Using the original Modigliani and Miller assumptions if a firm's cost of capital is 12% when it is all equity financed and it's cost of debt is 8%, the cost of equity will be ________% when the firm is financed with equal amount of debt and equity.
A) 12%
B) 24%
C) 16%
D) cannot be determined with the information given.

Question

Quizplus · Accepted Answer

According to Modigliani and Miller, when a firm is financed with equal amounts of debt and equity, the overall cost of capital remains the same. Therefore, the cost of equity will also remain the same as the cost of capital, which is 12%. However, since the firm is now also taking on debt, the cost of capital will be a weighted average of the cost of equity and the cost of debt. Using the formula for weighted average cost of capital (WACC), the calculation is: WACC = (E/V) x Re + (D/V) x Rd, where E is the market value of equity, D is the market value of debt, V is the total value of the firm (E + D), Re is the cost of equity, and Rd is the cost of debt. Assuming equal amounts of debt and equity, V = E + D = 2E, and D/E = 1. Therefore, WACC = (E/2E) x 12% + (E/2E) x 8% = 10%. Solving for Re, we get Re = (WACC - (D/V) x Rd) / (E/V) = (10% - (1/2) x 8%) / (1/2) = 12%. Therefore, the cost of equity is still 12%.

Using the Original Modigliani and Miller Assumptions If a Firm's