A firm has a debt-to-equity ratio of 1.0. If it had no debt, its cost of equity would be 12 percent. Its cost of debt is 9 percent. What is its cost of equity if there are no taxes?
A)21 percent
B)18 percent
C)15 percent
D)16 percent

Question

Quizplus · Accepted Answer

Using the formula for the weighted average cost of capital (WACC): WACC = (E/V) × rE + (D/V) × rD × (1 - Tc), where E = market value of equity, D = market value of debt, V = total value (equity + debt), rE = cost of equity, rD = cost of debt, and Tc = corporate tax rate.

Since debt-to-equity ratio is 1.0, we know that D = E. Therefore, V = E + D = 2E.

Let's assume that the market value of equity is $100, which means the market value of debt is also $100.

Plugging into the WACC formula: 
WACC = [(100/200) × 0.12] + [(100/200) × 0.09] 
WACC = 0.105 or 10.5%

Now we need to find the cost of equity if there were no taxes. We can use the Capital Asset Pricing Model (CAPM) formula: rE = rRF + β × (rM - rRF), where rRF = risk-free rate, β = beta, and rM = market return.

Since there's no information given on the risk-free rate, beta, or market return, we'll assume they're all constant for our analysis.

We know that rD = 0.09, and we can use the formula for the cost of debt in a no-tax scenario: rD = rD(1 - Tc). Therefore: 
0.09 = rD(1 - 0) 
rD = 0.09

Now we can use the WACC formula again, but this time assume rD = 0 since there's no debt. 
WACC = [(100/100) × rE] + [(0/100) × 0] 
WACC = rE

Therefore: 
rE = 0.105

Now we can use the CAPM formula: 
0.12 = rRF + β × (rM - rRF)

Assuming a risk-free rate of 2%, a beta of 1, and a market return of 10% (these are just example numbers), we can solve for rRF: 
0.12 = 0.02 + 1 × (0.10 - 0.02) 
0.12 = 0.08 + 0.08 
rRF = 0.04 or 4%

Now we can use the CAPM formula again to find the cost of equity with no taxes: 
rE = 0.04 + 1 × (0.10 - 0.04) 
rE = 0.10 or 10%

Therefore, the cost of equity with no taxes is 10%, which is answer choice C.

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