Did you ever have one of those days when you can’t decide if you want to break something or cry? I had one of those days last week. I was expressing my view in an online forum that credible investing strategies begin with an idea, something that derives one way or another from the body of financial theory that tells us how sock prices are established. Another participant who favored the process of searching the data­­ to see what worked in the past took the position that such factors could be used even without a determination that they relate somehow or other to core investment theory. He claimed “if you are creative enough, you can make up a theoretical basis for almost anything.”

#$(!@%! No! No matter how creative you are, you cannot make up a theoretical basis (of investing) for almost anything. Not even close! Well, actually, maybe I’m being a bit too broad. We’ve seen time and again how often investors do things that cause their savings to implode. But I’m taking it for granted that if you’re on this web site and took the trouble to click on this article, you’re not among them.

There are reasons why stocks are priced as they are. There’s nothing random about why Stock A may be priced at $20, Stock B at $4.83, and Stock C at $76.50. The reasons aren’t always easy to ascertain, and there is plenty of room for disagreement. But typically, if one person says Stock C is worth $76.50, another investor might say $70, another might say, $82, someone else might say $73.25, etc. But absent spectacular situations like Herbalife (HLF), nobody who knows what they’re talking about is likely to suggest $25 or $153.

And by the way, it’s not sufficient to brush the topic off by citing “supply and demand.” Any economist will tell you that neither supply nor demand exists in a vacuum and that there are reasons why they are what they are. So when I talk about stock prices being based on reasons, consider that a shorthand way of saying that there are reasons why supply and demand curves for a particular stock are such as to intersect at or near one price level rather than any number of others.

The theory is actually quite simple and completely firm. I’ll cover it all in this article and in just a few paragraphs.

The challenge is bridging the gap from theory to the real world, which I’ll do in subsequent installments. And by the way, this isn’t just for those who use fundamentals. Understanding stock pricing can even make the difference between successful technical analysis and technical analysis that doesn’t work. And by the time we’re done with this series, you’ll even understand why stocks like Tesla (TSLA) and Amazon.com (AMZN) are priced in the ranges you see.

Starting on Square One

To think about what a share of corporate stock is worth, we begin with the reason why the cooperation exists and what we, as shareholders, expect from it.  Actually, we can back up a bit more than that. Why would anybody be in any business at all? Answer: To make money!

Forgive me if the next few paragraphs seem overly basic. But I need to do it because although we know this stuff, we tend to forget it as soon as we focus on the stock market. That’s unfortunate. We need to really stay anchored in this material.

In the most basic form of business organization, a sole proprietorship, it starts with revenue - the money you get from customers or clients. From that, you need to pay the expenses of the business (including, I assume, your own salary if you work in the day-to-day operations). Everything left over is yours; it’s your profit. Sole proprietors do tend to think of profit and owner’s salary as being the same thing. Since this is an informal kind of organization, it’s tolerable (although it doesn’t make for the best kind of tracking and analysis).

In terms of formality, the next step up is a partnership. Now, because there’s more than one owner, it is important to dot the “i’s” and cross the “t’s” lest the partners constantly be at each other's throats over everything and anything. When a partner takes money out of the business (aside from a salary one gets for work done), it’s called a “draw.”

Corporations are like partnerships in that there’s typically more than one owner (we need not address the subtleties of single-owner corporations); often thousands or millions of owners. Now there’s a more formal gulf between the owners and the day-to-day business. In this setup, when an owner receives money from the corporation, it’s a dividend. In the world of publicly-owned corporations with which we’re concerned, most shareholders do not work for the business and, hence, do not get salaries, bonuses, 401K contributions, health insurance, or anything except for dividends. So dividends are important, very, very, very important.

The Theory of Stock Valuation: Simple and Ironclad

Therefore, nobody should be surprised when I say the value of your shares is determined by the present value (PV) of the dividends you get. How easy is that!

All you need to do is take an introductory finance class or look at a book and web site in order to learn what present value is. (For the uninitiated, if I guarantee to give you $100 one year from now, that would be the equivalent of getting $98.04 today if you can invest that money at an annual return of 2%. Hence the present value of the promise would be $98.04.)

