Question

A firm has a debt-to-equity ratio of 50%. The firm’s equity beta is 1.5 and the cost of debt is 6%. Assume the market risk premium is 6%, the 10-year Treasury bond yield is 3%, and the corporate income tax rate is 40%.

1. Estimate the firm’s WACC.
2. Estimate the firm’s unlevered cost of equity, k_u. (Hint: Since the debt ratio is constant, you can assume k_tax = k_u. Use Equation 3c2.)
3. If the firm plans to increase the debt-to-equity ratio to 80%, what will be the new WACC?
   (Hint: Keep in mind that the unlevered cost of equity, k_u, does not change even when the debt ratio changes.)

Answer 1

Debt to equity ratio = 0.5

Debt to capital (Wd) = 1 / 3

Equity to capital (We) = 2 / 3

Equity beta = 1.5

Cost of debt (Kd) = 6%

Market risk premium = 6%

Risk free rate = 3%

Tax = 40%

Cost of equity = Risk free rate + beta * (market risk premium)

Cost of equity (Ke) = 3 + 1.5 * 6 = 12%

Tax = 40%

WACC = Kd * Wd * (1-Tax) + Ke * We

WACC = 6% * 1 / 3 * (1-0.4) + 12% * 2 / 3

WACC = 9.2%

Unlevered Beta = Beta / ( 1+(1-tax)*Debt/Equity)

Unlevered Beta = 1.5 / (1+0.6*0.5) = 1.15

Unlevered Cost of equity = Risk free rate + unlevered beta * (market risk premium)

Unlevered Cost of equity = 3 + 1.15 * 6 = 9.9%

WACC using unlevered cost of equity

WACC = Kd * Wd * (1-Tax) + Ke * We

WACC = 6% * 1 / 3 * (1-0.4) + 9.9% * 2 / 3

WACC = 7.8%

Debt to Equity = 0.8

So

Wd = 8 / 18

We = 10 / 18

WACC = Kd * Wd * (1-Tax) + Ke * We

WACC = 6% * 8 / 18 * (1-0.4) + 9.9% * 10 / 18

WACC = 7.1%

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