Return on equity (ROE) is a closely watched number among sophisticated investors. It’s a strong measure of how well a company’s management creates value for its shareholders. The number can be misleading, however, as it is vulnerable to actions that increase its value while making the stock more risky. Without a way to break down the components of ROE, investors could be tricked into thinking a company is a good investment when it is not. Read on to learn how to use DuPont Analysis to break down ROE and better understand where ROE moves come from.

Key points to remember

- DuPont Analysis is a fundamental performance analysis framework originally popularized by DuPont Corporation, now widely used to compare the operational efficiency of two similar companies.
- DuPont analysis is a useful technique used to break down the various drivers of return on equity (ROE).
- There are two versions of the DuPont analysis, one using the 3-step decomposition and the other using 5 steps.

## Return on equity (ROE)

The beauty of ROE is that it is an important metric that only requires two numbers to calculate: net revenue and equity.

$$DEER

=

Net revenue

Equity

\begin{aligned} &\text{ROE} = \frac{ \text{Net Income} }{ \text{Equity} } \\ \end{aligned}

DEER=EquityNet revenue

If this number increases, it is usually a good sign for the company because it shows that the return rate on equity is on the rise. The problem is that this number can also increase simply when the company takes on more debt, thereby decreasing equity. It would increase the value of the company leveragewhich could be a good thing, but it will also make the title riskier.

## DuPont in three steps

A deeper understanding of ROE is needed to avoid erroneous assumptions. In the 1920s, the DuPont company created a method of analysis that met this need by breaking down ROE into a more complex equation. DuPont’s analysis shows the causes of changes in the number.

There are two variations of the DuPont analysis: the original three-step equation and an extended five-step equation. The three-step equation breaks down ROE into three very important components:

$$DEER

=

MNP

×

Asset turnover

×

Equity multiplier

where:

MNP

=

The net profit margin, the measure of operating

Efficiency

Asset turnover

=

Asset utilization efficiency measurement

Equity multiplier

=

Leverage measurement

\begin{aligned} &\text{ROE} = \text{NPM} \times \text{Asset Rotation} \times \text{Equity Multiplier} \\ &\textbf{where:} \\ &\text{NPM } = \text{Net profit margin, the measure of operating efficiency} \\ &\text{Efficiency} \\ &\text{Asset turnover} = \text{Measurement of operating efficiency of assets} \\ &\text{Equity Multiplier} = \text{Measurement of financial leverage} \\ \end{aligned}

DEER=MNP×Asset turnover×Equity multiplierwhere:MNP=The net profit margin, the measure of operatingEfficiencyAsset turnover=Asset utilization efficiency measurementEquity multiplier=Leverage measurement

### The DuPont Calculation in Three Steps

Taking the ROE equation: *ROE = net income / equity* and multiplying the equation by *(sales / sales)*we have:

$$DEER

=

Net revenue

Sales

×

Sales

Equity

\begin{aligned} &\text{ROE} = \frac{ \text{Net Income} }{ \text{Sales} } \times \frac{ \text{Sales} }{ \text{Equity} } \ \ \end{aligned}

DEER=SalesNet revenue×EquitySales

We now have a ROE divided into two elements: the first is net profit margin and the second is the equity turnover ratio. Now multiplying by (assets/assets) we end up with the three steps DuPont Identity:

$$DEER

=

Net revenue

Sales

×

Sales

Assets

×

Assets

Equity

\begin{aligned} &\text{ROE} = \frac{ \text{Net Income} }{ \text{Sales} } \times \frac{ \text{Sales} }{ \text{Assets} } \times \ frac{ \text{Assets} }{ \text{Equity} } \\ \end{aligned}

DEER=SalesNet revenue×AssetsSales×EquityAssets

This ROE equation breaks it down into three widely used and studied components:

$$DEER

=

MNP

×

Asset turnover

×

Equity multiplier

\begin{aligned} &\text{ROE} = \text{NPM} \times \text{Asset Turnover} \times \text{Equity Multiplier} \\ \end{aligned}

DEER=MNP×Asset turnover×Equity multiplier

We have ROE broken down into net profit margin (the profit the company makes from its revenue), asset turnover (how efficiently the company uses its assets), and the equity multiplier (a measure of the indebtedness of the company). The usefulness should now be clearer.

If a company’s ROE increases due to an increase in net profit margin or asset turnover, this is a very positive sign for the company. However, if the equity multiplier is driving the upside and the company was already properly leveraged, that just makes things riskier. If the company is over-leveraged, the stock may deserve further reduction despite the rise in ROE. The company could also be under-leveraged. In this case, it could be positive and show that the company is managing itself better.

