Saturday, April 23, 2011

Taking Stock of Stocks: Valuation, the Academic Way

In the first post in my series on stocks, I introduced the concept of a stock:  what it is, why a company would issue it, and why an investor would by it.  At the end of that article, I promised to talk about different ways to figure out what a stock's price should be.  Originally, I was going to put it all into one single post.  However, the concept of stock valuation is so important that I decided to split the discussion among multiple posts.  In this article, I will talk about how your friendly neighborhood economics professor might determine the value of a stock.  In other words, let's go back to school and talk about a stock's theoretical value.

[Note that the ideas contained in this article are based upon my old Finance textbook:  Principles of Finance by Robert W. Kolb.]

Dividend Valuation Model:
As with all investments, its value is based upon the cash that the investment generates, taking into account the time value of money.  For instance, if I ask you to buy a bond which will return you $105 a year from now and you want to earn 5% on your money, then you would pay me $100 for that bond.  One can apply the same principle to determining the price of a stock.  What are the cash flows that a stock generates? 


A dividend is the money that a company returns to its owners.  When you buy a stock, you do so because you hope that the company whose shares you are buying is going to make a profit, and as an owner, you are entitled to a share of those profits.  When a company makes a profit, it may choose to do two things with it.  It may hold on to those profits to help pay for acquisitions, expansion, or it might put them away for a "rainy day".  On the other hand, it may choose to return those profits to its owners in the form of a dividend.  If the Board of Directors decides to give back $1 million in profits to the owners, and there are one million shares of stock outstanding, each owner would get $1 for each share of stock he or she owns.

It stands to reason that the amount you would pay for a stock is based upon how much money that stock is going to generate for you.  This is the essence of what is known as the dividend valuation model.  The dividend valuation model tells you how much a stock is worth based upon the dividends that you expect to get from the stock. 

As with all investments, you hope to earn some interest on the money you invest.  Otherwise, you might as well stick your money in the bank instead.  Therefore, you expect some rate of return when you buy a stock.  Let's call that rate of return i.  A little later, we'll discuss how to determine the value of i.  Let's take a simple case of a company which plans to return a dividend of D one year from now, and then go out of business.  That means that you would pay the following for that stock:

Price = D / (1 + i)

If D is $105 and you want to earn 5% on your money, then you would pay $100 for that stock.

Of course, this is a somewhat unrealistic example.  Most companies (hope to) stay in business forever, and keep paying dividends forever.  Now what you pay for a company that pays a dividend D1 in year 1, D2 in year 2, D3 in year 3, and so forth?

Price = D1 / (1 + i) + D2 / (1 + i)^2 + D3 / (1 + i)^3 + ... + Dn / (1 + i)^n + ...


Price = Sum t = 1 to infinity (Dt / (1 + i)^t

Basically, we are summing up the value of all of the dividends discounted based upon what we would pay for that dividend today. 

Note that the denominator gets raised to the nth power in each period.  That is because we are assuming that i is an annual rate of return.  If you get a dividend in year 2, you would want to earn 5% each year, compounded yearly, or (1.05^2) - 1 or 10.25%.  Let's say that you are getting $100 in year 2.  You would pay 100 / 1.1025 or $90.70 for that dividend assuming you want to earn an annual rate of return of 5%.  Stated another way, you pay $90.70 now and you get $90.70 times 1.05 times 1.05 or $100 in year two.

Hidden Assumptions:

While this formula sounds very exacting, in practice it is very difficult to apply.  Why is that?  Because there are two big leaps of faith that you have to make.  First, this formula assumes that you know what a company's dividends are going to be now and in the future.  Of course, this is a near impossibility.  You cannot predict what a company's profits are going to look like years in the future.  If a company hits a rough patch, it may reduce or even suspend its dividends unexpectedly.  On the other hand, a company might do better than expected and pay a larger dividend than planned.  Therefore, any values of D that you would plug into this formula is speculation.

