# DuPont Identity Calculator

**
Instructions:
**
You can use this step-by-step DuPont Identity Calculator, by providing the Net Income, Sales, Total Equity and
Total Assets in the form below:

## DuPont Identity Calculator

More about the
*
DuPont Identity
*
so you can better use the results provided by this solver.

The DuPont Identity is an identity that helps you break-down the factors driving the Return on Equity, which is a very important profitability metric for investors.

### How is Dupont Identity calculated?

Du Pont's identity is broken down as follows

\[ \text{ROE} = \displaystyle \frac{\text{Net Income}}{\text{Total Equity}}\] \[ = \displaystyle \frac{\text{Net Income}}{\text{Sales}} \times \frac{\text{Sales}}{\text{Total Assets}} \times \frac{\text{Total Assets}}{\text{Total Equity}} \] \[ = \displaystyle \text{Profit Margin} \times \text{Total Asset Turnover} \times \text{Equity Multiplier} \]This identity is remarkable, since it allows to deconstruct the return on equity (ROE) into three profit ratios of importance for the performance of a company.

With this decomposition, it is possible to isolate the factors that directly his identity is remarkable, since it allows to deconstruct the return on equity (ROE) into three profit ratios of importance for the performance of a company.

### Example of DuPont identity application

**Question**: Suppose that a firm has $10,000 in net income, $40,000 in sales, $100,000 in equity and $200,000 in assets.
Compute the firm's return on equity using DuPont's calculator.

Solution:

This is the information we have been provided with:

Net Income = | \(\text{\textdollar}10000\) |

Sales = | \(\text{\textdollar}40000\) |

Total Assets = | \(\text{\textdollar}200000\) |

Total Equity = | \(\text{\textdollar}100000\) |

Therefore, the following is obtained from DuPont identity:

\[ \begin{array}{ccl} \text{Return on Equity} & = & \displaystyle \text{Profit Margin} \times \text{Total Asset Turnover} \times \text{Equity Multiplier} \\\\ \\\\ & = & \displaystyle \frac{\text{Net Income}}{\text{Sales}} \times \frac{\text{Sales}}{\text{Total Assets}} \times \frac{\text{Total Assets}}{\text{Total Equity}} \\\\ \\\\ & = & \displaystyle \frac{\text{\textdollar}10000}{\text{\textdollar}40000} \times \frac{\text{\textdollar}40000}{\text{\textdollar}200000} \times \frac{\text{\textdollar}200000}{\text{\textdollar}100000} \\\\ \\\\ & = & \displaystyle 0.25 \times 0.2 \times 2 \\\\ \\\\ & = & 0.1 \end{array} \]Therefore, using DuPont's identity we find that the return on equity is \(ROE = 0.1\).