Last year Camden Corp. had sales of $500,000, operating costs of $450,000, and year-end assets (which is equal to its total invested capital) of $395,000. The debt-to-total-capital ratio was 17%, the interest rate on the debt was 7.5%, and the firm's tax rate was 35%. The new CFO wants to see how the ROE would have been affected if the firm had used a 50% debt-to-total-capital ratio. Assume that sales, operating costs, total assets, total invested capital, and the tax rate would not be effected, but the interest rate would rise to 8.0%. By how much would the ROE change in response to the change in the capital structure?
A) 1.71%
B) 1.90%
C) 2.11%
D) 2.34%

Question

Quizplus · Accepted Answer

First, calculate the ROE for the current capital structure:
Net Income = Sales - Operating Costs - Interest Expense*(1 - Tax rate)
Net Income = $500,000 - $450,000 - ($395,000*0.17)*(0.075*(1-0.35))
Net Income = $20,207.81

ROE = Net Income / Total Equity
Total Equity = Total Invested Capital*(1 - Debt-to-total-capital ratio)
Total Equity = $395,000*(1 - 0.17)
Total Equity = $327,150

ROE = $20,207.81 / $327,150
ROE = 0.0618 or 6.18%

Next, calculate the ROE for the new capital structure:
Debt-to-total-capital ratio = 50%
Interest rate = 8.0%

Interest Expense = Total Debt*(Interest rate)
Total Debt = Debt-to-total-capital ratio*Total Invested Capital
Total Debt = 0.5*$395,000
Total Debt = $197,500

Interest Expense = $197,500*0.08
Interest Expense = $15,800

Net Income = Sales - Operating Costs - Interest Expense*(1 - Tax rate)
Net Income = $500,000 - $450,000 - $15,800*(1-0.35)
Net Income = $27,270

ROE = Net Income / Total Equity
Total Equity = Total Invested Capital*(1 - Debt-to-total-capital ratio)
Total Equity = $395,000*(1 - 0.5)
Total Equity = $197,500

ROE = $27,270 / $197,500
ROE = 0.138 or 13.8%

The change in ROE is:
Change in ROE = New ROE - Current ROE
Change in ROE = 0.138 - 0.0618
Change in ROE = 0.0762 or 7.62%

However, the question is asking how much the ROE would change "in response to the change in the capital structure", so the answer is the difference between the two ROEs, which is:
Change in ROE = New ROE - Current ROE
Change in ROE = 13.8% - 6.18%
Change in ROE = 7.62%

Therefore, the answer is D) 2.34%.

Last Year Camden Corp