Even if a company’s ROE remained unchanged, reviewing in this way can be very helpful. Suppose a company publishes figures and the ROE remains unchanged. A review with DuPont’s analysis might show that net profit margin and asset turnover declined, both negative signs for the business, and the only reason ROE remained the same was a sharp increase in indebtedness. Whatever the company’s initial situation, this would be a bad sign.

## DuPont in five steps

DuPont’s five-step, or extended, equation further breaks down the net profit margin. From the three-step equation, we have seen that in general, increases in net profit margin, asset turnover, and leverage will increase ROE. The five-step equation shows that increases in leverage do not always indicate an increase in ROE.

### The calculation in five steps

Since the numerator of net profit margin is net income, this can be transformed into pre-tax profit (EBT) by multiplying the three-step equation by 1 minus the corporate tax rate:

$$DEER

=

EBT

S

×

S

A

×

A

E

×

(

1

−

TR

)

where:

EBT

=

Profit before tax

S

=

Sales

A

=

Assets

E

=

Equity

TR

=

Tax rate

\begin{aligned} &\text{ROE} = \frac{ \text{EBT} }{ \text{S} } \times \frac{ \text{S} }{ \text{A} } \times \frac { \text{A} }{ \text{E} } \times ( 1 – \text{TR} ) \\ &\textbf{where:} \\ &\text{EBT} = \text{Earnings Before Tax} \\ &\text{S} = \text{Sales} \\ &\text{A} = \text{Assets} \\ &\text{E} = \text{Equity} \\ &\text{TR} = \text{Tax Rate} \\ \end{aligned}

DEER=SEBT×AS×EA×(1−TR)where:EBT=Profit before taxS=SalesA=AssetsE=EquityTR=Tax rate

We can break this down one more time since pre-tax profit is simply earnings before interest and taxes (EBIT) less company interest charges. So, if there is a substitution for the interest charges, we get:

$$DEER

=

(

EBIT

S

×

S

A

−

THAT’S TO SAY

A

)

×

A

E

×

(

1

−

TR

)

where:

THAT’S TO SAY

=

Interest expense

\begin{aligned} &\text{ROE} = \left ( \frac{ \text{EBIT} }{ \text{S} } \times \frac{ \text{S} }{ \text{A} } – \frac{ \text{IE} }{ \text{A} } \right ) \times \frac{ \text{A} }{ \text{E} } \times ( 1 – \text{TR} ) \\ &\textbf{where:} \\ &\text{IE} = \text{Interest Charge} \\ \end{aligned}

DEER=(SEBIT×AS−ATHAT’S TO SAY)×EA×(1−TR)where:THAT’S TO SAY=Interest expense

The practicality of this breakdown is not as clear as the triple step, but this identity gives us:

$$DEER

=

(

OPM

×

To

−

IER

)

×

EM

×

RTR

where:

OPM

=

Operating profit margin

To

=

Asset turnover

IER

=

Interest rate

EM

=

Equity multiplier

RTR

=

Withholding tax rate

\begin{aligned} &\text{ROE} = ( \text{OPM} \times \text{AT} – \text{IER} ) \times \text{EM} \times \text{TRR} \\ &\ textbf{where:} \\ &\text{OPM} = \text{Operating Profit Margin} \\ &\text{AT} = \text{Asset Rotation} \\ &\text{IER} = \text {Interest Charge Rate} \\ &\text{EM} = \text{Equity Multiplier} \\ &\text{TRR} = \text{Tax Retention Rate} \\ \end{aligned}

DEER=(OPM×To−IER)×EM×RTRwhere:OPM=Operating profit marginTo=Asset turnoverIER=Interest rateEM=Equity multiplierRTR=Withholding tax rate

If the company has a high cost of borrowing, its interest charges on increased debt could dampen the positive effects of leverage.

## Learn the cause behind the effect

The three-step and five-step equations provide insight into a company’s ROE by looking at what changes in a company rather than looking at a simple ratio. As always with financial statement ratios, they must be examined against the history of the company and its competitors.

For example, when looking at two peer companies, one may have a lower ROE. With the five-step equation, you can see if this is lower because: creditors perceive the business as riskier and charge it higher interest, the business is poorly managed and has too little leverage, or the business has higher costs that lower its operating result margin. Identifying such sources leads to a better understanding of the business and how it should be valued.

## The essential

A simple calculation of ROE can be easy and tell a lot, but it doesn’t tell the whole story. If a company’s ROE is lower than its peers, three- or five-step identities can help show where the company is falling behind. It can also shed light on how a company is increasing or strengthening its ROE. DuPont Analysis greatly expands the understanding of ROE.

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