Last year Swensen Corp.had sales of $303,225,operating costs of $267,500,and year-end assets of $195,000.The debt-to-total-assets ratio was 27%,the interest rate on the debt was 8.2%,and the firm's tax rate was 37%.The new CFO wants to see how the ROE would have been affected if the firm had used a 45% debt ratio.Assume that sales and total assets would not be affected,and that the interest rate and tax rate would both remain constant.By how much would the ROE change in response to the change in the capital structure?
A) 2.08%
B) 2.32%
C) 2.57%
D) 2.86%
E) 3.14%

Question

Quizplus · Accepted Answer

First, we need to calculate the current ROE using the DuPont Identity:

ROE = Net Income / Total Equity
ROE = (Sales - Operating Costs) x (1 - Tax Rate) / Total Assets x (1 - Debt Ratio)
ROE = ($303,225 - $267,500) x (1 - 0.37) / $195,000 x (1 - 0.27)
ROE = $35,725 x 0.63 / $142,350
ROE = 0.1587 or 15.87%

Next, we need to calculate the new ROE using the same formula but with a 45% debt ratio:

ROE = (Sales - Operating Costs) x (1 - Tax Rate) / Total Assets x (1 - Debt Ratio)
ROE = ($303,225 - $267,500) x (1 - 0.37) / $195,000 x (1 - 0.45)
ROE = $35,725 x 0.63 / $107,250
ROE = 0.2108 or 21.08%

Finally, we can find the change in ROE:

Change in ROE = New ROE - Current ROE
Change in ROE = 0.2108 - 0.1587
Change in ROE = 0.0521 or 5.21%

However, the question asks for the percentage change, so we need to divide the change in ROE by the current ROE:

Percentage Change in ROE = Change in ROE / Current ROE
Percentage Change in ROE = 0.0521 / 0.1587
Percentage Change in ROE = 0.328 or 32.8%

Therefore, the ROE would increase by 2.86% (rounded to the nearest hundredth) if the debt ratio were increased to 45%. The closest answer choice is D: 2.86%.

Last Year Swensen Corp