1. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-1 Concept and Measurement of Cost of Capital

2. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-2 Measurement of Specific Costs There are four types of specific costs 1)Cost of Debt 2)Cost of Preference Shares 3)Cost of Equity Capital 4)Cost of Retained Earnings

3. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-3 Cost of Debt Cost of debt is the after tax cost of long-term funds through borrowing. The debt carries a certain rate of interest. Interest qualifies for tax deduction in determining tax liability. Therefore, the effective cost of debt is less than the actual interest payment made by the firm by the amount of tax shield it provides. The debt can be either 1)Perpetual/ irredeemable Debt 2)Redeemable Debt

4. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-4 Perpetual Debt In the case of perpetual debt, it is computed dividing effective interest payment, i.e., I (1 – t) by the amount of debt/sale proceeds of debentures or bonds (SV). Symbolically k i = Before-tax cost of debt k d = Tax-adjusted cost of debt I = Annual interest payment SV = Sale proceeds of the bond/debenture t = Tax rate

5. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-5 Solution (i)Debt issued at par Before-tax cost, k i = (Rs 10,000 / Rs 1,00,000) = 10 per cent After-tax cost, k d = k i (1 – t) = 10% (1 – 0.35) = 6.5 per cent (ii)Issued at discount Before-tax cost, k i = (Rs 10,000 / Rs 90,000) = 11.11 per cent After-tax cost, k d = 11.11% (1 – 0.35) = 7.22 per cent (iii)Issued at premium Before-tax cost, k i = (Rs 10,000 / Rs 1,10,000) = 9.09 per cent After-tax cost, k d = 9.09% (1 – 0.35) = 5.91 per cent Example 1 A company has 10 per cent perpetual debt of Rs 1,00,000. The tax rate is 35 per cent. Determine the cost of capital (before tax as well as after tax) assuming the debt is issued at (i) par, (ii) 10 per cent discount, and (iii) 10 per cent premium.

6. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-6 Redeemable Debt In the case of redeemable debt, the repayment of debt principal (COP) either in instalments or in lump sum (besides interest, COI) is also taken into account. k d is computed based on the following equations: where CI 0 = Net cash proceeds from issue of debentures or from raising debt COI 1 + COI 2 +... + COI n = Cash outflow on interest payments in time period 1,2 and so on up to the year of maturity after adjusting tax savings on interest payment. COP n = Principal repayment in the year of maturityk d = Cost of debt. The cost of debt is generally the lowest among all sources partly because the risk involved is low but mainly because interest paid on debt is tax deductible.

7. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-7 Example 2 A company issues a new 10 per cent debentures of Rs 1,000 face value to be redeemed after 10 years The debenture is expected to be sold at 5 per cent discount. It will also involve floatation costs of 5 per cent of face value. The company’s tax rate is 35 per cent. What would the cost of debt be? Illustrate the computations using shortcut method.

8. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-8 (2) Shortcut Method The formula for approximating the effective cost of debt can, as a shortcut, be shown in the Equation whereI= Annual interest payment RV= Redeemable value of debentures/debt SV= Net sales proceeds from the issue of debenture/debt (face value of debt minus issue expenses) N m = Term of debt f= Flotation cost d= Discount on issue of debentures pi= Premium on issue of debentures pr= Premium on redemption of debentures t= Tax rate

9. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-9 Example 3 A company has issued 10 per cent debentures aggregating Rs 1,00,000. The flotation cost is 4 per cent. The company has agreed to repay the debentures at par in 5 equal annual instalments starting at the end of year 1. The company’s rate of tax is 35 per cent. Find the cost of debt.a Solution Net proceeds from the sale of debenture = Rs 96,000. Since the cash outflows are higher in the initial years than the average (Rs 24,500), let us try to determine PV at 7 per cent and 8 per cent. Cash outflowsPV factor atTotal PV at 7%8%7%8% 26,5000.9350.926Rs 24,777Rs 24,539 25,2000.8730.85722,00021,596 23,9000.8160.79419,50218,977 22,6000.7630.73517,24416,611 21,3000.7130.68115,18714,505 98,71096,228 @Rs 20,000 principal + Rs 10,000 interest (1 – 0.35) The value of k d = 8 per cent.

10. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-10 Cost of Preference Shares The cost of preference share (k p ) is akin to k d. However, unlike interest payment on debt, dividend payable on preference shares is not tax deductible from the point of view assessing tax liability. n Irredeemable Preference Shares n Redeemable Preference Shares

11. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-11 Irredeemable Preference Shares The cost of preference shares in the case of irredeemable preference shares is based on dividends payable on them and the sale proceeds obtained by issuing such preference shares, P 0 (1 – f ). In terms of equation: wherek p = Cost of preference capital D p = Constant annual dividend payment P 0 = Expected sales price of preference shares f = Flotation costs as a percentage of sales price D t = Tax on preference dividend

12. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-12 Example 4 A company issues 11 per cent irredeemable preference shares of the face value of Rs 100 each. Flotation costs are estimated at 5 per cent of the expected sale price. (a) What is the k p, if preference shares are issued at (i) par value, (ii) 10 per cent premium, and (iii) 5 per cent discount? (b) Also, compute k p in these situations assuming 13.125 per cent dividend tax Solution

13. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-13 Redeemable Preference Shares The cost of redeemable preference shares requiring lump sum repayment (P) is determined on the basis of the following equation: where P 0 = Expected sale price of preference shares f = Floatation cost as percentage of P 0 D p = Dividends paid on preference shares P n = Repayment of preference capital amount

14. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-14 Example 5 ABC Ltd has issued 11 per cent preference shares of the face value of Rs 100 each to be redeemed after 10 years. Flotation cost is expected to be 5 per cent. Determine the cost of preference shares (k p ). Solution Determination of PV at 11% and 12% YearCash outflows PV factor atTotal PV at 11%12%11%12% 1 – 10Rs 115.8895.65Rs 64.78Rs 62.15 101000.3520.32235.15 99.93 32.20 94.35 K p =11.9 per cent

15. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-15 The computation of cost of equity capital (k e ) is conceptually more difficult as the return to the equity- holders solely depends upon the discretion of the company management. It is defined as the minimum rate of return that a corporate must earn on the equity-financed portion of an investment project in order to leave unchanged the market price of the shares. There are two approaches to measure k e : 1) Dividend Valuation Model Approach 2) Capital Asset Pricing Model (CAPM) Approach. Cost of Equity Capital

16. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-16 As per the dividend approach, cost of equity capital is defined as the discount rate that equates the present value of all expected future dividends per share with the net proceeds of the sale (or the current market price) of a share. The cost of equity capital can be measured with the following equations: (A) When dividends are expected to grow at a uniform rate perpetually: whereD 1 = Expected dividend per share P 0 = Net proceeds per share/current market price g = Growth in expected dividends Dividend Valuation Approach

17. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-17 Example 6 Suppose that dividend per share of a firm is expected to be Re 1 per share next year and is expected to grow at 6 per cent per year perpetually. Determine the cost of equity capital, assuming the market price per share is Rs 25. Solution: This is a case of constant growth of expected dividends. The k e can be calculated by using Equation The dividend approach can be used to determine the expected market value of a share in different years. The expected value of a share of the hypothetical firm in Example 6 at the end of years 1 and 2 would be as follows

18. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-18 Example 7 From the undermentioned facts determine the cost of equity shares of company X: (i)Current market price of a share = Rs 150. (ii)Cost of floatation per share on new shares, Rs 3. (iii)Dividend paid on the outstanding shares over the past five years: YearDividend per share 123456123456 Rs 10.50 11.02 11.58 12.16 12.76 13.40 (iv)Assume a fixed dividend pay out ratio. (v)Expected dividend on the new shares at the end of the current year is Rs 14.10 per share.

19. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-19 Solution As a first step, we have to estimate the growth rate in dividends. Using the compound interest table (Table A-1), the annual growth rate of dividends would be approximately 5 per cent. (During the five years the dividends have increased from Rs 10.50 to Rs 13.40, giving a compound factor of 1.276, that is, Rs 13.40/Rs 10.50. The sum of Re 1 would accumulate to Rs 1.276 in five years @ 5 per cent interest).

20. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-20 CAPITAL ASSET PRICING MODEL (CAPM) APPROACH The CAPM describes the relationship between the required rate of return or the cost of equity capital and the non-diversifiable or relevant risk of the firm as reflected in its index of non-diversifiable risk, that is, beta. Symbolically, K e = R f + b (K m – R f )(14) R f = Required rate of return on risk-free investment b = Beta coefficient**, and K m = Required rate of return on market portfolio, that is, the average rate or return on all assets M = Excess in market return over risk-free rate, J = Excess in security returns over risk-free rate, MJ = Cross product of M and J and N = Number of years

21. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-21 Example 8 The Hypothetical Ltd wishes to calculate its cost of equity capital using the capital asset pricing model approach. From the information provided to the firm by its investment advisors along with the firms’ own analysis, it is found that the risk-free rate of return equals 10 per cent; the firm’s beta equals 1.50 and the return on the market portfolio equals 12.5 per cent. Compute the cost of equity capital. Solution K e = 10% + [1.5 × (12.5% – 10%)] = 13.75 per cent

22. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-22 Example 9: As an investment manager you are given the following information Investment in equity shares of Initial price Dividends Year-end market price Beta risk factor ACement Ltd Steel Ltd Liquor Ltd BGovernment of India Bonds Risk-free return, 8 per cent Rs 25 35 45 1,000 Rs 2 2 140 Rs 50 60 135 1,005 0.80 0.70 0.50 0.99 You are required to calculate (i) expected rate of returns of market portfolio, and (ii) expected return in each security, using capital asset pricing model

23. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-23 Solution (i) Expected Returns on Market Portfolio SecurityReturnInvestment DividendsCapital Appreciation Total ACement Ltd Steel Ltd Liquor Ltd BGovernment of India Bonds Rs 2 2 140 146 Rs 25 25 90 5 145 Rs 27 27 92 145 291 Rs 25 35 45 1,000 1.105 Rate of return (expected) on market portfolio = Rs 291/Rs 1,105 = 26.33 per cent (ii) Expected Returns on Individual Security (in percent) k e = R f + b(k m – R f ) Cement Ltd = 8% + 0.8 (26.33% – 8%)22.66 Steel Ltd = 8% + 0.7 (26.33% – 8%)20.83 Liquor Ltd = 8% + 0.5 (26.33% – 8%)17.16 Government of India Bonds = 8% + 0.99 (26.33% – 8%)26.15

24. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-24 Cost of Retained Earnings The cost of retained earning (k r ) is equally difficult to calculate in theoretical terms. Since retained earnings essentially involves use of funds, it is associated with an opportunity/implicit cost. The alternative to retained earnings is the investment of the funds by the firm itself in a homogeneous outside investment. Therefore, k r is equal to k e. However, it might be slightly lower than k e in the case of new equity issue due to flotation costs.

25. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-25 Computation of Overall Cost of Capital Weighted Average Cost of Capital Weighted average cost of capital is the expected average future cost of funds over the long run found by weighting the cost of each specific type of capital by its proportion in the firm;s capital structure. Assignment of Weights The aspects relevant to the selection of appropriate weights are: 1)Historical weights a)Book value weights or b)Market value weights 2)Marginal Weights

26. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-26 Historical Weights Historic weights either book or market value weights are based on actual capital structure proportion to calculate weights. Market Value Weights Market value weights use market values to measure the proportion of each type of capital to calculate weighted average cost of capital. Book Value Weights Book value weights use accounting (book) values to measure the proportion of each type of capital to calculate the weighted average cost of capital Marginal Weights Marginal weights use proportion of each type of capital to the total capital to be raised.

27. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-27 Mechanics of Computation Example 10: Book Value Weights (a) A firm’s after-tax cost of capital of the specific sources is as follows: Cost of debt Cost of preference shares (including dividend tax) Cost of equity funds 8% 14 17 (b) The following is the capital structure SourceAmount Debt Preference capital Equity capital Rs 3,00,000 2,00,000 5,00,000 10,00,000 (c) Calculate the weighted average cost of capital, k 0 using book value weights.

28. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-28 Table 1: Solution Computation of weighted average cost of capital (Book Value Methods) Source of funds (1) Amount (2) Proportion (3) Cost (%) (4) Weighted cost (3 x 4) (5) Debt Preference capital Equity capital Rs 3,00,000 2,00,000 5,00,000 10,00,000 0.3 (30) 0.2 (20) 0.5 (50) 1.00 (100) 0.08 0.14 0.17 0.024 0.028 0.085 0.137 Weighted average cost of capital 13.7% An alternative method of determining the k0 is to compute, as shown in Table 2, the total cost of capital and then divide this figure by the total capital. This procedure obviously avoids fractional calculations. TABLE 2 Computation of Weighted Average Cost of Capital (Alternative Method) SourcesAmountCost (%)Total cost (2 × 3) (1)(2)(3)(4) Debt Preference capital Equity capital Total Rs 3,00,000 2,00,000 5,00,000 10,00,000 8 14 17 Rs 24,000 28,000 85,000 1,37,000 Weighted average cost of capital = [(Rs 1,37,000 / Rs 10,00,000) x 100] = 13.7 per cent

29. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-29 Solution The computation is illustrated in Table 4. TABLE 4 Weighted Average Cost of Capital (Marginal Weights) Sources of fundsAmountProportionCost (%) (2 × 4)Total cost (1)(2) (3)(4)(5) DebtRs 3,00,0000.60(60)8Rs 24,000 Preference shares 1,00,0000.20(20)1414,000 Retained earnings1,00,0000.20(20)1717,000 5,00,0001.00(100)55,000 Weighted average cost of capital = (Rs 55,000/Rs 5,00,000) × 100 = 11 per cent Example 12 The firm of Example 10 wishes to raise Rs 5,00,000 for expansion of its plant. It estimates that Rs 1,00,000 will be available as retained earnings and the balance of the additional funds will be raised as follows: Long-term debtRs 3,00,000 Preference shares1,00,000 Using marginal weights, compute the weighted average cost of capital.

30. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-30 SOLVED PROBLEM

31. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-31 As a financial analyst of a large electronics company, you are required to determine the weighted average cost of capital of the company using (a) book value weights and (b) market value weights. The following information is available for your perusal. The company’s present book value capital structure is: Debentures (Rs 100 per debenture)Rs 8,00,000 Preference shares (Rs 100 per share)2,00,000 Equity shares (Rs 10 per share)10,00,000 20,00,000 All these securities are traded in the capital markets. Recent prices are: Debentures, Rs 110 per debenture Preference shares, Rs 120 per share Equity shares, Rs 22 per share

32. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-32 Anticipated external financing opportunities are: (i) Rs 100 per debenture redeemable at par; 10 year maturity, 11 per cent coupon rate, 4 per cent flotation costs, sale price, Rs 100. (ii) Rs 100 preference share redeemable at par; 10 year maturity, 12 per cent dividend rate, 5 per cent flotation costs, sale price, Rs 100. (iii) Equity shares: Rs 2 per share flotation costs, sale price = Rs 22. In addition, the dividend expected on the equity share at the end of the year is Rs 2 per share; the anticipated growth rate in dividends is 7 per cent and the firm has the practice of paying all its earnings in the form of dividends. The corporate tax rate is 35 per cent. Solution: Determination of specific costs:

33. © Tata McGraw-Hill Publishing Company Limited, Financial Management 11-33 Using these specific costs we can calculate the book value and market value weights as follows: (a)k 0 based on book value weights Source of capitalBook value (BV)Specific cost (k) (%)Total costs [BV (×) k] DebenturesRs 8,00,0007.7Rs 61,600 Preference shares2,00,00012.825,600 Equity shares10,00,00017.01,70,000 20,00,0002,57,200 k 0 = Rs 2,57,200/Rs 20,00,000 = 12.86 per cent (b) k 0 based on market value weights Source of capitalMarket value (MV) Specific cost (k) (%)Total costs [MV (×) k] DebenturesRs 8,80,0007.7Rs 67,760 Preference shares2,40,00012.830,720 Equity shares22,00,00017.03,74,000 Total capital33,20,0004,72,480 k 0 = Rs 4,72,480/Rs 33,20,000 = 14.23 per cent