If you pay too much for a stock, your return on investment won’t be satisfactory. In the AAII world of Shadow Stocks—companies with some history of growth, little or no dividend yield and a small amount of the stock outstanding owned by institutions—you hope to profit mainly through appreciation in the price. You expect that earnings will grow over time and that later on you can sell the stock to someone else for more than you paid for it. The key word is “expect.” Optimistic expectations can lead you to pay a share price that turns out to have been unrealistically high. The key question, then, is: What is a reasonable price?

Let me suggest one method of pricing. But first, let me comment on a theory of valuation which I don’t recommend. This theory says that a stock is worth the present value of all its future earnings. I have found this idea useless in trying to establish an acceptable price for the shares of a company with growing earnings. It frequently turns out that the projected earnings, even after discounting, keep increasing, and you never know when to stop adding them up. So, the indicated price just keeps getting bigger. The system works fine for looking over a history of actual earnings, so that you could determine what would have been an acceptable price at the beginning of the history, but that doesn’t help you now.

In fact, when you want to sell the stock, it will be exactly what someone will pay you for it—no more and no less. So, you have to guess what a stock of its type will be going for.

In order to help decide whether or not to pay today’s going price for a stock, investors should calculate the estimated return on investment based on the following:

- today’s price,
- today’s price-earnings (P/E) ratio,
- the price-earnings ratio five years from now, and
- the annual earnings growth rate for the next five years.

The formula for this is derived in the **accompanying box**, and the equations in it are used in the explanation below. To see why this method is useful, let’s look at some examples.

In the simple situation where the price-earnings ratio doesn’t change over the five years, your return on investment will exactly equal the growth rate in earnings. For example, XYZ is a fast-growing company. It just earned $1 per share, it has a five-year record of growing earnings, and its stock is selling for $25 per share; that puts the P/E at 25/1 = 25. At a growth rate of 20% per year, earnings five years from now (see **Equation 4**) will be:

$1.00 × (1 + 20/100)^{5} = $2.49 per share

At a price-earnings ratio of 25, I could sell the stock for 25 × $2.49 = $62.25 in five years. Since XYZ didn’t pay any dividends, my return on investment would be 1% from the appreciation of $25 to $62.25. The annual compound rate of return (see **Equation 1**) would be:

The example, though, assumes that the price-earnings ratio will be the same in five years. And it illustrates the point that you’re in danger of paying too much for a stock if the price-earnings ratio is high when you buy it and low when you sell it.

Price-earnings ratios decline for several reasons, such as:

- The earnings haven’t grown as fast as anticipated.
- The company has grown—price-earnings ratios tend to be smaller for larger companies.
- The supply of stock has grown.
- Investors believe other investments will yield more.

The price of a stock five years from now can be estimated simply by multiplying the expected annual earnings by the expected price-earnings ratio. For XYZ, you might want to know what the price and your return on investment would be if the price-earnings ratio was not today’s 25, but only 15 when you decided to sell. The answer, using equation 3: P = 15 × $2.49 = $37.35. The return on your $25 investment over five years would then be only 8%, quite a comedown from the 20% per year by which earnings are supposed to grow.

In this case, $25 may be too high a price to pay for the stock of XYZ. How about $20? Selling out at $37.35 in five years would bring you appreciation at the rate of 13% per year.

It’s possible, of course, that you may underestimate the price-earnings ratio five years out—a rarer error. Suppose XYZ was the investor’s dream: After five years, it seems capable of growing just as fast—the public’s appetite for the stock is even greater, the company refrains from issuing more shares and the price-earnings ratio goes to 35. You could sell for 35 × $2.49 = $87.15, achieve a rate of return of 28% annually and experience the joy of expanding multiples.

Perhaps you’re ready to try this method of pricing by now, but you don’t have a dandy exponentiating calculator to produce the earnings projections and return numbers as I have done in the examples and in the equations. I’ve made up a table so that you can calculate the return just by multiplying and adding. Here’s how it works:

- Estimate the percentage growth rate in earnings per year. Example: 20% per year
- Add 100. Example: 20 + 100 = 120
- Estimate the price-earnings ratio five years from now. Example: P/E in five years = 15×
- Find the factor in the
**table below**for your current P/E and the expected P/E five years from now: Example (assuming current P/E of 25): 0.90 - Multiply the number from the table by the growth rate plus 100 (from #2 above). Example: 0.90 × 120 = 108
- Subtract 100 to get the return. Example: 108 – 100 = 8% per year expected return on investment

If you start playing around with the table, doing expected return calculations for different possibilities, you may run into some results that startle you. Let me anticipate a few questions that may come up.

*Can the answer be a negative expected return?* You better believe it. The earnings growth hasn’t been enough to overcome a decline in the price-earnings ratio.

*Do you expect earnings to decline?* No problem—just plug in the negative growth rate. Perhaps you judged that the price-earnings ratio will deteriorate. Try an earnings decline of 20% per year, for example, and a P/E dropping from 20 currently to 10 in five years.

Result:

ROI = 0.87(–20 + 100) – 100 = –30% per year.

On the other hand, perhaps the price is already low and the multiple may expand. Would an increase in the price-earnings ratio from a current 5 to 10 in five years be enough to offset the earnings decline of 20% per year?

ROI = 1.15(–20 + 100) – 100 = –8% per year. Answer: No.

*Does the firm have negative earnings or no earnings?* Consider using a sales-based instead of an earnings-based projection, as suggested by Kenneth Fisher in his book “Super Stocks” (Dow Jones-Irwin, 1984; reissued 2007) to value companies that are losing money now but may become profitable.

The computation described here will work if the growth rate in sales per share is substituted for that of earnings per share and if the price-sales ratio is substituted for the price-earnings ratio. Price-sales ratios are usually smaller than price-earnings ratios, so use the row and column labels as if they were 10 times too large. Example: Suppose the price-sales ratio now is 2, and in five years it will be 1. Use the row labeled 20 and the column labeled 10 to get the factor 0.87 from the table. The factor is combined with the growth rate in sales per share, say 20% per year in this case, to obtain a return on investment:

ROI = 0.87(20 + 100) – 100

= 4.4% per year expected return.

May you avoid overpriced stocks and find underpriced ones.

## The article was written by AAII member C.R. McEwen for the October 1986 issue of the

AAII Journal.

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