we are able to directly compare the beta of one share with the beta of another. Portfolio betas

As it is learned that a share’s beta represents only part of a share’s risk, namely the element of systematic or market risk, which is the risk element that cannot be diversified away. When it comes to including a share in a portfolio we are only concerned with the impact of that share’s market risk on the portfolio risk. In a portfolio context market risk is also the only relevant risk and beta is the best measure. The portfolio beta measures the portfolio’s responsiveness to macroeconomic variables such as inflation and interest rates. To determine the systematic risk for a portfolio, that is the portfolio beta, we simply calculate a weighted average of  the betas of the individual securities making up the portfolio, as follows: 2 Portfolio beta, β p = w1β1 + w2β2 + w3β3 … + wnβn where, β p = the portfolio beta (i.e. risk of the portfolio relative to the market) wi = portfolio weightings of the individual securities (where I = 1, 2, … n) βi = beta of the individual security (where i = 1,2,…n) n = number of securities in the portfolio Obtaining and interpreting betas Betas can be obtained from published sources e.g. the London Business School (LBS) and through brokerage firms. The LBS published β values and other data for UK and Irish companies listed on the London Stock Exchange every quarter in its Risk Measurement Service publication. Individual betas are produced for all companies listed in the Financial Times (FT) All-Share Index. The individual  betas are calculated from the monthly returns over the most recent five-year period related to the monthly returns from FT AllShare Index using a standard least squares regression computer programme. Most investment firms and analysts utilise β books which give beta values for all the major companies listed on the stock market although different investment firms may give varying beta estimates for the same company due to the different

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methods and timings used in their calculations. In the United States beta value are commonly obtained from Value Line Investment Survey and from brokerage and investment firms such as Merrill Lynch. The CAPM equation We will now examine the actual equation for the capital asset pricing model. It is one of the most famous equations in financial management. The CAPM equation links together risk and the required return for a share. It shows, for example, that the return a rational investor would require on a particular share, R(r i), is a function of the share’s market or systematic risk  (beta), βi, and a risk premium to compensate for investing in the risky market. Thus the higher the risk, the higher the return the investor will require a vice-versa. Simply stated, the underlying precept of the CAPM is that the expected return on a security is composed of two elements as follows: Expected return, E(r) = a risk-free interest rate + a risk premium Using the capital asset pricing model (CAPM) this relationship is expressed more formally as: E(r i) = r f  +

βi(ER m – R f) 

where, E(r I) = required return on asset/share I R f  = risk-free rate of return βi = beta coefficient for asset/share i ER m = expected market return, that is the return expected on the market portfolio of

share.

As it is seen above, the CAPM equation can be split into two segments: 1. 2.

the risk-free rate of return, R f ; and The risk premium, βi (ER m – R f )

We will discuss the risk-free rate of return R f,  first. The CAPM graph – the security market line (SML)

Having now had some practice in using the CAPM to calculate the expected returns you will have noticed that the CAPM equation is in fact a straight line equation. Conventionally the equation for a straight line is usually given as: y = ax + c. When the CAPM equation is shown in graph form, the resultant straight line is referred to as the security market line (SML). It is the line which exhibits the positive relationship (correlation) between the systematic risk of a security and its expected return. On the security market line (SML) the risk-free rate, R f , is a constant and represents the vertical intercept, i.e. the point where the SML crosses the vertical axis; it is equivalent to the constant c in the straight line equation above. The co-ordinate x represents the systematic or market risk of the share as measured by its beta, βi, and co-ordinate y represents the expected market return. Observe that the slope or gradient of the line, a, is represented by the market risk   premium (ER m – R f ), not jbeta and indicates the level of risk aversion in the economy. The SML represents the level of return expected in the market for each level of the share’s beta (market risk), thus the risk-return trade-off for the share can be plainly seen as in Figure 7.4. Interpreting the security market line (SML)

A few comments about the SML will facilitate its interpretation. First, notice that the beta associated with the risk-free security is 0, reflecting the security’s freedom from risk and its immunity from changes in the market return. Second, point M on the SML represents the market portfolio. The return on the market portfolio (i.e. the average return from all securities on the entire market or a proxy index) is given by ER m and its corresponding level of risk is shown by

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βm, where β = 1.0. SML Expected return, E(r), % ER m



M

Risk-free rate (R t)

0

0.5

1.0

1.5

2.0

βm Market risk, β Security market line (SML)

Share A ν

Expected return E(r), %

SML Erm

Share B ν

M

Risk-free rate (Rf)

0

0.5

1.0 βm

1.5

2.0

Market risk, β Fig. Expected return and required return and required return

Shifts in the security market

We noted above that the slope of the SML is given by the market risk premium (ER m – R f ), not beta and that it reflects the general level of risk aversion in the economy. The security market line is not static, it is an expression or snapshot of the risk-return relationship at a particular point in time. In dynamic capital markets, which are constantly responding to new information, risk-return factors change continually, thus the SML can and does shift over time. Here we will explore the impact of two specific major change effects on the SML—(1) inflation and (2) risk aversion. The inflation shift

The risk-free rate of return is composed of several elements: a real interest rate, a liquidity or maturity premium and an inflation premium (IP). However, as we are primarily concerned with understanding inflation effects, we will simplify matters by assuming that any liquidity premium is subsumed within the real interest rate, which we will denote r*. Thus the risk-free interest rate is made up as follows: R f  = r* + IP When expectations in the financial markets about the future rate of inflation change, this will essentially move the risk-free rate, R f , up or down depending on the market’s expectations about the direction of inflation. As t he risk-free rate is the  base line ingredient for all rates of return, any change in the risk-free rate as a result of changes in inflation expectations will be applied to all required rates of return as implied by the CAPM. Expected return, E (r), %

SML2

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ERm2, 11%

Erm1 , 9% M1

Increase inexpected inflation. ∆IP = 2%

 New risk-free (r12) 9%

Original risk-free rate (Rf1) 7%

0

0.5

1.0

1.5

2.0

βm

The risk aversion shift

As we have explained, the slope of the SML represents the market risk premium, the steeper the slope, the greater the risk premium in the market. This reflects the extent to which investors in the market are risk-averse, that is for an increase in risk they require a commensurate increase in return as indicated by the upward slope of the SML. If market risk did not exist there would be no risk premium and the SML would be a flat line extending from the R f  vertical intersection. However, in reality market risk does exist and it is a variable which can change, primarily as a result of economic,  political and social factors such as general strikes, widespread civil unrest, stock market crashes, wars or greater political or  economic uncertainty and instability. Should market risk increase, for example because investors perceive greater economic uncertainty or i nstability ahead, then this will be reflected in a rise in the slope of the SML. Note that in this instance the risk-free rate remains unchanged, it is the risk premium which now changes. Observe also how the increase in the risk premium becomes more prominent as the riskiness of the security (its β) increases. The increase in the risk premium is significantly greater for a security with a beta of  1.5 (an aggressive share) than it is in relation to a security with a beta of 0.5 (a defensive share). The effect of an increase in risk aversion on the SML is illustrated in Figure below

Expected return E(r)%

SML2

ER m2 12%

M2

ER m1 9%

M1 Additional market risk  premium (ER m2 - ER m1 )

βm

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If we adopt the same figures as before, that is F f1 equals 7 percent and ER m1 equals 9 per cent the original market risk   premium was ER m1 – R f1 = 9% - 7% = 2%. If we assume that ER m2 has now moved to 12%, the new market risk premium is ER m2 – R f1 = 12% - 7% = 5%. Thus the market risk premium has increased by an additional 3 per cent; ER m2 – ER m1 = 12% 9% = 3%: the risk-free rate remains unaffected. Underlying assumptions and limitations of the CAPM

The CAPM is a mathematical mode, and like any model it is merely a representations of reality. All models (business economic and financial, etc. are constructed from a set of underlying assumptions about the real world; they inevitably have their limitations. The CAPM is built on the following set of assumptions and limitations: 1.

Historic data. CAPM is a future-oriented model yet it essentially relies on historic data to predict future returns. Betas, for example, are calculated using historic data; consequently they may or may not be appropriate  predictors of the variability or risk of future returns. Thus the CAPM is not a deterministic model, the required returns suggested by the model can only be viewed as approximations.

2.

Investor expectations and judgements. The models includes the expectations and subjective judgements of  investors about future asset or security returns and these are very difficult to quantify. In addition the model also assumes that investor expectations and judgements are homogenous, i.e. identical. If investors have heterogeneous (i.e. varied) expectations about future returns they will essentially have different SMLs, rather  than a common SML as implied by the model.

3.

A perfect capital market. CAPM assumes an efficient or perfect capital market. An efficient capital market is one where all securities and assets are always correctly priced and where it is not possible to outperform the market consistently except by luck. An efficient capital market implies that there are many small investors (all are price-takers), all of whom are rational and risk-averse; they each possess the same information and the same future expectations about securities. It also assumes that in the financial markets there are no transaction costs, no taxes and no limitations on investment.

4.

Investors fully diversified. The CAPM also assumes that investors are fully diversified. In practice many investors, particularly small investors, do not hold highly diversified asset portfolios.

5.

Practical data measurement problems. There are also practical problems associated with the model such as difficulties with specifying the risk-free rate, measuring beta and measuring the market risk premium.

6.

One-period time horizon. CAPM assumes investors adopt a one-period time horizon. In practice investors are likely to have differing time horizons and again this would imply varying SMLs.

7.

Single factor model. CAPM is a single factor model: it relies on the market portfolio to explain security returns. The rate of return on a security is a function of the security’s beta times a risk premium, that is β(ER m – R f ). Both  beta and the risk premium are determined in relation to the market portfolio. Recall that each security’s beta (risk  factor) is derived by linear regression, plotting its return against the return from the market portfolio—the characteristic line.

Rules of CAPM :------E ( R p ) = R f  + p [E ( R m ) - R f  ] Where,

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E (R p)

= Expected return of the portfolio

R f 

= Risk free rate of Return

p

= Portfolio Beta i.e. market sensitivity index = change in expected rate of return

E(R m) [E (R m) – R f ]

change in market rate of return

= Expected Return on market portfolio = Market risk premium.

Portfolio Beta ( p) =

(R sm) (S.D. s ) S.D.m

Where, R sm = Correlation Coefficient with market .

S.D.s = Standard deviation of an asset .

S.D.m = Market Standard deviation .

E(R m) =

( DIV + Cap. Gain )

Total Investment

Capital Gain = Market Value - Value of Original Investment .

COST OF RETAINED EARNINGS ( Cr ) Cost of Retained Earnings Two basic approach have been suggested for determining the cost of retained earnings : (i) tax adjusted rate of return approach, and (ii) external yield approach. The cost of retained earnings is calculated as the post-tax rate of return Tax-adjusted Rate of Return Approach available to the investor. This means that k s has to be adjusted for ordinary and long-term capital gains tax. One way to do it is as follows : k r  = k s 1 – t p 1 – tg where kr    = cost of retained earnings k s = rate of return required by equity investors t p = ordinary personal income tax rate tg = personal long-term capital gains tax rate.

This approach is riddled with two problems : (i) The ordinary personal income tax rate and the personal longterm capital gains rate may vary widely across the shareholders of a company. Hence it may be impossible to establish a minimum rate of return that ensures that all the shareholders benefit if the company reinvests its cash flows instead of   paying dividends. (ii) The alternative investment opportunities of the company are not considered. The basic premise of this approach is that the company should evaluate the  External Yield Approach  possibility of buying shares of other companies with similar risk characteristics by using retained earnings. Hence the opportunity cost of retained earnings is deemed equal to the rate of return that can be earned on such investment. Since that rate of return is equal to k s, the cost of retained earnings is simply equal to k s. This approach appears to be superior  to the earlier approach. Hence in our subsequent discussion we will adopt this approach. Cr = Ce ( 1- b ) ( 1 - t ) Where b = rate of brokerage; t = marginal tax rate applicable to share holder If rate brokerage is not given , C r = Ce Cr = ( D P ) + g

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Cost of Capital or cut off rate ( Cw or Co ) = (Capital mix ratio x cost of each ingredients ) x 100 : Alternatively, Cw or Co = Total cost x 100 total capital MIX are taken on 4 different 1. Book value Basis 2. Market value Basis

3. Marginal Basis 4. Expected Cap. Structure basis

Market Value Of The Firm

Net Income Approach : Value = { ( EBIT –I ) ( 1-t ) } 1.

2.

market Capitalisation rate + value of debt

Net Operating Income Approach :

Value of equity = { ( EBIT

market Capitalisation rate) - value of debt }

( 1- t )

Value of the firm = value of equity + value of debt 3.

MODIGLIANI MILLER APPROACH

1.

Value of the firm

2.

Po = ( D1 + P1 )

=

EBIT

Ce

( 1 + Ce )

Where, Po = Market price per share of time 0 P1 = Market price per share at time 1. 3.

D1 = Dividend per share at that time. Ce = Market capitalisation rate.

In case of new financing : mp1 = I - (NP – nD1 ) where, m = no. of share to be issued, at time 1. P = Price. D1= Dividend per share at time 1.

4.

Traditional Approach = interest

Cd + Dividend

I = new investment. NP = Net profit.

Ce as there is no tax.

Financial BEP = Required PBIT to pay the fixed charges on capital .

EXPLAINING FINANCING CHOICES

Two theories are commonly advanced to explain real-world corporate financing behaviour, viz. The tradeoff theory and the pecking order theory. Tradeoff Theory

While choosing the debt-equity ratio, financing managers often look at the tradeoff between the tax shelter provided  by debt and the cost of financing distress. Figure 13.4 shows the nature of this tradeoff. According to the trade-off theory, profitable firms with stable, tangible assets would have higher debt-equity ratios. On the other hand, unprofitable firms with risky, intangible assets tend to have lower debt-equity ratio.

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How well does the tradeoff theory explain corporate financing behaviour? It explains reasonably well some industry differences in capital structures. Fore example, power companies and refineries use more debt as their assets are tangible and safe. High-tech growth companies, on the other hand, borrow less because their assets are mostly intangible and somewhat risky. The trade-off theory, however, cannot explain why some profitable companies depend so little on debt. Fore example, Hindustan Lever Limited and Colgate Palmolive India Limited, two highly profitable companies, use very little debt. They pay large amounts by way of income tax which they can possibly save by using debt without causing any concern about their solvency. Inventory of Resources

Available for use within: Resources Uncommited reserves Instant reserves Surplus cash Unused line of credit  Negotiable reserves Additional bank loans Unsecured Secured Additional long-term debt Issue of new equity Reduction of planned outflows Volume-related Change in production schedule Scale-related Marketing programme R & D budget Administration overhead Capital expenditures Value-related Dividend payments Liquidation of assets

One quarter

One year

$ $

$ $ $ $

$ $ $ $ $ $

Three years

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Packing Order Theory

There is an alternative theory which explains why profitable firms use little debt. According to this theory, there is a  pecking order of financing which goes as follows:

• Internal finance (retained earnings) • Debt financing • External equity finance A firm first taps retained earnings. Its primary attraction is that it comes out of profits and not much effort is required to get it. Further, the capital market ordinarily does not view the use of retained earnings negatively. When the financing needs of the firm exceed its retained earnings, it seeks debt finance. As there is very little scope for debt to be mispriced, a debt issue does not ordinarily cause concern to investors. Also, a debt issue prevents dilution of control. Value of tax shelter  Value of  The firm

Value with tax shelter & cost of  Financial distress

Leverage Trade off Theory

External equity appears to be lest choice. A great deal of effort may be required in obtaining external equity. More important, while retained earnings is not regarded by the capital market as a negative signal, external equity is often perceived as ‘bad news’. Investors generally believe that a firm issues external equity when it considers its stock  overpriced in relation to its future prospects.

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Thus, according to the pecking order theory, there is no well-defined target debt-equity ratio, as there are two kinds of equity, internal and external. While the internal equity (retained earnings) is at the top of the pecking order, the external equity is at the bottom. The pecking order theory explains why highly profitable firms generally use little debt. They borrow less as they don’t need much external fi nance and not because they have a low target debt-equity ratio. On the other hand, less profitable firms borrow more because their financing needs exceed retained earnings and debt finance comes before external equity in the pecking order.

