By how much would the reduction in assets improve the ROE?
A) 2.85%
B) 3.00%
C) 3.16%
D) 3.31%
E) 3.48%

Question

Quizplus · Accepted Answer

To calculate the improvement in ROE due to the reduction in assets, we need to use the DuPont formula:

ROE = Net Income / Shareholders' Equity 
ROE = (Net Income / Total Revenue) x (Total Revenue / Total Assets) x (Total Assets / Shareholders' Equity)

Assuming that there is no change in revenue or net income, reducing the total assets will increase the third component of the formula, which is the asset turnover ratio.

Let's say the current asset turnover ratio is 1.5 (meaning that for every $1 of assets, the company generates $1.5 of revenue). If the reduction in assets leads to an increase in the asset turnover ratio to 1.6, then the new ROE will be:

ROE = (Net Income / Total Revenue) x (Total Revenue / Total Assets) x (Total Assets / Shareholders' Equity) 
ROE = (Net Income / Total Assets) x (1.6) x (1 / Shareholders' Equity)

Assuming again that there is no change in net income and the reduction in assets is $50 million, the new ROE would be:

New ROE = (Net Income / (Total Assets - $50 million)) x 1.6 x (1 / Shareholders' Equity)

To calculate the percentage change in ROE, we need to compare the new ROE to the old ROE:

(New ROE - Old ROE) / Old ROE x 100%

Plugging in the numbers:

New ROE = (Net Income / (Total Assets - $50 million)) x 1.6 x (1 / Shareholders' Equity) 
Old ROE = (Net Income / Total Assets) x 1.5 x (1 / Shareholders' Equity)

(New ROE - Old ROE) / Old ROE x 100% = [(Net Income / (Total Assets - $50 million)) x 1.6 x (1 / Shareholders' Equity) - (Net Income / Total Assets) x 1.5 x (1 / Shareholders' Equity)] / [(Net Income / Total Assets) x 1.5 x (1 / Shareholders' Equity)] x 100%

Simplifying:

[(Net Income / Total Assets) x (1.6 / 1.5) - (Net Income / Total Assets)] / (Net Income / Total Assets) x (1.5 / 1) x 100% 
= 0.067 x 100% 
= 6.7%

Therefore, the reduction in assets would improve the ROE by 6.7%, which is closest to choice C (3.16%).

By How Much Would the Reduction in Assets Improve the ROE