Question

Last year Ann Arbor Corp had $155,000 of assets (which equals total invested capital), $305,000 of...

Last year Ann Arbor Corp had $155,000 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?

a. 11.51%
b. 14.09%
c. 13.42%
d. 12.11%
e. 12.75%
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Answer #1

Solution:

Total Invested capital = $155,000

Debt to total capital ratio = 37.5%

Debts = Total Capital * Debt ratio = $155000*37.5% = $58,125

Equity Capital = Total Capital - Debts = $155000 - $58125 = $96,875

Existing ROE = Existing Net Income / Equity capital = $20,000 / $96,875 = 20.6451%

New ROE = Income after cost reduction / Equity Capital = $33,000 / $96,875 = 34.0645%

Improvement in ROE = 34.0645 - 20.6451 = 13.4194 or 13.42

Hence, option "c" is correct.

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