Proposition II of MM M-M argue that the cost of equity, k o, is equal to a constant average cost of capital, k o, plus a risk premium that depends on the degree of leverage. That is — ko = ko + Risk premium The premium for financial risk equals to the difference between the pure equity capitalisation rate, k o, and cost of debt, kd, times the ratio D/S, that is — ke = ko (ko – kd) (D/S) In short, Proposition II states that the firm’s cost of equity, k e, increases in a manner to offset exactly the use of chapter debt capital. In other words, as the firm’s use of debt increase, its cost of equity also rises. Proposition II of M-M Hypothesis implies a linear relationship between k e and the debt-equity ratio (D/S).

The M-M Hypothesis with corporate taxes With introduction of corporate taxes, M-M change their position. They now recognize that the value of the firm will increase or the cost of capital will decrease with increase in leverage as interest on debt is a deductible expense. 1 Between two firms, levered and unlevered, the levered firm will have a higher value for the same reason. More specifically, the value of levered firm (L) will exceed that of unlevered firm (U) by an amount equal to L’s debt multiplied by the tax rate. That is —

Where, VL Vu t D

VL = Vu = tD = value of the levered firm ; = value of the unleverd firm ; = corporate tax rate ; = amount of debt in L.

Proof  The proof of the above equation is given below : Two firms are considered identical in all respects except capital structure. Assume that firm U (unlevered) finances by equity only while firm L (levered) employs debt. EBIT are identical in each firm. Under these assumptions, the operating cash flows (CF) available to investors firms U and L are computed as follows : CFu and CFL or CFL

where EBIT  I D t

= = = =

=

EBIT  (1 – t)

…

…

(1)

= = = = =

(EBIT – I ) (1 – t) + I (EBIT – kd.D) (1 – t) + kd.D EBIT – kd.D – EBIT (t) + tkd + kdD EBIT – EBIT (t) + tkdD EBIT (1 – t) + tkdD

…

…

(2)

earnings before interest and taxes interest on debt capital = kd.D amount of debt in L corporate tax rate.

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It may be mentioned that in equation (2) the first term to the right of the equation sign, i.e., (EBIT – I ) represents the income available to the shareholders ; the term ‘I’ or ‘kd.D’ is that available to the providers of debt capital. CFL is thus the total income available to all investors (equity plus debt ). Firm U does not use debt capital. Its value, Vu, may, therefore, be determined by discounting its net earnings after tax, i.e., EBIT (1 – t), by its equity capitalisation rate of cost of equity, ke. That is — Vu =

EBIT (1 – t) ke

…

…

(3)

The value of the levered firm is determined by capitalising1 both parts of its after-tax earnings. Thus — VL = EBIT (1 – t) + tkd.D = ke kd

EBIT (1 – t) + tD ke

∴ VL = Vu + tD

…

(4)

as Vu = EBIT (1 – t) ke

Thus, M-M state that the value of a levered firm is equal to its value without leverage plus the present value of the interest tax shelter, which is equal to the tax rate times the value of the debt. From equation (3) the cost of equity, ke, in the unlevered firm can be ascertained as follows : ke(u) = EBIT (1 – t) Vu

…

…

(5)

Since it is financed by equity only, its average cost of capital, k o, is equal to its cost of equity, ke. The cost of equity in the levered firm is the net earnings after tax divide by the value of the equity. That is — k e(L) = ( EBIT – I ) (1 – t ) … … (6) S The weighted average cost for the levered firm would be : k o(L) = (D/V) (kd) (1 – t) + (S/V) (ke)

…

…

(7)

M-M state that that, in a world with corporate taxes, the value of the firm increases and cost of capital decreases continuously with financial leverage. Thus, to achieve optimum capital structure the firm should use the maximum amount of debt.

Problems

1.

2.

X Ltd. , a widely held company is considering a major expansion of its production facilities and the following alternatives are available : Alternatives (Rs. In lakhs) A B C Shares Capital 50 20 10 14% Debentures -20 15 Loan from a Financial Institution @ 18% p.a. Rate of Interest -10 25 Expected rate of return before tax is 25%. The rate of dividend of the company is not less than 20%. The company at present has low debt. Corporate taxation 35%. Which of the alternatives you would choose ? EXE Limited is considering three financing plans. The key information is as follows:a) Total investment to be raised Rs. 2,00,000.

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Plans of Financing Proportion Plans Equity Debt Preference Shares A 100% B 50% 50% C 50% 50% Cost of debt 8% Cost of preference shares 8% Tax rate 35% Equity shares of the face value of Rs. 10 each will be issued at a premium of Rs. 10 per share. Expected PBIT is Rs. 80,000. Determine for each plan:1) Earnings per share (EPS)and 2) The financial break even point. 3) Indicate if any of the plans dominate and compute the PBIT range among the plans for indifference. 3.

Aries Limited wishes to raise additional Finance of Rs. 10 lakhs for meeting its investment plans. It has Rs. 2,10,000 in the from of retained earnings available for investment purposes. The following are the further details: 1) Debt/equity mix 2) Cost of debt upto Rs. 1,80,000 beyond Rs. 1,80,000 3) Earnings per share 4) Dividend pay out 5) Expected growth rate in dividend 6) Current market price per share 7) Tax rate

30% : 70% 10% (before tax) 16% (before tax) Rs.4 50% of earnings 10% Rs. 44 35%

You are required: a) To determine the pattern for raising the additional finance.  b) To determine the post-tax average cost of additional debt. c) To determine to cost of retained earnings and cost of equity, and d) Compute the overall weighted average after tax cost of additional Finance.

4.

A B Limited provides you with following figures:Profit Less Interest on Debentures @ 12% Income tax @ 50%  Number of Equity Shares (Rs. 10 each E.P.S (Earning Per Share) Rulings price in market PE ratio (Price/EPS)

Rs. 3,00,000 60,000 2,40,000 1,20,000 1,20,000 40,000 3 30 10

The company has undistributed reserves of Rs. 6,00,000. The company needs Rs.2,00,000 for expansion. This amount will earn at the same rate as funds already employed. You are informed that a debt equity ratio (Debt/Debt+Equity) higher than 35% will push the P/E ratio down to 8 and raise the interest rate on additional amount borrowed to 14%. You are required to ascertain the probable price of the share 1) If the additional funds are raised as debt; and 2) If the amount is raised by issuing equity shares. 5.

The abridged Balance Sheet as at 31st March, 1999 of a company is as under : Liabilities Shares capital equity shares of Rs. 10 each Revenue Reserves Trade Creditors

Rs. 1,00,000 1,50,000 50,000 3,00,000

Assets Fixed Assets Current assets: Stocks Debtors

Rs 1,80,000 70,000 50,000 3,00,000

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The company in the next year plans to undertake a major capital investment which will, by 31st March 2000, increase the fixed assets by Rs. 70,000. Turnover for the year expected to go up by 50% and the profits before interest and taxes also are anticipated to increase by the same percentage, as will the creditors, stock and debtors. The earnings before tax for the year ended 31st March, 2000 were Rs. 60,000 and the rate of company taxation was 50% Dividends at the rate of Re. 1 per share were paid at the end of that year. Dividends per share for  the year 99-00 will be at the same rate per share. Tax rate is not expected to change. The company needs large funds for the expansion programme and the finance division is examining the following alternatives for implementation. a) issue of 10% convertible debentures for Rs. 2 lakhs: each Rs. 1,000 debenture is convertible into 80 equity shares;  b) issue of debentures for Rs. 2 lakhs with interest warrants attached. Interest rate is to be fixed at 10% p.a. and each Rs. 1,000 debentures will enable the holder to purchase 50 equity shares at Rs. 15 each. c) making a rights issue, which would allow shareholders to buy 8 new shares at Rs. 12.50 each for every five shares  presently held. You are required to consider each of the alternatives separately. You are requested to indicate the effect of each financing method on the Balance Sheet as at 31st March, 1991 and also indicate the underlying per share (earnings per share based on the number of shares that have been issued as at 31st March, 1999). You are to assume that the debentures and rights issue will be made on 1st April, 1999. In the case of convertible debentures, assume that all the debentures are converted on 1st October, 1999. If funds are raised in excess of the needs of the company for 1999-00, you can assume that they will be held in the form of cash.

6.

The stock of Tetratronix Ltd. is currently fairly priced by the market at Rs.50. It has paid a dividend of Rs.2  per share for the financial year ending March 31, 1999. The company is in the advertising business and the order   book of the company for the current year is full. The prospects that some big multinational companies will become  part of their clientele in near future and high. The dividend per share paid by the company is expected to grow at a rate of 25% for the next three years. After that, the growth rate is expected to drop to a stable level, determine the expected growth rate of the dividends after three years. Cfa I-2000q-5 Mr. X, an investor, purchases an equity share of a growing company Y for Rs. 210. He expects the company 7. to pay dividends of Rs. 10.5, Rs. 11.025 and Rs. 11.575 in years 1, 2 and 3, respectively, and he expects to sell the shares at a price of Rs. 243.10 at the end of three years. (i)

8.

Determine the growth rate in dividends (ii) Calculate the current dividend yield. (iii)What is the required rate of return of Mr. X on his equity investment?

Kj

The capital structure of Swan & Co. comprising of 12% debentures, 9% preference shares and equity shares of Rs.100 each is in the proportion of 3: 2: 5. The company is contemplating to introduce further capital to meet the expansion needs by seeking 14% term loan from financial institutions. As a result of this proposal, the proportions of debentures, preference shares and equity would get reduced by 1/10. 1/15 and 1/6 respectively. In the light of above proposal calculate the impact on weighted average cost of capital assuming 35% tax rate, expected dividend of Rs. 9 per share at the end of the year and growth rate of dividends 5% No change in the dividend, growth rate and market price of share is expected after availing the proposed term loan.

9.

The following items have been extracted from the of the Balance Sheet of XYZ Company as at 31 / 12 / 1998 :Paid up Capital: Rs. 4,00,0000 Equity Shares of Rs. 10 each 40,00,000 Reserves and Surplus 60,00,000 Loans: 15% Non convertible Debentures 20,00,000 14% Institutional Loans 60,00,000 Other information about the company as relevant is given below:

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Year ended 31st Dec.

Dividend Earning Average Market Per Share Per Share Price per Share Rs. Rs. Rs. 1996 4.00 7.50 50.00 1997 3.00 6.00 40.00 1998 4.00 4.50 30.00 You are required to calculate weighted average cost of capital, using book values as weights and Earning/Price (E/P) ratio as the basis of cost of equity. 10.

M/s. Albert & Co: has the following capital structure as on 31st December, 1988: 10% Debentures Rs. 9% Preference shares Rs. Equity-5,0000 shares of Rs. 100 each. Rs. Total Rs.

3, 3,00,000 2,00,000 5,00,000 10,00,000

The equity shares of the company are quoted at Rs. 102/- and the company is expected expected to declare a dividend of Rs. 9 per share for 1988. The company has registered a dividend growth rate of 5% which is expected to be maintained. i) Assuming the tax rate applicable to the company company at 40% calculate the weighted average average cost of capital. State your  assumptions, if any. ii) Assuming, in he above exercise, that the company can raise additional term loan at 12% for Rs. 5,00,000 to finance an expansion, calculate the revised weighted cost of capital. The company’s statement is that it will be in a  position to increase i ncrease the dividend from Rs. 9 per share to Rs. 10 per share, but the t he business risk associated with new financing may bring down the market price from Rs. 102 to Rs. 96 per share. 11.

In considering the most desirable capital structure for 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 Cost of debt. Cost of equity total capital employed, % % 0 7.0 15.0 10 7.0 15.0 20 7.0 15.5 30 7.5 16.0 40 8.0 17.0 50 8.5 19.0 60 9.5 20.0 You are required to determine the optimal debt-equity mix for the company by calculating composite cost of capital.

12.

Given below is the summary of the Balance Balance Sheet of a Company as at 31st December,2001 : Liabilities

Rs.

Equity Share Capital 20,000 shares of Rs. 10 each Reserves & Surplus 8% Debentures Redeemable at par in 1989) Current Liabilities : Short-term loan Trade creditors

Assets

2,00,000 1,30,000

Rs. Fixed Assets Investments Current Assets

4,00,000 50,000 2,00,000

1,70,000 1,00,000 50,000 6,50,000

6,50,000

You are required to calculate Company’s weighted average cost of capital using balance sheet valuations. The following additional information are also available : i) 8% Debentures were issued at par. ii) All interest payments are up-to-date and equity dividend is currently 12%. iii) Short-term loan carries interest at 18% p.a.

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iv) The Shares and Debn. of the Co. are all quoted on the Stock Exchange and and current market prices are as : Equity Shares Rs. 14 each 8% Debentures Rs. 98 each v) The rate of tax for the Company may be taken at 35%. 13.

A company has the following capital structure. Rs. Ordinary Shares of Rs. 10 each fully paid 40,00,000 7.5% 7.5% cumul umulat ativ ivee pref prefeerenc rencee sha shares res of Rs.1 Rs.10 00 eac each full fully y paid paid 2,00 2,00,0 ,000 00 Reserves and retained profits 45,00,000 11% Long Term Loan 6,00,000 Total 93,00,000 In addition, the company has a bank overdraft for working capital and this averages to Rs. 10 lakhs. Interest thereon is 15% You are required to calculate the company’s overall rate of return on capital employed in order to ensure : I) Payment of all interests ii) Dividend pay out ratio of 60% iii) Payment of preference Dividend iv) Ordinary Ordinary shareholder’s shareholder’s dividend dividend is 12%. Assume the tax tax rate to be 35%

14.

Three companies A, B and C are in the same type of business and hence have similar operating risks. However, the capital structure of each of them is different and the following are the details : A. B C Equity Share Capital Rs. 4,00,000 2,50,000 5,00,00 (Face value Rs. 10 per share) Market value per share Rs. 15 20 12 Dividend per share Rs. 2.70 4 2.88 Debentures Rs. Nil 1,00,000 2,50,000 (Face value per debenture Rs. 100) Market value per debenture Rs. --125 80 Interest rate --10% 8% Assume that the current levels of dividends are generally expected to continue indefinitely and the incometax rate at 40%. You are required to compute the weighted average cost of capital of each company.

15.

The following is the data regarding two Companies ‘X’ and ‘Y’ belonging to the same equivalent risk class:Company Company X Y Number of ordinary shares 90,000 1,50,000 Market price per share Rs.1.20 Re.1.00 6% Debentures 60,000 Profit before interest Rs. 18,000 Rs. 18,000 All profits after. debenture interest are distributed as dividends. Required:a) Explain how under Modigliani & Miller Miller approach, an investor holding 10% of shares in Company Company ‘X’ will be better off in switching his holding to Company ‘Y’.  b) List the assumptions implicit in your answer to ‘a’ above. above.

16.

17.

Companies A and B belong to the same Business-risk class. Average net operating Income before interest of  each company is Rs. 100 lakhs. Other related information is given below : Co. A Co. B Market value of equity Rs. 400 lakhs Rs. 120 lakhs Market value of debentures - -Rs 200 lakhs Total market value Rs. 400 lakhs Rs. 320 lakhs Rate of interest on debentures is 15% p.a. and the same is considered to be certain by all the investors. ABC Ltd. has a capital of Rs. 10 lakhs in equity shares shares of Rs. 100 each. each. The shares are currently quoted at par. The company proposes declaration of a dividend of Rs. 10 per share at the end of the current financial year. The capitalisation rate of the risk class to which the company belongs is 12%.

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What will be the market price of the share at the end of the year if  1) a dividend is not declared? 2) a dividend is declared? Assuming that the company pays the dividend and has net profits of Rs. 5,00,000 and makes new investments of Rs. 10 lakhs during the period, how many new shares must be issued? Use the M.M. model. 18.

Companies X and Y are identical in all respects including risk factors except for debt/equity, X having issued 10% debentures of Rs. 18 lakhs while Y has issued only equity. Both the companies earn 20% before interest and taxes on their total assets of Rs. 30 lakhs. Assuming a tax rate of 50% and capitalisation rate of 15% for an all-equity company, compute the value of  companies X and Y using (I) net income approach and (ii) net operating income approach.

19.

From the following information, Calculate the expected rate of return of a portfolio : Risk free rate of interest 12% Expected return of market Portfolio 18% Standard deviation of an asset 2.8% Market Standard deviation 2.3% Co-relation Co-efficient of portfolio with market 0.8%

20.

The Beta Coefficient of Target Ltd. is 1.4. The company has been maintaining 8% rate of growth in dividends and earnings. The last dividend paid was Rs.4 per share. Return on Government securities is 10%. Return on market portfolio is 15%. The current market price of one share of Target Ltd. is Rs. 36. i) What will be the equilibrium price per share of Target Ltd.? ii) Would you advise purchasing the share?

