Consider a retail firm with a net profit margin of 3.58 % , a total asset turnover of 1.75 , total assets of $ 42.6 million, and a book value of equity of $ 17.9 million. a. What is the firm's current ROE? b. If the firm increased its net profit margin to 4.30 % , what would be its ROE? c. If, in addition, the firm increased its revenues by 18 % (maintaining this higher profit margin and without changing its assets or liabilities), what would be its ROE?

(a) 14.9107%

(b) 17.9095%

(c) 21.13321%

Explanation:

Given that,

Net profit margin = 3.58%

Total asset turnover = 1.75

Total assets = $42.6 million

Book value of equity = $ 17.9 million

(a) firm's current ROE:

= Net income : Total equity

= Net profit margin * Assets turnover * (Assets : Equity)

= (Net income : sales) * (sales : assets) * (Assets : Equity)

= 3.58% * 1.75 * ($42.6 : $17.9)

= 3.58% * 1.75 * 2.38

= 14.9107%

(b) If the firm increased its net profit margin to 4.30 %,

ROE:

= 4.30% * 1.75 * ($42.6 : $17.9)

= 4.30% * 1.75 * 2.38

= 17.9095%

(c) If, in addition, the firm increased its revenues by 18%,

Asset turnover increases by:

= 1.75 * 1.18

= 2.065

ROE:

= 4.30% * 2.065 * ($42.6 : $17.9)

= 4.30% * 2.065 * 2.38

= 21.13321%