Last year Hamdi Corp.had sales of $500,000,operating costs of $450,000,and year-end assets (which is equal to its total invested capital)of $425,000.The debt-to-total-capital ratio was 17%,the interest rate on the debt was 7.5%,and the firm's tax rate was 25%.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 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? Do not round your intermediate calculations.
A) 1.65%
B) 2.41%
C) 2.60%
D) 2.17%
E) 1.80%

Question

Quizplus · Accepted Answer

To calculate the change in ROE due to the change in the capital structure, we first determine the initial and new ROE.Initial conditions:- EBIT = Sales - Operating Costs = $500,000 - $450,000 = $50,000- Interest = Debt * Interest Rate. With a 17% debt ratio, Debt = 0.17 * Total Capital = 0.17 * $425,000 = $72,250. Interest = $72,250 * 7.5% = $5,418.75- EBT = EBIT - Interest = $50,000 - $5,418.75 = $44,581.25- Taxes = EBT * Tax Rate = $44,581.25 * 25% = $11,145.31- Net Income = EBT - Taxes = $44,581.25 - $11,145.31 = $33,435.94- Equity = Total Capital - Debt = $425,000 - $72,250 = $352,750- Initial ROE = Net Income / Equity = $33,435.94 / $352,750 = 9.48%New conditions with 50% debt ratio:- New Debt = 0.50 * Total Capital = 0.50 * $425,000 = $212,500- New Interest = New Debt * New Interest Rate = $212,500 * 8.0% = $17,000- New EBT = EBIT - New Interest = $50,000 - $17,000 = $33,000- New Taxes = New EBT * Tax Rate = $33,000 * 25% = $8,250- New Net Income = New EBT - New Taxes = $33,000 - $8,250 = $24,750- New Equity = Total Capital - New Debt = $425,000 - $212,500 = $212,500- New ROE = New Net Income / New Equity = $24,750 / $212,500 = 11.65%Change in ROE = New ROE - Initial ROE = 11.65% - 9.48% = 2.17%

Last Year Hamdi Corp