If you were a newbie in the last stock market bubble, this article is for you. The purpose of this primer, and others that will follow in the near future, is to help you make the transition from newbie to experienced investor. You may have seen some instructional material on stock pricing before, and even heard of the dividend discount model (the most basic approach). But you may also have tuned it out after you recognized how impractical it was when applied to the real world. (It didn't help that making money seemed so easy in the late 1990s as to make theory seem a waste of time.) This primer will be different. There will be some math, but not much. Most of what I'll cover here will address how you can connect theory to what you see in the real world every single day.

What do shareholders own?

In our market economy, you go into business because you expect to make money. In a proprietorship, everything left over from the revenue you earned, minus expenses, is yours. In other forms of organization, you need to be a bit more formal because there are other owners. Partners "draw" money out of the business. And shareholders get money out of a corporation by receiving dividends. So the value of your shares is determined by the value of the dividends you get, your share of the profits plus two additional factors.

1. Let's say you consider buying shares of a corporation. How much will you pay if the annual dividend is $10 per share? That depends on how much of an annual "return" you want. If you want a 10 percent return, you'll offer $100 (math: a $10 dividend divided by a $100 investment equals a return of 10 percent). But just because you offer to pay $100 doesn't mean someone will sell to you at that price. Financial capital is subject to principles of supply and demand, just like wheat, copper, oil, etc. Suppose market conditions are such that prevailing rates of return for corporate shares are in the 5 percent range. If I'm selling stock that commands a $10 per share dividend I can demand a price of $200, and someone will give it to me. So one additional factor is prevailing market conditions.
2. Suppose this corporation is a bit riskier than most others. A buyer may say "If I'm willing to accept the prevailing 5 percent return, there are hundreds upon hundreds of better quality corporations I can invest in. So if you want me to buy your shares, you need to give me incentive to bypass all the others. The buyer and seller may settle on a 7 percent return, which is equivalent to a price of about $143. Hence the second additional factor is the desirability of this corporation relative to alternative investments.

In all cases, the price (P) is computed as dividend (D) divided by desired return (R). Often, though, investors use return (R) as the basis for comparing and pricing investments. R is computed as D (dividend) divided by Price (P). Mathematically, it looks like this:

R = D/P

Life is complicated

It would be delightful if we could stop there. But we can't because there are four major issues that complicate our lives.

1. Growth
   
   As profits grow over time (as we hope they will), dividends can be expected to grow. If profits and dividends are growing by 10 percent every year, the dividend this year may be $10, but by next year, it will be $11. If we divide $11 by today's $200 purchase price, next year's yield will be 5.5 percent (11/200). The year after, assuming further 10 percent growth, the dividend will be $12.10. Dividing that by the $200 purchase price produces a yield of 6.05 percent. The buyer might smile, but the seller won't accept it. The seller wants a price that truly is consistent with the prevailing 5 percent yield. At $200, the buyer gets too much of a good deal. If the latter holds the stock over time, he'll wind up with an annual return well in excess of 5 percent.
   
   Finance textbooks provide lots of great math to deal with this, including "present value." Simply stated, present value is a tool for computing today's equivalent of a cash payment to be made tomorrow. If I offer you $10 today or $10 a year from now, you'll probably choose $10 today. But the choice is $10 today or $11.50 a year from now, you have to pause. If you can invest today's $10 payment for one year at 5 percent, at the end of the year you'll have $10.50. But if you bypass the $10 for now and wait, you can get $11.50 a year hence. That's a better deal. The way to decide if you should wait is to do some math that helps you decide how much you must receive today to allow you to invest and wind up with $11.50 a year hence. In this example, the "present value" of $11.50 one year form now, assuming a 5 percent return, is $10.95. If I take $10.95 and invest it for one year at 5 percent, I'll wind up with $11.50 at the end of the year. If interest rates rise, to say 8 percent, it'll take less money today to generate $11.50 a year hence ($10.65 will be sufficient). So as interest rates rise, present values fall, and vice versa.
   
   Today's proper price for a share of stock is the "present value" of all the dividend payments that are likely to be received in the future. (Notice from the above paragraph how stock prices, or present values, go down when interest rates rise and vice versa.)
   
