Question

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

Answer 1

Answer:

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%.