Question

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?

Answer 1

To achieve a 20% ROE, the leverage ratio must be increased by 33.33%.

Step-by-step explanation:

In order to calculate the required increase in leverage ratio to achieve 20% return on equity (ROE), we need to use the DuPont formula.

The DuPont formula is ROE = Net Profit Margin x Asset Turnover x Leverage Ratio.

Given that the operating profit margin (Net Profit Margin) and asset turnover ratio remain unchanged at 8% and 1.25 respectively, we can rearrange the formula to solve for the leverage ratio: Leverage Ratio = ROE / (Net Profit Margin x Asset Turnover).

Plugging in the values, we have 15% = 0.08 x 1.25 x Leverage Ratio. Solving for Leverage Ratio, we find that it is equal to 1.875.

To achieve a 20% ROE, we need to increase the leverage ratio by (20% - 15%) / 15% = 0.33333 or 33.33%.

Answer 2

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%