# An Introduction to Stock Valuation

Note: This is a technique mostly gleamed from Phil Town’s Rule #1 book. If you haven’t a clue how to come up with an estimate of what price per share a given stock should be trading at, this is as good a place as any to start. Know that most institutional investors combine multiple valuation models to arrive at buy/sell target prices.

There are a variety of techniques one can use to determine whether a particular stock is over- or under-valued. And though the movements of the stock market often seem to defy logic, at least in the short term, I thought I’d present an introductory valuation approach that you might find appealing to your logical side.

I’ll do this by example, using a stock I currently own – Tractor Supply Company (ticker TSCO) – which is currently trading at \$38.38 per share (November 30, 2008).

Introduction
Just so the newbie doesn’t get lost in the details, here’s an overview of what we’re doing. First we estimate an annual rate of growth for the company’s earnings, based on how they’ve grown in the past. Then we grow the current earnings at that rate in order to predict what the earnings will be at some future date. We then convert that future earnings-per-share into a price-per-share via the expected P/E ratio (which is also based on the past). Finally, we figure out what price we’d have to buy at today in order to reach that future price while earning our desired rate of return.

Step #1: Find current EPS
The first step is just to locate the company’s most recent 4 quarters of earnings, known as the trailing-twelve-months (TTM) earnings-per-share (EPS). We can easily grab this popular statistic from any financial website. Today I went to the Key Statistics page of Yahoo Finance and read a diluted EPSTTM=\$2.52 for Tractor Supply.

Step #2: How will earnings grow over the next 10 years?
In this step, we’re looking for an estimate of the earnings growth rate. We can get this estimate from a variety of places, but we’ll start with the stock’s historical growth rates. This MSN Money link will give you a quick overview of the past 10 years.

Looking at the most recent and most distant entries in time, we see that sales (in millions) were \$2703 in 2007, and \$601 in 1998. This is an annualized growth rate of about 18%.

Sales Growth Rate = (\$2703 / \$601)1/9 – 1 = .1818 or 18%

Next we repeat the same calculation, but this time over historical EPS instead of sales. This yields an annualized growth rate of about 21%

Earnings Growth Rate = (\$2.40 / \$0.42)1/9 – 1 = .2137 or 21%

Finally, we compute the growth rate of equity (book value per share). These historical numbers are found on a different MSN money page and show an annualized growth rate of approximately 18%.

Equity Growth Rate = (\$15.08 / \$3.43)1/9 – 1 = .1788 or 18%

We might also check in with what the analysts are predicting about TSCO’s future long-term growth rate . See the third line item from the bottom (entitled “Next 5 Years”) here. Today the average of the analysts’ predictions is about 15%.

Average of Analysts’ Predicted Long-Term Growth Rate = 15%

So of all the above 4 growth rates (18%, 21%, 18%, and 15%), which provides the best estimate as to how earnings will grow in the future? You could average them, but a good conservative choice is just to pick the minimum. This turns out to be 15%.

Step #3: What will the EPS be in 10 years?
Well if the current EPS of \$2.52 grows at our 15% for 10 years, EPS will be

\$2.52 x 1.1510 = 10.19

… which turns out to be \$10.19 per share.

Step #4: Then what will the price per share be in 10 years?
The same link we used above to find a 10-year history of BV/S also has a 10-year history of Price-to-Earnings. If we now average the 10 entries (you could also use median if there is large yearly variation, or minimum if you’re ultra-conservative) we get that TSCO’s mean P/E over the last 10 years was 16.4. Therefore we use our future EPS and future best guess at P/E to estimate what the stock will be trading at.

Earnings/Share x Price/Earnings = Price/Share
\$10.19 x 16.4= \$167

Step #5: What minimum return per year do I require earning if I were to buy this stock?
If we’re going to tie up our money for 10 years, we might as well require a good return. 15% seems well worth the sacrifice, without getting too greedy.

Step #6: What price (P) would I have to buy that stock at today to earn my minimum required return?

So we’ll arrive at that future \$167 per share price and compound our money at the desired 15% per year if we buy today at…

P x 1.1510 = \$167

so…

P = \$167 / 1.1510 = \$41.28

Step #7: What is my margin of safety?
We know that our above “fair value” estimate of \$41.28 per share if we want to make 15% over the next 10 years is just that, an estimate. Therefore investors often look for a so-called margin-of-safety, which can best be defined as a discount to the fair value.

In this case, the difference between the current price per share (\$38.38) and our maximum price we’d pay (\$41.28) means about a 7% margin of safety, which wouldn’t be enough to trigger a buy for most conservative bargain hunters (who look for something more in range of 33% to 50%).

