Decomposing Return

We have talked about making comparisons, and there are lots of different ratios that we could talk about, and we talk about the different families of ratios. Here is something else you can do. You can actually combine ratios in a way that creates an insight.

Start with return on equity. This is just net profit divided by shareholder equity. That is something we understand. What we are asking is: how much money are we making, as a percentage of what the owners put into the business?

Well, it turns out that I can break this up into three other ratios. Let us walk through the math.

\[\frac{\text{Net profit}}{\text{Equity}} = \frac{\text{Net profit}}{\text{Sales}} \times \frac{\text{Sales}}{\text{Total assets}} \times \frac{\text{Total assets}}{\text{Equity}}\]

1. Net profit over sales
2. Sales over total assets
3. Total assets over shareholders’ equity

This is known as the DuPont decomposition. Here is what we are going to say. A measure of performance is return on equity - but where does that come from? Let us look at these three ratios in turn.

Net profit over sales. That ratio is just profitability. We want to know how much profit we are making as a percentage of sales.

Sales over total assets. This is a measure of efficiency and activity: how much sales activity, how much customers’ stuff are we driving through this business as a percentage of the total assets, the investments that we have made? This is a measure of efficiency. Are we doing a lot of activity given how much we have invested?

Total assets over shareholder equity. This is a measure of leverage. We remember from the balance sheet that total assets equals liabilities plus shareholder equity. If total assets is funded by either debt or shareholder equity, this ratio tells us how much of this stuff is financed by debt, by other people’s money.

There are two things to note.

The first is that return on equity can be decomposed into three parts: profitability, which is net profit over sales; efficiency, or asset turnover, which is sales over total assets; and leverage, which is total assets over shareholder equity.

The second thing to notice is how the math cancels out. You can cancel out both the numerator and the denominator. Sales are going to cancel out. Total assets are going to cancel out. And we are left with the fraction that we started with in the first place: net profit over shareholder equity.

If you look at this equation carefully, you will see that through cancellation we get return on equity.

So what is the insight here? If you are going to improve return on equity, it has got to come from one of three places. If it changes, it is because either profitability has changed, efficiency has changed, or leverage has changed. Those are the three levers for changing our return on equity.

All changes in return on equity must come through this.

Where does the cost of the borrowing show up?

One thing is worth pausing on, because it is the reason this version of the decomposition is the right one to use.

The third term counts the benefit of debt. More assets are working for every dollar the owner put in, so the ratio goes up and return on equity goes up with it. But the interest bill is inside the first term, because net profit is after interest.

So borrowing pushes the third term up and the first term down at the same time, and the decomposition tells you which effect won.

Why not just look at the number?

The DuPont decomposition can tell us a lot. It is not enough to know if something is performing. We want to know why.

If return on equity is improving, is it because we are more profitable, or because we are becoming more efficient? Depending on what we have been doing, we might be able to say this is a direct result of the efforts that we have made. If we are focusing a lot on efficiency but it is profitability that is increasing, perhaps masking the fact that we have not improved in efficiency, we would have a different diagnosis of our performance.

On the other hand there is also leverage. Higher leverage means higher return on equity. Are we getting higher return on equity numbers because we are performing better? We are more profitable? We are more efficient? Or are we just taking on more debt, taking on more risk? The stories behind these things are very different.

Say a business has improved its return on equity. That is nice, but how did it do this? You can decompose that trend in return on equity by disaggregating it into these three different kinds of ratios, to see if it was improved profitability, efficiency, or leverage that enabled them to do so.

Say the business improved performance by becoming more efficient. That sounds good, right? On the other hand, what if it improved return on equity simply by taking on more debt? In this case we might not be so impressed. We might even be a little concerned.

We need to know why things are happening, not just what is happening.

Watching it move over three periods

One decomposition on one year tells you how a business is put together. Several years of it tell you what is being done to the business. Here is a different firm, decomposed the same way across three periods.

