Serendipity Inc.is re-evaluating its debt level.Its current capital structure consists of 80% debt and 20% common equity,its beta is 1.60,and its tax rate is 35%.However,the CFO thinks the company has too much debt,and he is considering moving to a capital structure with 40% debt and 60% equity.The risk-free rate is 5.0% and the market risk premium is 6.0%.By how much would the capital structure shift change the firm's cost of equity?
A) −5.20%
B) −5.78%
C) −6.36%
D) −6.99%
E) −7.69%

Question

Quizplus · Accepted Answer

1. We need to calculate the unlevered beta of the company at the current capital structure.

Bu = B/(1 + (1 - tax rate) * (D/E))

Bu = 1.60 / (1 + (1 - 35%) * (80%/20%)) = 0.98

2. Then we use the Hamada equation to calculate the leveraged beta at the new capital structure.

Bl = Bu + (Bu - Bf) * (D/E)

Bl = 0.98 + (0.98 - 0.05) * (40%/60%) = 1.13

3. Finally, we can use the CAPM to calculate the cost of equity at the new capital structure.

Ke = Rf + Bl * (Rm - Rf)

Ke = 5.0% + 1.13 * 6.0% = 11.78%

So, the change in the capital structure would decrease the firm's cost of equity by 5.78%.