A firm has a debt-to-equity ratio of 1.75.If it had no debt, its cost of equity would be 9%.Its cost of debt is 7%.What is its cost of equity if the corporate tax rate is 50%?
A)7.73%
B)10.00%
C)10.75%
D)12.50%
E)None of the above.

Question

Quizplus · Accepted Answer

Step 1: Calculate the debt component of the firm's weighted average cost of capital (WACC).
Let E = equity and D = debt.
Debt-to-equity ratio = D/E = 1.75
So, D/(D+E) = 1.75/(1+1.75) = 0.6364 (debt component of WACC)
Cost of debt = rd = 7%
Tax rate = T = 50%
After-tax cost of debt = rd*(1-T) = 7%*(1-50%) = 3.5%
Debt component of WACC = D/(D+E)*rd*(1-T) = 0.6364*3.5% = 2.2273%

Step 2: Calculate the equity component of the firm's WACC.
Cost of equity without debt = re = 9%
Equity component of WACC = E/(D+E)*re = (1/2.75)*9% = 3.2727%

Step 3: Calculate the firm's WACC.
WACC = Equity component of WACC + Debt component of WACC = 3.2727% + 2.2273% = 5.5%

Step 4: Use the WACC to find the cost of equity with debt.
WACC = (E/(D+E))*re + (D/(D+E))*rd*(1-T)
Solving for re, we get:
re = (WACC - (D/(D+E))*rd*(1-T))/(E/(D+E))
re = (5.5% - 0.6364*7%*50%)/(1/2.75) = 10.75%

Therefore, the cost of equity if the corporate tax rate is 50% is 10.75%, which is option C.

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