This problem illustrates how an investor can use leverage within his/her own portfolio, to achieve the same effect as a firm using leverage (as argued in MM). We will assume a situation with no corporate taxes.

a. Firm A has sales of $100,000 in good years, $90,000 in average years, and $80,000 in bad years. Its variable operating costs are 60% of sales, and its fixed operating costs are $10,000 per year. It exists in a nation that has no corporate taxes, and pays all its earnings as dividends each year. The firm is all-equity financed, and its investors require an expected rate of return of % . Find the firm's EBIT in good, average and bad years, and its average EBIT, assuming the probability of each state of the world is 1/3. What is the total value of the firm's stock, Su, based on average EBIT? If there are 10,000 shares outstanding, what is the price per share? What is EPS under each state of the world? If an investor purchases 100 shares of this stock, how much will this investment cost, and what is their average dividend income per year?

b. Beth believes the firm would be a more attractive investment if it used leverage. Suppose there was a Firm B, identical to firm A except it is financed with ½ debt at Rd = 4%. The other half of its capital consists of 5000 shares of stock, selling at the same price per share as firm A's stock. Find this firm' EPS under each state of the world, and its average EPS. If an investor purchases 100 shares of this stock, how much will this investment cost, and what is the investor's average dividend income per year?

c. Since firm A's management does not use leverage as Beth prefers, she decides to do it herself. She purchases 200 shares of firm A's stock, borrowing half the purchase price at rate Rd = 4%. Show that her portfolio returns now look like the returns from owning 100 shares of Firm B.