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%. By how much would the capital structure shift change the firm's cost of equity?

a. −6.00% b. −6.60% c. −7.99% d. −7.26% e. −5.40%

Answer 1

Answer is -6.00%

Current Capital Structure:

Weight of Debt = 80%
Weight of Equity = 20%

Levered Beta = 1.60

Debt-Equity Ratio = Weight of Debt / Weight of Equity
Debt-Equity Ratio = 0.80 / 0.20
Debt-Equity Ratio = 4.00

Unlevered Beta = Levered Beta / [1 + (1 - Tax Rate) * Debt-Equity Ratio]
Unlevered Beta = 1.60 / [1 + (1 - 0.25) * 4.00]
Unlevered Beta = 1.60 / 4.00
Unlevered Beta = 0.40

Cost of Equity = Risk-free Rate + Levered Beta * Market Risk Premium
Cost of Equity = 5.00% + 1.60 * 6.00%
Cost of Equity = 14.60%

New Capital Structure:

Weight of Debt = 40%
Weight of Equity = 60%

Debt-Equity Ratio = Weight of Debt / Weight of Equity
Debt-Equity Ratio = 0.40 / 0.60
Debt-Equity Ratio = 0.6667

Unlevered Beta = 0.40

Levered Beta = Unlevered Beta * [1 + (1 - Tax Rate) * Debt-Equity Ratio]
Levered Beta = 0.40 * [1 + (1 - 0.25) * 0.6667]
Levered Beta = 0.40 * 1.50
Levered Beta = 0.60

Cost of Equity = Risk-free Rate + Levered Beta * Market Risk Premium
Cost of Equity = 5.00% + 0.60 * 6.00%
Cost of Equity = 8.60%

Change in Cost of Equity = Cost of Equity under New Capital Structure - Cost of Equity under Current Capital Structure
Change in Cost of Equity = 8.60% - 14.60%
Change in Cost of Equity = -6.00%