A critical thinker can immediately come up with potential problems with the above-presented valuation technique. To pick the low hanging fruit I’ll mention three…

• Historical average P/E may be higher than future average P/E, as a company goes from a rapidly expanding start-up to a more mature, slower growing company.

• The annualized growth rates we computed are entirely dependent upon the beginning and end points of the time period over which we’re annualizing. This causes distortions if, for example, our most recent EPS was extraordinary large (due to a non-operating sale of assets or peak of cyclical cycle) and/or our most distant EPS was extraordinarily small (due to trough of a cyclical cycle or middle of a recession). A work-around may be to use linear regression to come up with a “best-fit” growth rate that weights all years equally or smooth earnings over adjacent years before annualizing.

• The minimum required return of 15% that we picked in Step #5 does not need to be fixed for all stocks. Theoretically, the more risky a stock is, the more return you should require from it for taking on that risk. So use a higher discount rate for a Russian small-cap versus a US large-cap. Alternatively, you could just require a greater margin of safety before buying.

Finally, it’s important to remember that to “beat the street” so to speak, by recognizing a bargain before anyone else does, you not only have to be correct in your estimate of future earnings, you also have to be different. Therefore you might want to skip the factoring in of other analysts’ opinion as I did in Step #2 and just trust what you come up with on your own.

## 12 thoughts on “An Introduction to Stock Valuation”

1. Anonymous says:

Your required rate of return for this stock is based on what? Why don’t you try CAPM and calculate the beta yourself with regression.

2. I had a feeling that one was coming…

I used 15% because I’m basically reproducing the valuation method from the book this came from (Rule #1) and that is what the author used.

In the book, the author is not so much after valuation in order to determine intrinsic value as valuation in order to determine max price I would pay in order to earn 15%. Perhaps it’s incorrect to refer to the latter as “valuation”.

As you pointed out, the CFA-way to estimate a required rate-of-return for intrinsic value (as I’m now just learning in Vol. 4) is to use CAPM.

As Beta is larger for more volatile stocks, your required rate of return becomes larger for these automatically. Likewise with the equity risk premium – larger for small caps, emerging countries, etc.

Using CAPM makes intuitive sense but I don’t like the equating of variability with risk, which assumes all volatility vs. the index is symmetrical. I’m also a bit uncomfortable by the fact that Beta can vary dramatically over time and hasn’t shown a sharp correlation to returns since, what was it, the 1960’s?

But for determining intrinsic value today, I probably would use CAPM as you suggested, at least until something better comes along.

Thanks for the comment.

3. yellowman says:

Vol. 4 and it is only Dec! Congrats on your pace. If my calculations are right you can average a book a month from now which will leave you with 2/3 months of solid review time.

How many hours a day or if this fluctuates wildly how many hours a week do you try and put in for studying?

4. Hi Yellowman,

I try to put in an hour a day but probably average 45 minutes instead. I’ve actually been surprised at how little time it takes to make it through each volume – reading each page and working each problem once.

But one pass is of course nowhere near enough to internalize enough to pass so I’m counting on having a few months to review well.

Hope to keep good enough notes to have a full record of all logged hours before exam day.

– Lumi

5. John - San Jose says:

Lumilog, good write up on Rule #1 investing. I’ve being using this strategy for a couple of years now. For a quick way to gauge price vs. intrinsic value, rule #1 is great.

I want to add a few things to your write up, if you don’t mind.

1) When using this strategy, your confidence level won’t be as great relative to using the standard DCF valuation. As soon as you purchase your desired stock, there will be sleepless nights. Because of this, you might start to second guess 1) the method 2) your input numbers ie.. 15% of Req of Rtrn 3)Yourself (not good as a confidence builder).

So what will you do then? Revert back to DCF valuation. Or stick to Indexing.

When Markets are going up, the above scenario might not occur (sleepless nights). Because all strategie during a bull mkt. are good strategies.

It’s when we have a bear mkt that we find out if our strategy is any good.

From my experience, the best strategy is to FULLY understand the company you will invest in. Picture yourself as the CEO. Analyze every line in the Fin. Stmnt. Analyze competition, industry trends, vendors/suppliers, Customer wants and needs. More importantly, invest in a company you would be interested in running/owning, and that you can fully, easily understand. So, a G.E is out of the question for an avg. investor. Unless, you think you can run the many divisions of G.E.

