Chapter 13, Problem 13.5CP

Inferring Information from the DuPont Model Ratios

LO13-5 in this chapter, we discussed the DuPont model. Using that framework, find the missing amount in each of the following cases:

Case 1: ROE is 10 percent; net income is $200,000; the total asset turnover ratio is 5; and net sales are $1,000,000. What is the amount of average stockholders’ equity?

Case 2: Net income is $1,500,000; net sales are $8,000,000; average stockholders’ equity is $12,000,000; ROE is 22 percent; and the total asset turnover ratio is 8. What is the amount of average total assets?

Case 3: ROE is 15 percent; the net profit margin is 10 percent; the total asset turnover ratio is 5; and average total assets are $1,000,000. What is the amount of average stockholders’ equity?

Case 4: Net income is $500,000; ROE is 15 percent; the total asset turnover ratio is 5; net sales are $1,000,000; and financial leverage is 2. What is the amount of average total assets?

To determine

Compute the amount of average stockholders’ equity using the DuPont model.

Explanation of Solution

DuPont model: It is a model which allows the analyst to analyse a company’s performance using ratios. This model uses the ratios that indicate the company performance. DuPont model equation is as follows:

$\begin{array}{c}\text{ROE}\text{=}\left[\begin{array}{l}\text{Net profit margin}\text{×}\text{Total assets turnover}\text{×}\\ \text{Financial leverage}\end{array}\right]\\ \frac{\text{Net Income}}{\text{Average}\text{TotalStockholders'}\text{equity}}\text{=}\left[\begin{array}{l}\frac{\text{Net}\text{Income}}{\text{Net}\text{Sales}\text{Revenue}}\text{×}\frac{\text{Net}\text{Sales}\text{Revenue}}{\text{Average}\text{Total}\text{Assets}}\\ \text{×}\frac{\text{Average}\text{Total}\text{Assets}}{\text{Average}\text{TotalStockholders'}\text{equity}}\end{array}\right]\end{array}$

Return on equity ratio: Rate of return on equity ratio is used to determine the relationship between the net income available for the common stockholders’ and the average common equity that is invested in the company.

Determine the amount of average stockholders’ equity.

$\begin{array}{c}\text{Return on equity}=\frac{\text{Net income}}{\text{Average stockholders' equity}}\\ 0.10=\frac{\$200,000}{\text{Average stockholders' equity}}\\ \text{Average stockholders' equity =}\frac{\$200,000}{0.10}\\ \text{Average stockholders' equity =\$2,000,000}\end{array}$

Hence, the amount of average stockholders’ equity is $200,000.

To determine

Compute the amount of average total assets using the DuPont model.

Explanation of Solution

DuPont model: It is a model which allows the analyst to analyse a company’s performance using ratios. This model uses the ratios that indicate the company performance. DuPont model equation is as follows:

$\begin{array}{c}\text{ROE}\text{=}\left[\begin{array}{l}\text{Net profit margin}\text{×}\text{Total assets turnover}\text{×}\\ \text{Financial leverage}\end{array}\right]\\ \frac{\text{Net Income}}{\text{Average}\text{TotalStockholders'}\text{equity}}\text{=}\left[\begin{array}{l}\frac{\text{Net}\text{Income}}{\text{Net}\text{Sales}\text{Revenue}}\text{×}\frac{\text{Net}\text{Sales}\text{Revenue}}{\text{Average}\text{Total}\text{Assets}}\\ \text{×}\frac{\text{Average}\text{Total}\text{Assets}}{\text{Average}\text{TotalStockholders'}\text{equity}}\end{array}\right]\end{array}$

Total Asset turnover: Total asset turnover is a ratio that measures the productive capacity of the total assets to generate the sales revenue for the company. Thus, it shows the relationship between the net sales and the average total assets.

Determine the amount of average total assets.

$\begin{array}{c}\text{Total asset turnover}=\frac{\text{Net Sales}}{\text{Average total assets}}\\ 8=\frac{\$8,000,000}{\text{Average total assets}}\\ \text{Average total assets =}\frac{\$8,000,000}{8}\\ \text{Average total assets =\$1,000,000}\end{array}$

Hence, the amount of average total assets is $1,000,000.

