Last year Hamdi Corp. had sales of $500,000, operating costs of $450,000, and year-end assets of $395,000. The debt-to-total-assets 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 ratio. Assume that sales, operating costs, total assets, and the tax rate would not be affected, 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%
E) 2.58%

Question

Quizplus · Accepted Answer

First, let's calculate Hamdi Corp.'s ROE using the original capital structure:

Net Income = Sales - Operating Costs - Interest Expense - Taxes
Net Income = $500,000 - $450,000 - ($395,000 x 0.17 x 0.075) - ($55,250 x 0.35)
Net Income = $38,787.50

ROE = Net Income / Average Total Equity
Average Total Equity = (Beginning Total Equity + Ending Total Equity) / 2
Beginning Total Equity = Ending Total Equity = $395,000 x (1 - 0.17) = $327,150
Average Total Equity = ($327,150 + $395,000) / 2 = $361,075

ROE = $38,787.50 / $361,075 = 0.1073 or 10.73%

Now, let's calculate Hamdi Corp.'s ROE with a 50% debt ratio:

Debt = Total Assets x Debt Ratio
Debt = $395,000 x 0.5 = $197,500

Equity = Total Assets - Debt
Equity = $395,000 - $197,500 = $197,500

Interest Expense = Debt x Interest Rate
Interest Expense = $197,500 x 0.08 = $15,800

Net Income = Sales - Operating Costs - Interest Expense - Taxes
Net Income = $500,000 - $450,000 - $15,800 - ($55,250 x 0.35)
Net Income = $46,162.50

ROE = Net Income / Average Total Equity
Average Total Equity = (Beginning Total Equity + Ending Total Equity) / 2
Beginning Total Equity = Ending Total Debt = $197,500 / (1 - 0.17) = $237,650
Ending Total Equity = $395,000 x (1 - 0.5) = $197,500
Average Total Equity = ($237,650 + $197,500) / 2 = $217,575

ROE = $46,162.50 / $217,575 = 0.2127 or 21.27%

The change in ROE is:

Change in ROE = New ROE - Old ROE
Change in ROE = 0.2127 - 0.1073
Change in ROE = 0.1054 or 10.54%

The ROE would increase by 2.34% (Choice D).

Last Year Hamdi Corp