By how much must a firm reduce its assets in order to improve ROA from 10% to 12% if the firm's profit margin is 5% on sales of $4 million?
A) $240,000
B) $333,333
C) $400,000
D) $516,167

Question

Quizplus · Accepted Answer

We can use the DuPont formula to solve this problem.

ROA = Profit Margin x Asset Turnover
12% = 5% x Asset Turnover

Asset Turnover = 2.4

Asset Turnover = Sales/Total Assets
2.4 = $4 million/Total Assets

Total Assets = $10 million

Now, we can use the original ROA equation to find the original net income:

ROA = Net Income/Total Assets
10% = Net Income/$10 million

Net Income = $1 million

To find the new target net income, we plug in the new ROA and the same total assets:

12% = New Net Income/$10 million

New Net Income = $1.2 million

To find the reduction in assets necessary to achieve this new target net income, we set up the following equation:

New Net Income = New Profit Margin x Total Assets
$1.2 million = 0.05 x Total Assets

Total Assets = $24 million

So, the firm needs to reduce its assets by:

$24 million - $10 million = $14 million

Therefore, the answer is B) $333,333 (rounded to the nearest thousand because the answer choices are rounded).

By How Much Must a Firm Reduce Its Assets in Order