Question

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. 18 percent
B. 16 percent
C. 21 percent
D. 15 percent

Answer 1

The cost of equity for a firm with a debt-to-equity ratio of 1.0 and no taxes, given a cost of debt of 9 percent and no-debt cost of equity of 12 percent, would be 15 percent.

Step-by-step explanation:

The student asked what the firm's cost of equity would be if it has a debt-to-equity ratio of 1.0 and there are no taxes involved, given that its cost of debt is 9 percent and its cost of equity would be 12 percent if it had no debt.


To solve this, we use the Modigliani-Miller Proposition II without taxes, which states that the firm's cost of equity is equal to the cost of equity if the firm had no debt plus the debt-to-equity ratio times the spread between the cost of equity with no debt and the cost of debt. Therefore, the calculation would be as follows:

Cost of Equity = Cost of Equity if no debt + (Debt-to-Equity Ratio) * (Cost of Equity if no debt - Cost of Debt)

Cost of Equity = 12% + (1) * (12% - 9%)

Cost of Equity = 12% + 3%

Cost of Equity = 15%

So the correct answer to the student's question would be D. 15 percent.