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

-6.00%

Explanation:

The computation of the change in the capital structure is as follows;

Current Capital Structure:

Given that

Weight of Debt = 80%

Weight of Equity = 20%

Levered Beta = 1.60

Now  

Debt-Equity Ratio = Weight of Debt ÷ Weight of Equity

= 0.80 ÷ 0.20

= 4.00

Unlevered Beta = Levered Beta ÷ [1 + (1 - Tax Rate) × Debt-Equity Ratio]

= 1.60 ÷ [1 + (1 - 0.25) × 4.00]

= 1.60 ÷ 4.00

= 0.40

Now  

Cost of Equity = Risk-free Rate + Levered Beta × Market Risk Premium

= 5.00% + 1.60 × 6.00%

= 14.60%

New Capital Structure:

Weight of Debt = 40%

Weight of Equity = 60%

Now  

Debt-Equity Ratio = Weight of Debt ÷ Weight of Equity

= 0.40 ÷ 0.60

= 0.6667

Unlevered Beta = 0.40

Levered Beta = Unlevered Beta × [1 + (1 - Tax Rate) × Debt-Equity Ratio]

= 0.40 × [1 + (1 - 0.25) × 0.6667]

= 0.40 × 1.50

= 0.60  

Cost of Equity = Risk-free Rate + Levered Beta × Market Risk Premium

= 5.00% + 0.60 × 6.00%

= 8.60%

Now  

Change in Cost of Equity = Cost of Equity under New Capital Structure - Cost of Equity under Current Capital Structure

= 8.60% - 14.60%

= -6.00%

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