# Level 1 CFA® Exam:

DuPont Analysis

DuPont analysis is about decomposing return on equity into different items that affect it. The term 'DuPont analysis' is derived from the company for which this analysis was first conducted, namely 'E. I. du Pont de Nemours And Company', which is more commonly known as DuPont and is one of the biggest chemical companies in the world.

Return on equity (ROE) is calculated as net income divided by the average equity and is a measure of profitability. The main purpose of DuPont analysis is to indicate what affects the return generated by owners’ equity and to what extent.

In this lesson, we will analyze 3 formulas, where each subsequent formula will be an expanded version of the previous one.

We begin with illustrating ROE as the product of ROA and leverage. ROA is return on assets and it is calculated as net income over average total assets. Leverage, on the other hand, is average total assets divided by average equity. So, if we multiply ROA and leverage together, we get net income over average total assets times average total assets over average equity, thus we get net income over average equity, that is ROE.

\(ROE = \frac{NI}{E}=\frac{NI}{A}\times \frac{A}{E}=ROA\times{\text{leverage}}\)

- \(ROE\) - return on equity
- \(NI\) - net income
- \(E\) - average shareholders' equity
- \(A\) - average total assets

**Interpretation, relations, and usage:**

1. the higher the ratio >> the more net income is generated by a given level of equity

2. total equity = common equity + preferred equity + minority equity

Spades, Inc. is characterized by ROA equal to 6% and average total assets of USD 100 million. Assume that the company is financed by debt and equity in the same proportions. Compute:

- the value of ROE,
- the value of ROE assuming that the company repaid debt using cash in the amount of USD 10 million.
- the value of ROE assuming that the company increased its net income by 10%.

(...)

Let’s analyze ROE decomposition even further.

First, however, have a look at ROA. ROA can be presented as the product of return on sales (ROS) and total asset turnover. Return on sales, which is also called net profit margin, equals net income divided by revenue, and total asset turnover is revenue divided by average total assets. Therefore, ROA equals ROS times total asset turnover. Hence, ROE equals ROS times total asset turnover times leverage.

\(ROE = \frac{NI}{R} \times \frac{R}{A} \times \frac{A}{E}=\\ROS\times{\text{asset turnover}}\times{\text{leverage}}\)

- \(ROE\) - return on equity
- \(NI\) - net income
- \(R\) - revenue
- \(A\) - average total assets
- \(E\) - average shareholders' equity

According to this formula, we can say that ROE is a result of:

- net income earned on each unit sold, namely the profitability of the company,
- asset use efficiency, and
- financial leverage.

Spades, Inc. is characterized by the following ratios:

- ROE equal to 16%,
- net profit margin of 5%, and
- total asset turnover of 1.6.

What is the value of leverage?

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Now we will take one step further and decompose the net profit margin into:

- EBIT margin,
- interest burden, and
- tax burden.

EBIT margin is EBIT, which stands for earnings before interest and taxes, divided by revenue.

The interest burden is EBT, which is earning before taxes, divided by EBIT.

And, finally, the tax burden is net income divided by EBT.

Interest burden informs us what part of EBIT remains in the company after interest is deducted, and tax burden informs us what part of EBT remains after taxes.

Note that in the ratios we’ve just discussed, we sometimes use operating income instead of EBIT.

Back to our net profit margin. Net profit margin is equal to the product of EBIT margin, interest burden, and tax burden.

Knowing that we can present ROE as EBIT margin times interest burden times tax burden times total asset turnover times leverage:

\(ROE = \frac{NI}{EBT} \times \frac{EBT}{EBIT} \times \frac{EBIT}{R} \times \frac{R}{A} \times\frac{A}{E}=\\=\text{tax burden}\times{\text{interest burden}}\times\\\times{\text{EBIT margin}}\times{\text{asset turnover}}\times{\text{leverage}}\)

- \(ROE\) - return on equity
- \(NI\) - net income
- \(EBT\) - earnings before taxes
- \(EBIT\) - earnings before deducting interest and taxes
- \(R\) - revenue
- \(A\) - average total assets
- \(E\) - average shareholders' equity

DuPont analysis is about the decomposition of ROE into its components.

It gives us the answer to the following question: **What factors drive the changes in the ROE?**

As we can see ROE is a function of: tax rate, interest burden, operating profitability, efficiency, and leverage.

To sum things up, we started with the basic decomposition of ROE into ROA and leverage. Then, we presented ROA as the product of ROS and total asset turnover. Finally, we decomposed ROS into the product of EBIT margin, interest burden, and tax burden.

Thanks to these decompositions of ratios, you will be able to find out what are the sources of return on equity.

If for example in one year ROE is bigger than in the other, thanks to DuPont analysis, you will be able to find out what is the source of this increase in ROE and whether it is caused by a financial strategy, that is an increase in leverage, or by an operating strategy, that is an increase in ROA.

Furthermore, you will be able to see whether changes in ROA are related to changes in net profit margin or total asset turnover.

Finally, you will be able to find out whether changes in net profit margin result from changes in EBIT margin, interest burden, or tax burden.

The income statement of Spades, Inc. for 2022 is presented in the table:

Revenues | 250,000 |

Cost of goods sold | 130,000 |

Gross profit | 120,000 |

Selling, general, and administrative expenses | 50,000 |

Operating income | 70,000 |

Interest expense | 50,000 |

Earnings before taxes | 20,000 |

Taxes | 4,000 |

Net income | 16,000 |

All elements of the income statement are sales-driven, except for the tax burden and interest burden. The company’s tax rate in 2023 increases to 25% and interest expense remains at the same level as in 2022.

We also know that total asset turnover and leverage in 2023 are equal to 2.2 and 1.4, respectively. Compute ROE if the expected growth rate of revenue in 2023 is 10%.

(...)

- DuPont analysis is about decomposing return on equity (ROE) into different items that affect it.
- ROE can be calculated as the product of ROA and leverage.
- ROA can be presented as the product of return on sales (aka. ROS, net profit margin) and total asset turnover.
- Net profit margin is equal to the product of EBIT margin, interest burden, and tax burden.
- Interest burden informs us what part of EBIT remains in the company after interest is deducted.
- Tax burden informs us what part of EBT remains after taxes.