So to value a share of corporate stock, all you need to do is sum up the present values of all the dividends you expect to receive in the future, and voila, we’re done.

• P (or PV) = D/(1+RR)
  • P is the fair value of the stock (a present value)
  • D is the sum of all future dividends
  • RR is the assumed reinvestment rate or required rate of return (same thing) expressed, for convenience of computation, in decimal form, meaning a 2 percent required rate of return would be expressed as 0.02.

Would that life could be so simple. Obviously, it’s not. But the framework is simple. It’s ironclad. Everything else we’ll do in the area of stock pricing derives from that simple principle, the necessity that the stock price be equal to the present value of all dividends you, as a shareholder, expect to receive. More specifically, everything else we’ll do will one way or another help us cope with the always uncertain and sometimes downright perplexing ways that reality impacts this perfect theory.

So now, let’s turn to some realities that contribute to why, despite such a simple theory, we’re not all stock-market gazillionaires.

Reality #1: What is the Assumed Rate of Return?

To set up the simple present value (PV) example above, I casually tossed out 2% as an assumed one-year rate of return on invested money. In real life, rate of return is anything but casual. In fact, a bunch of guys back in the 1960s got a Nobel Prize for work done on this topic. And one of the reasons why we look toward a future that includes “big data,” is that we’ll need a heck of a lot of storage to preserve the volume of research done and still being done to refine this topic.

Here are some simple ways to think about the issue:

• 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 five percent range. If I'm selling stock that commands a $10 per share dividend I can demand a price of $200, and someone will likely give it to me. So one additional factor is prevailing market conditions.
• Suppose this corporation is a bit riskier than most others. A buyer may say “If I'm willing to accept the prevailing five 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 the others." The buyer and seller may settle on a seven 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.

So we understand that in the PV-of-dividends computation, we can’t just pull a number out of the air. It must relate to rates of return prevailing in the market, and to the desirability (i.e. the risk) associated with the specific corporation.

The Nobel Prize guys bequeathed to us a simple, elegant model for expressing this known as the Capital Asset Pricing Model (CAPM). It tells us that the return we should require in order to justify investing in an asset is

• The rate of return available on risk-free investments, such as Treasury securities; plus
• A premium, an extra amount of return, sufficient to induce us to invest in risky assets in general, such as the equity market
• And with the risk premium being adjusted (multiplied) by an indicator known as Beta, which measures the risk of an individual asset relative to risky assets in general.

Here’s a simple equation:

• RR = RF + (RP *B)
  • RR is rate of return
  • RF is risk-free rate of return
  • RP is risk premium, the bonus, so to speak, for bypassing RF in favor of risky assets
  • B is Beta, which be definitions 1.00 if the asset is exactly as risky as the market; a Beta of 1.156 indicates the asset is 15% riskier while a beta of .95 indicates the asset is 5% less risky

Here’s an alternative formulation:

• RR = RF + (RM-RF)*B

Here, we define RP as RM, the assumed Return on the Market, minus RF for the risk premium.

Please, please, please don’t try this precise formulation at home.

• You can easily look up RF (I typically assume it’s the 10-year Treasury rate.)
• But nobody really knows what RP is. Some people try to look at history and subtract observed market returns from observed Treasury returns. But that’s nonsense. The numbers you’ll get will vary wildly based on the observation period you chose, and can sometimes even be negative which, of course would make no sense (at times in the past, the market may have disappointed investors and delivered negative risk premiums, but no investor would ever buy a stock if he or she expects that in the future). In practice, when a risk-premium assumption is needed, many, including me, just assume something in the 4%-5% range and say “based on historical experience.” But please don’t ask that the start and end dates of the so-called history be identified; if you put the question to me, I’ll grab my mobile, pretend I got an urgent text message, and say “I’ll get back to you on that” as I run out the door.
• As to Beta, it’s a great theory. But you can’t use historical numbers (calculated by “regressing” historical stock returns against market returns) because they’re all over the place.

