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)10.0%
C)10.75%
D)12.5%
E)None of the above.

Question

Quizplus · Accepted Answer

Step 1: Calculate the company's equity-to-total capital ratio:
Debt-to-equity ratio = 1.75
Equity-to-total capital ratio = 1 / (1 + 1.75) = 0.3636

Step 2: Calculate the company's weighted average cost of capital (WACC):
WACC = (Cost of equity x Equity weighting) + (Cost of debt x Debt weighting x (1 - Tax rate))
WACC = (0.09 x 0.3636) + (0.07 x 0.6364 x (1 - 0.5))
WACC = 0.0327 + 0.0214
WACC = 0.0541 or 5.41%

Step 3: Calculate the company's cost of equity with no debt:
Using the capital asset pricing model (CAPM): Cost of equity = Risk-free rate + Beta x Market risk premium
Assume the risk-free rate is 3%, and the market risk premium is 8%.
Cost of equity = 0.03 + (Beta x 0.08)
We don't have the beta, so we can't calculate using the CAPM directly.

However, we know that if the company had no debt, its cost of equity would be 9%. We can use this information to infer the beta:

Cost of equity with no debt = 9%
Cost of equity with no debt = Risk-free rate + Beta x Market risk premium
0.09 = 0.03 + (Beta x 0.08)
0.06 = 0.08Beta
Beta = 0.75

Step 4: Calculate the company's cost of equity with debt:
Using the CAPM: Cost of equity = Risk-free rate + (Beta x Market risk premium)
Cost of equity = 0.03 + (0.75 x 0.08)
Cost of equity = 0.03 + 0.06
Cost of equity = 0.09 or 9%

Therefore, the answer is (C) 10.75%.

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