Occasionally I get questions and comments on my use of the risk-free rate (i.e. the interest rate on U.S. Treasury securities) to discount future cash flows. Such inquiries are definitely justified, seeing as my method runs counter to the discounted cash flow (NYSE:DCF) models typically taught in business programs all over the country. The standard approach specifies a “cost of capital,” which ostensibly includes a “risk premium.” Why, then, would I be satisfied using an opportunity cost equivalent to a low-yield government bond – which, of course, results in a much higher present value?
Not to appeal to authority, but this position has already been articulated by none other than the Oracle of Omaha himself. Just how exactly does Warren Buffett discount future cash flows – a key component of stock valuation? Surprisingly, this wonky topic is rarely brought up in interviews, but Buffett and Charlie Munger have sprinkled around some nuggets of wisdom over the years. Here I will review some of their comments and explain the approach in context.
False Sense of Precision
Buffett and Munger have been vocal in their criticism of academic finance. To quote one of Munger’s many famous zingers:
Munger: Some of the worst business decisions I've seen came with detailed analysis. The higher math was false precision. They do that in business schools, because they've got to do something.
Buffett followed up with a reference to Aesop, whom he frequently quotes as a font of basic investment advice.
Buffett: The priesthood has to look like they know more than "a bird in the hand." You won't get tenure if you say "a bird in the hand." False precision is totally crazy. The markets saw it in the Long-Term Capital Management [hedge fund] in 1998. It only happens to people with high IQs.
While Buffett accepts the principle of discounting cash flows, Charlie Munger says that he has never seen him perform a formal DCF analysis.
Munger: Warren often talks about these discounted cash flows, but I've never seen him do one. If it isn't perfectly obvious that it's going to work out well if you do the calculation, then he tends to go on to the next idea.
Buffett: It's true. If [the value of a company] doesn't just scream out at you, it's too close.
Source: Buffett FAQ
The value investor Joel Tillinghast advocates the use of a simple perpetual annuity formula, which shows the present value of a cash flow that stays constant forever, as a quick way of valuing a security. The equation merely consists of earnings divided by an interest rate.
The math behind discounting is not terribly complicated. The real trick is judging whether or not those cash flows will actually materialize, which is more of a qualitative exercise. This is where the science and art of investing blend together, and many high-IQ people probably find it easier to simply ignore the creative element.
Using the Risk-Free Rate
In Buffett’s view, it is foolish to account for risk by fiddling with the discount rate. For one, it only makes sense to “deal with things about which we are quite certain.” Buffett is only interested in opportunities where the probability of actually getting those future cash flows is as close to 100 percent as possible. In that case, it is appropriate to discount the cash flow using a risk-free rate.
Buffett: In a world of 7% long-term bond rates, we’d certainly want to think we were discounting the after-tax stream of cash at a rate of at least 10%. But that will depend on the certainty that we feel about the business. The more certain we feel about the business, the closer we’re willing to play. We have to feel pretty certain about anything before we’re even interested at all. But there are still degrees of certainty. If we thought we were getting a stream of cash over the thirty years that we felt extremely certain about, we’d use a discount rate that would be somewhat less than if it were one where we expected surprises or where we thought there were a greater possibility of surprises.
Moreover, using a single discount rate allows Buffett to compare the innumerable investing opportunities that cross his desk every day.
Buffett: In order to calculate intrinsic value, you take those cash flows that you expect to be generated and you discount them back to their present value – in our case, at the long-term Treasury rate. And that discount rate doesn’t pay you as high a rate as it needs to. But you can use the resulting present value figure that you get by discounting your cash flows back at the long-term Treasury rate as a common yardstick just to have a standard of measurement across all businesses.
Source: 1998 Annual Meeting
Rather than include a "risk premium" in his discount rate, he simply buys businesses at a large discount from calculated intrinsic value.
Shareholder: Following up on that other question – if you don’t adjust for risk by using higher discount rates, how do you adjust for risk – or do you?
Buffett: Well, we adjust by simply trying to buy it at a big discount from the present value calculated using the risk-free interest rate. So if interest rates are 7% and we discount it back at 7% (which Charlie says I never do anyway — which is correct), then we’d require a substantial discount from that present value figure in order to warrant buying it.