The first ratio is net profit over revenue. The second is asset turnover, revenues divided by total assets. The third is total assets over shareholder equity, which is our measure of leverage. What you see at the very bottom is the multiplication across each one of these. We multiply each one of these numbers together and we get that final return on equity, which ties out to what the return on equity number is.

We are going to walk through these periods - not what the numbers are, but the movements.

Period one to period two. The return on equity, that measure of performance, has gone up. That is a good thing. But why has it gone up?

The profits have increased a little bit, from 0.06 to 0.064. Asset turnover, revenue as a percentage of assets, has stayed flat. What we have really seen go up is total assets divided by shareholder equity. What that means is that our leverage has gone up. We are taking on more debt.

Period two to period three, where we saw a pretty significant drop in return on equity, from 13.4 percent to around 7.3 percent. What drove that?

First of all, when we look at net profitability, it eroded. Net profit over revenue declined. And we also got a little bit less efficient - when we talk about how much sales we are pushing over the assets that have been invested, that ratio eroded too.

However, a really big move driving this is that total assets divided by shareholder equity went down. What does that mean? It means that we have retired some debt. We have less leverage, so we have repaid that out, and our return on equity has gone down.

Generally, when we look at a return on equity going down, we think that is bad news - the performance has gone down. When we look at these numbers and decompose them using the DuPont decomposition, we see something really clearly. The effect of the leverage change is really what is driving this decline from 13.4 to 7.3. What does that mean? We are paying back debt. That is generally a good thing.

Now, if we found out that this whole thing went down because our profitability is eroding, or our efficiency is eroding, we would have a different level of concern. When we find out the reason our return on equity is going down is that we have a bigger share of equity because we are paying off our debt, that is generally considered a good thing. Certainly it is not pointing at the level of performance deterioration that the other two instances would have.

The same decomposition on our distributor

Let us do the DuPont decomposition for the distributor we have been working with. Everything here comes off the two statements we already have. Balances are the ending balances for each year.

Net margin has been 3.0 percent, then 3.8, then 1.9. Asset turnover was 2.03, then it went down to 1.95, then down again to 1.78. And assets over equity has gone from 1.97 up to 2.01, up again to 2.33. When you multiply all these out, we get return on equity of 12 percent, 14.9 percent and 7.9 percent - and this already agrees with the return on equity that we defined earlier.

Do the check line yourself once. Multiplying three ratios and landing exactly on the number you would have got by dividing net profit straight into equity is what convinces you the decomposition is not a trick.

Between 2020 and 2021. Profitability went up a little bit. We are doing a little bit better there, mostly driven by gross margins, perhaps because operating expenses are not how we won that game. We are slightly less efficient, but not too different. Total leverage went up a little bit. In the end we basically improved. We went from 12 percent to almost 15 percent on return on equity.

Between 2021 and 2022. That whole thing got cut in half. Return on equity really dropped. What happened?

Net profits took a big dive, from 3.8 percent to 1.9 percent. We can look and see what happened. This was a cost-getting-out-of-line story.

When we look at turnover, going from 1.95 to 1.78, that is also an erosion. We got less efficient, and this is primarily going to be around working capital. We have actually seen that our receivables and our payables have gone up, but they have gone up more than sales have. We are just moving slowly on that.

The last thing is taking on debt. We took on more debt, and we can see that in the financial statements and in the ratio of total assets to equity. Usually taking on more debt is going to make return on equity improve. The fact that our return on equity went down anyway suggests that there is a really big impact on profitability, or on efficiency.

Putting a number on each of the three

We can go one step further and say how many points of return on equity each component was worth. Change one component at a time and see what it does.

Between 2020 and 2021 it is a good year. It is almost entirely real, with very good fundamentals. Of the 2.9 points that we gained, about 3.2 came from an increase in profitability. From a borrowing standpoint there was a positive impact, but only by 0.3. Our turnover eroded a little bit and brought us back down by about 0.6. The business has improved. It has definitely gotten a little bit less efficient, but definitely a lot more profitable.

