Last year Ann Arbor Corp had $155,000 of assets, $305,000 of sales, $20,000 of net income, and a debt-to-total-assets ratio of 37.5%. The new CFO believes a new computer program will enable it to reduce costs and thus raise net income to $33,000. Assets, sales, and the debt ratio would not be affected. By how much would the cost reduction improve the ROE

13.42%

Explanation:

The computation of return on equity is shown below:-

Debt = Assets × ( Debt to assets ratio)

$155,000 × 37.5%

= $58,125

Equity = Total Assets - Debt

= $155,000 - $58,125

= $96,875

Old Return on equity = Old Net Income ÷ Equity

=$20,000 ÷ $96,875

= 20.64%

New Return on equity = New Net Income ÷ Equity

= $33,000 ÷ $96,875

= 34.06%

Increased in Return on equity = New Return on equity - Old Return on equity

= 34.06% - 20.64%

= 13.42%