The dupont equation

What Is the DuPont Analysis?

The DuPont analysis is a framework for analyzing fundamental performance popularized by the DuPont Corporation. DuPont analysis is a useful technique used to decompose the different drivers of return on equity (ROE). The decomposition of ROE allows investors to focus on the key metrics of financial performance individually to identify strengths and weaknesses. There are two versions of the tool—one which accounts for decomposition in three steps while the other does so in five steps.

Key Takeaways

• The DuPont analysis is a framework for analyzing fundamental performance originally popularized by the DuPont Corporation.
• The formula was developed in 1914 by F. Donaldson Brown, an employee of the DuPont Corporation.
• DuPont analysis is a useful technique used to decompose the different drivers of return on equity.
• An investor can use analysis tools like this to compare the operational efficiency of two similar firms.
• Managers can use DuPont analysis to identify strengths or weaknesses that should be addressed.

DuPont Analysis

Understanding the DuPont Analysis

The DuPont analysis is a formula used to track a company's financial performance. It was developed in 1914 by F. Donaldson Brown, who worked for the DuPont Corporation. His formula incorporates earnings, investment, and working capital together into a single figure that he called return on investment (ROI). It became a standard measure for all DuPont departments and was adopted by other companies.

A DuPont analysis is used to evaluate the component parts of a company's ROE. This allows an investor to determine what financial activities contribute the most to the changes in ROE. An investor can use tools like this to compare the operational efficiency of two similar firms. Managers can use DuPont analysis to identify strengths or weaknesses that should be addressed.

There are three major financial metrics that drive ROE:

• operating efficiency, which is represented by net profit margin or net income divided by total sales or revenue
• asset use efficiency, which is measured by the asset turnover ratio
• financial leverage—a metric that is measured by the equity multiplier, which is equal to average assets divided by average equity

Formula and Calculation of DuPont Analysis

The Dupont analysis is an expanded return on equity formula, calculated by multiplying the net profit margin by the asset turnover by the equity multiplier.

DuPont Analysis = Net Profit Margin × AT × EM where: Net Profit Margin = Net Income Revenue AT = Asset turnover Asset Turnover = Sales Average Total Assets EM = Equity multiplier Equity Multiplier = Average Total Assets Average Shareholders’ Equity \begin{aligned} &\text{DuPont Analysis} = \text{Net Profit Margin} \times \text{AT} \times \text{EM} \\ &\textbf{where:}\\ &\text{Net Profit Margin} = \frac{ \text{Net Income} }{ \text{Revenue} } \\ &\text{AT} = \text{Asset turnover} \\ &\text{Asset Turnover} = \frac{ \text{Sales} }{ \text{Average Total Assets} } \\ &\text{EM} = \text{Equity multiplier} \\ &\text{Equity Multiplier} = \frac{ \text{Average Total Assets} }{ \text{Average Shareholders' Equity} } \\ \end{aligned} ​DuPont Analysis=Net Profit Margin×AT×EMwhere:Net Profit Margin=RevenueNet Income​AT=Asset turnoverAsset Turnover=Average Total AssetsSales​EM=Equity multiplierEquity Multiplier=Average Shareholders’ EquityAverage Total Assets​​

DuPont Analysis Components

DuPont analysis breaks ROE into its constituent components to determine which of these factors are most responsible for changes in ROE.

Net Profit Margin

The net profit margin is the ratio of bottom line profits compared to total revenue or total sales. This is one of the most basic measures of profitability.

One way to think about the net margin is to imagine a store that sells a single product for $1.00. After the costs associated with buying inventory, maintaining a location, paying employees, taxes, interest, and other expenses, the store owner keeps $0.15 in profit from each unit sold. That means the owner's profit margin is 15%, which can be calculated as follows:

Profit Margin = Net Income Revenue = $ 0.15 $ 1.00 = 15 % \begin{aligned} &\text{Profit Margin} = \frac{ \text{Net Income} }{ \text{Revenue} } = \frac{ \$0.15 }{ \$1.00 } = 15\% \\ \end{aligned} ​Profit Margin=RevenueNet Income​=$1.00$0.15​=15%​

The profit margin can be improved if costs for the owner were reduced or if prices were raised, which can have a large impact on ROE. This is one of the reasons that a company's stock will experience high levels of volatility when management makes a change to its guidance for future margins, costs, and prices.

