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

Question

Quizplus · Accepted Answer

Using the formula for cost of capital with a debt-to-equity ratio of 1.0, we get:

Cost of capital = (cost of equity x equity weighting) + (cost of debt x debt weighting)

Let E = equity and D = debt, then E/(E+D) = 1/(1+D/E) = 1/2

And D/(E+D) = 1/2

So, Cost of capital = (0.12 x 1/2) + (0.09 x 1/2) = 0.105 or 10.5%

However, this is the cost of capital, not just the cost of equity. We need to solve for the cost of equity using the formula:

Cost of equity = Cost of capital - (debt-to-equity ratio x (cost of capital - cost of debt))

Substituting in the numbers:

Cost of equity = 0.105 - (1 x (0.105 - 0.09)) = 0.105 - 0.015 = 0.09 or 9%

But this is with taxes. We need to find the cost of equity without taxes, which is simply the cost of equity when the firm has no debt:

Cost of equity = 0.12

Therefore, the answer is C) 15% (since the cost of equity without taxes is higher than the cost of equity with taxes and debt).

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