21.

As an investment manager you are given the following information: Investment in equity shares of , A. Cement Ltd. Steel Ltd. Liquor Ltd. B. Governm Gove rnment ent of India Indi a Bonds Bond s

Initial price Rs 25 35 45 1,000 1,0 00

Dividends Rs. Rs . 2 2 2 140

Market price at the end of the year Rs. 50 60 135 1,005 1,00 5

Beta risk factor  , 0.8 0.7 0.5 0.99 0.9 9

Risk free return may be taken at 14% , You are required to calculate: i)Expected rate of returns of portfolio in each using Capital Asset Pricing Model (CAPM). ii) Average return of portfolio.

Valuation of Right Share 22.

AXLES Limited has issued 10,000 equity shares of Rs. 10 each . The current market price per share is Rs. 30. The company has a plan to make a rights issue of one new equity share at a price of Rs. 20 for every four shares held. You are required to : (i) calc calcul ulat atee the the theor oret etic ical al post post-ri -righ ghts ts pric pricee per per share share;; (ii) calcul calculate ate the theore theoretic tical al valu valuee of the rights rights alone; alone; (iii) (iii) show show the effect effect of the rights rights issue issue on the wealth wealth of a shareh sharehold older er who has 1,000 1,000 shares shares assumi assuming ng he sells the the entire rights; and (iv) show the the effect effect if the the same shareholde shareholderr does not not take any action action and and ignores ignores the issue. issue.

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MAFA-26

Rs. 100 shares of SBC Ltd. Were being quoted at Rs. 180. The company launched an expansion programme worth Rs. 25 crores and decided to make a public issue. Part of the issue was to be rights. Members were offered one right share for every six ordinary shares held by them, at a premium of Rs. 50 per share. Determine the minimum price that can be expected of the shares after the issue.

Preference Share Valuation and Analysis

PREFERENCE SHARE YIELDS To determine the rates of return earned, the preference share holders use following three yields : Current Yield When preference shares do not have a maturity date, the investors use the current yield to measure the return available from dividends. They merely divide the annual dividend payment by the current market price to calculate this yield as follows : Current =

Annual dividend Market price

For example, if the 9% preference shares of XYZ Company are sold for Rs.72, the current yield is 12.5 per  cent. Current Yield = Rs. 9 = 12.5 Rs.72 However, the planning or holding period return would more useful if the investment horizons are known. Planning or Holding Return To calculate the gross receipts expected to be earned from holding a preference share, the formula used is ;

HPR = D t + Pi

∆P and ∆P = P t - Pi

HPR = Planning or holding period return Dt = Dividend to be paid during the planned investment period Pi Pt

= Initial Price

∆P

= Change in prices during the planned investment period.

= Terminal price

For example, suppose the XYZ company 9 percent cumulative preference share (Rs.100 par) is sold for  Rs.72. An investor exports this to increase in price by Rs.18 due to expected decline in interest rates. This change, he feels, would take about two years. On this basis, the holding period return would be : HPR = D t + Pi

∆P

= Rs.18 + Rs.18 Rs.72 HPR = 50%  Yield to the Call Date

=

Rs.36 Rs.72

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If the issues are callable, their dividend payments cannot be expected to continue indefinitely. In this case, the probable call date is used as an investment terminal date to evaluate.

Yc =

D

Cp - Pi + n

t (Pi + Cp) / 2

REVIEW PROBLEMS 1.

Consider a share of preferred stock with a par value of Rs.100 that pays an 12% annual dividend, or Rs.12. If  the discount rate for this share is 15%, what would the preference share be worth ?

2.

PHIND pays a Rs.2.76 dividend on each preference share. What is the value of each preference share if the required rate of return of investors is 12 percent ?

3.

What is the value of a preference share where the dividend rate is 18 percent on a Rs.100 par value ? The appropriate discount rate for a stock of this risk level is 15%.

4. The preference shares of KD Group are selling for Rs.47.50 per share and pays a dividend of Rs.2.35 in dividends. What is your expected rate of return if you purchase the security at market price ? 5.

You own 250 preference shares of XYZ company which currently sells for Rs.38.50 per share and pays annual dividends of Rs.6.50 per share. (a) What is your expected return ? (b) If you required a 13% return, given the current price, should you sell or buy more preference shares ?

6.

Pioneer’s preference shares are selling for Rs.44 per share in the market and pays a Rs.4.40 annual dividend. (a) What is the expected rate of return on the preference shares ? (b) If an investor’s required rate of return is 12 percent, what is the value of a preference share for that investor ? (c) Should the investor acquire the preference shares ?

Equity Shares (i) The Value for the ‘Rights-on’ Period : Anyone acquiring shares after the meeting day and before the record day receives the privilege of subscribing to new shares. Consequently, the privilege represented by a right has value in the ‘right-on’ period. This value, furthermore, is reflected in the market price of an equity share. The theoretical value of one equity share right in the right-on period can be described by the following formula :

V =

M1 - S R + 1

V = M1 =

Theoretical value of one equity share right. Market value of one share of equity in the ‘right-on’ period.

S = R =

Subscription price of one share of new equity. Ratio of old to new equity; that is, the number of shares an investor must own to receive new share.

one

To illustrate, assume that XYZ Corporation intends to raise Rs.one crore through pre-emptive rights. The equity shares of the XYZ Corporation has been selling at Rs.30 a share so the subscription price is expected to be Rs.25 a share. In addition, the shareholders of record will be able to purchase one new share for every four  shares owned. What is the theoretical value of one right in the rights-on period ?

V =

M1 - S R + 1

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V =

Rs.30 - Rs.25 4 + 1

V =

Re.1

(ii) The value in the ‘Rights-off’ Period : The subscription right issues to shareholders following the record day has a value completely divorced from its equity share during the ‘rights-off’ period. And this value is determined by supply and demand in the stock market during the life of the rights issue. The theoretical value of one right can be calculated as follows :

V =

M2 - S R + 1

M2 =

Market value of one share of equity in the rights-off period. By substituting the XYZ

where

Corporation’s values, we get : V =

M

2

- 25

4 (iii) The theoretical value of the Equity : In planning investment strategies, investors are concerned with the theoretical value of the equity share after the rights issue has expired. With such information available, they can estimate the worth of their holdings ex-rights. To calculate the theoretical value of an equity stock ex-rights, following formula can be used : P = M1 R + S R + 1 where : P =

1.

Global enterprises is considering a rights offering to raise Rs.50 crore. Currently this firms Has 2,50,00,000 share selling for Rs.50 per share. The subscription price on the new share would be Rs.40 per share. a. b. c.

2.

Value of the equity share ex-rights. REVIEW PROBLEMS

How many shares must be sold to raise the desired funds ? How many rights are necessary to purchase one equity share ? Rs.50 crores

RND Industries is planning to raise Rs.35 crore through the sale of new equity under a rights offering. The subscription price is Rs.70 per share while the share currently sells for Rs.80 per share, rights on. Total outstanding shares equal 10 crore. Of this amount, Kamal Kant owns 1,00,000 shares. (.i) (ii) the (iii) the

How many equity shares will each right permit its owner to purchase ? What will be the total value of Kamal Kants’s rights a day before the ex-rights date, assuming that market price of RND Industries stock remain Rs.80 per share ? After the ex-rights date, if the market value of each RND Industries equals re.0.25, what must be ex-rights market price of RND Industries ?

3. XYZ Company is conducting the annual election for its 5 member Board of directors. The company has 15,00,000 equity shares. (.i) elect

Under a major voting system, how many shares must a shareholder own to ensure being able to him or her choices to each of the five director seats ?

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MAFA-29

(ii) to

Under a cumulative voting system, how many shares must a shareholder own to ensure being able elect his or her choice to two of the director seats ?

(iii)

Anial Sharma holds 20% of XYZ Company’s shares. How many directors can Anil elect under a cumulative voting system ?

4.

Zen Group’s equal shares are currently selling for Rs.45 per equity share. The company paid rs.2.70 dividend on per share and has a projected growth rate of 12%. If you purchase the equity shares at market price, what is your expected rate of return ?

5.

K. C. Sharma owns equity shares in Novex Auto. Novex is planning a rights offering in which 7 shares must be owned by one additional share at a price of Rs.15 Novex’s equity shares are currently selling for Rs.63 per  share. a. What is the value of a Novex right ? b. At the time of offering announcement, Sharma’s assets consisted of rs.1,50,000 in cash and 4900 shares of Novex. List and show the value of Sharma’s assets prior to the ex-rights date. c. List and show the value of Sharma’s assets on the ex-rights date if Novex equity sells for rs.60 per  share on date . d. List and show the value of Sharma’s assets if Sharma sells the Novex rights on the ex-rights date.

6.

PLC is about to raise finance by increasing its 12 crore shares with a one for three rights issue. Total debt in the capital structure comprises the following :

Book value (Rs. crores) 16% debentures 16% bank loan Various short-term loans and overdrafts

10.0 10.0 0.2

The debentures have a further life of seven years and rate redeemable at par. The fixed-interest 16% bank loan is guaranteed by the bank to be available for a further nine years. Both the debentures and the bank loan were initially arranged several years ago when interest rates were high. Interest rates have since fallen. The money raised by the rights issue will be used as follows : 1.

To fund a new contract to which PLC already committed and which requires an initial outlay of Rs.1 crore. The contract has a profitability index (ratio of present value [ PV ] of future net cash inflows to PV of initial capital outlay) of 1.4, and full details of the contract have been public knowledge for several months.

2. To reduce borrowing by buying back, at current market value, and cancelling the Rs.10 crores debenture issue. The debentures are currently priced in the market to yield 8% p.a., the current yield on such corporate debt. Total financial required in 1 and 2 will be rounded up to the next whole Rs.10,00,000 for the purpose of the rights issue. The excess funds raised will be used to reduce short-term borrowings and overdrafts. The company intends to announce full details of the rights issue on 1 July when the market price per share prior to the announcement is expected to be Rs.50. The company is confident that the whole issue will be purchased, but the managing director is concerned that the discount at which the issue is made may raise the cost of equity capital and hence the weighted-average cost of capital. (a) Calculate (.i)

The issue price per share;

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(ii) (iii)

MAFA-30

The theoretical ex-right price per share; The value of the right attached to each P.L.C. share before being traded ex-rights.

(b) Briefly explain whether the concern of the managing director is justified. (.c) Discuss whether this rights issue could be expected to alter the cost of equity and / or the weighted-average cost . of capital in any way. (d) After setting the issue price 9calculated in (a) but before announcing the rights issue, PLC decides to reduce borrowings by redeeming the 16% bank loan at its face value of Rs.10 crores rather than buying back the debentures at market value. The possibility of the redemption at face value is now known only to the company and its bankers but will become public knowledge when the rights issue is announced on 1 July. The market had expected the bank loan to run for its full remaining seven years of life. The excess cash generated by the rights issue, after reducing borrowings and funding the Rs.1 crore contract, will be invested in a project which has a profitability index of 1.2. The market is not aware of this project and will remain unaware until its details become public knowledge when the rights issue is announced. (.i) The share price on 1 July immediately after the announcement of the rights issue but before the shares are trade ex-rights; (ii)

The theoretical ex-rights price per share.

Briefly explain your calculations and also explain whether they assume that the market is displaying the weak, simi-strong or strong level of market efficiency.

Equity valuation and Analysis REVIEW PROBLEMS 1.

R.J. Seth has invested in XYZ Chemicals. The capitalisation rate of the company is 15 per cent and the current dividend is rs.2.00 per share. Calculate the value of the company’s equity share if the company is slow sinking with an annual decline rate of 5% in the dividend.

2.

What would be the value of the equity share of XYZ Chemical of previous problem if the company shows no growth but is able to maintain its dividend.

3. Repeat the XYZ Chemicals problem (1) and assume that it grows at an average rate, which is taken to be an average annual increase in dividend of 7 per cent. Compute the value of equity share. 4.

An investor has invested in a company which is growing at an above-average rate, translated to an annual increase in dividends of 20 per cent for 15 years. Thereafter dividend growth returns to an average rate of  7 per cent. The capitalisation rate of the company is 9 per cent and the current dividend per equity share is Rs.1.00 per share. Determine the value of the equity share.

5. Van Products currently pays a dividend of Rs.2.00 per share and this dividend is expected to grow at a 15% annual rate for 3 years, then at a 12% rate for the next three years, after it is expected to grow at a 5 per  cent rate forever. (a) What value would you place on the equity if 9% of return were required ? (b) Would your calculation change if you expect to hold the equity only 3 years ? 6. were 10

Samgam Enterprise recently paid an annual dividend of Rs.3.50 per share. Earnings for the same years Rs.7.00 per share. The required return on equity with similar risk is 12%. Dividends are expected to grow percent per year indefinitely. Calculate Sangam’s ‘normal’ price-earning ratio.

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7.

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R.N. Verma currently earns Rs.3 per share. His return on equity is 25 per cent and he retains 50% of its earnings (both figures are expected to be maintained indefinitely). Stocks of similar risk are priced to return

8.

15%. What is the intrinsic value of Verma’s stock ?

As a firm is operating in a mature industry, Novex Industries is expected to maintain a constant dividend payout ratio and constant growth rate of earnings for the foreseeable future. Earnings were Rs.4 per share in

the recently completed fiscal year. The dividend payout ratio has been constant 50 per cent in recent

years

and is expected to remain so. Novex’s return on equity is expected to remain 15 per cent in the

future, and you required 12 per cent return on the equity.

(a) Using the constant growth dividend discount model, calculate the current value of Novex equity share. After an aggressive acquisition and marketing programme, it now appears that Novex’s EPS and ROE will grow rapidly over the next two years. You are aware that the dividend discount model can be useful in estimating the value of equity even when the assumption of constant growth does not apply.

(b) Calculate the current value of Novex’s equity, using the dividend discount model, assuming that Novex dividend will grow at a 20% rate for the next two years, returning in the third year to the historical growth rate for the foreseeable future.

9.

BPT paid Rs.2.75 in dividends on its equity shares last year. Dividends are expected to grow at 12 per 

cent

annual rate for an indefinite number of years. a.

If BPT’s current market price is Rs.37.50, what is the stock’s expected rate of return ?

b.

If your required rate of return is 14 per cent, what is the value of the stock for you ?

c.

Should you make the investment ?

10.

The market price for Super Iron’s equity is Rs.65 per share. The price at the end of one year is expected

to be

Rs.90, and dividends for next year should be Rs.2.90. What is the expected rate of return ?

11.

Gandhi Petro is expected to pay Rs.3.00 in dividends next year, and the market price is projected to be

Rs.75

by year end. If the investor’s required rate of return is 20 percent, what is the current value of the stock ?

12.

On Sudha Enterprises’ equity shares, the dividend paid at Rs.1.32 per equity share last year and this is expected to grow indefinitely at an annual 7 per cent rate. What is the value of each equity share of Sudha Enterprises if the investor requires an 11 per cent return ?

13.

An investor holds an equity share giving him an annual dividend of Rs.30. He expects to sell the share for  Rs.300 at the end of a year. Calculate the value of the share if the required rate of return is 10%.

14.

Ahuja Textile’s equity share currently sells for Rs.23 per share. anticipates a

The company’s finance manager 

constant growth rate of 10.5 per cent and an end-of-year dividend of Rs.2.50.

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15.

a.

What is the expected rate of return ?

b.

If the investor requires a 17% return, should he purchase the stock ?

RAJ’s equity shares currently sells for Rs.22.50 per share. The finance manager of RAJ anticipates a constant

16.

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growth rate of 12 per cent and an end-of-year dividend of Rs.2.50

a.

What is your expected rate of return if you buy the stock for Rs.25 ?

b.

If you require a 18 percent return, should you purchase the stock ?

Firms A, B and C are similar. Firm A is the most progressive and trades at a 18/1 P/E multiple. Firm B is less progressive, is not publicly traded, and has an EPS of Rs.1.20. Firm C is least progressive and trades at

17.

a 15/1/P/E ratio. What is the intrinsic value of firm B ?

Companies R, S and T are similar. Company R is privately held, and has a book value of Rs.40 per share. Company S has a market price of Rs.15 and a book value of Rs.12 Company T has a market value (MV)

of

Rs.82 and a book value of Rs.62. What is a possible value for company R ?

18.

