# Solve problem for ROE Dupont 4 question.

1. A company has an ROE of 21.6%, Total Asset Turnover of 1.5 and EM of 1.2. If the company had sales of \$5,000,000, what was the company’s Net Income?

2. A company with \$800,000 in assets, has sales of \$1,000,000. Their net income was \$80,000 and they have \$500,000 in liabilities. According to the Dupont Identity, what is the company’s ROE?

3. Which of the following is LEAST likely to improve a company’s ROE?

 A. Increase profit margins B. Decrease the debt ratio C. Increase sales relative to assets D. Increase the equity multiplier

4. A company has an ROE of 28.16%, total asset turnover of 2.2x, profit margin of 8% and \$1,000,000 in equity. What does the company have in total assets?

1. To solve this problem, we can use the DuPont formula:

ROE = Net Income / Total Equity
ROE = Profit Margin x Total Asset Turnover x Equity Multiplier

Given:
ROE = 21.6%
Total Asset Turnover = 1.5
Equity Multiplier = 1.2
Sales = \$5,000,000

We need to find Net Income.

Using the DuPont formula, we can rearrange it to solve for Net Income:

Net Income = ROE / (Profit Margin x Total Asset Turnover x Equity Multiplier)

Net Income = 0.216 / (Profit Margin x 1.5 x 1.2)

We don’t have the profit margin information, so we cannot calculate the exact Net Income.

2. According to the DuPont Identity, Return on Equity (ROE) is calculated as:

ROE = Net Income / Total Equity
ROE = Profit Margin x Total Asset Turnover x Equity Multiplier

Given:
Assets = \$800,000
Sales = \$1,000,000
Net Income = \$80,000
Liabilities = \$500,000

To find the ROE, we need to calculate the Total Equity:

Total Equity = Assets – Liabilities
Total Equity = \$800,000 – \$500,000
Total Equity = \$300,000

Now we can calculate the ROE using the DuPont formula:

ROE = Net Income / Total Equity
ROE = \$80,000 / \$300,000
ROE = 0.2667 or 26.67%

So, the company’s ROE is 26.67%.

3. The correct answer is B. Decrease the debt ratio.

Decreasing the debt ratio would reduce the company’s equity multiplier, leading to a decrease in ROE. In contrast, increasing profit margins (A), increasing sales relative to assets (C), and increasing the equity multiplier (D) would typically result in an improvement in ROE.

4. To find the total assets, we can use the DuPont formula and rearrange it as:

ROE = Net Income / Total Equity
ROE = Profit Margin x Total Asset Turnover x Equity Multiplier

Given:
ROE = 28.16%
Total Asset Turnover = 2.2x
Profit Margin = 8%
Equity = \$1,000,000

We need to find the Total Assets.

Using the DuPont formula, we can rearrange it to solve for Total Assets:

Total Assets = Net Income / (Profit Margin x Total Asset Turnover x Equity Multiplier)

Total Assets = \$1,000,000 / (0.08 x 2.2 x 0.2816)

Total Assets = \$1,000,000 / 0.0492352

Total Assets ≈ \$20,318,121.98

Therefore, the company has approximately \$20,318,121.98 in total assets.