Final answer:
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.