Central Systems, Inc. desires a weighted average cost of capital of 7 percent. The firm has an after-tax cost of debt of 4 percent and a cost of equity of 10 percent. What debt-equity ratio is needed for the firm to achieve its targeted weighted average cost of capital?

1

Explanation:

Given that,

Weighted average cost of capital = 7%

After-tax cost of debt = 4 percent

Cost of equity = 10 percent

Let the debt of this firm be x, then the equity will be (1 - x),

wacc = (After-tax cost of debt * Debt) + (Cost of equity * Equity)

7% = (4% * x) + [10% * (1 - x) ]

0.07 = 0.04x + 0.1 - 0.1x

0.07 = 0.10 - 0.06x

0.06x = 0.10 - 0.07

0.06x = 0.03

x = 0.5

Therefore, if the debt is 0.5 then the equity is 0.5.

Hence, the debt to equity ratio will be:

= 0.5 : 0.5

= 1

The debt-equity ratio is 1 for the firm to achieve its targeted weighted average cost of capital.