## What is the 'DuPont Identity'

The DuPont identity is an expression that shows a company's return on equity (ROE) can be represented as a product of three other ratios: the profit margin, the total asset turnover and the equity multiplier. It is also commonly known as DuPont analysis, and it comes from the DuPont Corporation which began using the idea in the 1920s.

## BREAKING DOWN 'DuPont Identity'

The DuPont identity tells us that ROE is affected by three things:1. Operating efficiency, which is measured by profit margin;

2. Asset use efficiency, which is measured by total asset turnover;

3. Financial leverage, which is measured by the equity multiplier.

If the ROE is unsatisfactory, the DuPont identity helps analysts and management locate the part of the business that is underperforming.

The formula for the DuPont identity is:

ROE = profit margin x asset turnover x equity multiplier

This formula, in turn, can be broken down further to:

ROE = (net income / sales) x (revenue / total assets) x (total assets / shareholder equity)

## DuPont Identity Example Calculation

Assume a company reports the following financial data for two years:

Year one net income = $180,000

Year one revenues = $300,000

Year one total assets = $500,000

Year one shareholder equity = $900,000

Year two net income = $170,000

Year two revenues = $327,000

Year two total assets = $545,000

Year two shareholder equity = $980,000

Using the DuPont identity, the ROE for each year is:

ROE year one = ($180,000 / $300,000) x ($300,000 / $500,000) x ($500,000 / $900,000) = 20%

ROE year two = ($170,000 / $327,000) x ($327,000 / $545,000) x ($545,000 / $980,000) = 17%

With a slight amount of rounding, the above two ROE calculations break down to:

ROE year one = 60% x 60% x 56% = 20%

ROE year two = 52% x 60% x 56% = 17%

You can clearly see the ROE declined in year two. During the year, net income, revenues, total assets and shareholder equity all changed in value. By using the DuPont identity, analysts or managers can break down the cause of this decline. Here they see the equity multiple and total asset turnover remained exactly constant over year two. This leaves only the profit margin as the cause of the lower ROE. Seeing that the profit margin dropped from 60% to 52% while revenues actually increased in year two indicates that there are issues with the way the company handled its expenses and costs throughout the year. Managers can then use these insights to improve the following year.

Learn more about the DuPont analysis by readingĀ What are the main differences between return on equity (ROE) and return on assets (ROA)?