Value Investing Forum

I wrote an article on how Graham derived his formula a few years ago. I'll do some digging on my computer to see if I can find it. His factor  was derived by treasury bills and the average return on the total market up until 1936. That's where he came up with the idea of no growth. The market was averaging 8% per year and treasuries were yielding 4.41% (I believe, going off of memory). He never explained in detail, mathematically, how he arrived at his multiple but through trial and error I was confident enough that I had found out and therefore wrote an article. Essentially, it is defined, in the reverse and with an update, in Greenwald's From Graham to Buffett and Beyond. As is the case with most value investors, Greenwald diverts attention away from the discount factor even though I believe it's the single most important component to "fundamentally" valuing a business. It's been proven that one sized fits all discounts do not work and only do work when a great amount of luck is involved.

VIT, you wouldn't happen to know if Graham made any comments about where his formula came from do you? I've derived it as a simplification of the above relationship I give.

If we start with: P/E = 1/(R-G)

We can consider this to be a function of G and find the Taylor expansion of this which if I did this right (doubtful, I almost always botch a detail) it should give this:

P/E = 1/R + 1/R^2 x G + 1/R^3 x G^2 + … + 1/R^n x G^(n-1) + ….

The end terms get smaller and smaller. So you can lob off most of the end terms (there's an infinite number) and get a decent approximation.

If you want a simple formula (say a linear formula), you just lob off the nonlinear terms:

P/E = 1/R + 1/R^2 x G

So if I choose a discount rate of, say, 11.75% the formula looks like:

P/E = 8.5 + 72.4 x G

Note, my "G" is expressed as a decimal (3% = .03) so if we use 3% = 3 then we divide that 72 by 100 to get:

P/E = 8.5 + 0.72 x G.

The point of rounding up the linear term to 2 (instead of .72) would be to account for the fact that some of the terms we lobbed off weren't negligible. For example, if I use 11.75% as my discount rate and 5% as my growth rate, the first 3 terms I lobbed off would add 1.54, .655 and .279 respectively which are hardly negligible (at least the first 2 aren't negligible as far as a ballpark P/E. You can lob off the .279 and all the rest and the only add up to about .5 which isn't terrible.)

I don't know if this is how he derived it (or if he just did so via trial and error and didn't bother deriving it at all) but it does at least fit as an approximation to a simple DCF type model.

Was curious about the P/E discussion and did a quick search. Peter Lynch was talking about the PEG Ratio when he stated "The P/E ratio of any company that's FAIRLY priced will equal its growth rate." Not an advocate of Wikipedia for financial learning but it is talked about there.

http://en.wikipedia.org/wiki/PEG_ratio

So how would you practically use that P/E to growth formula? If something is trading at a P/E of 8, you assume that earnings will grow by 8% a year? But we predicate value investing on the fact that the current price paid can be way outta whack. Isn't this begging the question?

Here's a few interesting bits from Lynch's book (if you don't know Lynch, he recorded close to 30% annualized gains while managing the Magellan fund). The nice thing about reading Lynch is that (although I didn't technically do a tally) he talked far more about mistakes he made than about his successes.

That "growth" is synomous with "expansion" is one of the most popular misconceptions on Wall Street, leading people to overlook the really great growth companies such as Phillip Morris. You wouldn't see it from the industry – cigarette consumption in the U.S. is growing at about  a minus two percent a year.  [...] The key to it is that Phillip Morris can increase earnings by lowering costs and especially by raising prices. That's the only growth rate that really counts: earnings.

In general, he's fond of boring industries (or industries that don't have a standard classification) because no one else is paying attention. The hot, fast growing industries attract competition so there's a lot of "expansion" but not a lot of profit going around.

There are three phrases to a growth company's life: the start-up phase, during which it works out the kinks in the basic business; the rapid expansion phase, during which it moves into new markets; and the mature phase, also known as the saturation phase, when it begins to prepare for the fact that there's no easy way to continue to expand. Each of these phases may last several years. The first phase is the riskiest for the investor, because the success of the enterprise isn't yet established. The second phase is the safest, and also where the most money is made, because the company is growing simply by duplicating its successful formula. The third phase is the most problematic, because the company runs into its limitaitons. Other ways must be found to increase earnings.

Lynch seems to prefer the second phase the most. He does have some comments about what an appropriate multiple for P/E ought to be. He uses the rule of thumb that P/E should be the growth rate (e.g. 20 P/E ~ 20% growth in earnings). He's skeptical of growth greater than 25% and likes buying when the P/E is below the growth rate.

Lycnh also dislikes what he calls deworsification. While he acknowledges that mergers can create nice synergies, most of them (in his view) are bad. He does, however, like them on the other side when they go through some sort of restructuring (spin-off, selling off assets, etc).

There are also plenty of other good comments and interesting examples in the book.