Question

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?

Answer 1

Answer:

(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%