Last year Ann Arbor Corp had $195,000 of assets (which equals total invested capital), $305,000 of sales, $20,000 of net income, and a debt-to-total-capital 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. The firm finances using only debt and common equity. Assets, total invested capital, sales, and the debt to capital ratio would not be affected. By how much would the cost reduction improve the ROE? Do not round your intermediate calculations. Question 16 options: 8.85% 10.88% 10.45% 12.37% 10.67%

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andromache andromache · Answer 1 · 2019-10-10T07:23:11+02:00

Answer:

10.67%

Explanation:

For computing the change in ROE first we have to find out the debt and equity values which are shown below:

The debt value = Total invested capital × debt rate

= $195,000 × 37.5%

= $73,125

And, the equity value = Total assets - debt value

= $195,000 - $73,125

= $121,875

Now we apply the Return on Equity formula which is presented below:

= (Net income ÷ Total equity) × 100

The net income is $20,000 and the equity value would remain the same

So, the ratio would be = ($20,000 ÷ $121,875) × 100 = 16.41%

And if the net income raise to $33,000

Then the new ROE would be = ($33,000 ÷ $121,875) × 100 = 27.07%

So, the change in ROE

= New ROE - Old ROE

= 27.07% - $16.41%

= 10.67%