Ever wonder why some companies succeed while similar companies fail to generate the same returns for shareholders? One of the key elements is a company's ability to turn the shareholder equity it holds into profits. It's one of the key elements that Mathew Emmert looks for in his dividend-paying stocks featured in Motley Fool Income Investor. In fact, it's an element that every investor should keep in the ol' toolbox for evaluating securities.

It doesn't get the same treatment as earnings per share, it doesn't gain much cult status like free cash flow, and you'll never, ever hear the folks on Bubblevision using the term. But return on equity (ROE) matters. It shows how good a company is at generating money based on the retained shareholder equity, also known as money that the company could return to you. This is an important number for dividend payers as it shows how well the company is generating returns for the next dividend. A consistently low ROE is a sign that the company's management isn't effectively deploying the resources at its command.

Moreover, relative return on equity within an industry can tell investors which companies are well run, and which are not. Ever wonder why Ralph Lauren (NYSE:RL) was such a lousy investment for so many years even though everyone seemed to have one or two pieces of Polo clothing in their closets? Look no farther than a chronically anemic ROE.

The basic calculation for return on equity is dazzlingly simple: net income divided by shareholders' equity (book value). But this calculation hides some more nuanced information that not only indicates a company is generating poor returns, but also why. The return on equity calculation, as simple as it appears, is actually a combination of several critical components relating to profit margins, asset turnover, debt, and debt servicing. Break this calculation down into its elements and you'll get an astounding amount of information about a company, its trends, and its performance relative to its competition.

Permit me to demonstrate by looking at two similar companies: American Eagle Outfitters (NASDAQ:AEOS) and Abercrombie & Fitch (NYSE:ANF). American Eagle has 800 stores, Abercrombie 700. American Eagle's trailing 12-month revenues exceeded $1.5 billion, Abercrombie's $1.7 billion. These are not huge differences, and yet Abercrombie is valued 50% higher than American Eagle Outfitters. One hint why: Abercrombie & Fitch has an ROE exceeding 25%, while American Eagle Outfitters' is less than 10%.

Does this mean that the companies' book values are wide apart? Again, no -- they are quite close. Obviously, the return component for American Eagle is far inferior to that of Abercrombie. Let's dig in and figure out why. Keep in mind this formula for ROE: [(operating profit margin)(asset turnover) - (interest expense rate)](leverage)(tax retention rate).

Item 1. Operating profit margin
Simple enough. By dividing EBIT (earnings before interest and taxes) by sales, you find out how much money the company made from operating activities before the taxman and the noteholders get their lucre, and you want to see how much in revenues it took to generate this amount. A company could sell billions of dollars' worth of product, but if its expenses consistently equal or exceed its revenues, it's more like a turnstile than a business. Right out of the gate, we can see a big discrepancy between our two case-study companies. Abercrombie has an operating profit margin of 19.4%, while American Eagle's is 6.9%. At those rates, it would take American Eagle nearly three times the sales to generate the same gross operating profit.

Item 2. Asset turnover
I love this measure -- it's where places like Costco (NASDAQ:COST), Claire's (NYSE:CLE), and Home Depot (NYSE:HD) really shine. Compared to the level of assets, how much in revenues did the company generate? So we use this formula: sales divided by average assets. (Note we're talking average assets, not the raw number at the end of the reporting period.) For American Eagle, the turnover is 1.89 times, while for Abercrombie it's 1.53 times, so American Eagle is actually better in this regard.

Item 3. Interest expense rate
Remember, in Item 1 we backed out interest payments. That's because we want to be able to view leverage separately from operations. If a company is operating well but is simply drowning in debt, that would be useful information -- and if in future periods you notice the debt level dropping, you might have yourself an underappreciated stock. Stranger things have happened. What we're looking for here is how much interest the company is paying to maintain its asset base, so the formula is interest expense divided by assets. Abercrombie, rather than paying interest, generates it from the cash in the bank, so it actually has an interest expense rate of negative 0.3%. Ditto American Eagle, which comes in at minus 0.4% Nice.

Item 4. Leverage
Wait a minute, didn't we just get finished determining that neither company had any interest expenses? I guess that means we can scribble in a zero for both and move on, right? Not so fast. While neither had interest-bearing debt, both have plenty of operating, short-term leverage -- accrued expenses, accounts payable, even unredeemed gift cards. Still, this component's pretty simple to calculate. The formula is average assets divided by average shareholders' equity (remember the average part). American Eagle comes in at 1.31, while Abercrombie & Fitch is 1.37 times -- nearly identical.

Item 5. Tax retention rate
Can you hear Billy Bragg talking with the taxman about poetry? No? Well, Uncle wants his cut, and although we'd love to be able to quote returns net of tax, that doesn't really capture the whole picture. The calculation here is the reciprocal of the tax bite, that is: 1 minus the tax rate. To calculate, take the provision for income taxes and divide it by the income before income taxes, then take this sum and subtract it from 1. Abercrombie's tax rate is 38.8%, so its retention rate is 61.2%. American Eagle's tax rate is 43.4% (yikes!), so it retains 56.6%.

In sum we have the following equations:

Abercrombie & Fitch:
[(0.194)(1.53)-(-0.003)](1.37)(0.612) = 0.2514, or 25.1%

American Eagle:
[(0.069)(1.89)-(-0.004)](1.31)(0.566) = 0.0997, or a smidge below 10%

A look at most of these component numbers shows something striking. They're dramatically similar for the two companies with one glaring exception -- operating profit margins (though, I must admit I'm a bit perplexed by the high tax rate at American Eagle). Abercrombie is far more efficient at keeping costs down, and it shows in net profits -- and in return on equity. Here's where else it shows: On marginally higher annual sales, Abercrombie is valued at a billion dollars more in market capitalization than American Eagle. What's tougher for American Eagle shareholders is that the ROE has declined from well above 29% in 2001 to today's 10%. You can see this trend quite clearly in the most recent 10-K with the company having added more than 10% new retail space only to capture 3.9% higher revenues.

One thing to keep in mind is that companies granting tons of stock options without expensing them (neither of the two in the example) can skew results in two ways. First, earnings -- the numerator -- will be overstated. Second, many companies counteract the impact of options dilution by buying back shares. The money for this comes straight from the equity account, so the denominator may be substantially understated. I always read the management discussion and add back every penny to equity that was used to buy back shares to hide dilution. They don't call it shareholders' equity for nothing.

Fool on!
Bill Mann, TMFOtter on the Fool Discussion Boards

Bill Mann's own return on equity is dramatically hampered by his trips to Costco "to pick up just one thing." He owns shares of Costco. Please view his profile for a complete list of holdings. The Fool has its own community dedicated to financial analysis. Come share your thoughts on the Foolish Collective discussion board! Not yet a member? A free trial is required, and highly recommended.