   
2. Future selling of your shares
   
   Thus far, we thought about a stream of dividends stretching into the infinite future. Even long-term investors prefer a holding period that's something short of infinity. So we need to account for the fact that someday, you'll want to sell your shares. The books have lots more math for this, but I'll make it easy. The proceeds you expect to get when you sell are included, along with dividends, in the stream of cash you expect to get, and that goes into the present value calculation. Let's think about a projection of the future sale price. If you think you may sell in two years, imagine how a prospective buyer, two years into the future, will value the dividend stream that he'll get. Continuing with the above example, he'll be looking at an initial payout of $12.10 and a 5 percent return. So a price of $244 seems a reasonable starting point. Of course you'll need to make adjustments for probable growth beyond year two. And perhaps 5 percent won't be appropriate as a rate of return. Market rates may rise or fall, and/or the quality of the corporation may improve or deteriorate relative to alternative investments. And two years hence, the growth forecast may change. But in any case, we do have a $244 starting point. The changes may bring it up, perhaps to $275, or down, possibly to $175. But if an exuberant analyst publishes a target price of $1,000, you ought to raise an eyebrow and insist that the analyst get serious about justifying his presumably bold assumptions about market rates, growth or company quality, or else get some personal counseling or a new career.
   
   Does this like I'm stretching the point? I'm not. Remember some of the bold price targets published a few years ago for Qualcomm (QCOM) and Amazon.com (AMZN). This is why the stuffy suits (the old fogies who were ignored by the grass roots we-know-better Web sites) laughed and wagged their fingers at the dot-com crowd!
   
   
3. Reinvestmet of profits
   
   It's standard for corporations to refrain from paying out all annual profit as dividend. Some money is held in the business for a rainy day. And some money is simply reinvested for future growth. Either way, profits not paid out as dividends are known as retained earnings. Reinvestment is more desirable than dividend payments if the corporation can earn a higher return on the money than the shareholder could get (by reinvesting the dividends). If all goes well, the reinvestment will enable the corporation to pay a higher dividend in the future than would otherwise have been the case. Going back to the above example, if reinvestment gives the corporation the ability to set a year-five payout at $18 rather than $12.10, that raises the staring-point target price to $360. A shareholder who accepts a forecast like that would likely forego all or some immediate dividend payments in order to get that bigger future reward. As you can see, even if a corporation currently pays little or no dividend, we still have to acknowledge dividend as a major factor in our thoughts about share pricing.
   
   
4. The growth culture
   
   The above scenario sounds wonderful. But it is only good if it really works out as expected. For better or worse, a cultural phenomenon has occurred through which almost all corporations see themselves as "growth companies" and almost all shareholders buy into it hook, line, and sinker. It wasn't always like this. When I was in grad school in the late '70s, many academicians were still producing studies relating to their beliefs that corporations with high dividend payout ratios generated greater shareholder wealth than so-called growth companies. But today, shareholders, collectively speaking, have accepted a situation where most of today's publicly traded corporations pay little, if anything, as dividend, and reinvest most or all profits back into the business. Many companies don't deliver nearly as well on the growth dream as everybody hopes. But the growth culture remains alive and well, and dividend payouts remain paltry by historic standards.

Adapting to the complications: the EPS fiction

As a result of these four complications, modern stock prices have become uncoupled from dividends. So in the real world, you can't compute a fair price through the basic dividend formulas presented above. Nor will any of the dividend-based textbook math help you (unless you're still in school, in which case, you'd better use the all math, including the advanced stuff not presented here, if you want a decent grade in your finance course).

The solution is easy, sort of. We substitute EPS (earnings per share) for dividends. This doesn't really work in an ivory tower sense, but it does work within the context of our growth culture. Shareholders have so thoroughly accepted and adopted growth, that they act as if all corporate EPS (whether paid as dividends or reinvested back into the business) is in their hands. So instead of working with a dividend yield as presented above, we can substitute an earnings (E) yield which is computed as follows:

Earnings Yield = E/P

Here comes another culture thing. Does E/P look familiar? It should. Turn it upside down and we get something you see all the time: P/E!

If you're losing the train of thought, stop here and review from the top. This is important. I really want to drive home the point that P/E ratios aren't just one of those things we use for the heck of it. They have a serious and solid intellectual underpinning. They are equivalent to earnings yields, which are the modern-day substitute for dividend yields--which are the true basis for valuing ownership of corporate stock. So when somebody rants about how P/Es are no longer relevant, you'd best hold on tightly to your wallet and run away as fast as you can. Buying stocks without addressing P/Es is about as sensible as trying to fly a plane without addressing air currents. In both cases, well, you know . . .

