Last year Mason Inc. had a total assets turnover of 1.33 and an equity multiplier of 1.75. Its sales were $195,000 and its net income was $10,549. The CFO believes that the company could have operated more efficiently, lowered its costs, and increased its net income by $5,250 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

Return on equity (ROE) would have changed by 6.27%.

Explanation:

In accounting ratio, we know that:

Asset Turnover = Sales/Total Assets (1)

From equation (1), we can solve for Total Assets as follows:

Total Assets = Sales / Asset Turnover (2)

Substituting the values in the question into equation (2), we have:

Total Assets = $195,000 / 1.33 = $146,616.54

Also, we know that:

Equity Multiplier = Total Assets/Total Equity (3)

We can solve Total Equity from equation (3) as follows:

Total Equity = Total Assets / Equity Multiplier (4)

Substituting the relevant values into equation (4), we have:

Total Equity = $146,616.54 / 1.75 = $83,780.88

As a result, we have:

Return on Equity = Net Income/Total Equity = $10,549 / $83,780.88 = 0.1259, or 12.59%

If the company had operated more efficiently, we would have:

New net income = Net income + Amount of increase in net income = $10,549 + $5,250 = $15,799

New return on equity = New net Income / Total Equity = $15,799 / $83,780.88 = 0.1886, or 18.86%

Change in return on equity = New return on equity - Return on Equity = 18.86% - 12.59% = 6.27%

Therefore, return on equity (ROE) would have changed by 6.27%.

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