The Different Techniques Of Computing And The Cost of Various Sources of Capital Is Explained Here.
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Concept and Measurement of Cost of Capital Dr. Amit Gupta
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Cost of Capital In operational terms, it is defined as the weighted average cost of capital (ko) of all long-term sources of finance. The major long-term sources of funds are 1) 2) 3) 4) Debt, Preference shares, Equity capital, and Retained earnings. Dr. Amit Gupta
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Explicit and Implicit Costs Dr. Amit Gupta
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Measurement of Specific Costs There are four types of specific costs 1) Cost of Debt Cost of Preference Shares 2) Cost of Equity Capital 3) Cost of Retained Earnings 4) Dr. Amit Gupta
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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 Dr. Amit Gupta
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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 sv t (3) (4) = Before-tax cost of debt = Tax-adjusted cost of debt = Annual interest payment = Sale proceeds of the bond/debenture = Tax rate Dr. Amit Gupta
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Example A company has 10 per cent perpetual debt of Rs 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. Solution (i) Debt issued at par Before-tax cost, ki = (Rs 10,000 / Rs 1,00,000) = 10 per cent After-tax cost k k (1 t) 100/0 (1 -0.35) = 6.5 per cent (ii) Issued at discount Before-tax cost, ki = (Rs 10,000 / Rs 90,000) = 11.11 per cent After-tax cost, kd = 11.11% (1 — 0.35) = 7.22 per cent (iii) Issued at premium Before-tax cost, ki = (Rs 10,000 / Rs 1, 10,000) = 9.09 per cent After-tax cost, kd = 9.09% (1 — 0.35) = 5.91 per cent Dr. Amit Gupta
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Redeemable Debt Dr. Amit Gupta
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RV+SV 2 where I = Annual interest payment RV = Redeemable value of debentures/debt sv Net sales proceeds from the issue (face value of debt minus issue expenses) = Term of debt f = Flotation cost d = Discount on issue of debentures pi = Premium on issue of debentures pr = Premium on redemption of debentures = Tax rate t Dr. Amit Gupta of debenture/debt
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Yield to Maturity Yield to maturity (Y TM) is a rate of return that measures the total return of a bond/debenture (coupon/interest payments as well as capital gain or loss)from the time of purchase untilnaturity. The calculation of Y TM takes into account the current market price, the par value, coupon interest rates and the time to maturity. It is also assumed in yield to maturity that are reinvested at the rate. (1+YY Dr. Amit Gupta
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Yield to Maturity (Contd) In the formula, PO = issue price of debt It = the interest paid on debt Pn = repayment of debt on maturity Y = yield or return to maturity Dr. Amit Gupta
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Yield to Maturity (Contd) We canalso use the shortcut formula to calculate yield to maturity: + (M -PO+N YTM (11+11)+2 where Y TM = yield to maturity It interest paid on debt M = par or maturity value of debt or redemption value Pb = debt's issue price or its purchase price or net realized value M- 10b = Debt premium N = life of debt or number of years to maturity Dr. Amit Gupta
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Yield to Maturity: An Example ABC Ltd issues bonds of par value INR 2000 at 12 per cent interest, on 8 per cent discountfor 10 years, calculate its yield to maturity. Solution YTM (M+Pb)+2 240 + (2000-1840)+10 YTM (2000+1840) +2 Dr. Amit Gupta 240+16 = 13.33% 1920
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Cost of Preference Shares The cost of preference share (kp) 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. On the contrary, tax (Dt) may be required to be paid on the payment of preference dividend. Irredeemable Preference Shares n Redeemable Preference Shares n Dr. Amit Gupta
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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, PO (1 — f ). In terms of equation: where k po(l-f) Dp(1+Dt) po(l-f) = Cost of preference capital = Constant annual dividend payment = Expected sales price of preference shares = Flotation costs as a percentage of sales price = Tax on preference dividend Dr. Amit Gupta
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Example 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 kp, if preference shares are issued at (i) par value, (ii) 10 per cent premium, and (iii) 5 per cent discount? (b) Also, compute kp in these situations assuming 13.125 per cent dividend tax Solution (a) (i) Issued at par 11 Rs 1000 - 0.05) (ii) Issued at Premium Rsll = 10.5% Rs 1100-0.05) (iii ) Issued at Discount Rsll = 12.2% Rs 950-0.05) (b) (i) Issued at par Rs 11(1.13125) = Rs 12.44 Rs 95 (ii) Issued at Premium Rs 12.44 -11.9% Rs 104.5 (iii ) Issued at Discount Rs 12.44 = 13.8% Rs 90.25 = 13.1% Dr. Amit Gupta
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Cost of Redeemable Preference Shares Where kp is the cost of preference share, Dt is the dividend, PO is the issue price of preference share, Pn is the redemption price, n is the maturity period. Like redeemable debt we can also use the shortcut formula for calculating cost of preference shares: Dp + (M-Pb)+N Dr. Amit Gupta
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Cost of Redeemable Preference Shares (Contd) In the formula, cost Of preference shares, M par or maturity value of preference shares or redemption value, Pb = preference shares' issue price or its purchase price or net realized value, M- Pb share premium, N life of preference shares or no. of years to maturity Dr. Amit Gupta
