Practice_CostCapital

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Finance 6301 Cost of Capital Practice Interest is compounded annually unless stated otherwise. Payments are at the end of the year unless stated otherwise. All bonds have a face value of $1000. Taxes are 0 unless specified otherwise. 1. Using market values, a firm has a debt ratio (debt/value) of .25. The debt is risk-free. The risk-free rate is 6% and the return on the market is 16%. The (unlevered) asset beta is 2.0. Find the firm’s equity beta and the cost of equity. What is the cost of capital? 2. You have monthly returns for Acme and the market. Based on regression, you get the following information: y = .0575 + .5526x. The R-square is .29. The risk-free rate is 3%. a) Find beta and Jensen’s alpha. Based on Jensen’s alpha, how well did the stock perform? b) What portion of the variance can be explained by market risk? 3. Farm Furniture has a current stock price of $40 per share and 1,000,000 shares outstanding. Using market values, the debt-equity ratio is 2. The equity has a beta of 1.70 and debt has a beta of .4. The firm plans to issue $40,000,000 in equity to pay off existing debt. The beta on the debt will fall to .2. Assume the risk-free rate is 4% and the return on the market is 12%. a) Calculate the original cost of capital and asset beta. b) Find the beta and return on equity after the capital structure change. 4. A project has a beta of .2. The risk-free return is 2% and the return on the market is 12%. The project has an IRR of 6%. a) If the firm’s cost of capital is 14%, will they take the project? b) Using the CAPM to determine project risk, will they take the project? c) Which method is better for analyzing this project? Why? 5. Star plans to finance a new project with $5M in bonds, $1M in preferred stock and $2M in retained earnings. The bonds have a before-tax annual yield of 9%. The preferred stock has a $2.25 annual dividend and a price of $24. Star knows the Treasury bill rate is 3% and the market risk premium is 9%. The common stock has a beta of .80. The tax rate is 30%. Find the weighted average cost of capital. 6. Crook is planning a $100 million expansion to be financed with 20% debt, 5% preferred stock and the rest by issuing common stock.  The debt consists of 15-year bonds with a coupon rate of 12% paid annually. The face value is $1000 and the bonds are issued at par. (Assume issue costs are negligible).  The preferred stock pays an annual dividend of $3.50 a share and is sold to the public for $27 a share. Issue costs for preferred are $2 per share.  Crook expects dividends of $3.80 next year. The growth rate is 8%. Current price of the common stock is $40 per share. Crook will incur 5% in flotation costs if they issue additional common stock. Tax rate is 25%. Find weighted average cost of capital. 7. In mid-2022, RJR had AA rated 15-year bonds with an outstanding yield to maturity of 2.25%. a) What is the highest expected return these bonds could have? b) If you believe RJR bonds have a .85% chance of default per year and an expected loss rate in the event of default of 55%, what is your estimate of the expected return for these bonds?

8. Barn Corp. has two competitors: Coop and Silo. All three firms are relatively stable, so you assume a debt beta of 0. All three firms are also approximately the same size. Barn is 80% equity financed. Use the information below to estimate the equity beta for Barn. Competitor Equity Beta Equity/Value Asset Beta Coop 1.1 75% Silo 3.2 27% 9. Advanced : Jack Corp. needs to issue new debt to fund an asset expansion. They hire Fleece Capital, an investment banking firm, to assist them. Jack estimates that the cost of floating a new bond issue is about 2% of the proceeds. The tax is 25% and it plans to issue 30-year bonds with a $1,000 face and an annual 7% coupon. Find the after-tax cost of debt for Jack Corp. Solution 1.  E =  u + [(D/E)(  u -  D )] = 2 + [(.25/.75)(2-0)] = 2.67 R E = R f + [  E (R m - R f )] = 6% + [2.67(16%-6%)] = 32.67% Cost of capital = R u = R f + [  u (R m - R f )] = 6% + [2(16%-6%)] = 26% R u = (D/V)R D + (E/V)(R E ) = (.25×6%) + (.75×32.67%) = 26% 2. a) Beta = .5526. Alpha = .0575 . Since alpha > 0, the stock did better than average. b) R 2 = .29 so 29% is explained by market risk 3. Equity = 40  1,000,000 = 40,000,000. Debt/Equity = 2 so Debt = 2  40,000,000 = 80,000,000 Value = D+E = 40M + 80M = 120M a)  u = (E/V)  E + (D/V)  D = (40M/120M)  1.7 + (80M/120M)  .4 = .8333 r u = 4% + [.8333(12% - 4%)] = 10.67% You can also use the following: r D = 4% + [.4(12% - 4%)] = 7.2% and r E = 4% + [1.7(12% - 4%)] = 17.6% r u = (40M/120M)×17.6% + (80M/120M)×7.2% = 10.67% b) After: Debt falls 80M – 40M to 40M and Equity rises from 40M to 40M+40M = 80M  E =  u + [(D/E)(  u -  D )] = .8333 + [(40M/80M)(.8333-.2)] = 1.15 r E = 4% + [1.15(12% - 4%)] = 13.2% 4. a) No, because IRR of 6% < 14% cost of capital b) Project Beta = .2, so this is a very safe project. r = 2% + [.2(12%-2%)] = 4% . Accept since IRR > 4% required return based on the project’s risk c) CAPM because the project’s risk (.2) is far lower than the firm’s average risk . To see this, the firm’s cost of capital = 14% > return on the market of 12%. This suggests the firm’s overall beta > 1 (the beta of the market). 5. r D = 9% (given); r P = 2.25/24 = 9.4%; r E = 3% + [.8(9%)] = 10.2% WACC = [(E/V)r E ] + [(D/V)(1-T)r D ] + [(P/V)r P ] = [(2/8)10.2%] + [(5/8)(1-.3)9%] + [(1/8)9.4%] = WACC = 7.66% 6. r D = 12% since the price = 1000, the yield = coupon rate

r P = 3.50/(27-2) = 14% r E = (3.80/(40×(1-5%))) + 8% = 18% WACC = [(E/V)r E ] + [(D/V)(1-T)r D ] + [(P/V)r P ] = [.2×12%×(1-.25)] + [.05×14%] + [.75×18%] = 16% 7. a) If the bonds are risk-free, then the expected return = risk-free rate and the highest expected return is the yield to maturity of 2.25% . b) 2.25% - (.85% × 55%) = 1.78% 8. Competitor Equity Beta Equity/Value Asset Beta Coop 1.1 75% (.25×0) + (.75 ×1.1) = .825 Silo 3.2 27% (.73×0) + (.27 ×3.2) = .864 Average asset beta for Coop and Silo = ½ × (.825 + .864) = .8445 To get the equity beta for Barn: β E = .8445 + ((.2/.8)× (.8445 – 0)) = 1.056 9. Firm pays: PMT = 7% × 1000 × (1-.25) = -52.5. FV = -1000 N = 30 Receives: PV = 1000 × (1-.02) = 980 Calculate I/Y: 5.39% Since this is after-tax, you would use it directly in the WACC. For example, if r E = 20% and the firm was 40% debt, the WACC would be WACC = (.4× 5.39%) + (.6 × 20%) = 14.16%. The tax deduction was build into the calculation for I/Y.

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