91Ó°ÊÓ

MM Proposition I without Taxes Alpha Corporation and Beta Corporation are identical in every way except their capital structures. Alpha Corporation, an all-equity firm, has 10,000 shares of stock outstanding, currently worth \(\$ 20\) per share. Beta Corporation uses leverage in its capital structure. The market value of Beta's debt is \(\$ 50,000\), and its cost of debt is 12 percent. Each firm is expected to have earnings before interest of \(\$ 55,000\) in perpetuity. Neither firm pays taxes. Assume that every investor can borrow at 12 percent per year. 1\. What is the value of Alpha Corporation? 2\. What is the value of Beta Corporation? 3\. What is the market value of Beta Corporation's equity? 4\. How much will it cost to purchase 20 percent of each firm's equity? 5\. Assuming each firm meets its earnings estimates, what will be the dollar return to each position in part (d) over the next year? 6\. Construct an investment strategy in which an investor purchases 20 percent of Alpha's equity and replicates both the cost and dollar return of purchasing 20 percent of Beta's equity. 7\. Is Alpha's equity more or less risky than Beta's equity? Explain.

Cost of Capital Acetate, Inc., has equity with a market value of \(\$ 35\) million and debt with a market value of \(\$ 14\) million. Treasury bills that mature in one year yield 6 percent per year, and the expected return on the market portfolio is 13 percent. The beta of Acetate's equity is 1.15. The firm pays no taxes. 1\. What is Acetate's debt-equity ratio? 2\. What is the firm's weighted average cost of capital? 3\. What is the cost of capital for an otherwise identical all-equity firm?

Stock Value and Leverage Green Manufacturing, Inc., plans to announce that it will issue \(\$ 3\) million of perpetual debt and use the proceeds to repurchase common stock. The bonds will sell at par with a 6 percent annual coupon rate. Green is currently an all-equity firm worth \(\$ 9.5\) million with 600,000 shares of common stock outstanding. After the sale of the bonds, Green will maintain the new capital structure indefinitely. Green currently generates annual pretax earnings of \(\$ 1.8\) million. This level of earnings is expected to remain constant in perpetuity. Green is subject to a corporate tax rate of \(\mathbf{4 0}\) percent. 1\. What is the expected return on Green's equity before the announcement of the debt issue? 2\. Construct Green's market value balance sheet before the announcement of the debt issue. What is the price per share of the firm's equity? 3\. Construct Green's market value balance sheet immediately after the announcement of the debt issue. 4\. What is Green's stock price per share immediately after the repurchase announcement? 5\. How many shares will Green repurchase as a result of the debt issue? How many shares of common stock will remain after the repurchase? 6\. Construct the market value balance sheet after the restructuring. 7\. What is the required return on Green's equity after the restructuring?

MM with Taxes Williamson, Inc., has a debt-equity ratio of 2.5 . The firm's weighted average cost of capital is 15 percent, and its pretax cost of debt is 10 percent. Williamson is subject to a corporate tax rate of 35 percent. 1\. What is Williamson's cost of equity capital? 2\. What is Williamson's unlevered cost of equity capital? 3\. What would Williamson's weighted average cost of capital be if the firm's debt-equity ratio were .75? What if it were 1.5 ?

Weighted Average Cost of Capital In a world of corporate taxes only, show that the \(R_{\text {WACC }}\) can be written as \(R_{\text {WACC }}=R_0 \times\left[1-t_C(B / V)\right]\).

Unlevered Cost of Equity Beginning with the cost of capital equation-that is: $$ R_{\mathrm{waCC}}=\frac{S}{B+S} R_S+\frac{B}{B+S} R_B $$ show that the cost of equity capital for a levered firm can be written as follows: $$ R_S=R_0+\frac{B}{S}\left(R_0-R_p\right) $$