# Du Pont formula

Du Pont formula is a formula that expresses the relationship between return on assets (ROA), sales-to-assets, profit margin and measures of leverage[1]. An extended Du Pont formula measures ROE which gives us information about the returns earned on the owner's investment[2].

## The Origin of Du Pont Formula

E. I. Du Pont Nemorous Powder Company was the leading firm manufacturing high explosive materials in early 1900. Later it grew into one of the world's largest chemical companies. Du Pont managers developed the concept of return on investment to control and evaluate its operations[3].

The financial unit traced the cost and revenues for each product produced. This gave accurate information on profits, which provided a more precise way of evaluating financial performance. However, managers found product-line profits to be an incomplete measure of performance because these did not indicate the rate of return on capital invested[4].

Developing a rate of return on each segment of business required accurate data on investment. Du Pont undertook a careful valuation of each of its plants, properties and inventories by product line. With this information, management could track return on investment by product line[5].

Return on investment is the product of sales turnover (Sales/Total Investment) and return on sales (Earnings/Sales). With this data, managers can determine the causes of a product's change in return on investment. Du Pont managers used this information to calculate new capital appropriations by establishing the policy that there "be no expenditures for additions to the earning equipment if the same amount of money could be applied to some better purpose in another branch of the company's business"[6].

## ROA and ROE ratio

Du Pont developed ways to measure ROA and ROE ratios. The return on assets ratio developed by Du Pont breakdowns ROA into the product of turnover and margins [7]. $\text{ROA} = \frac{\text{After-Tax Interest + Net Income}}{\text{Assets}}= \frac{\text{Sales}}{\text{Assets}} \times \frac{\text{After-Tax Interest + Net Income}}{\text{Sales}}$

When the firm raises cash by borrowing, it must make interest payment to its lenders and this reduces net profits. However, if a firm borrows instead of issuing equity, it has fewer equity holders to share the remaining profits. An extended version of Du Pont formula helps us find out which effect dominates. It breaks down return on equity into four parts[8]: $\text{ROE} = \frac{\text{Net Income}}{\text{Equity}}= \frac{\text{Assets}}{\text{Equity}} \times\frac{\text{Sales}}{\text{Assets}} \times \frac{\text{After-Tax Interest + Net Income}}{\text{Sales}}\times\frac{\text{Net Income}}{\text{After-Tax Interest + Net Income}}$ Where[9]:

• ROE = leverage ratio;
• Assets/Equity = asset turnover;
• (After-Tax Interest + Net Income)/Sales = operation profit margin;
• Net Income/(After-Tax Interest + Net Income) = debt burden.

## Footnotes

1. Brealey R. A. i in. 2018, s. 768
2. Shim J. K. i in. 2012, s. 337
3. Lal J. (2017)
4. Lal J. (2017)
5. Lal J. (2017)
6. Lal J. (2017)
7. Brealey R. A. i in. 2018, s. 768
8. Brealey R. A. i in. 2018, s. 770
9. Brealey R. A. i in. 2018, s. 770

## References

Author: Michał Dembowski