2004: How do you value a company growing faster than your discount rate?

AUDIENCE MEMBER: Good morning, gentleman. My name is Tony Ado (PH) and I come from New Jersey.

Mr. Buffett, my question is on business valuation and growth. In one of your letters, you mentioned the discounting formula on earnings divided by the difference between the discount and the growth rate.

But if the growth rate is larger than the discount rate and if we use this formula, then we get a negative number. And one way around this — let’s call it method A — is to have two growth stages, one with a high growth and the second stage with a low growth.

And the second way, method B, would be to estimate how much the earnings is on the third year for the company and then multiply this by the average price-to-earning ratio to get the price in the tenth year.

I don’t know if you use the method A or method B, but if not, I would like to ask, Mr. Buffett, how do you estimate how much a company is worth if the growth rate is larger than the discount rate?

WARREN BUFFETT: Well, you put your finger on an interesting mathematical relationship. Because if you’re using a present value discount formula and you put in a growth rate that is higher than the discount rate, as you have postulated, the answer, of course, will be infinity.

And there are a lot of managements around who like to think their stocks are worth infinity, but we — (laughs) — haven’t found one yet.

That precise subject was covered in a paper called “The St. Petersburg Paradox” by a fellow named [David] Durand probably 30 years ago. And somewhere, we probably have a copy at our office. My guess, if you go to Google and you put in the name Durand and you put in St. Petersburg, you may be able to call up that article, although they aren’t necessarily terrific on old articles.

So if you’d like it, we would — if you’ll let somebody know in our office, we’ll look around a little and see if we can find that.

It gets very dangerous to project out high growth rates because you get into this paradox. If you say the growth rate of a company is going to be 9 percent between now and judgment day and you use a 7 percent discount rate, it goes off, you know, you get into infinity. And that’s where people get in a lot of trouble.

The idea of projecting out extremely high growth rates for very long periods of time has caused investors to lose, you know, very, very large sums of money.

There aren’t many companies — just take a look at the Fortune 500, go back 50 years — they’re commemorating that — and look at the companies that were there and how many have really maintained rates much above 10 percent. It’s not an easy hurdle. And when you get up to 15, you know, you’re in the atmosphere and rarified atmosphere.

So that’s — there’s a real danger in projecting out high growth rates. And Charlie and I will very seldom — virtually never — get up into high digits. You can lose a lot of money doing that.

You may miss an opportunity some time, but I haven’t seen people who have been consistently successful doing that. And you do run into this paradox you mentioned.

Charlie?

CHARLIE MUNGER: Well, you’re obviously right, when you get a mathematical result that is infinity, to back off and realize that can’t happen. And, of course, what people do is they project that the growth rate will reduce and, indeed, eventually stop. And then you get more realistic numbers. What else could anyone do?