Consider a retailing firm with a net profit margin of 3.6 %, a total asset turnover of 1.74, total assets of $ 44.4 million, and a book value of equity of $ 18.4 million. a. what is the firm's current roe? b. if the firm increased its net profit margin to 4.1 %, what would be its roe? c. if, in addition, the firm increased its revenues by 23 % (while maintaining this higher profit margin and without changing its assets or liabilities), what would be its roe?

a.15.09624%

b. 17.19294%

c.  18.56837%

Explanation:

In this question, we use the DuPont formula which is shown below:

a. Return on equity = Net profit margin × total assets turnover × leverage factor

where,

leverage factor = Total assets ÷ book value of equity

                         = $44.4 million ÷ $18.4 million

                         = 2.41

Now the ROE equals to

= 3.6% × 1.74 × 2.41

= 15.09624%

b. If net profit margin is 4.1%, so the New ROE equals to

= 4.1% × 1.74 × 2.41

= 17.19294%

c. If revenue is increase by 23% , so it increase the asset turnover, and the new asset turnover equals to

= 1.74 × 123%

= 2.1402

Now, New ROE equals to

= 3.6% × 2.1402 × 2.41

= 18.56837%

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