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29 July, 10:31

The board of directors is dissatisfied with last year's roe of 15%. If the operating profit margin and asset turnover ratio remain unchanged at 8% and 1.25, respectively, by how much must the leverage ratio (i. E., assets/equity) increase to achieve 20% roe?

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  1. 29 July, 10:34
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    Calculation of Increase in Leverage ratio to achieve 20% ROE:

    The current ROE is given 15% and operating profit margin and asset turnover ratio are 8% and 1.25, respectively.

    The formula for ROE is as follows:

    ROE = Operating profit margin * Asset turnover ratio * Leverage ratio

    We can say that:

    Leverage ratio = ROE / (Operating profit margin * Asset turnover ratio)

    Hence Current Leverage Ratio = 15% / (8%*1.25) = 1.5 times

    Now we are asked to get ROE 20% with operating profit margin and asset turnover ratio at 8% and 1.25, respectively.

    Hence,

    Required Leverage Ratio = 20% / (8%*1.25) = 2 times

    Hence Leverage Ratio should Increase by (2-1.5) 0.5 times to get the ROE of 20%
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