Last year Lowell Inc. had a total assets turnover of 1.40 and an equity multiplier of 1.75. Its sales were $295,000 and its net income was $10,600. The CFO believes that the company could have operated more efficiently, lowered its costs, and increased its net income to $20,850 without changing its sales, assets, or capital structure. Had it cut costs and increased its net income as expected, how much would the ROE have changed

ROE would have changed by 8.52%

Explanation:

First we calculate the current ROE using Dupont Equation which gives ROE as,

ROE = Net Income/Sales * Sales/Total Assets * Total Assets/Equity

or

ROE = Net Profit Margin * Total Assets Turnover * Equity Multiplier

Current ROE = 10600/295000 * 1.4 * 1.75 = 0.0880 or 8.8%

The condition says that the net income could have increased to 20850 but other factors will remain constant. Thus, to calculate new ROE, we will calculate the new Net Profit margin but the total assets turnover and the equity multiplier will remain constant as sales assets and capital structure is not changing.

New ROE = 20850/295000 * 1.4 * 1.75 = 0.17316 or 17.32% The ROE would have changed by 17.32 - 8.80 = 8.52%