Price on Value
April, 2001

The ABC of Value

John Price,  Ph.D.

What is the true value of a stock? Is there even such a thing as value? And if there is, can we calculate it? These are questions that we know we should try to answer but frequently we just dump them into the "too hard" basket.

A simple response to all three questions is that the worth of a stock is precisely what someone else will pay for it. From this perspective, the notion of true value is a will-o'-the-wisp that is a waste of time and energy to pursue. This view is related to the "greater-fool" theory that argues that the value of stock is irrelevant so long as there is an unsuspecting patsy who is willing to pay more.

At the other end of the spectrum are those that believe that stocks do have a value independent of immediate market activity. This is usually referred to as intrinsic value. Back in 1934 in their first edition of Security Analysis Benjamin Graham and David Dodd referred to intrinsic value as "the value which is justified by the facts, e.g., the assets, dividends, definite prospects, as distinct, let us say, from market quotations established by artificial manipulation or distorted by psychological excesses."

Let's run with this idea and see how we might be able to arrive at the intrinsic value of a stock. In situations like this I often find that a good place to start is with a simpler situation that has enough of the features of the original problem to throw light on a solution.

Some of the discussion might be a bit technical. Just try to get a general idea of what is going on. In a later article I will talk about implementation.

Bonds and discount rates

Instead of valuing a stock, suppose we are trying to value a bond. Even simpler, suppose we are trying to value a contract that says that we will receive $100 in one year's time. Start with the assumption that we can be completely certain that we will receive the payment. The first step would be to find out the rate for comparable investments. We could, for example, check the U.S. treasury rate and find that it is 5% for a one-year note. The rate of 5% is also called the risk-free rate.

An investment of $95.24 at 5% would pay $100 in a year. Since we could invest this $95.24 in a treasury note and receive $100 in twelve months, the rational price for the original contract is $95.24. This is because investing more than this does not make sense for us since we could achieve the same outcome by investing $95.24 in a treasury note. On the other hand, the person issuing the contact would not be happy with less than this amount.

The basic idea here is that to figure out how much to invest today for a guaranteed return in the future, we discount the return amount by the U.S treasury rate. In this case it means dividing by 1.05 for each year of the investment.

The next step is to allow for the fact that the return payment is not completely guaranteed. Suppose that all we know is that the best estimate of the payment is $100, but that it could be higher or lower. Now we would expect to pay less than $95.24 because we are taking on some risk. In other words, we would use a higher discount rate.

The difference between this higher rate and the U.S. treasury or risk-free rate is called the risk premium.

This is how bonds are valued. Each of the payments, whether they are quarterly, semi-annual or annual, are discounted back to the present time using a discount rate that is appropriate for the riskiness of the payments. If the bond is one that returns the face value at the end, then this amount is also discounted in the same way. The sum of all these amounts is the "intrinsic" value of the bond.

This is why riskier bonds are cheaper. Or, putting it around the other way, for the same cash outlay, you expect the coupon payments for riskier bonds to be higher than those for bonds with less risk.

You might recall the efforts of Michael Milken to persuade people to invest in "junk bonds." These are bonds that have a high level of risk and are typically priced using a discount rate 4 to 6 percentage points above the treasury rate. Milken argued that the risk of an occasional fault was more than offset by the low price and high returns.

Valuing Stocks

How can we transfer our technique for valuing bonds to valuing stocks? In An Owner's Manual that Warren Buffett sends to all new Berkshire Hathaway investors, he wrote that the intrinsic value of a stock is "the discounted value of the cash that can be taken out of a business during its remaining life."

There is an immediate parallel with bonds. The differences are that instead of discounting coupon payments, we discount "cash" and instead of the coupons running over a set period we have to allow for it to run over the "remaining" life of the business.

This leads to three questions.

Question 1. What do we mean by the cash that can be taken out of a business?

Question 2. How fast is this cash growing and for how long?

Question 3. What discount rate should we use?

The simplest answer to Question 1 is that cash refers to dividends. Obviously this does not work for companies that are expected to pay low or no dividends. Berkshire Hathaway is an excellent example of such a company. It has never paid dividends and, so long as Warren Buffett is in charge, it is unlikely that it will.

A better interpretation of cash is earnings, or earnings per share if we are working at the level of individual shares. But even this has drawbacks since earnings are the result of much accountancy processing such as making adjustments for depreciation.

The usual meaning of cash is free cash flow. This is defined as earnings plus depreciation and amortization less capital expenses. If necessary further adjustments are made for increases in working capital and tax allowances.

Note that we do not assume that the free cash flow actually gets paid directly to the investors. Rather, it is assumed that the free cash flow eventually ends up in the pockets of the investors through dividends and capital gains.

Estimating the rate and duration of growth of the free cash flow is the heart of successfully determining the intrinsic value of a stock. The three main approaches are the stable growth model, the two-stage model and the three-stage model.

The stable model assumes that the free cash flow grows at a constant rate. For how long? The standard answer is for the long term which, when inserted into the formulas, means running out to infinity. A little weird, but the formulas are simpler this way.

The two-stage model assumes that the company grows at a fast rate in an initial period and then at a stable rate after that. The three-stage model adds a transition period where the growth rate tapers from the initial rate to the long-term stable rate.

Estimating the size and duration of these growth rates uses past earnings, analyst forecasts and fundamental data. A touch of gypsy blood and necromancy is also a big help.

The third question concerns the discount rate. For Buffett it is very simple. He says that he only invests when there is no risk so he discounts using the risk-free rate. The more standard approach is to use the Capital Asset Pricing Model. For the average U.S. stock the CAPM gives a discount rate of around 4-5% above the risk-free rate.

Putting it Together

If you are mathematically inclined, or a bit of a whiz with spreadsheets, you can write formulas for the above methods. I used to do that but it was too clumsy. Every time I wanted to change something, particularly the lengths of the growth stages, then I would have to redo everything. This is the main reason why I wrote Valuesoft, a package of investment functions for Excel. One of the functions PRESVAL calculates the present value of any stream of payments using one, two or three stage growth rates.

In a later article I will give examples of how to implement the above methods for calculating the intrinsic value if stocks. Of course, once having done this, the idea is to buy stocks that are undervalued and sell them when they are overvalued. But does this always bring a decent profit? I will look at whether calculating the intrinsic value of a stock is something that we should really aim at or whether there are other approaches. ___________________________________ 

If you have any questions about this article or related topics, you can contact me at johnp@sherlockinvesting.com.