2. You own 10% of firm Z s stock. What cash flow will you get in the future? What combination of other assets will give you the same cash flow?

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1 MØA 155 PROBLEM SET: Capital Structure Exercise 1. A firm currently own assets worth $4 mill that have a beta of 1. The risk free interest rate is 10% and the market risk premium is 8%. Suppose the firm has the opportunity to invest in a project that will earn a 13% rate of return for certain into the indefinite future. The cost of the project is $1 mill. Should the firm make the investment? Exercise 2. Interest tax shields [4] Calculate the present value of interest tax shields generated by the following three debt issues. The firm s cost of capital is 16%. Assume that only corporate tax rates are relevant, and the marginal tax rate (τ c )=50%. 1. A $1000 zero coupon loan due one year from now. 2. A $1000, 1 year loan at 10% interest. 3. A $1000 perpetuity at 10% interest. Exercise 3. Arnold s kindergartens [7] As a financial consultant to Arnold s kindergarten s, you are given the following information about two companies, one levered and one unlevered: Firm U Firm L Before tax operating income $10,000 $10,000 Interest on debt 0 2,500 Cost of capital (WACC)? 16% Cost of Equity capital?? Cost of Debt capital -? Value of equity? 22,500 Value of debt 0? Value of firm?? Find the missing figures in the above table. Assume that the corporate tax rate is 40% and all cash flows are perpetual. Hint: Start by computing the value of the levered firm from the information given in the table. Exercise 4. Debt/Equity [7] Firm Z and Y have identical cash flows. Firm Z is 40% debt financed and 60% equity financed, while firm Y is 0% debt financed and 100% equity financed. The same required rate of return on their debt equals 10%. (Assume debt is perpetual) 1. Next period s cash flows for each firm are $100. Assume both firms pay out all excess cash in the form of dividends. What cash flows go to the debt and equity holders of both firms? Assume no corporate taxes. (Use D z for the value of firm Z s debt). 2. You own 10% of firm Z s stock. What cash flow will you get in the future? What combination of other assets will give you the same cash flow? 3. Suppose the value of firm Z is greater than firm Y. How can you become very rich? (You may assume no transactions costs, or other market imperfections) 4. Now, suppose there is a corporate tax rate of 40%. What should the value of each firm be? 1

2 Exercise 5. Sweeny Pie [5] Sweeny Pie Company s common stock has a beta of 1.0 and a total market value of $12 million. The expected risk premium on the market is 8% and the T-bill rate is 12%. If the company s cost of capital is 18%, what is the value of the company s risk free debt? Exercise 6. Charon Ferries The market value of Charon Ferries common stock is $16 million, and the market value of its (risk-free) debt is $4 million. The beta of the company s common stock is 1.5 and the expected risk premium on the market is 8%. If the Treasury Bill rate is 5%, what is the company s cost of capital? Exercise 7. Tax Rate Change [3] In a M&M world with US type taxation, the cost of equity is influenced by the tax rate. If the corporate tax rate increases from 34% to 40%, would you expect the required rate of return on equity to increase, decrease or stay the same? Exercise 8. B&N (WC 15.1) [5] The Bonner Company and the Kirkeby Company are identical except for their leverage ratios and the interest rate on debt. Each has $10 million in assets, each earned $2 million before interest and taxes in 1992, and each has a 40% corporate tax rate. Bonner, however, has a leverage ratio (debt/total assets) of 30% and pays 10% interest on debt, while Kirkeby has a 50% leverage ratio and pays 12% on debt. 1. Calculate the rate of return on equity (net income/equity) for each firm. 2. Observing that Kirkeby has a higher return on equity, Bonner s treasurer decides to raise the leverage ratio from 30% to 60%. This will increase Bonner s interest rate on debt to 15%. Calculate the new rate of return on equity for Bonner. 2