In any case, Buffett and Munger are pretty dismissive of the idea that one can even ascertain the cost of capital. Munger, in particular, has made no secret of his disdain for academia’s thoughts on the matter. Here he explains why it makes no sense to evaluate assets in total isolation:
Munger: In the real world, you uncover an opportunity, and then you compare other opportunities with that. And you only invest in the most attractive opportunities. That’s your opportunity cost. That’s what you learn in freshman economics. The game hasn’t changed at all. That’s why Modern Portfolio Theory is so asinine.
Munger: The trouble isn’t that we don’t have one [a hurdle rate] – we sort of do – but it interferes with logical comparison. If I know I have something that yields 8% for sure, and something else came along at 7%, I’d reject it instantly. It’s like the mail-order-bride firm offering a bride who has AIDS – I don’t need to waste a moment considering it. Everything is a function of opportunity cost.
Or, even more succinctly:
Munger: I’ve never heard an intelligent discussion on cost of capital.
One of Buffett's great strengths is his ability to say "no," even to otherwise attractive business opportunities. He refuses to jump into something new unless he thinks he can get even better return than what he judges as the best investment at the moment. When investors employ drastically different discount rates for different businesses, it is difficult to compare each company and ascertain which is the best buy.
Case Study: Copart, Inc.
Applying the Buffett/Munger method served me well when I looked at Copart (CPRT) last year. At the time, the company was on track to earn more than $1.60 per share for FY 2017. Copart's business model revolves around auctioning salvage vehicles wrecked in collisions and natural disasters, so its earnings are solid in both good times and bad. Therefore, the company passed the "certainty" filter with flying colors.
Shares traded at around $30 for less than 19 times earnings, which looked inexpensive for a company generating a return on equity of 30 percent. The annual report clearly explained a growth plan that revolves around infilling the U.S. market and expanding internationally. Copart also simply buys up smaller competitors and folds them into the company's existing online platform, adding instant value to the acquired firm through network effects. Using the perpetual annuity formula with a 4 percent discount rate, I quickly computed a value of $41 a share.
Once I estimated earnings 10 years out, it was clear that Copart was trading for a very low multiple of the present value of its future cash flow. Indeed, that multiple was lower than every other stock that I was considering at the time. Even though I saw other attractive opportunities in the market, I thought back to Munger's admonition to "instantly" dismiss them. Rather than dilute a great opportunity with so-so opportunities, as I had done in the past, I just kept buying Copart.
Using a higher discount rate (say, 7 percent) for Copart to account for risk also would have been a terrible mistake. The company's business risk is much lower than the average firm, so it deserves a much lower rate. Indeed, 7 percent would have given me a present value far below what the shares were changing hands for at the time.
In my first article on the company, I opined that shares were 25 - 50 percent undervalued. Since then, Copart stock is up more than 50 percent to $47 a share after the company smashed expectations for the most recent quarter.
A Few Caveats
Although Buffett has always remained modest and self-deprecating about his investing prowess, there is no question that he is a man of exceptional intelligence. In her biography The Snowball, Alice Schroeder writes how Buffett would often perform obnoxious feats of memory during his college years, frequently annoying professors by quoting long passages of their own work verbatim.
His mathematical ability is also said to be extraordinary. Robert Hagstrom describes a few choice examples of Buffett’s facility with numbers in The Warren Buffett Portfolio.
Despite what Buffett and Munger say about not needing a calculator, I do not think that most investors could be faulted for using simple spreadsheets to compute present value. The two men possess the advantage of being able to intuitively evaluate businesses based on experience, which few people can do. Not everyone can be Warren Buffett – otherwise, we would all be billionaires. Nevertheless, there is a lot to be said for eschewing the complex models and esoteric concepts that are common in academia and professional investment analysis.
So to conclude, I feel very comfortable sticking with a 4 percent discount rate. Even though the 10-year Treasury currently yields 3 percent, I hedge my bets by going with a rate that is closer to the long term average.
However, as former Fed chair Janet Yellen explained, there is a growing consensus among economists that the long run normal rate of interest may be closer to 3 percent. If that is the case, then the stock market is very cheap indeed. As long as investors plan to stay in the market and ride out any turmoil, it would be a terrible mistake to throw away fantastic opportunities by employing an arbitrarily high discount rate.
Of course, a 4 percent rate would not be appropriate for low-quality businesses. As Buffett cautions, he needs to be highly certain about earnings prospects before he is even interested in the first place. In my own investing, I try to minimize risk by identifying businesses with large moats, solid growth prospects, and strong balance sheets.
Disclosure: I am/we are long CPRT. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.