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Cost of Equity Capital The computation of cost of equity capital (ke) 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 Capital Asset Pricing Model (CAPM) Approach. 2) Dr. Amit Gupta
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Dividend Valuation Approach 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 equation: (A) When dividends are expected to grow at a uniform rate perpetually: where = Expected dividend per share = Net proceeds per share/current market price = Growth in expected dividends Dr. Amit Gupta
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(B) Under different growth assumptions of dividends over the years: t=l t=n-kl wheregb = Rate Of growth in earlier years gc = Constant growth in later years Dr. Amit Gupta
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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 kecan be calculated by using Equation + 0.06 = Rs25 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 Rs 1.06 (i) Price at the end of the first year (P ) = = 26.50 1 0.10-0.06 3 _ Rs1.124 = Rs 28 2 -g - 0.10-0.06 Dr. Amit Gupta
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Example 7 From the under mentioned facts determine the cost of equity shares of company X: (ii) (iv) (v) Current market price of a share = Rs 150. Cost of floatation per share on new shares, Rs 3. Dividend paid on the outstanding shares over the past five years: Year 1 2 3 4 5 6 Assume a fixed dividend pay out ratio. Dividend per share Rs 10.50 11.02 11.58 12.16 12.76 13.40 Expected dividend on the new shares at the end of the current year is Rs 14.10 per share. Dr. Amit Gupta
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Soludon As a first step, we have to estimate the growth rate in dividends. Using the compound interest table (Table A-I), 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 1276 in five years @ 5 per cent interest). Rs 14.10 Rs 147(Rs 150- Rs3) Dr. Amit Gupta
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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, Rf = Required rate of return on risk-free investment = Beta coefficient**, and b — Required rate of return on market portfolio, that is, the average rate or return on all assets Dr. Amit Gupta
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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 Ke = + [1.5 x (12.5% - 10%)] = 13.75 per cent Dr. Amit Gupta
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Example 9: As an information Investment in equity shares of A Cement Ltd Steel Ltd Liquor Ltd B Government of India investment manager you Initial Dividends are given the following price Rs 25 35 45 1 ,ooo 2 2 140 Year-end market price Rs 50 60 135 1 ,005 Beta risk factor 0.80 0.70 0.50 0.99 Bonds Risk-free return, 8 per cent 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 Dr. Amit Gupta
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Solution (i) Expected Returns on Market Portfolio Security A Cement Ltd Steel Ltd Liquor Ltd B Government of India Bonds Return Dividends Rs2 2 2 140 146 Capital Appreciation Rs 25 25 90 5 145 Total Rs 27 27 92 145 291 Investment Rs 25 35 45 1.105 Rate of return (expected) on market portfolio = Rs 291/Rs cent (ii) Expected Returns on Individual Security (in percent) Rf+ b(km- R) Cement Ltd = 80/0 + 0.8 (26.33% - Steel Ltd = 80/0 + 0.7 (26.33% - Liquor Ltd = 80/0 + 0.5 (26.33% - 8%) Government of India Bonds = 8% + 0.99 (26 33 / Dr. Amit Gupta 1,105 = 26.33 per 22.66 20.83 26.15
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Capital Asset Pricing Model Assume that Rf is 9 per cent and Rm is 18 per cent. If a security has a beta factor of: (a) 1.4, (b) 1.0 and (c) 2.3, determine the expected return of the security. Solution = + (18% 1.4 R,) = + (18% - 1.0 R,) = + (18% 2.3 Dr. Amit Gupta = 21.7% 29.7%
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Cost of Retained Earnings (Contd) Generally, the cost of retained earnings is slightly less than the cost of equity since no issuance costs are incurred. Floatation cost is considered when determining the cost of equity. Retained earnings is the residual earnings of a firm. where ke is cost of equity, kre is the cost of retained earnings and fis the floatation cost. Dr. Amit Gupta
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Weighted Average Cost of Capital (WACC) The capital that a company procures is derived from r) various sources. Each source of capital has a distinct cost attached r) toll, The overall cost of capital is termed as weighted r) average cost of capital (WACC). Dr. Amit Gupta
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Weighted Average Cost of Capital (Contd) WACC is calculated by multiplying the cost of each capital component by its proportional weighting and then summing them. Thus, WACC = Wd (cost of debt) + (cost of equity) + wp (cost of preferred stock)+ wre (cost of retained earnings) Where Wd is weight of debt, vvs is weight of equity, wp is weight of preference shares, wre is weight of retained earnings. Dr. Amit Gupta
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Weighted Average Cost of Capital: An Example Calculate the weighted average cost of capital from the figures shown inthe table below: Capital component Long-term debt (5,000 bonds) Common stock (62,500 shares) Preferred stock (20,000 shares) Retained earnings Dr. Amit Gupta Book value Cost 5.4% 13.9% 12.5% 12.0%
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Weighted Average Cost of Capital: An Example (Contd) The weighted average cost of capital is calculated as shown in the table below: Capital component Long-term debt Common stock Preferred stock Retained earnings Market value INR 52/50,000 INR INR INR Weight 7% Cost 5.4% 13.9% 12.5% 120% 9.2% Weighted cost 2.8% 9% Weighted average cost of capital Dr. Amit Gupta
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