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-earningsratio (P/E). Jeff Fischer (TMF Jeff) uses free cash flow in his work,which he feels is more reliable -- there are different ways toaccomplish this analysis. Anyway, let me go through the method I use.
Let's assume we have a company that is earning one dollar pershare. I expect that it will see earnings growth of 15% per year forthe next five years. At the end of that period, I feel its futureearnings growth will drop to 10%, so I think its P/E will probablyequal 10. To come up with the earnings at year five, I use thisformula: $1.00 *(1.15)^5 = $2.01 per share. Figuring a P/E of 10, thestock will be selling at around $20 a share.
Assume that I want an 8% return on my investment. The stock hasto 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, weneed to discount them back, too, in the same manner and add theresults. 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, Ineed to buy it at $13.61. If a developer were buying land she expectedto sell for $500,000 in five years, and wanted an 8% return, she coulduse the same method. In such a case, she'd pay $340,290.
Often you see articles talking about discounting a stock against thegoing interest rate on the 30-year Treasury bond. This is rathermisleading, because if you discounted the stock above against thecurrent 30-year rate (5.89%), it would have quite a high value. Thestock would be worth $15.02 per share. Certainly, investors would nottake on the risk of buying a stock to see the same return they couldget risk-free by purchasing a 30-year Treasury bond. However, manyinvestors feel the Treasury bond rate does serve well as the expectedrate of return from a stock.
My financial management text uses this formula to come up with anexpected rate of return using the Treasury bond: K = Krf + (Km-Krf) *Beta, where:
K = expected rate of returnIt may be fairly obvious by now what the weaknesses are of thismethod: Look at all the assumptions! I have to assume the earningsgrowth rate, the P/E of the investment at the end of the period (whichmay require yet another assumption of growth rate forward from there),and the expected rate of return. If I use the formula for the expectedrate of return, I'm assuming the beta of the stock will continue to bewhat it has been in the past. All these assumptions make meuncomfortable.
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
However, the method isn't without its merits. Using it, we can see if astock is selling fairly close to its assumed fair value. It doessuggest that a number of stocks are grossly overvalued with theirsky-high P/Es, since it's fairly safe to assume that most stocks won'tcarry triple-digit P/Es forever. Let's use our example again of thecompany that is making earnings of a dollar a share, and is now tradingat a P/E of 200. We think it will have a P/E of 50 in five years, sohow much will its earnings need to grow to make it worth a return of15%?
Let's play with some equations here. We can take the amount investedand 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, itsearnings 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 atthe beginning of our investment ($1.00). So, 8.04/1.00 = 8.04 (ofcourse), meaning our earnings have had to increase by 804% in fiveyears. Let's annualize that to see how much that is per year. To dothis, we take the fifth root of the increase and subtract one. It'sbasically 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 significantearnings increase, and for many stocks this kind of growth is notsustainable. Yet, we still see the sky-high P/E values. To many of us,some stocks have pretty absurd valuations. Conversely, if you workthis, you may find the "high" P/Es of some stocks are justified basedon the possibilities of high earnings growth.
Warren Buffett doesn't invest in technology stocks because he doesn'tfeel he can accurately predict their growth. How can anyone reasonablypredict the earnings growth for companies that are in markets that havenever existed before? For example, when Yahoo! (Nasdaq: YHOO)went public, could we predict its growth in revenues? Nobody ever had abusiness like this before, and there was no way to figure what kind ofmarket a search engine/Web portal would develop. While Warren uses thisline of reasoning to avoid tech stocks, it's also another reason thatit isn't possible to value many stocks, and it is just as well toinvest based on other criteria
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 whatwe should expect to pay for our investments.
