Question

Central Systems desires a weighted average cost of capital of 12 percent. The firm has an after-tax cost of debt of 5.4 percent and a cost of equity of 15.2 percent. What debt-equity ratio is needed for the firm to achieve its targeted weighted average cost of capital?

a. 0.67
b. 0.48
c. 0.56
d. 1.78
e. 2.06

Answer 1

The debt-equity ratio needed for the firm to achieve its targeted weighted average cost of capital is approximately 4.57.

Step-by-step explanation:

To calculate the debt-equity ratio needed for the firm to achieve its targeted weighted average cost of capital, we need to first determine the weights of debt and equity in the capital structure. The weighted average cost of capital (WACC) is the average rate of return required by both creditors and shareholders. We can use the formula: WACC = (Weight of Debt imes Cost of Debt) + (Weight of Equity imes Cost of Equity).

Let's assume the debt-equity ratio is D/E. Since the firm desires a weighted average cost of capital of 12%, we can set up the equation: 0.05D/E + 0.152(1 - D/E) = 0.12.

Simplifying this equation, we can solve for D/E to get the debt-equity ratio needed: D/E = (0.152 - 0.12) / (0.12 - 0.05) = 0.32 / 0.07 = 4.57.

Therefore, the debt-equity ratio needed for the firm to achieve its targeted weighted average cost of capital is approximately 4.57.