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Central Systems desires a weighted average cost of capital of 12.7 percent. The firm has an aftertax cost of debt of 4.8 percent and a cost of equity of 15.4 percent. What debt-equity ratio is needed for the firm to achieve its targeted weighted average cost of capital?

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Answer:

Debt-equity ratio = 0.34 or 34%

Explanation:

Weighted average cost of capital (WACC) = 12.7%

Cost of debt = 4.8%

Cost of equity = 15.4%

Let 'We' and 'Wd' be the fraction of capital corresponding to equities and costs, respectively, and that We + Wd =1.

The weighted average cost of capital is given by

[tex]WAAC = 0.154*W_e +0.048W_d\\0.127 = 0.154*W_e +0.048*(1-W_e)\\0.079 = 0.106W_e\\W_e=0.745\\W_d = 1-0.745=0.255[/tex]

The debt-equity ratio is:

[tex]DER = \frac{W_d}{W_e}=\frac{0.255}{0.745}\\DER =0.34[/tex]

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