A firm has a debt-to-equity ratio of 1.30.If it had no debt,its cost of equity would be 15%.Its cost of debt is 10%.What is its cost of equity if there are no taxes or other imperfections?
A)10.0%
B)15.5%
C)18.4%
D)21.5%
E)None of the above.

Question

Quizplus · Accepted Answer

We can use the formula for calculating the cost of equity with a given debt-to-equity ratio:

Cost of Equity = Rf + Beta(Equity risk premium)

where:

Rf = risk-free rate 
Beta = asset beta 
Equity risk premium = expected return on the market - risk-free rate

Since the firm has a debt-to-equity ratio of 1.30, we can use the following equation to calculate its asset beta:

Asset Beta = Equity Beta / (1 + (1 - Tax Rate) * Debt-to-Equity Ratio)

Assuming no taxes or other imperfections, the asset beta would be the same as the equity beta, which we can calculate using the formula:

Equity Beta = Unlevered Beta * (1 + (1 - Tax Rate) * Debt-to-Equity Ratio)

Assuming no debt, the firm's unlevered beta would be its equity beta:

Unlevered Beta = Asset Beta / (1 + (1 - Tax Rate) * Debt-to-Equity Ratio) = Equity Beta / (1 + 0) = Equity Beta

So we can rearrange the formula for the cost of equity to solve for the equity risk premium:

Equity risk premium = Cost of Equity - Rf = Beta^-1 (Cost of Capital - Rf)

Cost of Capital = Cost of Equity * (Equity / (Equity + Debt)) + Cost of Debt * (Debt / (Equity + Debt))

Plugging in the given values, we can solve for the equity risk premium:

Debt / (Equity + Debt) = 1 / (1 + 1.3) = 0.435 
Equity / (Equity + Debt) = 1 - 0.435 = 0.565

Cost of Capital = Cost of Equity * 0.565 + Cost of Debt * 0.435 
15% = Cost of Equity * 0.565 + 10% * 0.435 
Cost of Equity = (15% - 4.35%) / 0.565 = 21.50%

Therefore, the answer is D) 21.5%.

A Firm Has a Debt-To-Equity Ratio of 1