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Last year Ann Arbor Corp had $250,000 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 that a new computer program will enable the company 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.
a. 6.74%
b. 8.82%
c. 8.32%
d. 8.15%
e. 8.57%

Answer :

Answer:

Increase in ROE  = 8.32%

so correct answer is c. 8.32%

Explanation:

given data

assets ( total invested capital) = $250,000

sales = $305,000

old net income = $20,000

debt-to-total-capital ratio = 37.5%

raise new net income = $33,000

solution

we get here first debt that is

debt = total invested capital × debt-to-total-capital ratio .............1

debt = $250,000 × 37.5%  

debt = $93750

so here Equity will be as

Equity = Assets - debt  ..............1

Equity =  $250,000 - $93750

Equity = $156250

so here now we get  New ROE that is

New ROE = [tex]\frac{old\ net\ income}{equity}[/tex]      ..............3

New ROE = [tex]\frac{33000}{156250}[/tex]

New ROE = 21.12%

and

Old ROE = [tex]\frac{old\ net\ income}{equity}[/tex]  .....................4

Old ROE = [tex]\frac{20000}{156250}[/tex]

Old ROE = 12.8 %

so as that from equation 3 and 4 we get  Increase in ROE  that is

Increase in ROE = 21.12 % - 12.8%

Increase in ROE  = 8.32%

so correct answer is c. 8.32%

abiolataiwo2015

Based on the information given the amount that the cost reduction improve the ROE is 8.32%.

Cost reduction:

First step:

Equity = Assets - Debt

Equity=$250,000-( $250,000 × 37.5% )

Equity =  $250,000 - $93,750

Equity = $156250

Second step:

New ROE=$33,000/$156250×100

New ROE=21.12%

Old ROE=$20,000/$156250×100

Old ROE=12.8%

Third step:

Cost reduction=21.12%-12.8%

Cost reduction=8.32%

Inconclusion the amount that the cost reduction improve the ROE is 8.32%.

Learn more about cost reduction here:https://brainly.com/question/25537936

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