A firm’s current balance sheet is as follows: Assets $100 ...



A firm’s current balance sheet is as follows: Assets $100 Debt $10 Equity $90 a. What is the firm’s weighted-average cost of capital at various combinations of debt and equity, given the following information? Debt Asset After tax cost of debet Cost of equity Cost of Capital 0% 8% 12% ? 10% 8% 12% ? 20% 8% 12% ? 30% 8% 13% ? 40% 8% 14% ? 50% 10% 15% ? 60% 12% 16% ? b. Construct a pro forma balance sheet that indicates the firm’s optimal capital structure. Compare this balance sheet with the firm’s current balance sheet. What course of action should the firm take? Assets $100 Debt $? Equity $? c. As a firm initially substitutes debt for equity financing, what happens to the cost of capital, and why? d. If a firm uses too much debt financing, why does the cost of capital rise?

The cost of capital (k) is a weighted average:

k = (weight)(cost of debt) + weight(cost of equity)

Debt/ Weight x + Weight x = Cost of

Assets Cost Cost Capital

of Debt of Equity

0% (.0)(.08) + (1.0)(.12) = .120

10 (.1)(.08) + (.9)(.12) = .116

20 (.2)(.08) + (.8)(.12) = .112

30 (.3)(.08) + (.7)(.13) = .115

40 (.4)(.09) + (.6)(.14) = .120

50 (.5)(.10) + (.5)(.15) = .125

60 (.6)(.12) + (.4)(.16) = .136

b. The optimal capital structure is that combination, which minimizes the firm's cost of capital. In this case that occurs where debt is 20% of capital and the cost of capital is 11.2%. The balance sheet is

Assets $100 Liabilities $20

Equity 80

Since the firm is currently using only 10% debt financing, it is not at its optimal capital structure and should substitute some debt for equity.

c. The cost of capital initially declines because the effective cost of debt is less than the cost of equity.

d. As the firm continues to substitute debt for equity, the firm becomes more financially leveraged and riskier. This causes the interest rate to rise and the cost of equity to increase. These increases in the cost of debt and equity cause the cost of capital (i.e., the weighted average) to increase.

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