Question

Last year Harrington Inc. had sales of $325,000 and a net income of $19,000, and its year-end assets were $250,000. The firm's total-debt-to-total-assets ratio was 62.5%. Based on the DuPont equation, what was the ROE?

21.28%

15.40%

21.48%

20.87%

20.27%

Answer 1

Solution :

As per the Du pont Equation

Return on equity = Equity multiplier * Total asset turnover * Profit margin

= ( Assets / Common equity ) * ( Sales / Assets ) * ( Net Income / sales )

As per the information given in the question we have

Assets = $ 250,000   ; Sales = $ 325,000      ;   Net Income = $ 19,000 ;

Total debt to total assets ratio = 62.5% = 0.625 ;

The Formula for calculating the total debt to total assets ratio = Total Debt / Total Assets

Thus we have

0.625 = Total Debt / $ 250,000

Total Debt = $ 250,000 * 0.625 = $ 156,250

Further we know that

Debt + Common equity = Total Assets

$ 156,250 + Common equity = $ 250,000

Thus Common equity = $ 250,000 - $ 156,250 = $ 93,750

Applying the available information in the Du pont equation equation we have ROE as

= ( $ 250,000 / $ 93,750 ) * ( $ 325,000 / $ 250,000 ) * ( $ 19,000 / $ 325000 )

= 2.666667 * 1.3 * 0.058462

= 0.202667

= 20.2667 %                                                        

= 20.27 % ( when rounded off to two decimal places )

Thus based on the DuPont equation, the ROE = 20.27 %

The solution is Option 5 = 20.27 %