Close your books and take out your No. 2 pencils, folks. It's time for a math quiz: What's $100 times 102.4% divided by 102.4?

No peeking.

Oh, all right. Go ahead and peek.

The answer is $1 -- but you already knew that. It's intuitive. Here, then, is something that's just as true, but perhaps a bit less obvious: When a company you own issues new shares, or options convertibles into new shares, the company has to grow at least as fast as the speed at which its share count increases just to keep its earnings per share constant -- just to prevent a dollar earned this year from devaluing next year.

Say Company X has 100 shares outstanding and 100 shareholders. Say it earns $100 profit in Year 1, giving each shareholder a claim on $1 worth of profits. If Company X increases its profits 20% in Year 2, you might think that would mean that every shareholder now has a claim on $1.20 worth of profits.

And you'd be right, except for one thing: Most companies on the U.S. stock markets don't hold their share counts steady from year to year. Most companies, in fact, increase the number of their shares outstanding every year. As a result, whatever gains this hypothetical company makes in its annual profits, 2.4% gets shaved off the top before those profits reach the individual shareholder.

What's with the 2.4%?
Excellent question. According to a report by Institutional Shareholder Services, 2.4% is the average amount by which the 200 largest U.S. companies diluted outside shareholders annually over the three-year period from the end of 2000 through the end of 2003 (the most recent period for which data is available).

And that's just the number for the biggest, most conservatively run companies. According to the Investor Responsibility Research Center, the smaller the company, the more it tends to dilute outside shareholders. If the company is a "tech," dilution gets even worse. Presidio Pay Advisors puts the rate of stock options dilution at the average small software company at 3.5% in the 2000 to 2003 period. The average small telecom-equipment maker diluted at a 4% clip. And remember: Every percent of a company's shares that management grants itself is a percent of the company's profits that you'll never see. When management issues stock options, they're not just whittling away at your piece of the corporate pie -- each of the shares they grant themselves diverts profits from outside shareholders (that's you and me) to the insiders as well.

There's forgivable dilution ...
Now, sometimes buying a heavy diluter can be worthwhile. Apple (NASDAQ:AAPL) may have diluted its shareholders by a total of more than 17% since 2001, but it's also done a bang-up job of reversing its money-losing performance in 2001 over the subsequent years. Likewise, shareholders in EMC (NYSE:EMC), Electronic Arts (NASDAQ:ERTS), and Activision (NASDAQ:ATVI) can testify to the power of strong earnings growth to offset excessive share dilution.

... and then there's the other kind ...
On the flip side, if a company dilutes hand over fist, but its profits don't keep up with the pace of dilution -- watch out. Elan (NYSE:ELN), for example, boosted its share count by 19.7% from 2000 to 2003, but hasn't seen a profitable fiscal year since 2001. For largely unrelated reasons, its stock price plunged nearly 90% over the period, but the dilution certainly exacerbated the downturn.

... but if we had our druthers ...
At Motley Fool Hidden Gems, we focus our efforts on finding small companies that buck the trend on Wall Street, ones that don't dilute their shareholders just to enrich management insiders. Smaller versions of companies such as Dow Chemical (NYSE:DOW), which from 2000 to 2003 increased its share count by just 1.1% per annum -- less than half the average.

It would have been nice, however, if Dow increased its profits by more than the same 1.1% per annum rate. As things turned out, three years of holding the line on dilution benefited shareholders not at all, because profits per share remained flat. (After all, $100 times 101.1% divided by 101.1 = $1.)

Truly fortunate, however, is the investor who finds the corporate diamond in the rough -- one that eschews excessive stock option grants and grows profits for its owners. Small-cap "Dows" are fine, but what we're really searching for is a tiny company that follows the lead -- and can one day grow into the size -- of an International Paper (NYSE:IP). From 2000 to 2003, International Paper's share count barely budged. It began the period with 481.5 million shares. It ended with the same number. But when it came to profits, vive la difference! In three years' time, International Paper more than doubled its net profits. Because the share count held steady, shareholders saw their per-share earnings double as well.

At Hidden Gems, we actively seek out such companies. Indeed, we make finding shareholder-friendly management one of our highest priorities when researching potential investments. Before we recommend a company, we research its history to ensure that it has demonstrated a commitment to building shareholder value, growing profits, and restraining stock dilution. In fact, roughly one-third of our recommendations go a step further, buying back their shares to yield negative dilution -- "stock concentration" -- through which every shareholder's slice of the corporate pie grows, and every shareholder gets a larger and larger helping of the firm's total profits.

As a result, of Hidden Gems' 29 currently active recommendations, not one company matches or exceeds the confiscatory rates of dilution prevalent elsewhere on the market. On the contrary, from 2000 to 2003, our companies averaged just 2.0% in annual dilution -- half the rate of your run-of-the-mill small-cap tech firm.

While dilution is not the only criterion we consider when recommending a stock, it's certainly contributed to the gains our recommendations have scored over the past two years: up 35% vs. the S&P's 10% gain. If you'd like to see which companies make the Hidden Gems grade, you're welcome to try our service out for one month, free of charge. If you're not absolutely thrilled with the service after 30 days, you may cancel your subscription with no strings attached. To begin, just click here.

Fool contributor Rich Smith has no position in any company mentioned in this article. Activision and Electronic Arts are Motley Fool Stock Advisor recommendations. Dow Chemical is a Motley Fool Income Investor recommendation.The Motley Fool is investors writing for investors.