Between 2021 and 2022 is where we really understand the decomposition. The real thing that hurt us was lower profitability. It dropped us by 7.4 points when it comes to return on equity. Turnover also hurt us by a little bit, by 0.6.

Because we took on leverage, it did not go down as far. It added back 1.1. Which means that when we look at return on equity, we are understating the negative impact of profitability, because we took on more leverage. Taking on more leverage is generally not considered a good thing from a performance standpoint. Had we held leverage at its level, we can ask what would have happened - and our return on equity would have landed somewhere closer to 6.8 percent instead of 7.9 percent.

That is masking the erosion in profitability. There is a lot to feel grumpy about on profitability, and the effect of the leverage is actually masking it.

Why we look at asset turnover at all

Why do we look at asset turnover? If you think about it, when we invest in assets we are locking up our money, and we want to know that it is doing some work for us. Is it generating more business?

When we look at asset turnover we look at how much revenue you are producing for all the assets that we needed to invest in. This is the productivity of our invested capital.

It is the same idea that gave us inventory turnover. We have to hold this much inventory. If we have this much in stock, how much sales does it generate? If you want to have a lot of sales, you have got to have some ready inventory. It is a bit of the cost of doing business, but we want to know: are we getting a lot of sales out of the inventory we have held? Are we getting a lot of business return and activity given what we are committing to in investment in assets?

That is how we link up the income statement and the balance sheet into a comprehensive financial picture. It is not just that we want performance, and performance is revenue minus cost equals profits. Profit is performance. To get that performance, what did we have to invest? That is how we link the income statement and the balance sheet.

I buy assets in order to create revenue. How much revenue do I generate on the dollars I invest in assets? The more I generate, the more efficiently I am putting my assets to work. Operators or businesses that are able to have high turnover ratios, or improve them, show that they are creating more sales with the given assets they have.

When we talk about revenue divided by total assets, we are asking: how much money are we making for every dollar that we are putting into this business? For our distributor, that number went from 2.03 down to 1.78. It used to be that we would put a dollar into this business and generate $2.03 of sales. That dropped to just $1.78 in revenue for every dollar we were putting into assets.

That means we have to put more money into this business to get the same performance out of it. For every dollar we are putting in, we are getting less in terms of revenue out of this thing.

A timing problem, and how the book handles it

I have talked about before that an income statement covers a period and a balance sheet covers a snapshot. Matching these up, if we were to do this properly, what we want to do is match over the time. If you take an income statement that was for a whole year, the balance sheet is just something that is going to be at a given point in time.

Because income statement numbers are about a time period, and balance sheet numbers are a snapshot in time, we can match up the right time period by taking sales of one period and the average inventory of that period, taking the average of the starting and ending inventory numbers.

The common way of doing this is to take the average over that period of time. If we are going to compare an income statement account with a balance sheet, we take the income statement number - let us just say it is for a given year - and then we take the average of the beginning and the ending of the balance sheet number to compare to that.

That is because if you are really growing fast then perhaps your ending balances would be lower than your beginning balances, and it is not quite comparable. If you wanted to be really overkill about it, you would actually take all these data points of what your balance sheet was for every single day of the year and take a big blended average of that. For analyst purposes we often just take the two different end points and then take the average of that.

So which way do we use? In this book we use both, and that is fine. It depends on the insight we are trying to get out.

For a decomposition we use the ending balances, because all three years are computable that way and we can tie them out to the final number in return on equity. The three factors are going to multiply out cleanly. That is a nice analysis.

When we do efficiency ratios we are going to use averages. Neither of these is wrong, but it is wrong to switch without saying so, because then things are not comparable.

© 2026 Eric Lin. All rights reserved. This chapter is provided for students in BUSI 170 - please do not repost or redistribute without permission.