Question

2) A small, private firm has approached you for advice on its capital structure decision. It is in the specialty retailing business, and it had earnings before interest and taxes last year of $ 500,000. The book value of equity is $1.5 million, but the estimated market value is $ 6 million. The firm has $ 1 million in debt outstanding, and paid an interest expense of $ 80,000 on the debt last year. (Based upon the interest coverage ratio, the firm would be rated AA, and would be facing an interest rate of 8.25%.) The equity is not traded, but the average beta for comparable traded firms is 1.05, and their average debt/equity ratio is 25%.

a) Estimate the current cost of capital for this firm

b)Assume now that this firm doubles it debt from $1million to $2million, and that the interest rate at which it can borrow increases to 9%. Estimate the new cost of capital, and the effect on firm value.

Answer 1

MV of Equity = 6000000

MV OF Debt = 1000000

EBIT: 500000

Assuming no tax

500000 / Kc = 7000000

Kc = 7000000/500000 = 14%, current cost of capital for this firm

Kc = 6 / 7 * Ke + 1 / 7 * 8.25 = 14 %

Ke = 12.625%

Ke = Rf + MRP

MRP = 12.625 - 8.25 = 4.375

Levered Beta of Compareable firm = 1.05

D/E Ratio = 25%

Unlevered Beta = 1.05 / (1+ 0.25) = 0.84

Levered beta using Firm capital structure = 0.84 * (1+ 2 / 8) = 1.05

Ke = 8.25 + 4.375 * 1.05 = 12.84

Kd = 9%

Kc = 2/8 * 9% + 6 / 8 * 12.84 = 11.88%