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26 June, 09:42

A firm wants a sustainable growth rate of 2.55 percent while maintaining a dividend payout ratio of 35 percent and a profit margin of 4 percent. The firm has a capital intensity ratio of 2. What is the debt-equity ratio that is required to achieve the firm's desired rate of growth?

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  1. 26 June, 10:37
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    Debt to equity ratio = 0.92

    Explanation:

    In order to determine the required debt to equity ratio, we must first determine the equity multiplier. And to be able to determine the equity multiplier, we first need the return on equity (ROE).

    Debt to equity ratio = total liabilities / equity Equity multiplier (EM) = 1 + Debt to equity ratio

    First we must determine the return on equity (ROE)

    0.0255 = {ROE x (1-.35) } / {1-[ROE x (1-.35) ]}

    0.0255 = 0.65ROE / (1 - 0.65ROE)

    0.0255 (1 - 0.65ROE) = 0.65 ROE

    0.0255 - 0.016575ROE = 0.65ROE

    0.0255 = 0.666575ROE

    ROE = 0.0255/0.666575

    ROE = 0.0383

    0.0383 = 0.04 x (1 / 2) x EM

    0.0383 = 0.02EM

    EM = 0.0383 / 0.02 = 1.92

    1.92 = 1 + Debt to Equity ratio

    Debt to equity ratio = 1.92 - 1 = 0.92
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