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 $435,000. 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 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

1.74%

Explanation:

                               17% Debt       50% Debt

Sales                      $500,000      $500,000

Less: Cost              $450,000      $450,000

Less: Interest         $5,546           $17,400

Profit before tax   $44,454        $32,600

Less: Tax at 35%   $15,559          $11,410

Net Income           $28,895        $21,190

Equity                     $361,050        $217,500

Return on Equity   8.00%             9.74%

Change in ROE = 9.74% - 8.00% = 1.74%

Workings

Interest (17% Debt) = 43,500*17%*7.5% = $5,546

Interest (50% Debt) = 43,500*50%*8% = $17,400

Tax (17% Debt) = $44,454 * 0.35 = 15,559

Tax (50% Debt) = $32,600 * 0.35 = 11,410

Equity (17% Debt) =435,000*83% = 361,050        

Equity (50% Debt) = 435,000*50% = $217,500

Return on Equity = $28,895/$361,050 = 8.00%

Return on Equity = $21,190/$217,500 = 9.74%