An unlevered firm has an asset market beta of 1.5. The risk-free rate is 3%. The

Question

An unlevered firm has an asset market beta of 1.5. The risk-free rate is 3%. The equity premium is 4%. What is the firm's cost of capital? The firm refinances itself. It repurchases half of its stock with debt that it issues. Assume that this debt is risk free. What is the equity beta of the levered firm? According to the CAPM, what rate of return does the firm have to offer to its creditors? According to the CAPM, what rate of return does the firm have to offer to its levered equity holders? Has the firm's weighted average cost of capital changed?

Explanation / Answer

1

Asset market beta = 1.5

Risk free rate = 3%

Equity premium = 4%

Cost of capital = Risk free rate + Beta*Equity premium = 3% + 1.5*4% = 9%

2.

Asset beta = 1.5

Debt is risk free; Beta of debt = 0

Weight of debt = Weight of equity = 0.50

Asset beta = Weighted beta of equity + Weighted beta of debt

1.5 = (0.5*Beta of equity) + 0

Beta of equity = 1.5/0.5 = 3

3.

Rate of return to be offered to creditors = Cost of debt = Risk free rate = 3%

4.

Rate of return to be offered to levered equity holders = Cost of equity

Cost of equity = Risk free rate + Beta of equity*Equity premium = 3% + 3*4% = 15%

Rate of return to be offered to levered equity holders = 15%

5.

Weighted average cost of capital = (Weight of equity*Cost of equity) + (Weight of debt * Cost of debt)

WACC = (0.50*15%) + (0.50*3%) = 9%

NO, WACC has not changed because in absence of taxes the firm’s value and cost of capital is not affected by the change in the capital structure.

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