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9 March, 23:42

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?

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  1. 10 March, 00:04
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    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.
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