When I first started to invest, one question that nagged me was, "How much is a stock worth?" The answer is simple -- whatever people want to pay for it. However, there are different ways to come up with a stock's worth. One in particular is the discounted cash flow (DCF). As the name implies, cash flows in the future are discounted back to the present. It's certainly not a perfect valuation tool, but it does help give us an idea of what a stock is worth.

We have to come up with a few things to do this analysis:

  • an end value of the investment
  • an expected rate of return
  • a time period

To come up with the end value, I use an expected price-to-earnings ratio (P/E). Jeff Fischer (TMF Jeff) uses free cash flow in his work, which he feels is more reliable -- there are different ways to accomplish this analysis. Anyway, let me go through the method I use.

Let's assume we have a company that is earning one dollar per share. I expect that it will see earnings growth of 15% per year for the next five years. At the end of that period, I feel its future earnings growth will drop to 10%, so I think its P/E will probably equal 10. To come up with the earnings at year five, I use this formula: $1.00 *(1.15)^5 = $2.01 per share. Figuring a P/E of 10, the stock will be selling at around $20 a share.

Assume that I want an 8% return on my investment. The stock has to be discounted back at that rate. We do this with a similar formula: $20/(1.08) ^ 5 = $13.61. If the stock is paying dividends each year, we need to discount them back, too, in the same manner and add the results. To keep it simple, I won't do that. So, to get a return of 8% on an investment that I will expect to be worth $20 in five years, I need to buy it at $13.61. If a developer were buying land she expected to sell for $500,000 in five years, and wanted an 8% return, she could use the same method. In such a case, she'd pay $340,290.

Often you see articles talking about discounting a stock against the going interest rate on the 30-year Treasury bond. This is rather misleading, because if you discounted the stock above against the current 30-year rate (5.89%), it would have quite a high value. The stock would be worth $15.02 per share. Certainly, investors would not take on the risk of buying a stock to see the same return they could get risk-free by purchasing a 30-year Treasury bond. However, many investors feel the Treasury bond rate does serve well as the expected rate of return from a stock.

My financial management text uses this formula to come up with an expected rate of return using the Treasury bond: K = Krf + (Km-Krf) * Beta, where:

K = expected rate of return
rf = the risk-free return, which is often the 30-year Treasury bond
rm = the market return
beta = the stock's beta, which is a measure of its volatility compared to the rest of the market

It may be fairly obvious by now what the weaknesses are of this method: Look at all the assumptions! I have to assume the earnings growth rate, the P/E of the investment at the end of the period (which may require yet another assumption of growth rate forward from there), and the expected rate of return. If I use the formula for the expected rate of return, I'm assuming the beta of the stock will continue to be what it has been in the past. All these assumptions make me uncomfortable.

However, the method isn't without its merits. Using it, we can see if a stock is selling fairly close to its assumed fair value. It does suggest that a number of stocks are grossly overvalued with their sky-high P/Es, since it's fairly safe to assume that most stocks won't carry triple-digit P/Es forever. Let's use our example again of the company that is making earnings of a dollar a share, and is now trading at a P/E of 200. We think it will have a P/E of 50 in five years, so how much will its earnings need to grow to make it worth a return of 15%?

Let's play with some equations here. We can take the amount invested and compound it for five years at 15%. To do that we use this equation: P * (1+n) ^ t, where P is the amount invested, n is the desired return, and t is the number of years. In five years the company must sell for $200 * (1.15)^5 = $402.27 to return 15% annually. With a P/E of 50, its earnings must be 402.27/50 = $8.04 per share.

Let's work that backwards to see how much our earnings must grow. First, we divide the earnings ($8.04) at year five by the earnings at the beginning of our investment ($1.00). So, 8.04/1.00 = 8.04 (of course), meaning our earnings have had to increase by 804% in five years. Let's annualize that to see how much that is per year. To do this, we take the fifth root of the increase and subtract one. It's basically working the compounding equation backwards.

So, let's get our scientific calculator from Windows and do the math: 8.04^1/5 � 1 = 0.5174, or 51.74% annually. That's a pretty significant earnings increase, and for many stocks this kind of growth is not sustainable. Yet, we still see the sky-high P/E values. To many of us, some stocks have pretty absurd valuations. Conversely, if you work this, you may find the "high" P/Es of some stocks are justified based on the possibilities of high earnings growth.

Warren Buffett doesn't invest in technology stocks because he doesn't feel he can accurately predict their growth. How can anyone reasonably predict the earnings growth for companies that are in markets that have never existed before? For example, when Yahoo! (Nasdaq: YHOO) went public, could we predict its growth in revenues? Nobody ever had a business like this before, and there was no way to figure what kind of market a search engine/Web portal would develop. While Warren uses this line of reasoning to avoid tech stocks, it's also another reason that it isn't possible to value many stocks, and it is just as well to invest based on other criteria (as highlighted in Rule Breakers, Rule Makers by David and Tom Gardner).

In the end, DCF is just one of the ways that we can evaluate a stock. It doesn't provide all the answers, but it can give us an idea of what we should expect to pay for our investments.

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