Even if you have to invest in just ONE company, it’s a good start. As a matter of fact, for an avg. investor, probably the best way to invest, is to start with 1 or 2 stocks. Gradually increase your holdings or find other firms. But do not invest more than 5 companies at a time. You will not have time to go through all the readings of the 10k and other reports. Think of the entrepreneur who risk quitting their day job to start a small business. That’s how an avg. investor should think, except the quitting the job part. You might be best serve writing a business plan for the Company you want to invest in. Once, you have determined that it is safe to invest, I would do what Warren Buffett does, GO BIG, ALL IN, if you have too. Charlie Munger once commented that Berkshire was really built on no more than 10 decisions (investments)! That would be Coke, Americ. Express, Washington Post, Geico, I forget the rest…

If you don’t think you can run the business (not day-to-day ofcourse) or understand it’s many facets, then indexing is the way to go. And at times like we have now, learn how to hedge your bets with options. Good Investing to ALL!

6. John – thanks much for detailed comment. And it echoed what I was reading this morning in my latest library find, Trade Like Warren Buffett by James Altucher.

To paraphrase, in a study looking at mutual fund returns over 1984-1999, the conclusion was that actively managed, but highly concentrated portfolios tended to perform better than funds with diversified portfolios. What’s more, the they tended to outperform the market too, despite previous findings that actively managed funds in general, underperform the market.

This is attributed to the “information advantage” that the concentrated portfolio manager has – able to closely track and understand the businesses of his few holdings. No chance in doing that with a 200-stock diversified portfolio.

And that was a good reminder for me on GE. I tend to equate old, large-cap businesses with being easy to understand. Not always so.

– Lumi

7. Thibaut says:

Lumi,

Could you point me to the study on highly concentrated portfolios you’re talking about? Studies usually point out that actively managed portfolios don’t beat the market over the long run…

Thanks!

Thibaut

8. Hi Thibaut,

Here is some information that I hope will steer you toward what you’re looking for.

First, my source for this is Trade Like Warren Buffett. In chapter 2 the author says that Buffett’s investing style is a mixture of Philip Fisher and Ben Graham. But Fisher advocated a “focused” portfolio of just a few stocks you can easily follow, research and manage, whereas Graham-Dodd advocated more extensive diversification.

Which does Buffett subscribe to? To answer that, the author reprints a famous Buffett quote:

“Wide diversification is only required when investors do not understand what they are doing.”

The author goes on to say that there are two excellent books on the value of such “focused” portfolios and lists these two by Hagstrom:

Finally, he says that academic research in this area received a boost from the following paper:

“On the Industry Concentration of Actively Managed Mutual Funds”, by Clemens Sialm, Lu Zheng, and Marcin Kacperczyk, Journal of Finance, 2005

If you google the paper title, you’ll come across a few links with the PDF.

Below is the abstract:
Mutual fund managers may decide to deviate from a well-diversified portfolio and concentrate their holdings in industries where they have informational advantages. In this paper, we study the relation between the industry concentration and the performance of actively managed U.S. mutual funds from 1984 to 1999. Our results indicate that, on average, more concentrated funds perform better after controlling for risk and style differences using various performance measures. This finding suggests that investment ability is more evident among managers who hold portfolios concentrated in a few industries.

The abstract does not detail conclusions about beating the market as a whole, and perhaps suggests that “focused” does not mean few stocks, but few industries. But this seems to be the main source that the author is citing. If you read the whole 50-page PDF, I’d be interested to know your conclusions!

-Lumi

9. momo says:

doesn’t being conservative mean using a higher P/E ratios ?
higher P/E’s mean high stock priced companies relative to earnings, so how is using minimum P/E is being conservative? or am I wrong?

and about the growth rate, shouldn’t we look how the growth for a specific company is? (linear,avg,exp.) and then try to forecast upcoming growth, to be more reliable on data.

Just my thoughts!

10. hey momo,

we’re trying to be conservative with respect to what we can sell the stock for 10 years from today.

if future estimated earnings per share is \$2.00 and future P/E is 20, someone will buy our shares for \$40 each. but if that future P/E is a lower 15, then the market would only give us \$30 per share.

regarding estimating the growth rate, there are of course a large variety of ways to do this and you should use what you trust! the CFA program teaches a sort of top-down approach (what is the economic outlook for this region of the world, this industry in this region of the world, this sector of this industry in this region of the world, …).

but i don’t consider myself a good enough economist (yet) to trust my economic forecasts. so i do as i believe you’re suggesting, compute a “best-fit” curve over the historical data and extrapolate it out to the future. and i tone down the growth rate a bit if the historical computes out to be something i think is unreasonable, like 45%.

– lumi