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?

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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