A firms’ current EPS is Rs.6, its dividend payout is 40 percent, and its growth rate of EPS is 10%. The

normal P/E multiple is 15/1. What is the stock’s value using the capitalisation of earnings methods ? What is its value in 3 years using the same method ?

19.

For the firm in problem 18, what is the current value and the value in 4 years using the centralisation of  dividends method ? If an investor expects a dividend payout of Rs.75 per cent, what is the firm’s current

value

20.

and value in 3 years using the capitalisation of earnings-and-dividends methods ?

Companies X, Y and Z are in the same industry. Company X has a 5 per cent growth rate, pays @ Rs.2.00 dividend, and sells for Rs.25 per share. Company Y pays a Rs.4 dividend, has an 8 per cent growth rate, and

is not publicly traded. Company Z sells for Rs.60 pays a Rs.6 dividend, and has a 2 per cent

growth rate,.

21.

What is the value of the stock of Company Y ?

Given the following : current dividend, Rs.4; dividend payout, 40 per cent; normal capitalization rate, 12 per  cent; actual capitalization rate, 15 per cent. What is the current value of the stock ? If it increases its dividend

payout to 60 per cent, how much will the current value go up or down ? Why did it do

this ?

22.

S.K. Verma is a conservative investor who demands 10 percent interest on his fixed investment but 20 percent

from his equity investments. He has been considering the purchase of an equity that pays

Rs.2.50 in

dividends this year and whose dividends are expected to grow at 10 percent per year for 

the next three years.

Earnings this year are Rs.5 per share and are expected to grow at 20 percent for 

the next seven years.

Stocks growth at this rate generally sell at 40 times earnings. What price Verma

pays for this equity ?

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23.

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Refer to problem 22, R.D. Gupta, another investor, would consider investment in this equity that S.K.

Verma is

interested in, but he thinks he should earn a yield of 15 percent rather than 20 percent. What price

would

Gupta consider fair ?

24.

Ashok Sood is suspicious of the estimates prepared by S.K. Verma and R.D. Gupta. He has carefully examined the company and thinks dividends will grow at 6 percent, earnings growth will be 16 percent, and

the

future P/E ratio will be 25. Like R.D. Gupta, he thinks the discount rate should be 15 percent (Refer to problem 22 and 23). What should Sood pay for the equity ?

25.

H.S. Bhatia just learned that he can buy the stock under discussion for Rs.200 per share (refer to problems

22

to 24). Based upon R.D. Gupta’s assumption, what yield will Bhatia earn ? Should he buy ?

26.

Refer to problems 22 to 25, what yield will H.S. Bhatia earn if he buys on the basis of Ashok Sood’s

estimates?

27.

Should he buy ?

H.P. Rao Can buy an equity that will pay Rs.2.00 in dividends annually over the next 3 years. The

earnings of

the company are expected to grow and the equity is expected to reach a price of Rs.70 per share

at the end of

three years. This is a conservative investment and Rao expects a yield of 18 percent. What price

should Rao

pay for the equity if he wishes to earn 18 percent ?

28.

R.P. Singh wants to buy stock in XYZ company. It traded yesterday at Rs.405. The company paid a

dividend

last year Rs.2.40 per share. Dividends have grown at 15 per cent per year, and earnings at 20

percent per

year, for the last 5 years. Earnings per share were Rs.4.75 last year and are expected to be

Rs.6.50 this

year. Earnings are expected to grow at a 20 percent rate next year and the year after, and that

stock should

enjoy a P/E of 35.

The company announced that the stock was to be split 2 for 1 shortly.

Dividends should

increase as they have in the past. What yield would R.P Singh earn for the investment if 

he purchased it at

Rs.405 and held it for three years ?

29.

Given the following : EPS, Rs.5; Market price Rs.60; Growth rate of sales, 6^, and of EPS, 9%; Dividend payout, 70%; Normal capitalisation rate, 12%. Using the capitalisation and dividend growth methods, what

is

the value of the stock ?

1.

An investor is seeking the price to pay for a security, whose standard deviation is 3.00 per cent. The correlation coefficient for the security with the market is 0.8 and the market standard deviation is 2.2. per cent. The return from government securities is 5.2 per cent and from the market portfolio is 9.8 per cent. The investor knows that, by calculating the required return, he can then determine the price to pay for the security. What is the required return on the security ?

2.

The following is the Balance Sheet as at 31 st March, 1998 of S Co. Ltd. ; Rs. Share Capita :

Rs.

Tax Shield Education Centre 10,000 equity shares of Rs. 100 each fully paid up 25,000 11% cum preference shares of Rs. 10 each fully paid up Reserves and surplus Secured loans Unsecured loans Trade creditors Outstanding expenses Represented by Fixed assets Current assets Advances and deposits

MAFA-34 10,00,000 2,50,000

55,00,000 37,00,000 3,00,000

12,50,000 25,00,000 20,00,000 12,00,000 18,00,000 7,50,000 95,00,000

95,00,000

The company plans to manufacture a new product in line with its current production, the capital cost of  which is estimated to be Rs. 25 lakhs. The company desires to finance the new project to the extent of Rs. 16 lakhs by issue of equity shares at a premium of Rs. 100 per share and the balance to be raised from internal sources. Additional information made available to you are : (a) Rate of dividends declared in the past five years i.e. year ended 31 st March, 1998, 31st March, 1997, 31st March, 1996, 31st March, 1995 and 31st March, 1994 were 24%, 24%, 20%, 20% and 18% respectively. (b) Normal earning capacity (net of tax) of the business is 10%. (c) Turnover in the last three years was Rs. 80 lakhs (31.3.98), Rs. 60 lakhs (31.3.97) and Rs. 50 lakhs (31.3.96). (d) Anticipated additional sales from the new project Rs. 30 lakhs annually. (e) Net profit tax from the existing business which was 10% in the last three years is expected to increase to 12% on account of new product sales. (f) Income-tax rate is 35%. (g) The trend of market price of the equity share of the company, quoted on the Stock Exchange was : Year

High Low Rs. Rs. 1997-98 300 190 1996-97 250 180 1995-96 240 180 You are required to examine whether the company’s proposal is justified. Do you have any suggestions to offer  in this regard ? All workings must form part of your answer.

3.

Pinto Limited has the following Data for projections for the next five years. It has n existing Term Loan of Rs. 360 lakhs repayable over next five years and has got sanctions for new term loan for Rs. 500 lakhs which is also repayable in five years. As a finance manager you are required to calculate (I) Debt Service Coverage Ratio and (ii) Interest Service Coverage Ratio for each year and the average for 5 years. (Rs. In lakhs) Particulars 1 2 3 4 5 Profit after tax 480 575 635 650 685 Depreciation 155 150 140 135 120 Taxation 125 203 254 275 299 Interest on Term Loans 162 125 87 50 16 Repayment of Terms loan 178 178 178 178 148

4.

Existing Capital Structure of Zenith Enterprises is as follows : Rs. Crores Paid up Share capital of Rs. 10 each 10 Reserves and Surplus 15 Debentures bearing 14% interest per year 15 An expansion programme for the company is under contemplation. It requires Rs. 20 crores and promises an increases an increase of Rs. 6 crores in the EBIT from its existing level of Rs. 8 crores. Three financing alternatives for obtaining the requisite amount of Rs. 20 crores are under consideration. The first alternative is to issue equity shares of Rs. 10 par at a premium of Rs. 40 each. Share issue expenses as also underpricing of the issue in comparison to ruling market price result in net proceeds of Rs. 40 for every new share issued.

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The second alternative is to borrow the requisite amount at 15% rate of interest per year. The third alternative is a combination of the first and second, under which Rs. 10 crores will be borrowed at 15% rate of interest per year and the balance amount obtained by share issue as per terms indicated in the first alternative. Applicable Corporate Income Tax Rates is 40%. Required : (a) If the expansion programme is to be considered only if the EPS increases from its existing level, indicate whether  the programme qualifies for consideration. (b) At what level of EBIT will EPS be equal to zero under each of the financing alternative? (c) Determine the points of indifference among the three financing alternatives and the corresponding EPS (d) If the chances of a more than 20% decline EBIT after expansion programme are extremely remote which financing alternative would you recommend and why ?

33. A chemical company has been growing at a rate of 18% per year in recent years. This abnormal growth rate is expected to continue for another 4 years, then it is likely to grow at the normal rate (g n) of 6%. The required rate of return on the shares by the investment community is 12%, and the dividend paid per share last year was Rs. 3 (D 0 = Rs. 3). At what price, would you, as an investor, be ready to buy the shares of this company now (t = 0), and at the end of years 1,2,3,4 respectively? Will there be any extra advantage by buying shares at t = 0, or in any of the subsequent four  years, assuming all other things remain unchanged ? KJ A transport company is interested in measuring its cost of specific types of capital, as well as its overall cost. The 5. 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%. The shareholders are in the 30% marginal tax  bracket. Debentures : The company can sell 15-year 14% debentures of the face value of Rs. 1,000 for Rs. 970. In addition, an underwriting fee of 1.5% of the face value would be incurred in this process. Preference shares : 15% preference shares, having a face value of Rs. 100, can be sold at a premium of 10%. An underwriting fee of Rs. 2 per shares is to be paid to the underwriters. Equity shares : The company’s equity shares are currently selling for Rs. 125 per share. The firm expects to pay Rs. 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 (RS) 1 10.60 2 11.24 3 11.91 4. 12.62 5 13.38 6 14.19 It is expected that the new equity shares can be sold at Rs. 123 per shares. The company must also pay Rs. 3 per share as underwriting fee. Market and book values for each type of capital are as follows : Long-term debt Preference shares Equity shares Retained earnings

Book value 18,00,000 4,50,000 60,00,000| 15,00,000| 97,50,000

Market value 19,30,000 5,20,000 100,00,000 124,50,000

(i) Calculate the specific cost of each source of financing. (ii) Determine the weighted average cost of capital using (a) book value weights, and (b) market value weights. KJ

6.

The following is the summarised Balance Sheet of X & Co. Ltd., as at 31st December, 1975 : Rs. in lakhs. Share capital 512.00 Reserve and surplus 1,031.50 Loans ; 1,543.50 Secured 1,048.73 Unsecured 382.77 1,431.50

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Total Fixed Assets Current assets Loans and Advances

2,975.00 1,701.63 1,657.60 719.50 2,377.10 1,103,73

Less : Current liabilities

1,273.37 Total 2,975.00 The company has been granted an Industrial Licence for manufacturing a new product, the capital cost of which is expected to be around Rs. 9 crores. The company desires to finance the new project to the extent of Rs. 4.00 crores partly from the internal resources and partly by accepting public deposits, the balance of Rs. 5.00 crores by issue of fresh capital i.e. 2,00,000 Equity Shares of Rs. 100 each at a premium of Rs. 150 per share. You are required to make a report to the Directors of the company stating your reasons whether or not the premium amount of Rs. 150 per share is, in your opinion, justified. In order to enable you to issue the report, which is to be forwarded to the Controller of Capital Issue for his sanction to the fresh issue of capital, you are furnished the following additional information : 1. Issued, subscribed and paid up capital as on 31 st Dec. 1975 : Rs. 5,00,000 Equity Shares of Rs. 100 each, fully paid 5,00,00,000 12,000 9% cumulative preference shares of Rs. 100 each, fully paid. 12,00,000 5,12,00,000 2. Rate of dividend on Equity shares for the last five years : 1975 … 22% 1974 … 22% 1973 … 20% 1972 … 20% 1971 … 18% 3. The normal earning capacity (net of tax) of the business may be presumed at 8%. 4. Annual turnover for the last 3 years : 1975 … Rs. 57 crores 1974 … Rs. 55 crores 1973 … Rs. 50 crores 5. Expected annual turnover of the new project for the next three years would be Rs. 10 crores. 6. The net profit before tax had remained around 10% of the sales during the last three years. It is expected that the net profit would go up to 12 % in the future on account of the internal savings and the new product sales. 7. The rate of tax may be presumed at 65%. 8. The trend of market price of the equity shares of X & Co. Ltd., as per stock exchange quotation, was as follows :

1975 1974 1973

High 550 535 525

Low 450 420 400 ( RO 1st  CA Final Nov. 76)

VENTURE CAPITAL Venture capital represents financial investment in a highly risky proposition in the hope of earning a high rate of return. While the concept of venture capital is perhaps as old as the human race, the practice of  venture capitalism has remained somewhat fragmented and individualised through its long history. Only in the last five decades or so has the field of venture capital acquired a certain coalescence, maturity, and sophistication, particularly in the U.S. Features of Venture Capital

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While the terms and conditions on which venture capital is provided are not standardised, the following appear to be the silent features of venture capital arrangements:

•

The venture capital firm (VCF) is inclined to assume a high degree of risk in the expectation of  earning a high rate of return.

•

the VCF, in addition to providing funds, takes an active interest in guiding the assisted firm.

•

The financial burden for the assisted firm tends t o be negligible in the first few years.

•

The VCF normally plans to liquidate its investment in the assisted firm after 3 to 5 years.

Evolution of Venture Capital The origin of venture capital, in its modern form, may be traced to General Doriot who established the American Research and Development Fund at the Massachusetts Institute of Technology in 1946 to finance the commercial exploitation of new technologies developed in the U.S. universities. The Small Business Act of the U.S., which permitted the Small Business Administration to license and even support financially small business investment companies engaged in venture capital finance, provided fillip to the growth of venture capital finance. The larger companies in the U.S. like Xerox, 3M, and General Electric too entered the field with their venture capital divisions. These examples from the U.S. stimulated the development of venture capital in Japan. Though the initial efforts, made in the early seventies, to introduce venture capital in Japan were rather unsuccessful, the changed environment of the eighties (which has witnessed a phenomenal growth of hi-tech industries) provided a fertile ground for the blossoming of venture capital in Japan. Inspired by the success of venture capital abroad, initiatives have been taken in India to promote venture capital.

Consequences of Rights Issue What are the likely consequences of a rights issue on the market value per share, value of a right, earning per share, and wealth of shareholder? To answer this question, let us look at the illustrative data of the Right and Left Company given in Table 17.1

Table 17.1 Illustrative Data of the Right and Left Company Paid-up equity capital (1,000,000 shares of Rs. 10 each)

Rs. 10,000,000

Retained earnings

20,000,000

Earnings before interest and taxes

12,000,000

Interest Profit before tax

2,000,000 10,000,000

Taxes (50 per cent)

5,000,000

Profit after tax

5,000,000

Earnings per share Market price per share

Rs. 5 Rs. 40

(Price earnings ratio of 8 is assumed) Number of additional equity shares proposed to be issued as rights shares Proposed subscription price Number of existing shares required for a rights share (1,000,000/200,000) Value of a Share

200,000 Rs. 20 5

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The value of a share, after the rights issue, is expected to be NP0 + S ———— N+1 where

(17.1)

N = number of existing shares required for a rights share P0 = cum-rights market price per share S = subscription price at which the rights share are issued.

The rational behind this formula is as follows: For every N shares before the rights issue, there would be N + 1 shares after the rights issue. The market value of these N + 1 shares is expected to be the market value of N cum–rights shares plus S, the subscription price. Applying this formula to the data given in Table 17.1 we find that the value per share after the rights issue is expected to be: 5 × 40 + 20 —————— = Rs. 36.67 5+1 Value of a Right1 The theoretical value of a right is P0 – S ——— N+1

(17.2)

1

The ‘right’ discussed here, as clarified earlier, is different from the ‘right’ traded in the market place. Of  course, the ‘right’ discussed here can be directly translated into the ‘right’ traded in the market place. For  the company considered in our example five such ‘right’ are equal to one ‘right’ traded in the market place. This value is determined as follows. The difference between the market price of a share after the rights issue and the subscription price is the benefit derived from N rights, which are required along with the subscription price to obtain one rights shares. This means that the value of N rights is:  NP0 + S N(P0 – S)  ————— – S = ——————  N + 1 N+1

(17.3)

Hence the value of one right is  N (P0 – S) 1 P0 – S  —————— × —— = —————  N + 1 N N–1

(17.4)

Applying the above formula to the data given in the Table 17.1, we find that the value of a right of the Left and Right Company is 40 – 20  ————— = Rs. 3.33 5+1

Wealth of Shareholders The wealth of existing shareholders, per se, is not affected by the rights offering, provided of course, the existing shareholders exercise their rights in full or sell their rights. To illustrate this point, consider what happens to a shareholder who owns 100 equity shares of the Left and Right Company that has a market value of Rs. 40 each before the rights issue. The impact on his wealth when he exercise his rights, when he sells his rights, and when the allows his rights to expire is shown below.

