Question

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 25%. 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%. What's the firm's new cost of equity under 40% debt?

Group of answer choices

7.5%

7.8%

8.1%

8.3%

8.6%

Answer 1

Given about Serendipity Inc.

Its current capital structure consists of 80% debt and 20% common equity, its beta is 1.60, and its tax rate is 25%

=> D/E ratio = 80/20 = 4

Levered beta = 1.6

So, unlevered beta = Levered beta/(1 + (D/E)*(1-T))

=> firm's unlevered beta = 1.6/(1 + 4*(1-0.25)) = 0.4

Under new capital structure with 40% debt and 60% equity.

D/E ratio = 40/60 = 2/3

=> Levered beta = 0.4*(1 + (2/3)*(1-0.25)) = 0.6

risk-free rate Rf = 5.0%

market risk premium MRP = 6.0%

Based on CAPM, company's cost of equity = Rf + beta*MRP

=> New cost of equity = 5 + 0.6*6 = 8.6%

Option E is correct.