3 Empirical Solutions MØA 155 PROBLEM SET: Capital Structure Exercise 1. The company-wide cost of capital currently is r = = 18% If the firm compared the 13% return on the new project to its cost of capital, they would reject the project. But this would be a mistake since the company-wide cost of capital ignores the risk of the project. The NPV of the project is NP V = $1, 000, $1, 000, = $300, 000 Note that the appropriate discount rate for this project is r f = 10%. If the firm issued stock worth $1 mill. to finance the project, the market value of the firms assets would increase to $5.3 mill and the company-wide cost of capital would decline to 16.04%. r = = 16.04% Thus, the required rate of return on the firm s equity would fall after the investment. The reason that the required return on the firm s equity falls to 16.04% is because the beta of the firm s assets decline to β = = Exercise 2. Interest tax shields [4] P V = ($1, %) 50% 1.16 = ( ) = $ P V = t=1 ($1, %) 50% (1.16) t ( ) 0.5 = = 0.16 = $

4 Exercise 3. Arnold s kindergartens [7] Exercise 4. Debt/Equity [7] 1. Cash flows. 2. Future cash flows: $10, 000(1 0.4) V L = = $37, D L = V L E L = $15, 000 $2, 500 D L = $15, 000 = r D r D = 16.67% (10, 000 2, 500)(1 0.40) E L = $22, 500 = = 20% 22, r = 16% = (1 0.4)15, 37, , 500 V U = V L τ c D = $37, $15, 000 = $31, , 000(1 0.4) V U = E U = 31, 500 = = r = 19.05% Firm U Firm L Before tax operating income 10,000 10,000 Interest on debt 0 2,500 Cost of capital 19.05% 16.0% Cost of Equity capital 19.05% 20.0% Cost of Debt capital % Value of equity 31,500 22,500 Value of debt 0 15,000 Value of firm 31,500 37,500 Alternative assets to replicate these cash flows: 3. We then recognise an arbitrage opportunity. Firm Z Firm Y Cash flow Debt payment 0.10D Z Equity payment D Z ( D Z ) Buy 10% of Y Borrow 10% of D Z at 10% rate 0.1 (0.10 D Z ) Net 0.1 ( D Z ) Cost Next period Buy Y V Y 100 Short Z V Z D Z ( D Z ) BorrowD Z D Z 0.1D Z Net V Y + V Z > 0 0 4

5 4. New firm values after tax of 40%. Let V Y, V Z be the no tax values of Y and Z. Since Y has no debt, its value goes down by 40%, to 0.60 V Y. For firm Z, its value is adjusted for the tax shelter of debt: Firm Z goes to 0.6V Z + 0.4D Z Exercise 5. Sweeny Pie [5] Given Want to find D. Remember r = r f = 12% E[r m ] r f = 8% E = $12mill r = 18% = 0.6V Y + 0.4D Z D D + E r D + E D + E Since the equity has a β of 1, it has the same return as the market E[r m ]: Hence We are also given that the debt is risk-free. Hence Thus, we have everything but D in the equation: E[r m ] = (E[r m ] r f ) + r f = = 20% = 20% r D = 12% Solve for D, find r = D D + E r D + E D + E 0.18 = D D + 12 D D = 4 mill Exercise 6. Charon Ferries First find the asset beta for the company: β = = D D + E β D + E D + E β E = =

6 Cost of capital: r = r f + (E[r m ] r f )β = = 14.6%. Exercise 7. Tax Rate Change [3] Decrease. Exercise 8. B&N (WC 15.1) [5] 1. Each firm has assets V = 10 mill. Bonner Kirkeby Debt 3 mill 5 mill Equity 7 mill 5 mill Earnings 2 mill 2 mill Interest 300, ,000 Net earnings 1,700,000 1,400,000 Taxes 680, ,000 Net income 1,020, ,000 1, ,000 = 14.57% 5,000 = 16.80% 2. b: Bonner changes leverage to 60%. Bonner Kirkeby Debt 6 mill 5 mill Equity 4 mill 5 mill Earnings 2 mill 2 mill Interest 900, ,000 Net earnings 1,100,000 1,400,000 Taxes 440, ,000 Net income 660, ,000 = 16.5% 16.80% 660 4,000 6