12-4: At your company, sales and their probabilities are forecast for next year as follows: $300,000 at 25% probability; $400,000 at 50% probability; $500,000 at 25% probability. Fixed annual operating costs are expected at $150,000. Variable operating costs are pegged to operating revenue at 35% of sales. The current capital structure stands at 100% common stock (no preferred shares, no debt) at 30,000 shares and $8 per share book value. The current marketplace points to the following estimated required returns with regard to earnings per share (EPS):

Coefficient of variation of EPS: Required Return:

0.42 14%

0.44 16

0.45 18

0.46 21

0.51 23

0.60 25

If the company moves to change its capital structure from common stock to debt, analysts have determined that three possible debt ratios would be feasible: (1) a debt ratio of 25% at an interest rate of all debt of 8%; (2) a debt ratio of 35% at an interest rate of all debt of 12%; and (3) a debt ratio of 55% at an interest rate of all debt of 15%. The firm's tax rate is 36%. Use the simplified method, Equation(12.12), to determine the market value of equity for a leveraged firm.

(A) Compute the required earnings per share (EPS); the standard deviation of EPS; and the coefficient of variation of EPS for each of the three capital structures.

(B) Scenario 1: If the management wants to maximize the earnings per share, identify the best capital structure of the three. Scenario 2: If the management wants to maximize share value, identify the best capital structure of the three.

(C) Using Figure 12.7 as your guide, graph the results of Part B for scenarios 1 and 2. You will have only 3 data points on each graph. Compare the maximums for each scenario.

HINT: Part a calls for several EPS calculations from income statement scenarios. You could construct income statements for each probability in the 0% debt category; that is, a column of the income statement for a 0.20 probability at Sales of $200,000, a column for the 0.60 probability at Sales of $300,000, and a column for the 0.20 probability at Sales of $400,000. Do this also for the 20% debt ratio, another for the 40% debt ratio, and another for the 60% debt ratio. Your bottom line for each debt ratio should be the EPS for each probability. Finally in part a, set up a table for the share price of each scenario (each debt ratio). In parts b and c, use part a to determine the optimal capital structure to maximize EPS, and the optimal capital structure to maximize share price. Use the same format for the graph's axes as Figure 12.7 on p. 499. You will have a graph for share price to compare with a graph for EPS.