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5 August, 13:50

A firm currently has a debt-equity ratio of 1/2. The debt, which is virtually riskless, pays an interest rate of 6%. The expected rate of return on the equity is 12%. What would be the expected rate of return on equity if the firm reduced its debt-equity ratio to 1/3? Assume the firm pays no taxes.

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  1. 5 August, 14:00
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    Expected return on equity is 11.33%

    Explanation:

    Using Weighted Average Cost Capital without tax formula, overall rate of return is given by the formula:

    WACC = (Ke*E/V) + (Kd*D/V)

    Kd is the cost of debt at 6%

    Ke is the cost of equity at 12%

    D/E=1/2 which means debt is 1 and equity is 2

    D/V=debt/debt+equity=1/1+2=1/3

    E/V=equity/debt+equity=2/1+2=2/3

    WACC = (12%*2/3) + (6%*1/3)

    WACC=10%

    If the firm reduces debt-equity ratio to 1/3,1 is for debt 3 is for equity

    D/V=debt/debt+equity=1/1+3=1/4

    E/V=equity/debt+equity=3/1+3=3/4

    WACC=10%

    10% = (Ke*3/4) + (6%*1/4)

    10% = (Ke*3/4) + 1.5%

    10%-1.5%=Ke*3/4

    8.5%=Ke*3/4

    8.5%=3Ke/4

    8.5%*4=3 Ke

    34%=3 Ke

    Ke=34%/3

    Ke=11.33%
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