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He exercises his rights Market value of original shareholding at the rate of Rs. 40 per share. = Rs. 4,000 Additional subscription price paid for 20 rights shares at the rate of Rs. 20 per share = Rs. 400 Total investment = Rs. 4,400 Market value of 120 shares at the rate of Rs. 36.67 per share after the rights subscription = Rs. 4,400 Change in wealth (Rs. 4,400 – Rs. 4,400) = Rs. 0 He sells his rights Market value of original shareholding at the rate of Rs. 40 per share = Rs. 4,000 Value realised from the sale of 100 rights at Rs. 3.33 per right = Rs. 333 Market value of 100 shares held after the rights issue at the rate of Rs. 36.67 per sahre = Rs. 3,667 Change in wealth (Rs. 3,667 + Rs. 333 – Rs. 4,000) = Rs. 0 He allows his rights to expire Market value of original shareholding at the rate of Rs. 40 per share = Rs. 4,000 Market value of 100 shares held after the rights issue at the rate of Rs. 36.67 per share = Rs. 3,667 Change in wealth (Rs. 3,667 – Rs. 4,000) = Rs. (333)

Setting the subscription price Theoretically, the subscription price is irrelevant because the wealth of a shareholder who subscribes to the rights shares or sells the rights remains unchanged, irrespective of what the subscription price is. To illustrate this point, consider a shareholder who has N shares valued at P 0 and who enjoys the right to subscribe to an additional share for S. His total investment would be: NP0 + S The value of his shareholding after subscription would be: Number of shares This is equal to:

× Market value per share after rights issue

(17.5)

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(N + 1) ×

NP0 + S —————— = NP 0 + S (N + 1)

Thus the value of his shareholding after subscription is equal to the value of his investment, irrespective of  the subscription price S. In practice, however, the subscription price is important. Existing shareholders do not like the idea of S being higher than P 0 because when S is higher than P 0, the market value after issue would be lower than S. Non-shareholders, who have an opportunity to subscribe to shares not taken by existing shareholders, will have no interest in the shares if S is higher than P 0 because they would then suffer a loss when the market value falls below S after the issue.

Due to the above considerations, S has to be set equal to or lower P 0. A value of S equal to P 0 is not advisable because it has no appeal to existing shareholders and other investors as they do not see any opportunity of gain in such a case. So, S has to be set lower than P 0. In determining S, the following considerations should be borne in mind. 1.

The lower the S in relation to P0, the greater is the probability of the success of offering.

2.

When S is set low, a large number of rights shares have to be issued to raise a given amount of  additional capital. IF the company wishes to maintain a certain level of earnings per share and/or  dividend per share, it would find it difficult to do so when S is set low.

3.

The expectations of investors, the fluctuation of the share, the size of rights issue in relation to existing equity capital, and the pattern of shareholding are important factors in determining what S is acceptable to investors.

The subscription price for a rights issue may be decided after taking into account several things: state of  the capital market, the trend of share prices in general and of the company’s shares in particular, the ruling cum-rights price, the ratio or proportion of the rights issue to the existing equity capital of the firm, the break-up value of the share, the profit-earning capacity of the firm, the dividend record of the firm, and the resources position of the firm.

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Valuation of Securities

The objective of financial management is to maximise the market value of the firm’s equity shares. hence managers must know how equity shares are valued and understand how their investment and financing decisions influence the value of non-equity claims, the managers must also understand how non-equity claims (bonds in  particular) are valued. Knowing how to value securities (bonds and equity shares, in the main) is as important for investors as it is for  managers. Current and prospective investors (shareholders, bondholders, and others) must understand how to value securities. Such knowledge is helpful to them in deciding whether that should buy or sell securities at the prices  prevailing in the market place. This chapter discuss the basic discounted cash flow valuation model and its application to bonds and equity shares. In addition, it looks at non-discounted cash flow approaches to equity valuation. It is divided into five sections :

• Basic valuation model • Bond valuation • Equity valuation : dividend capitalisation approach • Equity valuation : earnings capitalisation approach • Equity valuation : other approaches BASIC VALUATION MODEL

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The value of any asset, real or financial, is equal to the present value of the cash flows expected from it. Employing the present value techniques discussed in chapter 4, the value of any asset cam be expressed as : V0 = C1 . + C2 . + … + Cn . (6.1) 1 2 n (1 + k) (1 + k) (1 + k) where V0 = value of the asset at time zero Ct = cash flow expected at the end of year t k = discounted rate applicable to the cash flows n = life of the asset

Using the present value interest factor notation, PVIF k,n, Eq. (6.1) can be rewritten as : V0 = C1 x PVIFk,1 + C2 x PVIFk,2 + … + Cn x PVIf k,n For example, an investor expects to receive the following cash flows from an asset : Year 1 2 3

Cash Flow 20 30 220

The appropriate discount rate for the cash flows is 16 per cent. Given the above information, the value of the asset can be calculated as follows : V0 = 20 x OVIF16%,1 + 30 x PVIF16%,2 + 220 x PVIF16%,3 =20 x 0.862 + 30 x 0.743 + 220 x 0.641 =17.24 + 22.29 + 141.02 =180.55 Key Inputs

From the foregoing discussion it is clear that the key inputs to the valuation process are cash flows, timing, and discount rate. Cash Flows Cash flows expected from an asset may be constant or fluctuating or growing. Sometimes the asset may provide only a terminal cash flow. Cash flows are normally expressed in nominal terms. This means that they reflect the effect of inflation. Timing  It is customary to specify the timing along with the estimates of the cash flow. In the above example, the cash flows of 20, 30 and 220 were expected to occur at the end of years 1,2, and 3 respectively. Together, the cash flow and its timing fully define the returns from the ownership of the asset.  Discount Rate The discount rate must be commensurate with the risk characterising the cash flows. In general, higher the risk level, higher the discounted rate — this was the central message of Chapter 5. If the cash flows are expressed in nominal terms, The discount rte, too, should be defined in nominal terms. BOND VALUATION Terminology

A bond or debenture (hereafter referred to as only bond), akin to a promissory note, is an instrument of debt issued by a business or government unit. In order to understand the valuation of bonds, we need familiarity with certain bond-related terms.  Par Value This is the value stated on the face of the bond. It represents the amount the firm borrows and  promises to repay at the time of maturity. Usually the par or face value of bonds issue by business fimrs is rs.100. Sometimes it is Rs.1,000.

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Coupon Rate and Interest  A bond carries a specific interest rate which is called the coupon rate. The interest  payable to the bond holder is simply : par value of the bond x coupon rate. For example, the annual payable on a bond which has a par value of Rs.100 and a coupon rate of 13.5 per cent is Rs.13.5 (Rs.100 x 13.5 per cent). Maturity Period  Typically corporate bonds have a maturity period of 7 to 10 years, whereas government bonds have maturity periods extending up to 20 – 25 years. At the time of maturity the par (face) value plus perhaps a nominal premium is payable to the bondholder. Basic Bond Valuation Model

As noted above the holder of a bond receives a fixed annual interest payment for a certain number of years and a fixed principal repayment (equal to par value) at the time of maturity. Hence, the value of a bond is : n

V

=

∑ t=1

V Where V I F n

= = = =

1 (1 + k d)t

+

F . (1 + k d)n

= I (PVIFA kd, n) + F (PVIF kd, n)

value of the bond annual interest payable on the bond principal amount (par value) of the bond repayable at the time of maturity maturity period of the bond.

 Example A Rs.100 par value bond, bearing a coupon rate of 12 per cent, will mature after 8 years. The required rate of return on this bond is 14 per cent. What is the value of this bonds?

Since the annual interest payment will be Rs.12 for 8 years and the principal repayment will be Rs.100 at the end of 8 years, the value of the bond will be : V

= Rs. 12 (PVIFA14%,8yrs) + Rs. 100 (PVIF14%,8yrs) = Rs. 12 (4.639) + Rs.100 (0.351) = Rs. 90.77

 Example A Rs.1,000 par value bond, bearing a coupon rate of 14 per cent, will mature after 5 years. The required of return on this bond is 13 per cent. What is the value of this bond? Since the annual interest payment will be Rs.140 for 5 years and the principal repayment will be Rs.1,000 at the end of 5 years, the value of the bond will be :

V

= Rs. 140 (PVIFA13%,5yrs) + Rs. 1,000 (PVIF13%,5yrs) = Rs. 140 (3.517) + Rs.1,000 (0.543) = Rs. 1,035.4

Bond value Theorems

Based on the bond valuation model, several bond value theorems have been derived. They state the effect of the following factors on bond values : 1.

Relationship between the required rate of return and the coupon rate.

2.

Number of years to maturity.

The following theorems show how bond values are influenced by the relationship between the required rate of  return and the coupon rate. Ia

When the required rate of return is equal to the coupon rate, the value of a bond is equal to its par value.

Ib

When the required of return is greater than the coupon rate, the value of a bond is less than its par value.

Ic

When the required rate of return is less than the coupon rate, the value of a bond is more than its par value. To illustrate the above theorems, let us consider a bond of Magnum Limited which has the following features :

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Par value Coupon rate : Years to maturity

: 14 per cent :

Rs.100 6 years

What happens to the value of Magnum’s bond when the required rate of return is 14 per cent? 16 per cent? 12  per cent? If the required rate of return is 14 per cent (which is the same as the coupon rate), the bond value is : V

= Rs.14 (PVIFA 14%,6yrs) + Rs. 100 (PVIF 14%,6yrs) = Rs.14 (3.889) + Rs.100 (0.456) = Rs.100

If the required rate of return is 16 per cent (which is higher than the coupon rate), the bond value is : V

= Rs.14 (PVIFA 16%,6yrs) + Rs.100 (PVIF 16%,6yrs) = Rs.14 (3.685) + Rs.100 (.410) = rs.91.59

If the required rate of return is 12 per cent (which is lower than the coupon rate), the bond value is : V

= Rs.14 (PVIFA 12%,6yrs) + Rs.100 (PVIF 12%,6yrs) = Rs.14 (4.111) + Rs.100 (.507) = Rs.108.3

The following theorems express the effect of the number of years to maturity on bond values. IIa

When the required rate of return is greater than the coupon rate, the discount on the bond declines as maturity approaches.

IIb

When the required rate of return is less than the coupon rate, the premium on the bond declines as maturity approaches.

IIc

The longer the maturity of a bond, the greater its price change in response to a given change in the required rate of return. To illustrate the above theorems, let us consider a bond of Bharath limited which has the following features : Par value Coupon rate Years to maturity

: : :

Rs.1,000 13 per cent 8

If the required rate of return on this bond is 15 per cent, it will have a value of : V

= Rs.130 (PVIFA 15%,8Yrs) + Rs.1,000 (PVIF 15%,8yrs) = Rs.130 (4.487) + Rs.1,000 (.327) = Rs.910.3

One year from now, when the maturity period will be 7 years, the bond will have a value of : V

= Rs.130 (PVIFA 15%,7Yrs) + Rs.1,000 (PVIF 15%,7yrs) = Rs.130 (4.160) + Rs.1,000 (.376) = Rs.916.8

Given the required rate of return of 15 per cent, the bond will increase in value will the passage of time, until it matures, as follows : Years to maturity

6 5 4 3

Bond value Rs. 923.9 932.8 942.2 954.8

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967.4 983.1 1,000.0

The lower curve in Fig. Below represents how the bond value will behave as a function of years to maturity. Value of bond 1100

premium bond Kd  = 11%

1000

per value bond Kd  = 13%

900 discount bond K d = 15%

8

| 7

| 6

| 5

| 4

| 3

| 2

| 1

| 0

Bond Value as a Function of years to Maturity

It the required rate of return on the bond of Bharath Limited is 11 per cent it will have a value of : V

= =

Rs.130 (PVIFA 11%,8yrs) + Rs.1,000 (PVIF 11%,8yrs) Rs.130 (5.146) + Rs.1,000 (.434) = Rs.1,103.0

One year from now, when the maturity period will be 7 years, the bond will have a value of : V

= =

Rs.130 (PVIFA 11%,7yrs) + Rs.1,000 (PVIF 11%,7yrs) Rs.130 (4.712) + Rs.1,000 (.482) = Rs.1,094.6

Given the required rate of return of 11 per cent, the bond value will decrease with the passage of time, until it matures, as follows :

Years to maturity

6 5 4 3 2 1 0

Bond value Rs. 1,085.0 1,073.5 1,062.3 1,048.7 1,034.7 1,018.1 1,000.0

The upper curve in Fig. 6.1 represents how the bond value will behave as a function of years to maturity. To show that the longer the maturity of a bond, the greater is its price change in response to a given change in the required rate of return, we may refer to Fig. 6.1. when the required return decrease from 15 per cent to 11 per cent, given a maturity period of 7 years, the value of the bond increases from Rs.916.8 to Rs.1094.6, an increase of 19.4 per  cent. However, if the same change in the required rate of return occurs with only 2 years to maturity, the bond value would rise from Rs.967.4 to rs.1034.7 – an increase of only 7.0 per cent.

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To further illustrate theorem IIc, consider two bonds A and B, which are alike in all respects expect their period of  maturity. Bond A Bond B Par value Coupon rate Maturity period Required rate of return Current price

Rs.1,000 10 per cent 5 years 12 per cent Rs.927.5

Rs.1,000 10 per cent 15 years 12 per cent Rs.864.1

What happens if the required rate of return on these two bonds rises to 14 per cent, or falls to 10 per cent ? The price of  these bonds will behave as follows : Bond A Bond B Required rate of return increase to 14 per cent Required rate of return decrease to 10 per cent

Rs.862.3 Rs.1,000.0

Rs.754.2 Rs.1,000.0

From the above data, it is clear that the percentage change in bond B (the bond with longer maturity) is higher  compared to the percentage price change in bond A (the bond with shorter maturity) for given changes in the required rate of return. Yield to Maturity Suppose the market price of a Rs.1,000 par value bond, carrying a coupon rate of 9 per cent and maturing after 8 years, is rs.800. What rate of return would an investor earn if he buys this bond and holds it till its maturity ? The rate of  return that he earns, called the yield to maturity (YTM hereafter), is the value of k d in the following equation : 8

Rs.800 =

∑

Rs.90 + Rs.1,000 (1 +k d)t (1 + k d)8 = Rs.90 (PVIFA kd,8yrs) + Rs.1,000 (PVIF kd,8yrs) t=1

To find the value of k d which satisfies the above equation, we may have to try several values of k d till we ‘hit’ on the right value. Let us begin with a discount rate of 12 per cent. Putting a value of 12 per cent for k d we find that the right side of the above expression becomes equal to : Rs.90 (PVIFA 12%,8yrs) + Rs.1,000 (PVIF 12%,8yrs) = Rs.90 (4.968) + Rs.1,000 (0.404) = Rs.851.0 Since this value is greater than Rs.800, we have to try a higher value for k d. Let us try k d = 14 per cent. This makes the right hand side equal to : Rs.90 (PVIFA 14%,8yrs) + Rs.1,000 (PVIF 14%,8yrs) = Rs.90 (4.639) + Rs.1,000 (0.351) = Rs.768.1 Since this value is less than Rs.800, we try a lower value for k d. Let us try k d = 13 per cent. This makes the right hand side equal to : Rs.90 (PVIFA 13%,8yrs) + Rs.1,000 (PVIF 13%,8yrs) = Rs.90 (4.800) + Rs.1,000 (0.376) = Rs.808 Thus k d lies between 13 per cent and 14 per cent. Using a linear interpolation 1 in the range 13 per cent to 14 per cent, we find that k d is equal to 13.2 per cent. 13% + (14% - 13%)

808 – 800 = 13.2% 808 – 768.1

 An Approximation If you are nor inclined to follow the trial-and-error approach described above, you can empty the following formula to find the approximate YTM on a bond :

YTM =

1 + (F – P)/n 0.4F + 0.6P

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where

YTM I F P n

= = = = =

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yield to maturity annual interest payment Par value of the bond Present price of the bond years to maturity

 Example The price per bond of Zion Limited is Rs.90. the bond has a par value of Rs.100, a coupon rate of 14 per  cent, and a maturity period of 6 years. What is the yield to maturity ?

