Problem 1:
Integrative – Optimal capital structure. Nelson Corporation has made the following forecast of sales, with the associated probability of occurrence noted.
Sales Probability
R200,000 .20
R300,000 .60
R400,000 .20
The company has fixed operating costs of R100 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 R10 per share book value. No other capital items are outstanding. The marketplace has assigned the following discount rates to risky earnings per share.
Coefficients of Estimated required
variation of EPS return, ks (%)
.43 15%
.47 16
.51 17
.56 18
.60 22
.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 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 levered 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) maximisation of earnings per share and (2) maximisation of share value.
c) Construct a graph showing the relationships in b.