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(10) Imagine a firm has EBIT that varies, with a mean of $20 million.
1. (10) Imagine a firm has EBIT that varies, with a mean of $20 million. The firm satisfies the Modigliani and Miller assumptions (for instance, all earnings are paid out as dividends or interest to investors). Investors' required rate of return on the unlevered stock of this firm is Reu = 8%, and the required rate of return on bonds is Rd = 2%.
a. First assume that the firm is located in a country that has no corporate taxes. If the firm is unlevered, what is its value? If it instead chooses to sell $15 million in bonds, and use the proceeds to buy back shares, what will be the new firm value? What levered rate of return will investors require on the stock? What is the weighted average cost of capital?
b. Repeat part a, but assume the firm is located where there is a tax rate of T=.3
2. (4) In the Modigliani and Miller model without taxes, proposition I states that the value of the firm is unaffected by leverage: Vu = VL. Under MM assumptions that the firm pays out all its earnings as dividends or interest to investors, and is a no-growth firm, the firm's overall value must equal its EBIT/WACC, regardless of the degree of leverage used (since the firm's cash flow is a perpetuity, except for the random fluctuations in EBIT around its mean). And since Vu = VL, it must be true that WACCu = WACCL. Write the formulas for WACCu and WACCL, set them equal, and show that this implies Proposition II.
3. (14) 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 Reu=10% . 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.