Use CAPM to understand the three things you need to consider in setting an assumed required rate of return, which would serve as the assumed reinvestment rate in a PV computation: (1) the easily identifiable risk free rate, (2) market rates of return in general, and (3) the risks associated with a specific stock.

So now you know why the stock market goes down if interest rates go up. As RF rises, so, too, does RR. And as RR rises, PV would decline. For example, the PV of $100 received one year from now assuming a 2% RR is $98.04, but if we assume a 5% RR, the PV drop to $95.24.

You now also understand why a stock could tank if a company loses an important customer, even if management swears it expects new customers to enable it to maintain ongoing trends in profitability and dividends. The level of risk (uncertainty) has gone up since you’ll probably not accept management’s claims without seeing them play out in the real world. Higher risk is equivalent to higher B, which means a higher RR is needed and higher RR spells lower PV.

Reality #2: What is the Dividend?

Going back to our original equation, P = D/(1+RR), we saw above how to think about RR. And we know it can be challenging in the real world. But if you aren’t sitting now, please do so. The challenges of dealing with RR are nothing compared to what we have to put up with to address D. And just to get started, I have to ask your indulgence as I pretend all companies pay dividends. Yes, yes I know that’s not even close to being true. But we have to start somewhere. I’ll address the non-dividend-payers later.

A simpler version of the PV formula we’ve already seen would be to assume that a stock’s price (P) is computed as dividend (D) divided by required return (RR). Often, though, investors use return (RR) as the basis for comparing and pricing investments. Toward this end, we can easily reshuffle the basic equation to state that RR is computed as D divided by Price. Mathematically, it looks like this:

R = D/P

You've seen this before. It's a dividend yield.

But as noted, this is a simplification. As important as it is, we can’t get a real-world valuation tool unless we adapt to five kinds of curve balls life throws at us.

• A Multi-period Approach    

While investors hold shares for very short periods of time, equity valuation requires us to accommodate the fact that many hold long enough to collect or expect more than one dividend. And that, in turn, leads to some other complications . . .

• Growth

Let’s assume a company pays a $10 dividend and that its stock sells for $200, consistent with a five percent market rate or return. 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 divided by 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 as he contemplates the escalating yield, but the seller won't be happy. 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.

This is why we can’t stay with our simple R=D/P computation but must go instead back to the more involved PV concept with which we started. The $100 a year from now example works to introduce the idea of PV, but it doesn’t really shed much light on what happens in stock valuation.

Here’s a more relevant view of the situation.

• Assuming a RR of five percent, the first $10 dividend, payable one year from today, has a PV of $9.52 (($10 divided by 1.05). But that’s just one dividend. We need more.
• The second dividend, assumed to be $11 is divided by 1.05 raised to the second power, to accommodate the two-year time frame. In other words, it’s $11 divided by 1.05^2, which is $9.98. (If you’re not convinced about the math, you can do it the longer way: $11 payable at the end of Year 2 divided by 1.05 is $10.48. That’s the value at the end of Year 1. To get from the end of Year 1 to today, we divide $10.48 by 1.05, and get $9.98.)
• The dividend at the end of Year 3 is assumed to be $12.10. Because its a three year time frame, we compute PV by dividing $12.10 by 1.05 to the third power; $12.10/(1.05^3). The result is $10.45.
• So at the end of three years, we’ve accounted for a total valuation of $29.95 (which is $9.52 + $9.98 + $10.45). That’s a long way from $200. But then, who is to say we’re not going to hold for longer than three years. We could divided the Year 4 dividend by 1.05^4, the Year 5 dividend by 1.05^5, etc., etc., etc. Or we could bag the idea of owning shares forever and pull ourselves back in the direction of reality . 

• Future selling of your shares

Even long-term investors prefer a holding period that's something short of forever. So we need to account for the fact that someday, you'll want to sell your shares. The books have lots more mathematics to help us handle 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 grand PV 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 you see a forecast of a $1,000 stock price, you ought to raise an eyebrow and ask that the presumably bold assumptions about market rates, growth or company quality be justified.

