The Modigliani-Miller theorem assumes that the firm has only two classes of securities, perpetual debt and equity. Suppose that the firm has issued a third class of securities (preferred stock) and that X% of preferred dividends may be written off as an expense (0 X1). a) What is the appropriate expression for the value of the levered firm?

b) What is the appropriate expression for the weighted average cost of capital? (2 Marks)

2. The XYZ Company has a current market value of Kshs.1000000, half of which is debt. Its current weighted average cost of capital is 9%, and the corporate tax rate is 40%. The treasurer proposes to undertake a new project, which costs Kshs.500000 and which can be financed completely with debt. The project is expected to have the same operating risk as the company and to earn 8.5% on its levered after-tax cash flows. The treasurer argues that the project is desirable because it earns more than 5%, which is the before-tax marginal cost of the debt used to finance it. What do you think? (2 Marks)

3. Consider firm B as an unlevered firm and firm C as a levered firm with target debt-toequity ratio (B/S = 1. Both firms have exactly the same perpetual net operating income, NOI = 180, before taxes. The before-tax cost of debt, kb, is the same as the risk-free rate. The corporate tax rate = 50%. Given the following market parameters, E(Rm) = 0.12, m = 0.0144, Rf = 0.06 B =1 c = 1.5 a. Find the cost of capital and value for each firm. [Ignore any effect from personal income taxes.] b. Evaluate the following four projects to determine their acceptance (or rejection) by firms B and C. What do the results of this evaluation tell you about leverage in a world with corporate taxes but no personal taxes? [Note: rjm is the correlation between the unlevered free cash flows of each project and the market.] Project j Cost j E(NOIj)(After Tax) j rjm Correlation of j with the market 1 100 9 .10 .6 2 120 11 .11 .7 3 80 9 .12 .8 4 150 18 .20 .9 (3 Marks)

4. The firm's cost of equity capital is 18%, the market value of the firm's equity is $8 million, the firm's cost of debt capital is 9%, and the market value of debt is Kshs.4 million. The firm is considering a new investment with an expected rate of return of 17%. This project is 30% riskier than the firm's average operations. The riskless rate of return is 5%; the variance of the market return is .08. Is the project profitable? [Assume a world without taxes.] (1 Marks) 2

5. Susan, a treasurer of the Gammamax Company, has proposed that the company should sell equity and buy back debt in order to maximize its value. As evidence, she presents the financial statements given in Table below. Income Statement Before After Net Operating Income 100 100 Interest expense 80 40 Earnings Before Tax 20 60 Tax at 50% 10 30 Net Income 10 30 The company currently has a price/earnings ratio of 50. Before the change in capital structure it has 10 shares outstanding; therefore its earnings per share are Kshs.1.00, and the price per share is Kshs.50. If 10 new shares are issued at Kshs. 50 each, Kshs.500 is collected and used to retire Kshs.500 of debt (which pays a coupon rate of 8%). After the capital structure change, earnings per share have increased to Kshs.1.50 (since there are now 20 shares outstanding); and with a price/earnings ratio of 50, presumably the price per share will increase from Kshs.50 before the capital structure change to Kshs.75 afterward. Given your understanding of modern finance theory, discuss the above proposal. (2 Marks)