DATA NUMBER OF SHARES 1000 PRICE PER SHARE 10 MARKET VALUE O

Solution

An Example of Proposition 1 Macbeth Spot Removers is reviewing its capital structure. Table 13.1 shows its current posi-tion. The company has no leverage and all the operating income is paid as dividends to the common stockholders ( we assume still that there are no taxes). The expected earnings and dividends per share are $ 1.50, but this figure is by no means certain— it could turn out to be more or less than $ 1.50. The price of each share is $ 10. Since the firm expects to produce a level stream of earnings in perpetuity, the expected return on the share is equal to the earnings– price ratio, 1.50/ 10.00 .15, or 15%. Ms. Macbeth, the firm’s president, has come to the conclusion that shareholders would be better off if the company had equal proportions of debt and equity. She therefore pro-poses to issue $ 5,000 of debt at an interest rate of 10% and use the proceeds to repurchase 500 shares. To support her proposal, Ms. Macbeth has analyzed the situation under dif-ferent assumptions about operating income. The results of her calculations are shown in Table 13.2 . To see more clearly how leverage would affect earnings per share, Ms. Macbeth has also produced Figure 13.1 . The brown line shows how earnings per share would vary with oper-ating income under the firm’s current all- equity financing. It is, therefore, simply a plot of the data in Table 13.1 . The green line shows how earnings per share would vary given equal proportions of debt and equity. It is, therefore, a plot of the data in Table 13.2 . Ms. Macbeth reasons as follows: “ It is clear that the effect of leverage depends on the company’s income. If income is greater than $ 1,000, the return to the equityholder is increased by leverage. If it is less than $ 1,000, the return is reduced by leverage. The return is unaffected when operating income is exactly $ 1,000. At this point the return on the market value of the assets is 10%, which is exactly equal to the interest rate on the debt. Our capital structure decision, therefore, boils down to what we think about income prospects. Since we expect operating income to be above the $ 1,000 break- even point, I believe we can best help our shareholders by going ahead with the $ 5,000 debt issue.”

As financial manager of Macbeth Spot Removers, you reply as follows: “ I agree that leverage will help the shareholder as long as our income is greater than $ 1,000. But your argument ignores the fact that Macbeth’s shareholders have the alternative of borrowing on their own account. For example, suppose that an investor borrows $ 10 and then invests $ 20 in two unlevered Macbeth shares. This person has to put up only $ 10 of his or her own money. The payoff on the investment varies with Macbeth’s operating income, as shown in Table 13.3 . This is exactly the same set of payoffs as the investor would get by buying one share in the levered company. [ Compare the last two lines of Tables 13.2 and 13.3 .] Therefore, a share in the levered company must also sell for $ 10. If Macbeth goes ahead and borrows, it will not allow investors to do anything that they could not do already, and so it will not increase value.” The argument that you are using is exactly the same as the one MM used to prove proposition 1.

Data

Number of shares 1,000
Price per share $ 10
Market value of shares $ 10,000
Outcomes
Operating income ($) 500 1,000 1,500 2,000
Earnings per share ($) .50 1.00 1.50 2.00
Return on shares (%) 5 10 15 20 Expected outcome

Number of shares 500 Price per share $ 10 Market value of shares $ 5,000 Market value of debt $ 5,000 Interest at 10% $ 500 Outcomes Operating income ($) 500 1,000 1,500 2,000 Interest ($) 500 500 500 500 Equity earnings ($) 0 500 1,000 1,500 Earnings per share ($) 0 1 2 3 Return on shares (%) 0 10 20 30 Expected outcome

Operating Income ($) 500 1,000 1,500 2,000 Earnings on two shares ($) 1 2 3 4 Less interest at 10% ($) 1 1 1 1 Net earnings on investment ($) 0 1 2 3 Return on $ 10 investment (%) 0 10 20 30 Expected outcome






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