Obviously, the kinds of computations we’re talking about would be quite cumbersome. Fortunately (in theory anyway), the academic community copes with the uncertainty of selling by inviting us to forget the sale and simply use an infinite-dividend-stream assumption. That’s really not so crazy since as we saw above, if we assume a sale in two years, the price will presumably reflect the future buyer’s expectations about the dividend stream he’ll receive, and so on and spot forth for all buyers in the future. Deriving a formula for the infinite-stream scenario is heady stuff for someone with my mathematical proclivities (not great). But the rocket scientists did the dirty work and handed us a formula that’s pretty simple, which is known as the Gordon Dividend Discount Model. It equates a fair price to the dividend divided by the difference between the required return and the dividend growth expectation.

• P = D/(k-g)
  • D is the Dividend
  • k is required return (the same as RR; I have no idea why the academicians call it k in this context, but I’ll go along)
  • g is the expected dividend growth rate

We Now Have Our Starting Point

P = D/(k-g). That’s it. That’s the theory of stock valuation. The good news is that the theory is just this easy.

The bad news is that you can’t actually use it to make money in the market, which probably explains why you don’t see it discussed in the financial media every day.

• We know what the dividend is, assuming the company pays one. So right away, we’ll see that we need to adapt to on-dividend paying stocks.
• We saw above how we can deal with k. We can’t compute it per se, but if we’re aware of the issues to which CAPM calls our attention, we ought to be able to come up with reasonable, albeit imprecise, assumptions.
• But g is a nightmare, a complete, total and absolute nightmare; way beyond the challenges of forecasting growth more than a month or two ahead. Suppose we assume RR is eight percent, but that expected dividend growth is 20 percent per year. Now, the expression k-g is negative, implying a negative stock price, something we know is impossible. The answer, nerdy as it is, is that the growth rate is supposed to be for now through infinity, and no company can grow 20 percent annually through infinity. We’re supposed to always assume a very low, “mature” company growth rate. Yeah. Right.

But although we don’t have a genuine plug-and-play formula, we have established the building blocks of a fair stock price, so much so that we can now pretty much interpret a lot of what we see and hear in the media and start to see that there is, indeed, an underlying logic to what goes on out there.

• We know that dividends are important and that higher dividends are associated with higher stock prices.
  • Assume k is .07 and g is .05. If D is $1, then P is $50 ($1 divided by .07-.05, or $1 divided by .02).
  • If k and g are unchanged but D is $1.50, then P is $75
• We understand that stock process vary inversely (in an opposite direction) to changers in k (which is influenced by market conditions and company risk).
  • Assume again k is .07 and g is .05. We’ve seen that P is $50 ($1 divided by .02).
  • Assume D and g the stay the same but k rises to .08. Now, P falls to $33.33 ($1 divided by .08-.05 or .03).
  • Assume D and g continue to stay the same but now, k falls to .06. P jumps to $100 ($1 divided by .06-.05 or .01).
• We recognize that that stock process vary directly (in the same direction) as changes in g, growth expectations (which is influenced by market conditions and company risk).
  • Assume again k is .07 and g is .05. We’ve seen that P is $50 ($1 divided by .02).
  • Assume D and k stay the same but g rises to .055. Now, P jumps to $66.67 ($1 divided by .07-.055 or .025).
  • Assume D and k continue to stay the same but now, g slides to .035. P drops to $28.57 ($1 divided by .07-.035 or .025).

It’s not yet perfect. We’re still talking about dividends instead of EPS, Sales, Cash Flow, EBITDA, etc. And we’re still working with the nerdy infinite growth (lower than k or else) assumption. In the next installment, we’ll expand the roster of realities with which we deal and expand what we’ve done here to discussion points that will be much more familiar.

>>Read Part 2: From Dividends To EPS – Why Stock Prices Are What They Are

>>Read Part 3: Out Of The Ivory Tower – Why Stock Prices Are What They Are