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Last year Swensen Corp. had sales of $303,225, operating costs of $267,500, and year-end assets of...

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 25%. 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?

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Expert Solution

Year-end Total assets = $195,000 Debt-to-total-assets ratio = 27%

Interest rate on the debt = 8.2% Firm's tax rate = 25%

Debt-to-total-assets ratio = Total Debt / Total Assets

27% = Total Debt / $195,000

Total Debt = 0.27 x $195,000 = $52,650

Total Equity = Total Assets - Total Debt = $195,000 - $52,650 = $142,350

Current ROE is:

Sales = $303,225 Operating costs = $267,500

Operating income = Sales - Operating costs = $303,225 - $267,500 = $35,725

Interest Expense = 8.2% of $52,650 = 0.082 x $52,650 = $4,317.3

Earnings Before Tax = Operating income - Interest Expense = $35,725 - $4,317.3 = $31407.7

Earnings After Tax = Earnings Before Tax x (1 - Tax Rate) = $31407.7 x ( 1-0.25) = $31407.7 x 0.75

Earnings After Tax = $23,555.775

Return on Equity (ROE) = Earnings After Tax / Total Equity = $23,555.775 / $142,350 = 0.1655 = 16.55%

Current ROE is 16.55%

Now, ROE when debt ratio is 45%

Debt-to-total-assets ratio = Total Debt / Total Assets

45% = Total Debt / $195,000

Total Debt = 0.45 x $195,000 = $87,750

Total Equity = Total Assets - Total Debt = $195,000 - $87,750 = $107,250

Sales = $303,225 Operating costs = $267,500

Operating income = Sales - Operating costs = $303,225 - $267,500 = $35,725

Interest Expense = 8.2% of $87,750 = 0.082 x $87,750 = $7,195.5

Earnings Before Tax = Operating income - Interest Expense = $35,725 - $7,195.5 = $28,529.5

Earnings After Tax = Earnings Before Tax x (1 - Tax Rate) = $28,529.5 x ( 1-0.25) = $28,529.5 x 0.75

Earnings After Tax = $21,397.125

Expected ROE = Return on Equity (ROE) = Earnings After Tax / Total Equity = $21,397.125 / $107,250 = 0.1995

Expected ROE= 19.95%

Change in ROE in response to the change in the capital structure = Expected ROE - Current ROE = 19.95% - 16.55%

Change in ROE in response to the change in the capital structure = 3.40%

jeff jeffy answered 1 year ago

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