Nelson Corporation has made the following forecast of sales, with the associated probabilities of occurrence noted.

Sales Probability

$200,000 ..... 0.20

300,000 ...... 0.60

400,000 ...... 0.20

The company has fixed operating costs of $100,000 per year, and variable operating costs represent 40% of sales. The existing capital structure consists of 25,000 shares of common stock that have a $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 Estimated required variation of EPS 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 Interest rate

ratio on all debt

20% ....... 10%

40 ........ 12

60 ........ 14

The tax rate is 40%. The market value of the equity for a leveraged firm can be found by using the simplified method.

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 showing the relationships in part b.