Question

1. A firm has debt-equity ratio of 1 (i.e. the value of the debt divided by the value of the equity euqals one). The beta of the equity is 1.2 and the beta of the debt is 0.1. The risk free rate is 5% and the return on the market index is 10%. What is the WACC (weighted average cost of capital) for the firm?

2. Suppose the firm above increases its borrowing so that the debt-equity ratio is 2. The recapitalization is done in such a way that no new capital is raised or spent, i.e. the firm issues new debt and uses the proceeds to buy back old equity. The beta of the debt increases to 0.15 following the recapitalization. Assuming Modigliani-Miller Irrelevance of Captial Structure Proposition holds, what is the beta of the equity after the recapitalization?

3. Now suppose the static trade off theory is correct, and that the optimal capital structure for the firm is a debt-equtiy ratio of 2. Do you expect that the beta of the equity is higher or lower in this case than your answer in the question above? Explain.

Answer 1

WACC = [(Equity / Equity + Debt) x Cost of Equity] + [(Debt / Equity + Debt) x Cost of Debt x (1-tax rate)

Equity / Equity + Debt = 0.5 / 1 = 0.5

Debt / Equity + Debt = 0.5 / 1 = 0.5

Cost of Equity using the CAPM method = Risk-free rate + Beta of equity (Market return - Risk-free rate)

= 0.05 + 1.2 (0.1-0.05) = 0.11

Cost of equity = 0.11

Debt Beta = (Cost of Debt - Risk-free rate) / (Market return - Risk-free rate)

Cost of Debt = [Debt Beta(Market return-Risk-free rate)] + Risk-free rate

= [0.1(0.10-0.05)] + 0.05

Cost of Debt = 0.055

WACC = (0.5 x 0.11) + (0.5 x 0.055) (Since tax rates are not given there is no tax shield on the cost of debt)

WACC = 0.0825 or 8.25%

First, we will unlever the equity beta and then relever it with the new capital structure.

Unlevered Beta = Levered Beta / (1 + D/E)

= 1.2 / (1 + 1)

= 0.6

Levered Beta = Beta unlevered) x [1 + (Debt / Equity)]

= 0.6 x [1 + 2]

= 1.8

The new beta of equity is 1.8.

According to the static trade off theory, the company has used the correct amount of debt and equity. As the capital structure is optimal the beta of the equity is lower.