The DuPont decomposition
Return on equity splits into three things: how much each sale earns, how hard the assets work, and how much debt is underneath. Two companies with the same ROE can be opposite businesses, and this is what shows it.
Chapter 10 · Intermediate
Return on equity is one number hiding three decisions. Separating them is a piece of arithmetic from the 1920s that still does more work than most modern analysis.
The identity
ROE = net margin × asset turnover × equity multiplier
Or written out:
net profit net profit revenue assets
---------- = ---------- × ---------- × --------
equity revenue assets equity
Revenue cancels, assets cancel, and you are back to profit over equity. It is an identity, so it is always true — the value is in what each term means.
What each one says
Net margin — what each sale earns. Chapter 8. Pricing power and cost control.
Asset turnover — how hard the assets work. Revenue divided by assets. A supermarket turns its assets over several times a year; a steel plant does not. This is the component people forget, and it is why a 3% margin business can be excellent.
Equity multiplier — how much debt is underneath. Assets divided by equity. A company funded entirely by owners has a multiplier of 1. One with half its assets funded by debt has a multiplier of 2, and doubles its ROE without the business changing at all.
Why this matters
Three companies, each with 18% ROE:
| Margin | Turnover | Multiplier | ROE | |
|---|---|---|---|---|
| A branded goods maker | 15% | 1.2 | 1.0 | 18% |
| A retailer | 3% | 6.0 | 1.0 | 18% |
| A leveraged manufacturer | 6% | 1.0 | 3.0 | 18% |
Identical ROE, three completely different investments.
A earns its return from pricing power. Durable if the brand is, and the risk is a competitor or a changing taste.
B earns it from throughput. Durable if the operation stays efficient, and vulnerable to a sales slowdown with fixed costs in place.
C earns it from borrowing. The business itself produces 6% on its assets; debt multiplies it to 18%. If rates rise or profits dip, the same leverage works in reverse — and chapter 12 is what that does.
Anyone comparing the three on ROE alone would call them equivalent. They are not remotely equivalent, and the decomposition takes two minutes.
Where a return on equity comes from
What each rupee of sales leaves as profit.
Revenue ÷ assets. A retailer turns over several times; a steel plant does not.
Assets ÷ equity. 1 means no debt at all. Drag it and watch ROE move.
Return on equity
18%
- The business earned
- 18%margin × turnover, before any debt
- Borrowing added
- 0%1× on the equity base
With no debt at all, the whole 18% is the business: 15% on each sale, 1.2× of sales for each rupee of assets. Raise the multiplier and the return rises without anything about the operation changing — which is the point of the chapter.
The question it answers best
Is this return earned or borrowed?
A high ROE with a multiplier near 1 is a business genuinely earning well. A high ROE with a multiplier of 4 is mostly an arrangement with lenders.
That is also why chapter 9 preferred ROCE for judging the business: ROCE is indifferent to the third term. Running both and comparing them is the fastest way to see how much of the owners' return is leverage.
Reading changes over time
More useful than the level, and it is where the decomposition really earns its keep. If ROE fell from 20% to 14%, which term moved?
Margin fell. Competition or costs. Chapter 8.
Turnover fell. Assets grew faster than sales — a factory not yet full, or working capital ballooning. Chapter 11.
Multiplier fell. The company repaid debt. ROE fell and the business got safer, which is a good outcome that looks like deterioration in the headline.
That last case is the one the decomposition is worth knowing for. A falling ROE caused by deleveraging is close to the opposite of a falling ROE caused by margin collapse, and the single number cannot distinguish them.
The honest caveats
Averages again. Use average equity and average assets, for chapter 9's reason.
It is an identity, not an explanation. It tells you where the return comes from, not why. Why the margin is 15% is a question about the business, which the accounts cannot answer.
Financial companies do not fit. For a bank, borrowing is the raw material rather than a financing choice, and a multiplier of 10 is normal. This decomposition is for non-financial businesses.
The point
ROE equals margin times asset turnover times leverage. Three companies with the same ROE can be a branded goods maker, a retailer and a borrower, and they are not the same investment. When ROE moves, the component that moved tells you whether the business improved, the assets got less productive, or the debt changed.
Check yourself
4 questions. Every answer is explained afterwards, including the ones you get right — guessing correctly is not the same as knowing. Score 70% or more and the chapter is marked done.
Question 1 of 4
0 of 4 answered. You can submit with questions unanswered — they simply score zero.
Now do it with your own numbers
Take two companies in different industries with similar ROE and decompose both. Write one sentence each saying where the return comes from. They will not be the same sentence.
Net margin times asset turnover times the equity multiplier. Each is a division you can do from the two statements.