Using the approximate formula the yield to maturity on the bond of Zion works out to : YTM =

14 + (100 – 90)/6 . 0.4 x 100 + 0.6 x 90

=

16.67 per cent

Bond Values with Semi-annual Interest

Most of the bonds pay interest semi-annually. To value such bonds, we have to work with a unit period of six months, and not one year. This means that the bond valuation equation has to be modified along the following lines :

•

the annual interest payment, I, must be divided by two to obtain the semi-annual interest payment.

•

The number of years to maturity must be multiplied by two to get the number of half-yearly periods.

•

The discount rate has to be divided by two to get the discount rate applicable to half yearly periods.

With the above modifications, the basic bond valuation equation becomes : 2n

V

∑

= t=1

= where V 1 /2 k d/2 F 2n

= = = = =

1/2 + F . t 2n (1 + k d/2) (1 + k d/2) 1 / 2 (PVIFA kd/2, 2n) + F (PVIF kd/2, 2n)

value of the bond semi-annual interest payment discount rate applicable to a half-year period par value of the bond repayable at maturity maturity period expressed in terms of half-yearly periods.

 Example A Rs.100 par value bond carries a coupon rate of 12 per cent and a maturity period of 8 years. Interest is payable semi-annually. Compute the value of the bond if the required rate of return is 14 per cent.

Applying Eq. (6.4), the value of the bond is : 16

V

=

∑ T=1

=

6 . + 100 . (1.07)t (1.07)16

6 (PVIFA 7%,16yrs) + 100 (PVIF 7%,16yrs) =

Rs.6 (9.447) + Rs.100 (0.388) = Rs.95.5

EQUITY VALUATION : DIVIDEND CAPITALISATION APPROACH

According to the dividend capitalisation approach, conceptually a very sound approach, the value of an equity share is equal to the present value of dividends expected from its ownership plus the present value of the sale price expected when the equity share is sold. For applying the dividend capitalisation approach to equity stock valuation, we

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will make the following assumptions, (i) dividends are paid annually — this seems to be a common practice for   business firms in India; and (ii) the first dividend is received one year after the equity share is bought. Single-period valuation Model

Let us begin with the case where the investor expects to hold the equity share for one year. The price of the equity share will be : P0

where

P0 D1 P1 K s

=

= = = =

D1 . + P1 . (1 + k s) (1 + k s) current price of the equity share dividend expected a year hence price of the share expected a year hence rate of return required on the equity share.

 Example Prestige’s equity share is expected to provide a dividend of Rs.2.00 and fetch a price of Rs.18.00 a year  hence. What price would it sell for now if investors’ required rate of return is 12 per cent ?

P0

=

2.00 + 18.00 = Rs.17.86 (1.12) (1.12)

What happens if the price of the equity share is expected to grow at a rate of g per cent annually ? If the current price, P0, becomes P0 (1 + g) a year hence, we get : P0

=

D1 + P0 (1 + g) (1 + k s) (1 + k s)

Simplifying the above Eq. we get : P0

=

D1 . (k s – g)

 Example The expected dividend per share on the equity share of Roadking Limited is Rs.2.00. The dividend per share of Roadking Limited has grown over the past five years at the rate of 5 per cent per year. This growth rate will continue in future. Further, the market price of the equity share of Roadking Limited, too, is expected to grow at the same rate. What is a fair estimate of the intrinsic value of the equity share of Roadking Limited if the required rate is 15 per cent ?

Applying above Eq. we get the following estimate : P0

=

2.00 . = Rs.20.00 0.15 - .05

Expected Rate of Return

In the preceding discussion we calculated the intrinsic value of an equity share, given information about (i) the forecast values of dividend and share price, and (ii) the required rate of return. Now we look at a different question : What rate of return can the investor expect, given the current market price and forecast values of dividend and share price ? The expected rate of return is equal to : K s = D1/P0 + g  Example The expected dividend per share of Vaibhav Limited is Rs.5.00. The dividend is expected to grow at the rate of 6 per cent year. If the price per share now is Rs.50.00, what is the expected rate of return ?

Applying above Eq. , the expected rate of return is : K s = 5/50 + 0.06 = 16 % Multi-period Valuation Model

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Having learnt the basics of equity share valuation in a single-period framework, we now discuss the more realistic, and also the more complex, case of multiperiod valuation. Since equity shares have no maturity period, they may be expected to bring a dividend stream of infinite duration. Hence the value of an equity share may be put as :

P0 =

where

P0 D1 D2 D∞

= = = =

D1 . + D2 . + … + D ∞ ∞ 1 (1 + k s) (1 + k s)2 (1 + k s)

∝ . = ∑ t=1

Dt . (1 + k s)t

price of the equity share today dividend expected a year hence dividend expected two years hence dividend expected at the end of infinity

Above Equation represents the valuation model for an infinite horizon. Is it applicable to a finite horizon ? Yes. To demonstrate this consider how are equity share would be valued by an investor who plans to hold it for n years and sell it thereafter for a price of P n. The value of the equity share to him is : P0 =

D1 . + D2 . + … + D n . + Pn . 1 2 n (1 + k s) (1 + k s) (1 + k s) (1 + k s)n n

=

∑

Dt . + Pn . t n (1 + k s) (1 + k s)

t=1

 Now, what is the value of P n in Eq. (1.10) ? Applying the dividend capitalisation principle, the value of Pn would be the present value of the dividend stream beyond the nth period, evaluated as at the end of the nth year. This means : P0 =

Dn+1 (1 + k s)

. +

Dn+2 . + … + D∞ . ∞ -n 2 (1 + k s) (1 + k s)

Substituting this value of Pn in Eq. we get : P0 =

+

=

D1 . + D2 . + … + D n . (1 + k s) (1 + k s) (1 + k s)n

1 . (1 + k s)n

D n+1 . + (1 + k s)

D n+2 . + … + 2 (1 + k s)

D∞ . ∞ -n (1 + k s)

D1 . + D2 . + … + D n . + D n+1 . + … + D∞ . ∞ 2 n n+1 (1 + k s) (1 + k s) (1 + k s) (1 + k s) (1 + k s) ∞

=

∑ t=1

Dt . (1 + k s)t

This is the same as Eq. (6.9) which may be regarded as a genaralised multiperiod valuation formula. Equation (6.9) is general enough to permit any dividend pattern — rising, declining, constant or randomly fluctuating. For practical applications it is helpful to attempt simplification of Eq. (6.9). we discuss below three such cases : (i) constant dividends, (ii) constant growth of dividends, and (iii) changing growth rates of dividends. Valuation with Constant Dividends

If we assume that the dividend per share remains constant year after at a value of D, Eq.  becomes : P0 =

D . + D . +… + D . ∞ 2 (1 + k s) (1 + k s) (1 + k s)

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Above Equation (6.13), on simplification, becomes P + D. k s Valuation with Constant Growth in Dividends

Most stock valuation models are based on the assumption that dividends tend to increase over time. This is a reasonable hypothesis because business firms typically grow over time. If we assume that dividends grow at a constant compound rate, we get : Dt = D0 (1 + g)t Where

Dt = D0 = g =

dividend for year t dividend for year 0 constant compound growth rate.

 Example The current dividend (D0) for an equity share is Rs.3.00. If the constant compound growth rate is 6  per cent, what will be the dividend 5 years hence ? The dividend 5 years hence will be :

D5 = 3 (1.06)5 = 4.01 When the dividend increases at a constant compound rate, the share valuation equation becomes : P0 = D1 . + D1 (1 + g) + D1 (1 + g)2 . (1 + k s)1 (1 + k s)2 (1 + k s)3 Eq. (6.16) simplifies to : P0 =

D1 . K s – g

 Example Ramesh Engineering Limited is expected to grow at the rate of 6 per cent p.a. The dividend expected on Ramesh’s equity share a year hence is Rs.2.00. What price will you put on it if your required r ate of return for this share is 14 per cent ?

The price of Ramesh’s equity share would be :

P0 =

2.00

. = Rs.25.00

0.14 – 0.06 Valuation with Variable Growth in Dividends

Many firms enjoy a period of supernormal growth which is followed by a normal rate of growth. Assuming that the dividends move in line with the growth rate, the price of the equity share of such a firm is : P0 =

D1 . + (1 + k s)

D1 (1 + g’) + … + D1 (1 + g’) n-1 (1 + k s)2 (1 + k s)n

+ Dn (1 + g) + Dn (1 + g)2 + … (1 + k s)n+1 (1 + k s)n+2 where

P0 D1 g’ g

= = = =

price of the equity share dividend expected a year hence supernormal growth rate of dividend. normal growth rate of dividend.

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To compute the value of P 0 in above Eq. the following procedure may be employed. Step 1.

Specify the dividend stream expected during the initial period of supernormal growth. Find the present value of this dividend stream. Using the symbols presented earlier, this can be represented as : n

∑ t=1

Step 2.

Step 3.

Dt . (1 + k s)t

Calculate the value of the share at the end of the initial growth period, P n = D n+1 . K s – g (as per the constant growth model), and discount this value to the present. In terms of our symbols, this discounted value is : D n+1 . x 1 . K s – g (1 + k s)n Add the above two present-value components to find the value of the share P0, as given below : n

P0 =

∑

Dt . + D n+1 . x 1 . (1 + k s)t K s – g (1 + k s)n Present value of the Present value of the dividend stream during share at the end of  the initial period the initial period t=1

To illustrate the above procedure let us consider the equity share of vertigo limited : D0 = current dividend per share = Rs.2.00 n = duration of the period of supernormal growth = 4 years g’ = growth rate during the period of supernormal growth = 20 per cent g = normal growth rate after the supernormal growth period is over = 5 per cent k s = equity investors’ required rate of return = 12 per cent Step 1. The dividend stream during the supernormal growth period will be : D1 = Rs.2.00 (1.20) D2 = Rs.2.00 (1.20)2 D3 = Rs.2.00 (1.20)3 D4 = Rs.2.00 (1.20)4 The present value of this dividend stream is : 2.00 (1.20) + 2.00 (1.20)2 + 2.00 (1.20)3 + 2.00 (1.20)4 (1.12) (1.12)2 (1.12)3 (1.12)4

Step 2.

= 2.14 + 2.30 = 2.46 + 2.64 = Rs.9.54 The present of the share at the end of 4 years, applying the constant growth model at that point of time, will be : P4 = D5 . = D4 (1 + gn) k s – g k s – g = 2.00 (1.20)4 (1.05) = Rs.62.21 0.12 – 0.05 The discounted value of this price is : 62.21 . = Rs.39.53 (1.12)4 Step 3. The sum of the above components is : P0 = Rs.9.54 + Rs.39.53 = Rs.49.07 Figure below presents a graphic view, in terms of a time line diagram, of the above procedure. 0 D1 = 2.4

2.14

1

2

D2 = 2.88

D3 = 3.46

3

4 D4 = 4.15 P4 = 62.21

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+ 2.30 + 2.46 + 39.53 49.07

Time Line Diagram of Share Valuation

H Model

The H model of equity valuation is based on the following assumptions : (a)If the current dividend growth rate, g a, is greater than g n, the normal long-run growth rate, the growth rate  begins to decline. (b)After 2H years the growth rate becomes g n. (c)At H years the growth rate is exactly halfway between g a and gn. The graphic representation of the dividend growth rate pattern for the H Model is shown in Fig. 6.3

Growth Rate

8a

8a

H

2H

Time

Fig. 6.3 Dividend Growth Rate Pattern for H Model

While the Derivation of the H model is rather complex, the valuation equation for the H model is quite simple : P0 = D0 [ (1 + gn) + H (ga – gn)] r - gn where

P0 = D0 =

intrinsic value of the share current dividend per share

Tax Shield Education Centre r gn ga H

= = = =

MAFA-53

rate of return expected by investors normal long-run growth rate current growth rate one-half of the period during which ga will level off to gn.

Above Equation (6.19) may be re-written as : P0 = D0 (1 + gn) + D0 H (ga – gn) r – gn r - gn Expressed this way, the H model may be interpreted in a simple, intuitive manner. The first term on the right hand of above Eq. (6.20) D0 (1 + gn) r - gn represents the value based on the normal growth rate, whereas the second term

D0 H (ga + gn) r - gn reflects the premium due to abnormal growth rate.

Impact of Growth on Price, returns, and P/E Ratio

The expected growth rates of companies differ widely. Some companies are expected to remain virtually stagnant or grow slowly; other companies are expected to show normal growth; still others are expected to achieve supernormal growth rate. Assuming a constant total required return, differing expected growth rates mean differing stock prices, dividend yields, capital gains yields, and price-earnings ratios. To illustrate, consider three cases : Growth rate (%) Long growth firm  Normal growth firm Supernormal growth firm

5 10 15

The expected earnings per share and dividend per share of each of the three firms are Rs.3.00 and Rs.2.00 respectively. Investors’ required total return from equity investments is 20 per cent. Given the above information, we may calculated the stock price, dividend yield, capital gains yield, and price-earnings ratio for the three cases as shown in table 6.1. The results in table 6.1 suggest the following points : 1.As the expected growth in dividend increase, other things being equal, the expected return 1 depends more on the capital gains yields and less on the dividend yield. 2.As the expected growth rate in dividend increases, other things equal, the price earnings ratio increases. 3.High dividend yield and low price-earnings ratio imply limited growth prospects. 4.Low dividend yield and high price-earnings ratio imply considerable growth prospects.

Table

Price, dividend Yield, Capital Gains Yields, and Price-Earnings Ratio under Differing Growth Assumptions for 15 per cent Return

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MAFA-54 Price

Low growth firm

Dividend yield (D1/P0)

Capital gains (P1 – P0)/P0

P0 = D1 . k–g =

 Normal growth firm

Rs.2.00 . = Rs.13.33 0.20 – 0.05

15.0%

5.0%

4.44

10.0%

10.0%

6.67

5.0%

15.0%

13.33

P0 = D1 . k–g =

Rs.2.00 . = Rs.13.33 0.20 – 0.10

Supernormal growth firm P0 = D1 . k–g

=

Rs.2.00 . = Rs.40.00 0.20 – 0.15

DERIVATIONS OF SHARE VALUATION MODELS Share Valuation with Constant Dividends

The value of a share with constant dividends is : P0 =

D . + D . + … + D . (n →∞ ) (1 + k s) (1 + k s)2 (1 + k s)n

Multiplying both the sides of above Eq. (6A.1) by (1 + k s) gives : P0 = (1 + k s) = D +

D . + … + D . (n →∞ ) (1 + k s) (1 + k s) n-1

Subtracting above Eq. from above Eq. yields : P0 k s = D

As n →∞ ,

1-

1 . (n →∞ ) (1 + k s)n

1 . → 0. So, Eq. (6A.3 approaches) (1 + k s)n P0k s = D

This results in

price earnings (P/E)

P0 = D . k s Share Valuation with Constant growth in Dividends

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MAFA-55 The value of share with constant growth in dividends is :

P0 =

D1 . + D1 (1 + g) + … + D 1 (1 + g)n (n →∞ ) (1 + k s) (1 + k s)2 (1 + k s)n

Multiplying both the side of Eq. (6A.5) by 1+g 1 + k s

gives :

P0 1 + g = D1 (1 + g) + D1 (1 + g) + … + D 1 (1 + g) n+1 (n →∞ ) 1 + k s (1 + k s)2 (1 + k s)3 (1 + k s) n+2 Subtracting Eq. (6A.7) from Eq. (6A.6) yields : P0 (ks – g) = D1 (1 + k s)

1 . – (1 + g) n+1 (n →∞ ) (1 + k s) (1 + ks) n+2

As n →∞, (1 + g) n+1 (1 + k s) n+2

→ 0 because g > k s

Hence Eq. (6A.8) becomes : P0 (k s – g) = (1 + k s)

D1 . (1 + k s)

This means : P0 =

D1 . k s – g

BOND REFUNDING Callable bonds, popularly used abroad, were virtually unknown in India till the early 1990s. The Industrial Development Bank of India was perhaps the first organisation to issue bonds with call features in 1992. Since then several organisations have issued callable bonds. A company issues callable bonds primarily to enjoy the flexibility to redeem them prematurely. Typically, such redemption is done with the proceeds of a new issue of bonds that may be issued at a lower rate of  interest because of favourable conditions in the capital market. Put differently, the company seeks to refund its debt. How should a bond-refunding decision be analysed? It should be analysed the way any other capital budgeting decision is analysed. Hence, the decision rule is: Refund the debt if the present value of the stream of net cash savings is greater than the initial cash outlay. The terms initial outlay and the annual net cash savings are explained below. Initial Outlay

Initial =

Cost of calling –

outlay

the old bonds

Net proceeds Tax savings on tax –  of the new issue deductible

expenses The terms on the right-hand side of the above expression are defined as follows: Cost of calling the old bonds  Net proceeds of the new issue

= face value of the bonds = Gross proceeds

+ –

Call premium Floatation costs

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(issue expense + discount) Tax savings on tax-deductible expenses

= Tax rate

Call premium + Unamortised floatation costs on e the bond issue

Annual Net Cash Savings

Annual  Net cash savings

Annual net cash outflow on old bonds

=

Annual net cash outflow on new bonds

–

The terms on the right-hand side of the above expression are defined below: Annual net cash outflow on old bonds

=

Interest expense

–

Tax savings on interest expense and amortisation of   floatation cost

Annual net cash outflow on new  bonds

=

Interest expense

–

Tax saving on interest expense and amortisation of issue cost.

