This led to a decrease in Days of Sales Outstanding (DSO), which in turn led to a decrease in accounts receivables. Total assets therefore declined, so borrowings were reduced, leading to an increase in ROE as interest expense went down.

After all, how do you get operating management to understand all of this? In the case above, for example, our fear was that our salespeople might react to the new incentive by cutting selling prices, leading to an offsetting decline in operating margins and a net zero (or worse) impact on ROE.

Fortunately, and because the sales force was incented both on gross margins and on DSO, they eventually

*raised* prices on many items to restore gross margins. We ended up with the best of both worlds; we maintained margins and decreased interest expense.

The point is,

**when it comes to its management and measurement, there are many interrelated components which drive ROE** - actions that improve one component often harm another.

A clear understanding of what these components are and how they interact is critical.

**What is ROE?** Simply put, Return on Equity is Net Income (after tax profits) divided by Average Shareholder's Equity for a given period.

A helpful tool in unpacking the elements involved is something known as

**the DuPont formula, a simple algebraic equation that breaks down ROE into five major components** (and that was developed nearly a century ago in 1919):

- EBIT (earnings before interest and taxes) Margin,
- Total Asset Turnover,
- Interest Burden,
- Tax Burden and
- Leverage.

Let's start with the obvious basics: Return on Equity is Net Income (the final bottom line, income after interest and taxes ) divided by Average Shareholder Equity for the period being measured. Or, ROE = NI/ASE.

So,

**ROE increases if Net Income increases or if Average Shareholder Equity decreases** (through dividends, for example). If things move in the opposite direction, ROE does as well.

Since, ROE is such a straightforward measure,

**how does the DuPont model come up with five components in its make up?** First, ROE can also be stated as Return on Assets (ROA) multiplied by Leverage (L). Where ROA = NI/Average Total Assets (ATA) and L = ATA/ASE. So,

ROE = ROA x L, or

ROE = (NI/ATA) x (ATA/ASE).

**You can think of ROE as (mostly) business-driven ROA multiplied by CFO-controlled leverage.** (Note the algebra: The average total assets in ROA and in Leverage cancel each other out.)

Second, ROA can be further broken down as Net Profit Margin (NPM, often commonly called Return on Sales or ROS) multiplied by Total Asset Turnover (TAT). Where NPM is NI/Revenues (R) and TAT is R/ATA, or

ROA = NI/R x R/ATA.

In our Foodservice example, Total Asset Turnover increased. By focusing management on TAT that they control, they don't have to consider the impact on borrowings and interest expense to know they are improving ROE.

**There is a basic trade-off between higher ROS and lower asset turnover.** High volume retailers and distributors, for example, typically have lower margins and higher asset turnover than do manufacturers. Because manufacturers have expensive equipment, and also sizable inventories and receivables, they turn their assets less frequently. To get a competitive ROE, they drive net profit margins. (Again, note the algebra. The R or revenue in both NPM and TAT cancel each other out.)

Third, Net Profit Margin (NPM), can be thought of as Tax Burden (TB) multiplied by Interest Burden (IB) multiplied by EBIT (earnings before interest and taxes) margin (EM). Where Tax Burden, TB, Net Income divided by Earnings Before Taxes (after interest) and Interest Burden, IB is Earning Before Taxes (EBT) divided by EBIT and EBIT Margin is EBIT divided by Revenues, R. So,

NPM = TB x IB x EM, and

TB = NI/EBT, and

IB = EBT/EBIT, and

EM = EBIT/R. So,

NPM = NI/EBT x EBT/EBIT x EBIT/R.

**At this point (still with me?), we have isolated operating management impact on margins to the profit before interest and taxes line.** (For you operating managers, this is why your published margins in the annual report are much less than the net profit margin you generate.)

Put these all back together and we get the five components of the DuPont formula for ROE:

**ROE = TB x IB x EM x TAT x L**

Or, for those who prefer words:

Return on Equity = Tax Burden X Interest Burden X Earnings Margin X Total Asset Turnover X Leverage

**Using the DuPont Formula** Okay, so how can we use this tool?

Well,

**let's say your company is thinking of taking on more debt** (i.e. boosting leverage) as a way to boost ROE. If nothing else changed, as our formula demonstrates, that would certainly help.

But there is a cost to debt - interest expense - so boosting leverage has an effect on the interest burden. The DuPont formula allows us to see if the higher debt will boost ROE.

**Or consider the example of a grocery store.** Ever wonder how these operations survive on such slim operating margins? It's a function of their exceedingly high asset turnover and leverage. Here as well, the DuPont Formula demonstrates how these two numbers are capable of offsetting the lower earnings numbers.

[Interestingly, Whole Foods increases margins for premium products at the expense of lower inventory turns and more expensive stores that combine to reduce asset turnover.]

One last example.

**A CEO I met with recently was undertaking a strategy of backward integration,** to capture the profits of his company's vendors. Some of the vendors had higher margins than the company, so why not buy them up? I reminded the CEO that these vendors had more capital intensive businesses and so even higher margins would be needed. The result was a slower and more price-conscience backwards integration that boosted profits and maintained ROE.

**ROE is a critical measure of business profitability.** And while accountants don't charge the cost of equity in the business, the market does. As my

March newsletter regarding the cost of capital discussed,

**if the cost of equity exceeds the return on equity, the equity value of the business declines,** even if there are profits.

The DuPont Formula, with its simple ability to break out the components of ROE into levers controlled by the operators and levers controlled by the CFO or Corporate, is a handy tool for assigning responsibility to different programs that improve profitability and returns.