Asset Turnover Ratio

The asset turnover ratio measures how efficiently a company uses its assets to generate revenue. Imagine a company had $100 of assets, and it made $1,000 of total revenue last year. The assets generated 10 times their value in total revenue, which is the same as the asset turnover ratio and can be calculated as follows:

Asset Turnover Ratio = Revenue Average Assets = $ 1 , 000 $ 100 = 10 \begin{aligned} &\text{Asset Turnover Ratio} = \frac{ \text{Revenue} }{ \text{Average Assets} } = \frac{ \$1,000 }{ \$100 } = 10 \\ \end{aligned} ​Asset Turnover Ratio=Average AssetsRevenue​=$100$1,000​=10​

A normal asset turnover ratio will vary from one industry group to another. For example, a discount retailer or grocery store will generate a lot of revenue from its assets with a small margin, which will make the asset turnover ratio very large. On the other hand, a utility company owns very expensive fixed assets relative to its revenue, which will result in an asset turnover ratio that is much lower than that of a retail firm.

The ratio can be helpful when comparing two companies that are very similar. Because average assets include components like inventory, changes in this ratio can signal that sales are slowing down or speeding up earlier than they would show up in other financial measures. If a company's asset turnover rises, its ROE improves.

Financial Leverage

Financial leverage, or the equity multiplier, is an indirect analysis of a company's use of debt to finance its assets. Assume a company has $1,000 of assets and $250 of owner's equity. The balance sheet equation will tell you that the company also has $750 in debt (assets - liabilities = equity). If the company borrows more to purchase assets, the ratio will continue to rise. The accounts used to calculate financial leverage are both on the balance sheet, so analysts will divide average assets by average equity rather than the balance at the end of the period, as follows:

Financial Leverage = Average Assets Average Equity = $ 1 , 000 $ 250 = 4 \begin{aligned} &\text{Financial Leverage} = \frac{ \text{Average Assets} }{ \text{Average Equity} } = \frac{ \$1,000 }{ \$250 } = 4 \\ \end{aligned} ​Financial Leverage=Average EquityAverage Assets​=$250$1,000​=4​

Most companies should use debt with equity to fund operations and growth. Not using any leverage could put the company at a disadvantage compared with its peers. However, using too much debt in order to increase the financial leverage ratio—and therefore increase ROE—can create disproportionate risks.

A point to note, though, is that some companies use balance sheet averages when one of the components is an income statement metric. In the case noted above, no averaging is necessary as the equation takes balance sheet/balance sheet figures into account.

DuPont Analysis vs. Return on Equity (ROE)

The return on equity metric is net income divided by shareholders’ equity. The Dupont analysis is still the ROE, just an expanded version. The ROE calculation alone reveals how well a company utilizes capital from shareholders.

With a Dupont analysis, investors and analysts can dig into what drives changes in ROE, or why an ROE is considered high or low. That is, a Dupont analysis can help deduce whether its profitability, use of assets, or debt that’s driving ROE.

Drawbacks of Using DuPont Analysis

The biggest drawback of the DuPont analysis is that, while expansive, it still relies on accounting equations and data that can be manipulated. Plus, even with its comprehensiveness, the Dupont analysis lacks context as to why the individual ratios are high or low, or even whether they should be considered high or low at all.

Example of DuPont Analysis

Here's a hypothetical example to show how the DuPont analysis works. Let's say an investor has been watching two similar companies, SuperCo and Gear Inc. Both of these companies have improved their return on equity compared to the rest of their peer group, which could be a good thing if the two companies make better use of assets or improving profit margins.

In order to decide which company is a better opportunity, the investor decides to use DuPont analysis to determine what each company does to improve its ROE and whether that improvement is sustainable.

