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# Cost of Capital

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Lecture #1 FinMan2

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### Cost of Capital

1. 1. After this module, the student isexpected to:1. Identify the most important characteristics of cost of capital2. Compute cost of capital using common stock, debt, preferred stock and retained earnings3. Apply the use of cost of capital4. Compute weighted cost of capital
2. 2. Cost of capital is defined as the rate of returnthat is necessary to maintain the market valueof the firm (or price of the firm’s stock).Also known as1. hurdle rate,2. discounted rate,3. benchmark,4. minimum required of return
3. 3. Applications1. It is used in making capital budgeting decisions;2. It helps in establishing the optimal capital structure, and3. Making decisions such as leasing, bond refunding, and working capital management.
4. 4. Each element of capital has a component costthat is identified by the following: ki = before-tax cost of debt kd = ki (1-t) = after-tax cost of debt, where t = tax rate kp = cost of preferred stock ks = cost of retained earnings (or internal equity) ke = cost of external equity, or cost of issuing new common stock ko = firm’s overall cost of capital, or a weighted average cost of capital
5. 5. The before-tax cost of debt can be found by determiningthe internal rate of return (or yield to maturity) on thebond cash flows. However, the following shortcutformula may be used for approximating the yield tomaturity on a bond. ki = I + (M-V)/ n (M+V)/2where I = annual interest payments in dollars M = par value, usually P1,000 per bond V = value or net proceeds from the sale of a bond n = term of the bond in years
6. 6. Since the interest payment are tax-deductible, thecost of debt must be stated on an after-tax basis.The after-tax cost of debt is: k d = ki ( 1 – t )where t is the tax rate.
7. 7. Assume that the Carter Company issues a P1,000, 8%, 20-year bond whose net proceeds are P940. the tax rate is 40percent. Then, the before-tax cost of debt, k I, is: ki = I + (M-V)/ n (M+V)/2 = P80 + (P1,000 - P940)/20 = P 83 = 8.56% (P1,000 + P940)/2 P970Therefore, the after-tax cost of debts is kd = ki ( 1 – t ) = 8.56% (1 – 0.4 ) = 5.14%
8. 8. The cost of preferred stock, kp, is found bydividing the annual preferred stockdividend, dp, by the net proceeds from the sale ofthe preferred stock, p, as follows: kp = dp p-fSince preferred stock dividends are not a tax-deductible expense, these dividends are paid outafter-taxes. Consequently, no tax adjustment isrequired.
9. 9. Carter Company has preferred stock that pays a P13dividend per share and sells for P100 per share in themarket. The flotation (or underwriting) cost is 3percent, or P3 per share. Then the cost of preferredstock is:Then the cost of preferred stock is: kp = dp p-f = 13 = 13.4% P100 - 3
10. 10. The cost of common stock, ks, is generallyviewed as the rate of return investors requireon a firm’s common stock.Three techniques for measuring the cost ofcommon stock equity capital are available:(1) the Gordon’s growth model,(2)the capital asset pricing model(CAPM) approach and(3) the bond plus approach.
11. 11. Gondon’s Growth Model (GGM) ks = D1 + g PowherePo = value of common stockD1 = dividend to be received in 1 yearks = investor’s required rate of returng = rate of growth (assumed to be constant over time)
12. 12. Assume that the market price of the CarterCompany stock is P40. The dividend to be paidat the end of the coming year is P4 per shareand is expected to grow at a constant annualrate of 6 percent. Then the cost of thirdcommon stock is:ks = D1 + g = P4 + 6% = 16% Po P40
13. 13. The cost of new common stock, or externalequity capital, is higher than the cost of existingcommon stock because of the flotation costsinvolved in selling the new common stock.If f is flotation cost in percent, the formula for the costof new common stock is: ke = D1 +g Po (1 – f )
14. 14. Assume the same data in previous example, exceptthe firm is trying to sell new issues stock of A andits flotation cost is 10 percent. Then: ke = D1 + g Po (1 – f ) = P4 + 6% P40 (1 – 0.1) = P4 + 6% = 11% + 6% = 17.11% P36