When we flip P/E back over and think of earnings yield, we can understand, from the prior discussion of dividend yield, that a bad company's stock will have to offer a higher yield to attract buyers. Similarly, the yield for a great company will be low (otherwise, there would be too many would-be buyers). Let's see how this works when we flip the earnings yields back to P/Es. If EPS equals $3.00 and the earnings yield is 5 percent, the price will be $60. If it's a bad company and the yield is higher, at 8 percent, the stock price will be $37.50. If it's a good company and the yield is lower, say 3 percent, the stock price will be $100.

The starting number translates to a P/E as follows: a $60 price divided by $3.00 EPS gives us a P/E of 20. A bad-company stock price of $37.50 divided by EPS of $3.00 produces a P/E of 12.5. A good-company stock price of $100 divided by EPS of $3.00 produces a P/E of 33.3.

That's the basis for the generally recognized phenomenon of good stocks having higher P/Es and bad stocks generally having lower P/Es. So once again, this isn't just one of those things. It's an inevitable result of the basic principles of finance and math. When evaluating companies, good or bad is usually determined based on growth prospects and risk.

We handled the complicating factors through what I call "the EPS fiction," where we treat EPS as if it were the same as a dividend. But notwithstanding introduction of the fiction, we still have a reasonably rational basis for stock prices. We can argue over what the growth prospects are and what the market return ought to be (based on differing assessments of market conditions and company-quality issues). So there will always be disagreement on what, exactly, a fair stock price ought to be. But all rational investors ought, at least, be somewhere in the same ballpark. We may have a big ballpark and debate if a stock that commands $25 today is worth $15 or $35. But we are unlikely to seriously considering a price of, say, $350 (unless you're a circa 1999 day-trader).

Before we wrap up, let's just extend the fiction a bit more. Suppose a company has no earnings, but we agree it should still have a value above zero. Maybe a temporary recession is causing losses. Or perhaps it's a startup company that will take time to achieve initial profitability. We can cheat and use a Price/Sales ratio assuming that today's sales will translate to tomorrow's EPS (which will translate to dividends further out into the future). Or if we fancy ourselves to be accounting philosophers, we may substitute cash flows or EBITD for earnings. But even in these cases, we're still doing the same thing: we're allowing the corporation to reinvest our money because we believe the corporation can generate higher returns (and larger future dividends) than we could get if we received and reinvested the dividends.

Investing's main law of nature

Here's the moral of the story. You should always, always, always, always be able, in your mind, to construct some sort of logical connection between today's stock price and a stream of future dividends. The logical chain might be long: you might assume years of startup losses will be followed by more years of all profits being reinvested. But you should be able to envision some connection between today's stock prices and a stream of dividends that will commence someday in the future. You don't actually have to do the math. But you should feel comfortable that the numbers are such that if you wanted to take the time to do it as an interesting exercise, you could come up with some plausible set of assumptions that make the present-day price seem somewhere in the ballpark.

This is true even in an asset play, where you buy because you expect the business to be liquidated and the sale proceeds to exceed the current market capitalization of the stock. You need to imagine how the prospective buyers will view future dividend streams and calculate prices they are willing to pay. Again, there may be a long and convoluted logical chain (involving restructuring, perhaps). But you still need at least some sort of chain.

As noted above, you don't have to actually do these calculations, unless you're stuck indoors in a snowstorm and want an interesting way to kill some time (assuming your cable TV isn't working). You may have to make many assumptions that are to tenuous to use with real money (when a startup company will start paying dividends, what market rates of return will look like years hence, an extremely long-term growth forecast, etc.). The key is that you be aware that on some theoretical level, this sort of thing could be done.

Even though we're not getting strict about the math, at least respect the theory. Many investors, especially newbies, failed to do this in the late 1990s. Some analysts tried to sound alarms. I remember some write-ups that said bubble-era stock prices couldn't be justified unless one was willing to assume Yahoo!, or Amazon, or whomever, would single-handedly account for something like 25 percent of the U.S. economy in 2010, or something like that. The grass roots investors who thought they discovered a new P/E-free era laughed and ignored that sort of analysis. That was too bad. The party-poopers were right. And all they really did was implement the rainy-day math applicable to the concepts discussed above.