The DuPont Identity
Table of Contents
The DuPont Identity breaks Return-on-Equity (ROE) into 3 separate components, the Profit Margin (PM), Total Asset Turnover (TAT) and the Equity Multiplier (EM).
1. Derivation
We'll first state ROE in terms of ROA because it gives and important insight for using each as a measure of management performance.
1.1. The First Step: ROA
Let NI denote Net Income, E denote equity, and A denote assets. ROA is Return-on-Assets.
\[ROE = \frac{NI}{E} = \frac{NI}{A}(\frac{A}{E}) = ROA(EM)\]
This is not yet the DuPont Identity, but it does show us something very useful. ROE is equal to ROA multiplied by a measure of the firm's capital structure. Remember EM is the firm's debt-to-equity ratio plus 1.
The important point here is managers can change EM easily. In fact if they want to increase EM (and thereby likely1 increase ROE) they just have to issue debt and buy back stock. We will see ROA is solely a function of operating measure of the firm, and cannot easily be changed by management.
So if you were to measure management performance would you use the measure that management can easily increase or decrease via the capital structure? Or would you use the measure of operating performace they cannot easily change?
1.2. DuPont Identity
Decomposing ROA:
\[ROA = \frac{NI}{A} = \frac{NI}{S}(\frac{S}{A}) = PM(TAT)\]
where S denotes sales, and PM and TAT is profit margin and total asset turnover respectively. Inserting this into the ROE equation above affords:
\[ROE = PM(TAT)(EM)\]
which is the DuPont Identity. It says that a firm's return on equity is the product of the firm's profit margin, total asset turnover, and equity multiplier.
2. Application
This is particularly useful when you realize that profit margin measures a firm's profitability. That is, it measures how well a firm controls its costs. Total asset turnover, however, measures how efficiently a firms uses its assets. Lastly, the equity multiplier (which is one plus the debt-to-equity ratio) is a measure of the firm's use of debt in its capital structure.
So the DuPont Identity allows you to see what is driving a firm's ROE. Does the firm have a high ROE because it controls is costs, or because it uses its assets efficiently? Or does it simply have a high ROE because it is highly leveraged (not a particularly good reason).
Author note: I once was asked by upper management for an analysis of the performance of our wind farms in north Texas. While going through their financial statements I realized I had everything I needed to calculate the DuPont Identity. I was thus able to point to profitability as the driver of our wind farm returns.
ROE (DuPont) Calculator
| Profit Margin: | |
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| Debt-to-Equity Ratio: |
ROE:
3. Self-Quiz Questions
1. Assume Mohawk Valley Skateboards has a 10% profit margin, 1.6 in total asset turnover, and a 1.75 equity multiplier. What is the firm's return on equity?
2. New Hartford Paving Inc has a 10% profit margin, a 30% return on equity, and a debt-to-equity ratio of 1.2? What is the firm's total asset turnover?
3. If a firm has a 15% return on assets and a debt to equity ratio of 2, what is its return on equity?
4. Reading Ease Score
"Flesch-Kincaid reading ease score: 76.38 Fairly easy (7th grade)"
"Flesch-Kincaid grade level score: 4.95"
Footnotes:
There are unlikely situations where increasing a firm's EM will decrease ROE because the effect of interest expense on reducing PM more than offsets the increase in the debt-to-equity ratio.