The board of directors is dissatisfied with last year's ROE of 15 percent.If the profit margin and asset turnover remain unchanged at 8 percent and 1.25 respectively, by how much must the total debt ratio increase to achieve 20 percent ROE?
A)Total debt ratio must increase by .5
B)Total debt ratio must increase by 5
C)Total debt ratio must increase by 5 percent
D)Total debt ratio must increase by 16.67 percent Last Year:
ROE = .15 = Profit margin x Asset turnover x leverage rate
= )08 x 1.25 x 1.5
This Year:
ROE = .20 = .08 x 1.25 x?

Question

Quizplus · Accepted Answer

Using the DuPont Identity, we can manipulate the ROE formula to solve for the change in the total debt ratio:
ROE = Profit margin x Asset turnover x leverage rate
ROE = (Net income/Sales) x (Sales/Assets) x (Assets/Equity)
ROE = Net income/Equity
0.2 = 0.08 x 1.25 x (Total assets/Total equity)
Total debt ratio = (Total assets - Total equity)/Total assets

Assuming total assets remain constant, we can solve for the change in the total debt ratio needed to achieve a 20% ROE:
0.2 = 0.08 x 1.25 x (1 + Total debt ratio)
Total debt ratio = 0.1667, or a 16.67% increase in the total debt ratio. Therefore, the correct answer is D.

The Board of Directors Is Dissatisfied with Last Year's ROE