Nadir Corporation has made the following forecast of sales, with the associated probabilities of occurrence noted.
Sales Probability
US$200,000...................0.20
300,000........................0.60
400,000........................0.20
The company has fixed operating costs of US$100,000 per year, and variable operating costs represent 40 percent of sales. The existing capital structure consists of 25,000 shares of common stock that have a US$10 per share book value. No other capital items are outstanding. The marketplace has assigned the following required returns to risky earnings per share.
Coefficient of variation of EPS Estimated required return, rs
0.43..............................................................15%
0.47................................................................16
0.51................................................................17
0.56................................................................18
0.60................................................................22
0.64................................................................24
The company is contemplating shifting its capital structure by substituting debt in the capital structure for common stock. The three different debt ratios under consideration are shown in the following table, along with an estimate, for each ratio, of the corresponding required interest rate on all debt.
Debt ratio Interest rate on all debt
20%...........................................10%
40.....................................12
60.....................................14
The tax rate is 40 percent. The market value of the equity for a leveraged firm can be found by using the simplified method (see Equation 12.12).
a. Calculate the expected earnings per share (EPS), the standard deviation of EPS, and the coefficient of variation of EPS for the three proposed capital structures.
b. Determine the optimal capital structure, assuming (1) maximization of earnings per share and (2) maximization of share value.
c. Construct a graph (similar to Figure 12.7) showing the relationships in part b