A firm has an equity multiplier of 1.57,an unlevered cost of equity of 14 percent,a levered cost of equity of 15.6 percent,and a tax rate of 21 percent.What is the cost of debt?
A)11.25 percent
B)10.50 percent
C)10.45 percent
D)11.00 percent
E)10.33 percent

Question

Quizplus · Accepted Answer

The cost of debt can be found using the Modigliani and Miller Proposition II with taxes, which states that the levered cost of equity (Re) is equal to the unlevered cost of equity (Ru) plus the debt-to-equity ratio (D/E) times the difference between the unlevered cost of equity and the cost of debt (Rd) times (1 - tax rate). Rearranging the formula to solve for Rd gives us:$$Re = Ru + (D/E) \times (Ru - Rd) \times (1 - Tax Rate)$$Given:- Equity Multiplier (EM) = 1.57, which implies that $D/E = EM - 1 = 0.57$- Levered cost of equity (Re) = 15.6%- Unlevered cost of equity (Ru) = 14%- Tax rate = 21%We can rearrange the formula to solve for Rd:$$15.6\% = 14\% + 0.57 \times (14\% - Rd) \times (1 - 0.21)$$Solving for Rd gives us approximately 10.45%, which is option C.

A Firm Has an Equity Multiplier of 1