# The DuPont Equation

One of the more interesting measures of a company's financial performance is the DuPont Equation. This model allows stock analysts and investors to examine the profitability of a company using information from both the income statement as well as the balance sheet.

In this article, we're going to explain how to use the DuPont Equation to examine the performance of a company.  As part of that explanation, we'll first talk about the history of the measure.  Next, we'll begin with the high-level equation, then work our way down to what is known as the extended DuPont Equation.  Finally, we'll finish up with some brief examples that demonstrate the power of this financial calculation.

## The DuPont Equation

Also known as the DuPont Model, DuPont Method, and DuPont Identity, this equation was first used by Donaldson Brown in 1918 when DuPont purchased a substantial stake in General Motors.  The equation was used by Brown to examine the fundamental drivers of profitability at G.M.

The advantage of this model is that it uses information from both the balance sheet and income statement.  This gives the analyst a thorough view of a company's financial health and operating efficiency.  The disadvantage of the model is that it relies on accounting data, which can be manipulated by companies to hide weaknesses in the short term.

There are two forms of the DuPont Equation; the first examines return on assets, while the second examines return on equity.  The model relies on expanding, or extending, a well-known financial ratio using simple mathematical techniques.

### Return on Assets

The model begins by looking at the company's return on assets (ROA) or return on investment (ROI):

Return on Assets (ROA) = Profit Margin x Total Asset Turnover

By substituting:

Profit Margin = Net Income / Sales
Total Asset Turnover = Sales / Total Assets

This equation can be expanded into the following form:

ROA = (Net Income / Sales) x (Sales / Total Assets)

In the same way, this equation can be further extended into a final form:

ROA = ((Sales - Total Costs) / Sales) x (Sales / (Current Assets + Non-Current Assets))

By extending the return on assets formula, it's possible to see the power of this equation, and how it can be used to identify the strengths and weaknesses of a company.  We begin with elements of total cost such as the cost of goods sold, SG&A (selling, general and administrative expenses), interest expense, and income taxes.  These first measures tell us how effectively a company uses its assets to produce profits.

Current assets include cash, accounts receivable, inventories, and marketable securities.  The strength of this second measure comes from its ability to predict how working capital is used to help maintain the company's operation.  Finally, there are non-current assets such as buildings, land, and machinery / equipment.  These elements are viewed as long-term, income-producing assets.

### Return on Equity

The DuPont model can also be applied to return on equity, which is a measure of the rate of return to stockholders:

Return on Equity (ROE) = Net Profit / Average Equity

Once again, this equation can be expanded into the following form:

ROE = (Net Profit Margin) x (Asset Turnover) x (Asset / Equity Ratio)

This equation can be further extended into its final form:

ROE = (Net Profits / Sales) x (Sales / Average Assets) x (Average Assets / Average Equity)

Here again, the expanded DuPont Equation provides insights into a company's profit margins, which tells the analyst how efficiently a company is operated.  It also provides insights into the company's use of assets via turnover.  By examining the average assets and average equity, there is a greater understanding of the financial leverage of the company.

## The Equation in Practice

The power of the DuPont Equation stems from its ability to demonstrate the levers a company has at its disposal to return to shareholders above average returns.  Once again, the three components of interest include:

• Net Profit Margin:  a measure of a company's operational effectiveness.
• Asset Turnover:  a measure of the company's ability to use assets efficiently.
• Leverage Ratio:  a measure that is equal to a company's debt to equity ratio plus 1, also referred to as financial gearing.

Every company has at least one of these tools available to their management team for use in increasing shareholder value:  controlling expenses or margins, use of assets, capital funding.

### High Margins

Companies competing in a high margin industry will typically rely on those margins rather than sales.  For example, software companies usually have a high profit margin on each sale.  In turn, those margins are used to fund research into new products or services.  The company is profitable because of the large margin (or profit) obtained from each sale.  These companies usually do not compete on price, and their value proposition would be quality over quantity.

### High Turnover

At the opposite end of the spectrum, there are high turnover businesses.  These companies have relatively low profit margins on each sale, and rely on a large volume of sales to create profits.  For example, the margin that grocery stores derive from the sale of each item may be relatively small.  Instead, these companies rely on a large volume of sales, and high turnover of inventory, to provide shareholders with an adequate level of net income.

### High Leverage

Finally, there are certain sectors of the market that rely on financial leverage to produce adequate returns to shareholders.  For example, the banking industry relies on relatively high leverage to generate sufficient earnings to stockholders.  By contrast, most industries would view the leverage used by banks as unacceptably risky.  In fact, this risk proved too much for many banks and lenders as evidenced by the credit market and stock market crash of 2008.

### Predicting Performance

Analysts can use this information to benchmark the performance of companies within the same industry.  By comparing the relative strengths and weaknesses of each measure against those of similar companies, an investor can predict the relative performance of each company.  The beauty of the DuPont Equation is the information needed to perform these calculations is freely available to the public.

While benchmarking can provide information on each company's relative strengths and weaknesses, the measure does rely on accounting data.  As such, this is a record of past performance, and history is not always a reliable indicator of future results.

About the Author - The DuPont Equation