Final answer:
The target debt-equity ratio for Central Systems to achieve its desired weighted average cost of capital of 12% is approximately 0.56. This is calculated by setting up the WACC formula and solving for the debt-equity ratio.
Step-by-step explanation:
The student's question relates to the determination of the debt-equity ratio that Central Systems requires in order to achieve its targeted weighted average cost of capital (WACC) of 12 percent. The firm has given its after-tax cost of debt as 5.4 percent and cost of equity as 15.2 percent.
To solve this problem, we use the WACC formula: WACC = (E/V) * Re + (D/V) * Rd * (1 - Tc), where E is the firm's equity, D is the firm's debt, V is the total value of the firm (E + D), Re is the cost of equity, Rd is the cost of debt, and Tc is the tax rate. In this scenario, tax effects are already considered in the after-tax cost of debt.
Since the WACC is the weighted average of the cost of equity and the cost of debt, and the target WACC is 12%, we can set up the equation as follows: 0.12 = (E/V) * 0.152 + (D/V) * 0.054. To find the target debt-equity ratio (D/E), which is D/V divided by E/V, we can rewrite this formula to solve for D/E.
Doing the calculation, we find that the required debt-equity ratio for Central Systems to achieve the 12% WACC is approximately 0.56.