Last year oliver inc had a total assets turnover of 1.60 and an equity multiplier of 1.85. its sales were $200,000 and its net income was $10,000. the cfo believes that the company could have operated more efficiently, lowered its costs, and increased its net income by $5,000 without changing its sales, assets, or capital structure. had it cut costs and increased its net income in this amount, by how much would the roe have changed

7.4%

Explanation:

As we know that

ROE = Profit margin ×  Total asset turnover × Equity multiplier

where,

Profit margin = (Net income ÷ Sales) × 100

                     = ($10,000 ÷ $200,000) × 100

                     = 5%

So, the ROE would be

= 5% × 1.60 × 1.85

= 14.8%

Now if the net income is increased by  $5,000

So, the updated profit margin would be

= (Net income ÷ Sales) × 100

= ($15,000 ÷ $200,000) × 100

= 7.5%

And updated ROE would be

= 7.5% × 1.60 × 1.85

= 22.2%

So, the change in ROE would be

= 22.2% - 14.8%

= 7.4%

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