Over the years, Warren Buffett (Trades, Portfolio) has written and talked extensively about the ways he goes about assessing the intrinsic value of a business. He generally relies on simple formulae and easy-to-follow heuristics, rather than needlessly complicating the issue with advanced computations. These formulae work quite well in most cases; however, there are instances in which they seem to break down. At the 2006 annual Berkshire Hathaway (BRK.A,)(BRK.B, Financial) investor conference Buffett was asked about just one such case.
High growth rates
Buffett’s preferred method for calculating the intrinsic value of a business is as follows: divide owner earnings by the difference between the discount rate and growth rate. Eagle-eyed scholars of mathematics will note that if the growth rate is higher than the discount rate, the number generated by this simple formula would be negative, an obvious nonsense result in terms of applied finance, which seems to suggest an infinite valuation. What is the problem?
“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% between now and judgement day and you use a 7% discount rate it goes off into infinity. That’s where people get into a lot of trouble. The idea of projecting out extremely high growth rates for very long periods of time has caused investors to lose very, very large sums of money ... Charlie [Munger] and I will very seldom, virtually never get up into high digits. You may miss an opportunity sometime, but I haven’t seen people who have been consistently successful doing that.”
The paradox the Buffett is referring to is Daniel Bernouilli’s St. Petersburg paradox. It describes a lottery game in which a player flips a coin and is paid $2 if it lands on heads. Thereafter, each subsequent heads doubles the amount, and the game continues until tails comes up. The question is: how much should the player pay for the right to play the game?
Probability theory states that the player should pay an infinite sum of money to compete, because the expected payoff tends to infinity. From a common-sense perspective, this seems nonsensical, and so the St. Petersburg paradox is used to describe the divergence between what the mathematics dictates and what a real-life person would do in this situation.
Don’t mistake the map for the territory
There are many detailed and interesting attempts to reconcile this paradox, which are unfortunately outside the scope of this piece. However, note the similarity between the lottery game and our hypothetical growth stock -- in both cases there is a clear disconnect between what common sense and mathematics dictate. What does this mean?
It means that when using formulae and heuristics, we must always remember that not every method is equally applicable in every single scenario. Discount formulae can provide very good approximation for the intrinsic value of fixed-income securities, and even some slow-growing equities. But when it comes to high-growth enterprises, we may need a new set of tools.
Disclosure: The author owns no stocks mentioned.
