Nearly a century ago, an engineer from DuPont named F. Donaldson created an algebraic decomposition of the now famous return on equity ratio. At the time, DuPont owned a large stake in a struggling General Motors. In 1920, with the specter of bankruptcy looming, Pierre du Pont joined GM's board and pushed for operational changes. It's believed that Donaldson's analysis played a crucial role in du Pont's thinking and in the eventual turnaround of the automobile manufacture. By the time Pierre du Pont left GM's board in 1928, the company had become the largest corporation in the world.

The basic DuPont model starts by decomposing return on assets into two parts, net income and asset turnover. The breakdown is as follows;

From there, a leverage factor is included to find return on equity;

This is the basic DuPont formula. It's simply the product of net income, asset turnover, and leverage. The breakdown can be useful for understanding the driving factors of ROE. It acts as a window into a company's business model and helps answer questions such as;

- Is a company's ROE high because of high profit margins, large amounts of leverage, efficient use of assets, or some proportion of all three?
- How do the ROE drivers of one company compare with those of another in that industry?

**Expansion for Retail Operations**

Fortunately, the Dupont breakdown can be expanded to allow for a more granular analysis of the company's operations. There are many possibilities depending on one's focus. The specific expansion presented below was derived by the author to analyze retail operations, and is one that works well for companies which hold inventory. The complete derivation can be found at the end of this article.

__Notes:__

- Many of the inputs used in this analysis are accrual accounting values and are subject to manipulation by the presenting company. The Dupont analysis does a poor job spotting accrual accounting manipulations, and should be used in conjunction with other cash flow analysis techniques.
- The above equation uses NET PPE to represent fixed capital invested. One can include off-balance sheet capital by replacing NET PPE with [GROSS PPE + CAPITALIZED OPERATING LEASES]. Additionally, ASSETS can be replaced by (ASSETS + COL) in the denominator of both (NET PPE/ASSETS) as well as the numerator of the leverage ratio, (ASSETS/EQUITY). This allows one to view the adjusted leverage ratio corrected for operating leases.

This ROE breakdown is designed to illuminate critical characteristics of a company's business operations. The equation is written in such a way to allow for quick analysis of popular metrics such as inventory turns or interest coverage. Each term represents an element in the operations story. In a retail environment, inventory is purchased from a supplier and then stocked on shelves in a layout and density designated by the company. The product is then marked up and turned. Each square foot of that retail space is supported by property plant and equipment. Once the inventory is sold, funds from the inventory markups are combined. Out of that pool, SG&A expenses are paid, then interest, then taxes. The return to shareholders is leveraged in this entire process by using assets that the equity holders do not own.

Since ROE is simply a product of all terms (excluding net PPE per sqft, in this case), one may have an initial instinct to simply maximize each term, thus increasing ROE. Unfortunately, there's no free lunch. Changing the conditions of one term tends to affect a neighboring term in an opposing manner. For instance, increasing the resale markup or inventory-per-sqft will also have the effect of decreasing inventory turns. The problem is not one of maximization, but optimization. The retailer must decide what type of model works best for that company. Is the business one of low margins and high volumes, or one of higher margins and lower volumes? Understanding ones market, and the company's place in it, will help management find the optimal solution to their unique ROE equation. It will also give analysts a deeper understanding of management's strategic approach.