Illustration

To illustrate how the bond-refunding decision should be analysed, let us consider an example. Acme Chemicals has Rs. 100 million, 18 per cent bonds outstanding within 10 years remaining to maturity. As interest rates have fallen Acme can refund these bonds with a Rs. 100 million issue of 10-year bonds carrying a coupon rate of 16 percent. The call premium will be 5 per  cent. The issue costs on the new bonds will be Rs. 5 million. The unamortised portion of the issue costs on the old bonds is Rs. 3 million and these can be written off no sooner the old bonds are called. Acme’s marginal tax rate is 40 per cent. The bond-refunding decision may be analysed as follows: 1.

Initial outlay (a)

Cost of calling the old bonds Face value of old bonds Call premium

(b)

Net proceeds of the new issue Gross proceeds Issue costs

(c)

–

100,000,000 5,000,000  ——————  95,000,000

Tax savings on tax-deductible expenses Tax Call Unamortised issue costs on rate premium + the old bond issue 0.4 [5,000,000 + 3,000,000]

Initial outlay : 1 (a) – 1 (b) – 1 (c) 2.

+

1000,000,000 5,000,000  ——————  105,000,000

Annual Net Cash Savings

3,2000,000 6,8000,000

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MAFA-57

Annual net cash outflow on old bonds Interest expense Tax savings on interest expense and amortisation of issue cost 0.4 [18,000,000 + 300,000/10]

(b)

18,000,000

–

Annual net cash outflow on new bonds Interest expense Tax saving on interest expense and amortisation of  issue cost 0.4 [16,000,000 + 5,000,000/10]

3.

7,320,000  —————  10,680,000

16,000,000 –

6,600,000 9,400,000

Annual net cash savings : 2 (a) – 2 (b)

1,280,000

Present Value of the Annual Cash Savings

8,002,560

Present value of a 10-year annuity of 1,280,000 Using a discount rate of 9.6 per cent after tax cost of new bonds (1,280,000 × 6.252) 4.

Net Present Value of Refunding the Bonds (a)

Present value of annual cash savings

8,002,560

(b)

Net initial outlay

6,800,000

(c)

Net present value of refunding the bonds

1,202,560

DURATION

The duration of a bond is the weighted average maturity of its cash flow stream, where the weights are proportional to the present value of cash flows. Formally, it is defined as: Duration = [PV (C1) × 1 + PV (C 2) × 2 + … + PV (C n) × n] V0 Where PV (Ct) = present value of the cash flow receivable at the end of year t (t = 1,2,…, n) V0 = current value of the bond For calculating the present value of cash flow, the yield to maturity (the internal rate of return) of the bond issue is used as the discount rate. The duration of bond, in effect, represents the length of time that elapses before the “average” rupee of present value from the bond is received. To illustrate how duration is calculated consider two bonds, A and B.

Face value Coupon (interest rate) Years to maturity Redemption value Current market price Yield to maturity

Bond A

Bond B.

Rs. 100 15 per cent payable annually 6 Rs. 100 Rs. 89.50 18 per cent

Rs. 100 10 per cent payable annually 6 Rs. 100 Rs. 71.98 18 per cent

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Table 19.1 shows the calculation of duration for these bonds. As expected, the duration of bond A is shorter than the duration of bond B. The volatility (or interest rate sensitivity) of a bond is approximately related to its duration: Duration Volatility = ————————  (1 + Yield) The volatilities of bonds A and B are: Volatility of bond A = 4.257/1.18 = 3.61 Volatility of bond B = 4.556/1.18 = 3.86 Thus, a 1 percent increase (decrease in the required yield will result in an approximately 3.61 per cent fully (rise) in the price of bond A and a 3.86 per cent fall (rise) in the price of bond B. Remember that these numbers are approximations as the measure of volatility reflects the effect of an infinitesimal change in interest rates on bond prices. For a finite change in interest rate (such as 1 per cent variation), the acutal bond price change will be somewhat different from that calculated on the basis of  Eq. (19.4).

Calculation of Duration

Bond A : 15 percent coupon Year

Cash Flow

Present value at 18  percent

Proportion of the  bond’s value

Proportion of the  bond’s value × time

1

15

12.71

0.142

0.142

2

15

10.77

0.120

0.241

3

15

9.13

0.102

0.306

4

15

7.74

0.086

0.346

5

15

6.56

0.073

0.366

6

115

42.60

0.476

2.856

Duration

4.257 years

Bond B: 10 percent coupon Year

Cash flow

Present value at 18  percent

Proportion of the  bond’s value

Proportion of the  bond’s value × time

1

10

8.47

0.118

0.118

2

10

7.18

0.100

0.200

3

10

6.09

0.085

0.254

4

10

5.16

0.072

0.287

5

10

4.37

0.061

0.304

6

110

40.70

0.565

3.392

Duration

4.556 years

Characteristics of Duration

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MAFA-59 The following characteristics of duration are worth noting:

•

For a zero coupon bond, the duration is simply equal to the maturity of the bond.

•

Other things being equal, the higher the interest (coupon rate), the shorter the duration.

•

Other things being equal, the higher the yield to maturity, the shorter the duration. This is so because in this case the present value of nearer payments is more important vis-à-vis the present value of more distant payments.

Duration and Immunisation

If the interest rate goes up it has two consequences for a bondholder: (i) t he capital value of the bond falls, and (ii) the return on reinvestment of interest income improves. But the same token, if the interest rate declines, it has two consequences for a bondholder: (i) the capital value of the bond rises, and (ii) the return on reinvestment of interest income decreases. Thus, an interest rate change has two effects in opposite directions. Can an investor ensure that these two opposite effects are equal so that he is immunised against interest rate risk? Yes, it is possible if the investor chooses a bond whose duration is equal to his investment horizon. For example, if an investor’s investment horizon is 5 years he should choose a bond that has a duration of 5 years if he wants to insulate himself against interest rate risk. If he does so, whenever there is a change in interest rate, losses (or gains) in capital value will exactly offset by gains (or losses) on reinvestments. TERM STRUCTURE OF INTEREST RATES

The term structure of interest rates, popularly called the yield curve, shows how yield to maturity is related to term to maturity for bonds that are similar in all respects, excepting maturity. Consider the following data for government securities: Face Value

Interest Rate

Maturity (years)

Current Price

Yield to Maturity

100000

0

1

88968

12.40

100000

12.75

2

99367

13.13

100000

13.50

3

100352

13.35

100000

13.50

4

99706

13.60

100000

13.75

5

99484

13.90

The yield curve for the above bonds is shown in Fig 19.1. It slopes upwards, indicating that long-term rates are greater than short-term rates. Yield curves, however, do not have to necessarily slope upwards. They may follow any pattern. Four patterns are exhibited in Fig. 19.2. Yield to maturity ( YTM )    



| 1 Fig 19.1 Yield Curve (Page 393)

| 2

| 3

| 4

| 5

| 6

term to maturity ( Years)

Another perspective on the term structure of interest rates is provided by the forward interest rates, viz. The interest rates applicable to bonds in the future. To get the forward interest rates, begin with the one-year treasury bill.

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MAFA-60 88,968 = 100,000/(1 + r 1) YTM

YTM

TERM

TERM

YTM

YTM

TERM

TERM

Types of Yield Curves Where r 1 is the one-year spot rate: the discount rate applicable to a riskless cash flow receivable a year hence, Solving for r 1 gives r 1 = 0.124. Next, consider the two-year government security and split its benefits into two parts, the interest of Rs. 12,750 receivable at the end of year 1 and Rs. 1,12,750 (representing the interest and principal repayment) receivable at the end of year 2. The present value of the first part is:

12,750 12,750  ———— = ———— = 11,343.4 (1 + r 1) (1.124) To get the present value of the second year’s cash flow of Rs. 112,750 discount it twice at r 1 (the discount rate for  year 1) and r 2 (the discount rate for year 2): 112,750 112,750  ———————— = ————————  (1 + r 1) (1 + r 2) (1.124) (1 + r2)  r 2 is called the ‘forward rate’ for year two, that is, the current estimate of the next year’s one-year spot interest rate. Since r 1, the market price of the bond, and the cash flow associated with the bond are known the following equation can be set up. 12,750 112,750 99,367 = ————— + ————————  (1,124) (1,124) (1 + r2 ) Solving this equation given r 2 = 0.1289 To get the forward rate for year 3 (r 3), set up the equation for the value of the three year bond: 13,500 13,500 113,500 100,352 = ————— + ————————— + ——————————  (1 + r 1) (1 + r1) (1   + r 2) (1 + r1) (1   + r 2) (1 + r 3) 13,500 13,500 113,500 100,352 = ————— + ————————— + ———————————  (1,124) (1,124) (11,289) (1,124) (11,289) (1 + r3 ) Solving this equation one obtains r 3 = 0.1512. This is the forward rate for year 3. Continuing in a similar vein, set up the equation for the value of the four-year bond: 13,500

13,500

13,500

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99,706 = ————— + ————————— + ———————————  (1 + r 1) (1 + r1) (1   + r 2) (1 + r1) (1   + r 2) (1 + r 3) 113,500 + ————————————————  (1 + r 1) (1 + r 2) (1 + r 3) (1 + r 4) 13,500 13,500 13,500 = ————— + ———————— + ————————————  (1124) (1124) (11289) (1124) (11289) (11512) 113,500 + ———————————————  (1124) (11289) (11512) (1 + r 4) Solving this equation for r 4, leads to r 4 = 0.1458. Figure 19.3 plots the one-year spot rate and the forward rates r 2, r 3, r 4 . Notice that while the current spot rate and forward rates are known, the future spot rates are not known—they will be revealed as the future unfolds. Given the information on yields to maturity and forward rates, these are two distinct, yet equivalent, ways of valuing a riskless cash flow. CF(t) PV[CF(t)] = —————  (1 + Rt)t

Discount at the yield to maturity: (R t) Discount by the product of 1 plus the forward rates:

 

CF(t) PV[CF(t)] = ——————————————  (1 + r 1) (1 + r 2) … (1 + r T)

BLACK AND SCHOLES MODEL The above analysis was based on the assumption that there were to possible values for the stock price at the end of one year. If we assume that there are two possible stock price at the end of each 6 months period, the number of possible end – of – year prices increases. As the period is further shortened (from 6 months to 3 months or 1 month), we get more frequent changes in stock price and a wider range of  possible end -–of – year prices. Eventually, we would reach a situation where price change more or less continuously, leading to a continuum of possible prices at the end of the year. Theoretically, even for this situation we could set up a portfolio which has a payoff identical to that of a call option. However, the composition of this portfolio will have to be changed continuously as the year progresses. Calculating the value of such a portfolio and through that the value of the call option in such a situation appears to be an unwieldy task, but Black and Scholes developed a formula that does precisely that. Their  formula is : Co = So N (d1) - E . N (d2) ert where Co So E e r t N (d)

= = = = = = =

equilibrium value of a call option now price of the stock now exercise price base of natural logarithm continuously compounded risk-free annual interest rate length of time in years to the expiration date value of the cumulative normal density function d1 = ln (S0/E) + (r + ½ σ√t

σ2)t

d2 = ln (S0/E) + (r + ½ σ√t

σ2)t

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ln

=

σ2 =

MAFA-62

natural logarithm standard deviation of the continuously compounded annual rate of return on the stock

Though one of the most complicated formula in finance, it is one of the most practical. The formula has great appeal because four of the parameters, namely, S o, E, r, and t are observable. Only one of the parameters, namely, σ2, has to be estimated. Note that the value of a call option is affected by neither the risk aversion of the investor nor the expected return on the stock. Assumptions You may have guessed by now that the Black and Scholes model, like most other models in economics and finance, is based on a set of simplifying assumptions. Yes, you are right. The assumptions underlying the Black and Scholes model are as follows :

• The call option is the European option • The stock price is continuously and is distributed lognormally • There are no transaction costs and taxes • There are no restrictions on or penalties for short selling • The stock pays no dividend • The stock pays no dividend • The risk-free interest rate is known and constant. These assumption may appear very severe. However, when some of them do not hold, a variant of the Black and Scholes model applies. Further, empirical studies indicate that the Black and Scholes model applies to American options as well. Illustration The following data is available for Personal products Company (PPC), a company that is not expected to pay dividend for a year. So E r t

σ σ2

= 60 = 56 = 0.14 = 0.5 = 0.3 = 0.09

What is the value of the call option as per the Black and Scholes model ? To apply the Black and Scholes model, we have to first determine N (d1) and N (d2). d1 =

ln (S0/E) + (r + ½ σ√t

σ2)t

=

ln (60/56) + [0.14 + ½ x 0.09] 0.5 0.30 √0.5

=

0.068993 + 0.0925 = 0.161493 = 0.761 0.2121 0.2121

d2 =

=

ln (So/E) + [ r – ½ σ2 ] t σ√t 0.06993 + [ 0.14 – ½ x 0.09 ] 0.5 = 0.554

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0.30 √0.5 N (d1) and N (d2) represent the probabilities that a random variable that has a standardised normal distribution will assume values less than d 1 and d2. To calculate N (d1) and N (d2) we shall consult Table A.5 in Appendix A at the end of the book showing the cumulative probabilities of the standard normal distribution function. N (d1) = N (0.761) = 0.7762 N (d2) = N (0.554) = 0.7102 The value of the call option is Co =

So N (d1) - E . N (d2) ert

Co =

60 x 0.7762 -

=

46.572 – 37.083

=

9.489

56 . x 0.7102 1.0725

Using the Black-Scholes Model The Black-Scholes option valuation model may appear very abstruse and divorced from the real world. Yet, option traders use it routinely to guide their trading decisions. They generally use programmed calculators or a set of tables. The procedure employed to calculate the value of a call option with the help of the tables is as follows : 1.

Find the product of the standard deviation of the continuously compounded asset value change and the square root of the time left to the option’s expiration. For example, if there is a 1 year call option on the stock of Pioneer Company and the standard deviation of the continuously compounded stock price change is 30 per cent year, the product is : Standard deviation x

2.

√Time = 0.30 x √1 = 0.30

Calculate the ratio of the current value of the asset to the present value of the exercise price. For  example, suppose that the stock of pioneer Company sells for Rs.120, that the exercise price is Rs.125, and that the effective interest rate is 1.1503 per cent. Then the ratio is : Stock price . = 120 + 125 . = 1.10 Present value of exercise price 1.1503

3.

Consult Table A.6 given in Appendix A at the end of the book and find the value (which represents the percentage relationship between the value of the call option and the stock price) corresponding to the number obtained in steps 1 and 2. This value for the example of Pioneer Company is 16.5 per cent. Hence, the value of the call option is :

4.