To determine

Compute the amount of average stockholders’ equity.

Explanation of Solution

DuPont model: It is a model which allows the analyst to analyse a company’s performance using ratios. This model uses the ratios that indicate the company performance. DuPont model equation is as follows:

$\begin{array}{c}\text{ROE}\text{=}\left[\begin{array}{l}\text{Net profit margin}\text{×}\text{Total assets turnover}\text{×}\\ \text{Financial leverage}\end{array}\right]\\ \frac{\text{Net Income}}{\text{Average}\text{TotalStockholders'}\text{equity}}\text{=}\left[\begin{array}{l}\frac{\text{Net}\text{Income}}{\text{Net}\text{Sales}\text{Revenue}}\text{×}\frac{\text{Net}\text{Sales}\text{Revenue}}{\text{Average}\text{Total}\text{Assets}}\\ \text{×}\frac{\text{Average}\text{Total}\text{Assets}}{\text{Average}\text{TotalStockholders'}\text{equity}}\end{array}\right]\end{array}$

Total Asset turnover: Total asset turnover is a ratio that measures the productive capacity of the total assets to generate the sales revenue for the company. Thus, it shows the relationship between the net sales and the average total assets.

Return on equity ratio: Rate of return on equity ratio is used to determine the relationship between the net income available for the common stockholders’ and the average common equity that is invested in the company.

Determine the amount of average stockholders’ equity.

$\begin{array}{c}\text{Return on equity}=\frac{\text{Net income}}{\text{Average stockholders' equity}}\\ 0.15=\frac{\$500,000\left(2\right)}{\text{Average stockholders' equity}}\\ \text{Average stockholders' equity =}\frac{\$500,000}{0.15}\\ \text{Average stockholders' equity =\$3,333,333}\end{array}$

Working Note:

Determine the amount of average asset turnover.

$\begin{array}{c}\text{Total asset turnover}=\frac{\text{Net Sales}}{\text{Average total assets}}\\ 5=\frac{\text{Net Sales}}{\text{\$1,000,000}}\\ \text{Net Sales = }\$1,000,000\times 5\\ \text{Net Sales =\$5,000,000}\end{array}$ (1)

Determine the amount of net income.

$\begin{array}{c}\text{Net profit margin}=\frac{\text{Net Income}}{\text{Net Sales }\left(1\right)}\\ 5=\frac{\text{Net Sales}}{\text{\$1,000,000}}\\ \text{Net Income = }\$1,000,000\times 5\\ \text{Net Income =\$5,000,000}\end{array}$ (2)

Hence, the amount of average stockholders’ equity is $3,333,333.

To determine

Compute the amount of average total assets using the DuPont model.

Explanation of Solution

DuPont model: It is a model which allows the analyst to analyse a company’s performance using ratios. This model uses the ratios that indicate the company performance. DuPont model equation is as follows:

$\begin{array}{c}\text{ROE}\text{=}\left[\begin{array}{l}\text{Net profit margin}\text{×}\text{Total assets turnover}\text{×}\\ \text{Financial leverage}\end{array}\right]\\ \frac{\text{Net Income}}{\text{Average}\text{TotalStockholders'}\text{equity}}\text{=}\left[\begin{array}{l}\frac{\text{Net}\text{Income}}{\text{Net}\text{Sales}\text{Revenue}}\text{×}\frac{\text{Net}\text{Sales}\text{Revenue}}{\text{Average}\text{Total}\text{Assets}}\\ \text{×}\frac{\text{Average}\text{Total}\text{Assets}}{\text{Average}\text{TotalStockholders'}\text{equity}}\end{array}\right]\end{array}$

Total Asset turnover: Total asset turnover is a ratio that measures the productive capacity of the total assets to generate the sales revenue for the company. Thus, it shows the relationship between the net sales and the average total assets.

Determine the amount of average total assets.

$\begin{array}{c}\text{Total asset turnover}=\frac{\text{Net Sales}}{\text{Average total assets}}\\ 5=\frac{\$1,000,000}{\text{Average total assets}}\\ \text{Average total assets =}\frac{\$1,000,000}{5}\\ \text{Average total assets =\$200,000}\end{array}$

Hence, the amount of average total assets is $200,000.