As you can see in the table, SuperCo improved its profit margins by increasing net income and reducing its total assets. SuperCo's changes improved its profit margin and asset turnover. The investor can deduce that SuperCo also reduced some of its debt since average equity remained the same.

Looking closely at Gear, the investor can see that the entire change in ROE was due to an increase in financial leverage. This means the company borrowed more money, which reduced average equity. The investor is concerned because the additional debt didn't change the company's net income, revenue, or profit margin. As such, the leverage may not add any real value to the firm.

Real-World Example

Now let's consider Walmart (WMT). For the fiscal year ending Jan. 31, 2021, the company reported:

• Net income over the trailing 12 months (TTM) of $4.75 billion
• Revenue of $559.2 billion
• Assets of $252.5 billion
• Shareholders' equity of $80.9 billion

So from these figures, we can use the information above to deduce that the company had the following:

• Profit margin of 0.8% or $4.75 billion/$559.2 billion
• Asset turnover of 2.22 or $559.2 billion/$252.5 billion
• Financial leverage (or equity multiplier) is 3.12 or $252.5 billion/$80.9 billion

According to these figures, Walmart's return or equity (ROE) for the fiscal year was 5.5% (or 0.8% x 2.22 x 3.12).

What Does DuPont Analysis Tell You?

DuPont analysis is a useful technique used to decompose the different drivers of return on equity for a business. This allows an investor to determine what financial activities are contributing the most to the changes in ROE. An investor can use an analysis like this to compare the operational efficiency of two similar firms.

What Is the Difference Between 3-Step and 5-Step DuPont Analysis?

There are two versions of DuPont analysis, one utilizing decomposition of ROE via three steps and another utilizing five steps. The three-step equation breaks up ROE into three very important components:

ROE=Net IncomeSales×SalesAssets× AssetsShareholders’ Equity\begin{aligned} &\text{ROE} = \frac{ \text{Net Income} }{ \text{Sales} } \times \frac{ \text{Sales} }{ \text{Assets} } \times \frac{ \text{Assets} }{ \text{Shareholders' Equity} } \\ \end{aligned}​ROE=SalesNet Income​×AssetsSales​×Shareholders’ EquityAssets​​

The five-step version instead is:

ROE=EBTS×SA×AE×(1−TR)where: EBT=Earnings before taxS=SalesA=Assets E=EquityTR=Tax rate\begin{aligned} &\text{ROE} = \frac{ \text{EBT} }{ \text{S} } \times \frac{ \text{S} }{ \text{A} } \times \frac{ \text{A} }{ \text{E} } \times ( 1 - \text{TR} ) \\ &\textbf{where:} \\ &\text{EBT} = \text{Earnings before tax} \\ &\text{S} = \text{Sales} \\ &\text{A} = \text{Assets} \\ &\text{E} = \text{Equity} \\ &\text{TR} = \text{Tax rate} \\ \end{aligned}​ROE=SEBT​×AS​×EA​×(1−TR)where:EBT=Earnings before taxS=SalesA=AssetsE=EquityTR=Tax rate​

Why Is It Called DuPont Analysis?

A DuPont employee by the name of F. Donaldson Brown developed a formula in 1914 that was used by the company as an internal management tool to better understand where its operating efficiency was coming from and where it was falling short. By breaking down ROE into a more complex equation, DuPont analysis shows the causes of shifts in this number.

What Are Some Limitations of Using DuPont analysis?

While the DuPont analysis can be a very helpful tool for managers, analysts, and investors, it is not without its weaknesses. Its expansive nature means that it requires several inputs. As with any calculation, the results are only as good as the accuracy of the inputs.

This tool utilizes data from a company's income statement and balance sheet, some of which may not be entirely accurate. Even if the data used for calculations are reliable, there are still additional potential problems, such as the difficulty of determining the relative values of ratios as good or bad compared to industry norms.

Seasonal factors, depending on the industry, can also be an important consideration since these factors can distort ratios. For instance, some companies always carry a higher level of inventory at certain times of the year. Different accounting practices between companies can also make accurate comparisons difficult.

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