The second assumption you need to make is the value that you choose for i.  The rate of return you choose usually reflects the riskiness of the venture.  If you've read my first article on stocks, you know that stocks are riskier than bonds, because if the company loses money and goes bankrupt, you get nothing.  Therefore, as a rational investor, you would want to compensate yourself for that risk by demanding a higher rate of return.  For example, if you can earn 5% by buying a safe investment like a bank CD or a Government Bond, you would demand something higher than 5% when you buy a stock.  The riskier the stock, the high rate of return you would like to get in return. 

For a share of a company that is stable, profitable, and is likely to stay in business for awhile, you might demand a 7% return.  It is higher than the risk-free rate of return, but not that much higher.  On the other hand, for a startup company that doesn't have a track record of making money, you might demand 10%, 15%, or even more.  You do this because there is a strong possibility that you might lose your entire investment.  Therefore, if the investment does pan out, you want to be rewarded handsomely.

What About Non-Dividend Paying Stocks?:

Many stocks, particularly young companies that are still expanding, don't pay any dividend.  Based upon the dividend valuation model, the price of the stock should be zero because you are not getting any cash from your investment.  However, we all know that non-dividend paying stocks still have a positive value on the stock market.  How can that be?  That's because investors hope, at some point in the future, that company will be stable and mature enough to be able to return money to its investors.  For years Microsoft didn't pay any dividend and its stock kept going up and up and up.  However, it finally reached a point where it no longer needed that cash to fund its growth, and it started return profits to its shareholders.

What About the Money I Get From Selling My Stock?:

The other thing astute readers will note is that the formula doesn't include the sale of the stock.  For most investors, the biggest return on investment is when the they sell the stock.  However, the sale price is not reflected in the formula anywhere.  There is a reason for that.  The price that a future investor will pay for the stock is based upon the company's future dividends.

Let's say that you plan on selling the stock in year 2 after you get the year 2 dividend.  Here is what your cash flows will look like:

Price =  D1 / (1 + i) + D2 / (1 + i)^2 + Selling Price / (1 + i)^2

Note that the Sale Price is discounted by the rate of return, because you want to earn your rate of return on the cash flow you get from the sale of the stock.  Now what should the Selling Price of the stock be?  It should be the value of the future dividends from year 3 on:

Selling Price in Year 2 = D3 / (1 + i) + ... + Dn / (1 + i)^(n-2) + ...

If we substitute this value of the Selling Price in Year 2 into the previous formula we get:

Price = D1 / (1 + i) + D2 / (1 + i)^2 + D3 / (1 + i)^3 + ... + Dn / (1 + i)^n + ...

This is exactly the same formula we stated earlier.  In conclusion, you don't need to include the selling price cash flow in the equation, because your selling price is based upon the future dividends from that point on.

Is This Valuation Method Really Useful In Practice?:

Yes and no.

Let's look at the "no" side first.  On first blush the formula gives you the sense that the price of any stock can be calculated with precision.  This couldn't be further from the truth.  Nobody can know the exact composition of future dividends.  They may grow.  They may stay stable.  They may fall.  They may disappear altogether.  We may have some sense of what dividends are going to look like.  However, if we think we can predict them with certainty, we are setting ourselves up for some serious disappointment.

Therefore, what can we glean from this formula?  There are a couple of useful observations we can make.  First is that a stock investment should be treated like any other.  The price we pay for this investment should be based upon the amount of cash we expect the investment to generate.  Stocks are no different.  Investors are often blinded by hype when it comes to investing that they pour money into stocks which have no chance of making any money (ex:  dotcom bubble).  However, if these investors remembered that a stock is only worth what type of cash flow it will generate, there wouldn't be any bubbles.

Second is that a stock's price is dependent upon its dividends and the desired rate of return investments want.  Since dividends are in the numerator, we can say that the higher the dividend, the more we should pay for the stock.  This makes sense, since dividends represent profits.  The more profits a company makes, the more valuable it is to its owners.  On the other hand, since the rate of return is in the denominator, we can say that the higher the rate of return, the lower the price of the stock.  Again, this makes sense.  If a stock is risky, we would demand to earn more of a return on our investment.  In order to do this, we would pay a lower price for that stock.  Note how the stock price of small, risky companies often is quite low, hence the term "penny stocks".

In the next installment of this series, I will talk about the fundamental analyst's model, popularized by the late Benjamin Graham.

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