**3. The Dupont Equation (return on equity)**

ROE = (net income/sales) x (sales/assets) x (assets/equity)

Return on equity is a useful return measure, but I'm less interested in ROE, per se, than its components. The traditional version of the Dupont equation demonstrates that return measures can be broken down into useful segments. There are actually many ways to express ROE:

ROE = net income / average shareholder's equity

ROE = (net income/sales) x (sales/equity)

ROE = [(earnings before interest and taxes/sales) x (sales/assets) - (interest expense/assets)] x (assets/equity) x (1-taxes)

Don't panic. You don't have to memorize all these formulas. What they demonstrate, however, is a fact often forgotten by investors: Margins are just one component of profitability. Focus on the first equation.

Let's say we know a company's ROE is increasing. This is good information, but we need to know why it's happening if we expect to learn anything about the business. The traditional version of the Dupont equation opens the door.

The first part *(net income/sales) *is net margin. Most investors know about profit margins. Yes, they are important. The second part *(sales/assets) *is the lesser-known asset turnover, which measures the efficiency with which a firm uses assets. This is also a vital part of profitability, and explains why low-margin companies such as **Wal-Mart ****Southwest Airlines **

The last part of the equation *(assets/equity) *is called the equity multiplier, and is a measure of leverage. Leverage, or debt, used smartly can magnify returns. We need to know to what extent the companies we invest in are using leverage, and get a feel for whether it's being used smartly.

Other return measures such as return on assets and return on invested capital can also be broken down into their components and analyzed, giving us a much fuller picture of how a company is performing. Using the Dupont equation not only gives us practice analyzing financial statements, but also allows us to see how items from the income statement, balance sheet, and cash flow statement fit together.

**4. Expected return formula**

ER = Sum (probability of return) x (possible return)

This equation starts with the understanding that investing is an uncertain business, and then gives us a way to mitigate the uncertainty. It does so by using probabilities.

The power of probability is that it gives us a way to look at a number of these different scenarios. Since we don't know what will happen, it's useful to find a way to aggregate (the "sum" in the above equation) a number of possibilities into one expected return figure.

Here's an example of how it could work. Let's say we're trying to figure out what kind of a return a company such as **Amgen **

It's not easy coming up with good estimates. You can see that you must be careful with this equation. If you put junk in, you're going to get junk out. Nevertheless, uncertainty is part of the business. We must find ways of coping, and this was my way of looking at Amgen at the time. Here's how the math looks:

ER = Sum(probability of return) x (possible return) *[as many as you have]*

ER = (0.60)(1) + (0.20)(0.50) + (0.20)(-.20) *[we have three probabilities for Amgen]*

ER = 0.60 + 0.10 - 0.04

ER = 66%

An expected return of 66% is equivalent to a mean annualized return of 10.6%. The formula provided a simple way to combine three different scenarios into one number, one that's more powerful than any single estimate. Investors can then decide whether they think these estimates make sense, and, if so, whether a 10.6% return on a stock like Amgen is a reasonable payoff.

I've thrown a lot at you in a short space, yet probably omitted formulas worth a closer look such as the dividend discount model and earnings multiplier. But this is enough for now. It's a good start. Maybe, with effort and study, one of these formulas can play a small role in the discovery of a new investing idea, a company as yet unseen in the far reaches of the market.

Have a great day.

**« Back: Four Great Equations, Part 1**

*Richard McCaffery doesn't own shares in any company mentioned in this report. To see his stock holdings, check his profile. The Motley Fool is investors writing for investors.*

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