15. 15. An alternative approach to measuring the cost of commonstock is to use the CAPM, which involve the following steps:1. Estimates the risk-free rate,rf, generally taken to be the Treasury bill rate.2. Estimate the stock’s beta coefficient, b; which is an index of systematic (or nondiversifiable market) risk.3. Estimate the rate of return on the market portfolio such as Phisix or Dow Jones.4. Estimate the required rate of return on the firm’s stock, using the CAPM (or SML) equation. ks = rf + b (rm – rf)
16. 16. Assuming that rf is 7 percent , b is 1.5 and rm is 13percent, then:ks = rf + b (rm – rf) = 7% + 1.5 (13% - 7%) = 16%The 16 percent cost of common stock can be viewed asconsisting of a 7 percent risk-free rate plus a 9 percentrisk premium, which reflects that the firm’s stock price is1.5 times more volatile than the market portfolio to thefactors affecting nondiversifiable, or systematic, risk.
17. 17. Another simple but useful approach to determiningthe cost of common stock is to add a risk premium tothe firm’s own cost of long-term debt, as follows:ks = long-term bond rate + risk premium = ki(1-t) + risk premiumA risk premium of about 4 percent is commonly usedwith this approach.
18. 18. The cost of common stock using the bond plusapproach is :ks = long-term bond rate + risk premium = ki(1-t) + risk premium = 5.14% + 4% = 9.14%
19. 19. The firm’s overall cost is the weighted average of theindividual capital costs, with the weights being theproportions of each type of capital used. Let ko be theoverall cost of capital.ks =Σ % of total capital structure cost of capital for supplied by each type x each type of capital of capital = wd x k d + wp x kp +We x ke + ws x ks
20. 20. Book Value Weights.The use of book value weights in calculating the firm’sweighted cost of capital assumes that a new financing will beraised using the same method the firm used for its presentcapital structure. The weights are determined by dividingthe book value of each capital component by the sum of thebook values of all the long-term capital sources.Assume the following capital structure for the Carter Co.:Mortgage bonds (P1,000 par) P20,000,000Preferred stock (P100 par) 5,000,000Common stock (P40 par) 20,000,000Retained earnings 5,000,000Total P50,000,000
21. 21. The book value weights and the overall cost of capital arecomputed as follows:Source Book Value Weights Cost Weighted CostDebt P20,000,000 40% 5.14% 2.06%PS 5,000,000 10 13.40% 1.34CS 20,000,000 40 17.11% 6.84RE 5,000,000 10 16.00% 1.60Totals P50,000,000 100% 11.84%Overall cost of capital = ko = 11.84%
22. 22. Market value weights are determined by dividing the market value of eachsource by the sum of the market values of all sources. The use of market valueweights for computing a firm’s weighted average cost of capital is theoreticallymore appealing than the use of book value weights because the market valuesof the securities closely approximate the actual peso to be received from theirsale. Assume that the security market prices are as follows: Mortgage bonds = P1,100 per bond Preferred stock = P90 per share Common stock = P80 per share The firm’s number of securities in each category is: Mortgage bonds = P20,000,000 = 20,000 P1,000 Preferred stocks = P5,000,000 = 50,000 P100 Common Stock = P20,000,000 = 500,000 40
23. 23. The market value weights are:Source Number of Price Market Value SecuritiesDebt 20,000 P1,100 P22,000,000Preferred stock 50,000 90 4,500,000Common stock 500,000 80 40,000,000 P66,500,000
24. 24. The P40 million common stock value must be split in the ratio of4 to 1 (the /P20 million common stock versus the P 5 millionretained earnings in the original capital structure), since themarket value of the retained earnings has been impounded intothe common stock. The firm’s cost of capital is as follows:Source Market Weights Cost Weighted Value AverageDebt P22,000,000 33.08% 5.14% 1.70Preferred stock 4,500,000 6.77 13.40% 0.91Common stock 32,000,000 48.12 7.11% 8.23Retained earnings 8,000,000 12.03 16.00% 1.92 P66,500,000 100.00% 12.76%Overall cost of capital = ko = 12.76%