Question

Agave group has an unlevered cost of capital of 11.6 percent, a cost of debt of 7.9 percent, and a tax rate of 23 percent. what is the target debt-equity ratio if the targeted levered cost of equity is 12.6 percent?

a. 35
b. 39
c. 53
d. 56
e. 44

Answer 1

The target debt-equity ratio is determined using the Modigliani-Miller Proposition II with taxes. After applying the provided numbers to the formula, the target debt-equity ratio is calculated to be approximately 35.1%, which corresponds to option A (35%).

Step-by-step explanation:

The student has asked about determining the target debt-equity ratio given the unlevered cost of capital, cost of debt, tax rate, and the targeted levered cost of equity.

To find the target debt-equity ratio, we use the Modigliani-Miller Proposition II with taxes, which states that the levered cost of equity is equal to the unlevered cost of capital plus the debt equity ratio times the spread between the unlevered cost of capital and the cost of debt, adjusted for taxes.

The formula is:
Re = Ru + (Ru - Rd)(1-Tc)(D/E)
Where:
Re = Levered cost of equity (12.6%)
Ru = Unlevered cost of capital (11.6%)
Rd = Cost of debt (7.9%)
Tc = Tax rate (23%)
D/E = Debt-equity ratio we want to find

Rearranging the formula to solve for D/E gives us:
D/E = (Re - Ru) / [(Ru - Rd)(1-Tc)]

Plugging in the values we have:
D/E = (0.126 - 0.116) / [(0.116 - 0.079)(1-0.23)]
D/E = 0.010 / [0.037 * 0.77]
D/E = 0.010 / 0.02849
D/E ≈ 0.351, or 35.1%

Therefore, the closest answer to the target debt-equity ratio is 35%, which corresponds to option A.