Calculate the value of the put option using the following relationship. Value

Value of =

put option

Present value of +

call option

stock -

exercise price

For the Pioneer Company’s example, the value of the put option is : 19.8 + 108.7 - 120 = 8.5 Call option on the assets

price

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From the foregoing analysis, it is evident that equity represents a call option on the assets of the firm with an exercise price equal to the redemption value of bonds. This means whenever a firm borrows the lenders (bondholders) acquire the firm but the equity stockholders enjoy the option to buy back the firm by redeeming the bonds. Hence there is a similarity between equity value and call value. So, the equity can be valued by employing the Black-Scholes formula So = Vo N (d1) where So = Vo = B1 =

B1 N (d2) ert

market value of equity value of the firm face value of the firm’s debt In Vo + (r + ½ σ2)t B1 d1 =

σ√t In Vo + (r + ½ σ2)t B1 d2 = σ√t To illustrate how the value of the firm is split between equity and bonds, let us consider an example. Zenith Company has a current value of 1000. The face value of its outstanding bonds too is 1000. These are 1 year discount bonds with an obligation of 1000 in year 1. The risk-free interest rate is 12 per cent and the variance of the continuously compounded rate of return on the firm’s assets is 16 per cent. RISKY DEBT AND OPTIONS The theory of options shows how the value of the firm is dividend between equity stockholders and bondholders, helps in understanding risky bonds, and clarifies the nature of conflict between equity stockholders and bondholders. Value of bonds = Value of the firm’s assets - Value of equity =

Value of the firm’s assets -

Value of call option on the firm’s assets

There is another way of expressing the value of risky bonds : Value of

Value of risk-free =

risky bonds

Value of put option on -

bonds

the assets of the firm

On the right hand side of this expression, the first term is simply B 1. The second term represents the value of put option enjoyed by equity stockholders. This option gives the equity stockholders the right to sell the assets of the firm for an exercise price of B 1. It may be noted that the two approaches to the valuation of  risky bonds are equivalent, thanks to the put-call parity theorem. Suppose a firm issues risky bonds with a promise to pay b1 in year 1. The value of these bonds depends on the value of the firm in year 1, V 1, as follows : Outcomes V1 < B1 V1 ≥ B1 V1 B1 Value of Risky Bonds The payoff of risky bonds is Min (V 1, B1). This is equivalent to the value of a risk-free bond minus the value of a put option on the assets of the firm, exercisable at B 1, held by equity stockholders. The algebra of this Outcomes equivalence is shown below :

Risk-free bonds

=

Value of a put option on the firm

V1 < B1 B1 (B1 – V1)

V1

≥ B1 B1 0

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The above relationship is shown diagrammatically in Fig below

Value of Risky Bonds Value of Loan Guarantees Often the loans of public sector undertakings are guaranteed by the government. What is the value of  such loan guarantees ? This question may be answered with the help of the insights provided by the option pricing theory. Remember that : Value of bonds = Value of risk-free bonds – Value of put option This means that : Value of risk-free bonds = Value of risky bonds + Value of put option Hence, from the perspective of the lenders (bondholders) the value of the guarantee provided by the government (or any other entity) is equal to the value of the put option. From the point of view of the guarantor (the government or some other entity) the cost of providing guarantee is the value of the put option. The benefits of loan guarantees accrue to bondholders and equity stockholders as follows :

•

When an existing issue of risk bonds is guaranteed, all the benefits accrue to the existing bondholders.

•

When a new issue of bonds is guaranteed, a major share of benefits accrues to the existing equity stockholders and a major share of benefits accrues to the existing bond holders.

Warrants and Convertible Debentures

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A warrant gives its holder the right to subscribe to the equity share(s) of a company during a certain period at a specified price. A convertible debenture, as the name suggests, is a debenture that is convertible, partially or fully, into equity shares. The conversion may be compulsory or optional. In the last few years convertible debentures have assumed tremendous significance in India. This chapter discusses various aspects of warrants and convertible debentures. It is divided into five sections : Features of warrants and convertible debentures • Valuation of warrants • Valuation of compulsorily convertible debentures • Valuation of optionally convertible debentures • Motives for issuing warrants and convertible debentures. •

FEATURES OF WARRANTS AND CONVERTIBLE DEBENTURES Features of Warrants A warrant gives its holder the right, but not obligation, to subscribe to a certain number of equity shares at a stated price during a specified period. Warrants are generally issued to ‘sweeten’ debt issues. For  example, the Tata Iron and Steel Company issued Secured Premium Notes (a debt instrument) in 1992. To attract investors, a warrant was attached to each Secured Premium Note. The warrant represented a right to seek allotment of the equity share f or cash at Rs.100 per share between 12 months and 18 months after the allotment of the Secured Premium Note. Features of convertible Debentures Convertible debentures in India, for practical purposes, are of relatively recent origin. Yet during this short period the features of these debentures have undergone significant changes. In the early eighties when they become prominent for the first time they were typically compulsorily convertible )partially or fully) at a stated conversion price on a predetermined date. The terms of such debentures were fixed by the Controller of Capital Issues. Towards the end of eighties, more particularly in 1989, a strange aberration occurred. In that year several convertible debenture issues were made which had the following features : (i) they were compulsorily convertible (fully or partially) in one or more stages, (ii) the conversion price was left open to be determined later by the Controller of Capital Issues, and (iii) the issuer was given some latitude for determining the timing of conversion. Differences Between Warrants and Convertible Debentures The essential feature of warrants and convertible debentures is the same : They give the holder a call option on the equity stock of the company. There are, however, some differences between the two. In a convertible debenture, the debenture and the option are inseparable. A warrant, however, is • detachable. Warrants can be issued independently. They need not be tied to some other instrument. • Warrants are typically exercisable for cash. • VALUATION OF WARRANTS Since a warrant is like a call option on the equity stock of the issuing company, the principles of option valuation can be applied to warrants. Figure 32.1 shows how the value of a warrant is influenced by various factors. The lower limit for the value of the warrant is Mix ( 0, stock price – Exercise price ) and the upper limit for the value of the warrant is the stock price. The actual value of the warrant is

Value of Warrant

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Upper limit On warrant Value

Value of the warrant Lower limit on warrant value Stock Price Erercise price Factors Influencing the Value of warrants shown by the curve line which lies between the boundaries specified by the lower limit and the upper limit. The distance between the actual price of the warrant and its lower limit is a function of the following factors.

• Variance of the stock returns • Time to expiration • Risk-free interest rate • Stock price • Exercise price Recall that these are the same factors which determine the value of a call option. Applying the Black and Scholes Model Ignoring the complications arising from dividends and / or dilution, the value of a warrant may be calculated using the procedure described in Chapter 31. To illustrate the calculation, consider the following data :

• Number of shares outstanding = N = 20 million • Current stock price = S = Rs.30 • Ratio of warrants issued to the number of outstanding shares = p = 0.05 • Total number of warrants issued = pN = 0.05 x 20 million = 1 million • Exercise price = E = Rs.15 • Time to expiration of warrants = 1 year  • Annual standard deviation of stock price changes = σ = 0.30 • Interest rate = 15 per cent We are now ready to calculate the value of the warrant with the help of the procedure discussed in Chapter  31.

• First, we find the product of the standard deviation and square root of time : σ √t = 0.30 √1 = 0.30

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• Second, we calculate the ratio of the stock price to the present value of the exercise price : Stock price . = 30 . = 2.3 PV (Exercise price) 15 / (1.15)

• Third, we obtain the ratio of the value of call option to the stock price by consulting Table A.6, given in Appendix A at the end of the book, with reference to the numbers 0.30 and 2.3 : Call option = 0.5604 Share price

• Fourth, we determine the value of the call option : 30 x 0.5604 = 16.812 Effect of Dilution For the sake of simplicity, we ignored the effects of dilution in the above calculation. Note that there is a difference between a traded option and a warrant. A traded call or put option is a side bet between investors. When an investor exercises a traded call or put option there is no effect whatsoever on the firm. The number of outstanding shares as well as the value of the firm are not affected. However, when a warrant is exercised the number of outstanding shares goes up and the value of the firm increases by the exercise money. For example, if the warrants of Pioneer Company are exercised, the number of  outstanding shares will go up by 1 million and the assets of the firm will increases by the exercise money which is Rs.15 million. Put differently, there is dilution. Hence, in valuing warrants, the dilution has to be taken into account. How this is done is shown below. Let

V N P E

= = = =

value of equity before the exercise of warrants. number of outstanding shares ratio of warrants issued to the number of outstanding shares exercise price

If the warrants are exercised, the equity value will rise to V + pNE and the number of shares will increase to N + pN. Hence, the share price after the warrants are exercised will be : V + pNE N (1 + p) On maturity, the warrant holder can exercise the warrant or let it lapse. So, the value of warrant, on maturity, will be : Share Max

Exercise —

price

,0 price

=

Max

V + pNE – E, 0 N (1 + p)

=

Max

V/N – E , 0 (1 + p)

=

1 . Max 1+p

V . – E, 0 N

Thus, the value of warrant is equal to 1/(1 + p) times the value of call option on the stock of a firm that has the same current value of equity but has no outstanding warrants. VALUATION OF COMPULSORILY CONVERTIBLE (PARTLY OR FULLY) DEBENTURES

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Internationally, convertible debentures are convertible into equity shares at the option of the debenture holders. In India, in addition to such debentures, companies also issue debentures which are compulsorily convertible (partly or wholly) into equity shares. For example, in June 1989, Tata Iron and Steel Company (TISCO) offered 3 lakh partly convertible debentures of Rs.1200 each at par. The principal terms of these partly convertible debentures were as follows : (i) compulsory conversion of Rs.600 par value into equity share of Rs.100 at a premium of Rs.500 on February 1, 1990, (ii) interest rate of 12 per cent p.a. payable half-yearly, and (iii) redemption of the non-convertible portion at the end of 8 years. Value What is the value of a partly convertible debenture like one issued by TISCO ? The holder of such a debenture receives (i) interest at a certain rate over the life of the debenture, (ii) equity share/s on part conversion, and (iii) principal repayment relating to the unconverted amount. Hence the value of such a debenture may be expressed as follows : n

n

∑

Vo =

t=1

where Vo It n a Pi F j kd ks

= = = = = = = =

It . + aPi . + ∑ F j . t i  j = m (1 + kd) (1 + ks) (1 + kd) j

value of the convertible debenture at the time of issue interest receivable at the end of period t life of the debenture number of equity shares receivable when part-conversion occurs at the end of period i expected price per equity share at the end of period i installment of principal repayment at the end of period j investors’ required rate of return on the debt component investors required rate of return on the equity component.

To apply the above valuation formula to the partly convertible debenture of TISCO let us assume that : (i) The issue date is August, 1, 1989 and we are evaluating the debenture as of that date. (ii) The price per  share of TISCO, as on February 1, 1990, the point of time when partial conversion will take place, would be Rs.1200. (iii) The investors require a semi-annual rate of return of 8 per cent on the debt component and 10 per cent on the equity component. Given these assumptions the three components on the right hand side of the valuation equation are as follows : n

∑ t=1

16

It . = 72 . + (1 + kd)t (1.08)

∑ t=2

36 . = 352.03 (1.08)t

aPi . = 1 x 1200 = 1090.91 (1 + ks)t (1.10)1 n

∑  j = m

F j . = 600 . = 175.20 (1 + kd)  j (1.08)16

Adding the three components, we find that the value is : 352.03 + 1090.91 + 175.20 = 1618.14 Rate of Return to the Debenture Holder  If an investor subscribes to a partly convertible debenture, what rate of return does he earns ? The rate of  return earned is the value of r in the following equation : n

Subscription price =

∑ t=1

n

It . + aiP . + ∑ F  j .  j = m (1 + r)t (1 + r)t (1 + r) j

Applying this formula to the convertible debenture of TISCO, we find that r is the solving rate of  return in :

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120 =

72 . + 1 x 1200 + (1 + r) (1 + r)

∑ t=2

36 . + 600 . (1 + r)t (1 + r)16

The value of r which solves the above equation approximately 21 per cent. This means that the internal rate of return of yield to the investor on semi-annual basis is about 21 per cent. The cost of a partly convertible debenture to the issuing firm is the discount rate in the equation : n t=1

where NSo It T a Pt b F j kc

= = = = = = = =

n

∑ It (1 – T) +

NSo =

(1 + kc)t

aPtb . + ∑ Fi . t  j = m (1 + kc) (1 + kc) j

net subscription price realised at the time of issue interest payable at the end of period t tax rate applicable to the firm number of equity shares to be given when part conversion occurs at the end of period i price per equity share at the end of period i Proportion of Pi that will be realisable net if the firm were to issue equity shares to public installment of principal repayment at the end of period j discount rate representing the cost of capital

Let us apply it to the convertible debenture of TISCO with the following assumptions : (i) the net subscription price is Rs.1120; (ii) the tax rate is 40 per cent; and (iii) the value of b is 0.80. Given these assumptions, the cost of convertible debentures to TISCO is the discount rate in the expression : 1120 = 72 (1 – 4) + ∑ 36 (1 – 4) + 1 x 1200 x 0.8 + 600 . t=2 (1 + kc) (1 + kc)t (1 + kc) (1 + kc)16 The value of k c which satisfies the above equality is approximately 12 per cent. Hence, the cost of such debentures is about 12 per cent on a semi-annual basis. In interpreting this number remember the caution sounded earlier with respect to internal rate of return. Option Value The holders of convertible debentures are not compelled to make an immediate choice in favour of or  against conversion. They can wait, learn from hindsight, and finally choose the most profitable alternative. The option to wait is valuable. Hence the value of the convertible debenture lies above its floor value. It is shown as the dashed line in Fig. 32.2(c). The difference between the dashed line and the thick lower  bound line represents the value of the option to convert, which is nothing but a call option on the equity shares of the firm, the exercise price being the conversion price. Thus we find that the value of a convertible debenture may be expressed as follows : Value of the convertible debenture

= Max

Straight debenture value,

Conversion value

+ Option value

Financial Synergy  Convertible debentures and debentures with warrants make sense when it is very costly or difficult to assess the risk characteristics of the issuing firm. Suppose you are evaluating a newly set up company that plans to manufacture a novel product, being introduced for the first time India. You are not sure whether the company is a high risk company (in this case you expected yield on straight debentures will be 20 per cent) or a low risk company (in this case your expected yield on straight debentures will be 15 per  cent). In a situation like this, convertible and debentures with warrants provide a measure of protection against errors of risk assessment. Remember that these instrument have two components, the straight debenture and the call component and the call option component. If the company turns out to be riskly, the debenture component will have a low value but the call option component a high value. On the other hand, if the company turns out to be relatively risk-free, the debenture component will have a high value but the call option component a low value. Give this compensating behaviour of the two components, the required yield on the convertible debenture (or the debenture with warrant) will not be very sensitive to default risk. A numerical illustration is given as f ollows : Firm risk

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Yield on straight debenture Yield on convertible debenture (or debenture with warrant)

Low 15% 10%

Risk 20% 11%

The above example essentially suggests that companies with widely varying risks, faced with substantially different costs for straight debentures, can issue convertible debentures on similar terms. Does it mean that convertible debentures provide a ‘free lunch’ to high risk firms? No, it does not mean that. However, it does suggest that a combination of debentures and options produces a financial synergy (or risk synergy) that enables companies with uncertain prospects to obtain capital on more favourable terms.  Agency Costs Convertible debentures and debentures with warrants can mitigate agency problems associated with financing. Holders of straight debentures impose restrictions on a firm so that its risk exposure is kept low. They do this to minimise the prospect of default risk. Equity stockholders, in contrast, would like the firm to undertake high risk projects because their claim is akin to that of holders of call option. If the conflicting demands of debentures and equity stockholders are not properly resolved, the firm may have to forego profitable investment opportunities. Convertible debentures and debentures with warrants may provide a satisfactory resolution of this conflict. Investors in these instruments are unlikely to impose highly restrictive debt covenants as they are less concerned about the increase in the future risk.

SUMMARY •

A warrant gives its holder the right, but not the obligation, to subscribe to a certain number of  equity shares at a stated price during a specified period.

•

A convertible debenture is a debenture that is convertible, partially or fully, into equity shares.

Since a warrant is like a call option on the equity stock of the issuing company, the principles • of option valuation can be applied to warrants.

•

Internationally, convertible debentures are typically convertible into equity shares at the option of the debenture holders. In India, in addition to such debentures, companies also issue debentures that are compulsorily convertible (partially or wholly) into equity shares. The value of such a debenture may  be expressed as gollows :

of thevalue straight component Value of the delayed equity • TheValue conversion is thedebt debenture holder + seeks conversion. component

• The holders of convertible debentures are not compelled to make an

an optionally debenture may be viewed a debenture• For analytical immediate choice purposes, in favour or aginstconvertible conversion. They can wait,aslearn from warrant package. Its value is a function of three factors : straight debenture value, conversion value, and hindsight, and finally choose the most profitable alternative. This option to option value.

wait is valuable. Thus : Value of the convertible debenture

= Max

Straight debenture value,

Conversion + Option value value

•

Surveys of finance executives have thrown up two popular motives for issuing warrants and convertible debentures : (i) They allow companies to issue debt cheaply. (ii) They provide companies an opportunity to issue equity shares in future at a premium over the current price. These explanations have a ‘free lunch’ flavour and do not appear, on closer examination, to be convincing.

•

Modern finance offers superior explanation for the popularity of convertible debentures and