A firm has a debt-to-equity ratio of 1.75.If it had no debt, its cost of equity would be 14%.Its cost of debt is 10%.What is its cost of equity if the corporate tax rate is 50%?
A)14.0%
B)16.0%
C)17.5%
D)21.0%
E)None of the above.

Question

Quizplus · Accepted Answer

First, we need to calculate the firm's current cost of equity:
Debt/Equity ratio = 1.75
Equity portion = 1 / (1.75+1) = 0.3636 (rounded to four decimal places)
Debt portion = 1 - 0.3636 = 0.6364
Cost of debt = 10%
Tax rate = 50%

Cost of equity = Cost of capital - (Debt/Equity ratio x (Cost of capital - Cost of debt) x (1 - Tax rate))
14% = Cost of capital - (1.75 x (Cost of capital - 10%) x (1 - 50%))
14% = Cost of capital - (0.875 x (Cost of capital - 10%))
14% = Cost of capital - (0.875 x Cost of capital - 8.75%)
14% = 0.125 x Cost of capital + 8.75%
5.25% = 0.125 x Cost of capital
Cost of capital = 42%

Now, we can calculate the cost of equity if there was no debt:
Cost of equity = 14%
However, this is not the cost of equity for the current situation. We need to adjust for the tax shield provided by the debt:
Cost of equity = Cost of equity with no debt + (Tax rate x (Cost of debt - Cost of equity with no debt))
Cost of equity = 14% + (50% x (10% - 14%))
Cost of equity = 14% - 2%
Cost of equity = 12%

Finally, we use the Hamada equation to calculate the cost of equity for the current situation:
Cost of equity = Cost of equity with no debt + (Debt/Equity ratio x (Cost of equity with no debt - Cost of debt) x (1 - Tax rate))
Cost of equity = 12% + (1.75 x (12% - 10%) x (1 - 50%))
Cost of equity = 17.5%

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