Wednesday, August 19, 2009

Discount Rate

In business school, many learn the risk-free rate (long-term Treasury rate) plus a risk premium should be used to determine the proper discount rate.

If there's more risk, the use of a higher discount rate should account for that risk. Sounds harmless enough so far, right? Here's where it becomes a bit less so. Somehow, a stock's volatility or beta (fluctuation compared to a benchmark) is supposed to be a proxy for risk. Well, at least it is based upon what seems a highly flawed model.

No doubt more than a few who went to business school have carried this way of thinking into their business and investing endeavors.

Yet Warren Buffett has said he believes none of this makes any sense. So what rate does he use to discount the future cash flows of an investment?

The long-term U.S. Treasury rate.*

"Don't worry about risk the way it is taught at Wharton. Risk is a go/no go signal... We don't discount the future cash flows at 9% or 10%; we use the U.S. Treasury rate. We try to deal with things about which we are quite certain. You can't compensate for risk by using a high discount rate." - Warren Buffett at the 1998 Berkshire Hathaway (BRKa) Shareholder Meeting

"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." - Warren Buffett at the 1998 Berkshire Hathaway Shareholder Meeting

"...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." - Warren Buffett at the 1997 Berkshire Hathaway Shareholder Meeting

To me, the Buffett way of thinking not only makes more sense, it's also less complex and more useful.

Complexity is fine if it's warranted; it's fine if it has some incremental utility.

So the idea is to use one discount rate to create a "common yardstick" across different investments, calculating present value using that discount rate, then buying at a substantial discount to that present value to create a margin of safety.

Note that there's no real attempt to quantify risk in the process.

There is no shortage of ideas, formulas, and theories that are more or less directly related to the efficient market hypothesis. The capital asset pricing model (CAPM)** is just one good example. Charlie Munger thinks the creation of such a model comes down to, at least in part, what he calls "physics envy":

"Well, Berkshire's whole record has been achieved without paying one ounce of attention to the efficient market theory in its hard form. And not one ounce of attention to the descendants of that idea, which came out of academic economics and went into corporate finance and morphed into such obscenities as the capital asset pricing model, which we also paid no attention to." - Charlie Munger Speech at UC Santa Barbara

Then, later in the speech, Munger talked about nine different categories of things wrong with economics. Here's what he says is the third weakness:

"The third weakness that I find in economics is what I call physics envy. And of course, that term has been borrowed from...one of the world's great idiots, Sigmund Freud. But he was very popular in his time, and the concept got a wide vogue.

One of the worst examples of what physics envy did to economics was cause adaptation and hard-form efficient market theory. And then when you logically derived consequences from this wrong theory, you would get conclusions such as: it can never be correct for any corporation to buy its own stock. Because the price by definition is totally efficient, there could never be any advantage. QED. And they taught this theory to some partner at McKinsey when he was at some school of business that had adopted this crazy line of reasoning from economics, and the partner became a paid consultant for the Washington Post. And Washington Post stock was selling at a fifth of what an orangutan could figure was the plain value per share by just counting up the values and dividing. But he so believed what he'd been taught in graduate school that he told the Washington Post they shouldn't buy their own stock. Well, fortunately, they put Warren Buffett on the Board, and he convinced them to buy back more than half of the outstanding stock, which enriched the remaining shareholders by much more than a billion dollars." - Charlie Munger Speech at UC Santa Barbara

CAPM adjusts the expected return based upon a stock's volatility or beta. The expected return minus the risk-free rate is the risk premium.

To me, this way of thinking about risk and return has major defects.

The end result of all this is a discount rate (or expected return) based upon a risk premium that gets added to the risk free rate. Now, some would view CAPM as insufficient for companies with debt because it doesn't take into account the capital structure. That leads, unfortunately, to things like weighted average cost of capital (WACC).

Well, feel free to explore how to calculate WACC.

The WACC formula attempts to take the capital structure of a business into account.

It's also, if not exactly useless, closer to being useless than not as far as I'm concerned.

So the rates calculated via formulas like this are intended to then be used for discounting whatever the expected cash flows of a business might be.

Unwarranted complexity that is more than just a bit less than satisfactory and adds little to zero insight.

Exchange Between Charlie Munger & Professor William Bratton

The following pretty well captures how Buffett and Munger think about cost of capital:

Buffett: Charlie and I don't know our cost of capital. It's taught a[t] business schools, but we're skeptical. We just look to do the most intelligent thing we can with the capital that we have. We measure everything against our alternatives. I've never seen a cost of capital calculation that made sense to me. Have you Charlie?

Munger: Never. If you take the best text in economics by Mankiw, he says intelligent people make decisions based on opportunity costs -- in other words, it's your alternatives that matter. That's how we make all of our decisions. The rest of the world has gone off on some kick -- there's even a cost of equity capital. A perfectly amazing mental malfunction. - From the 2003 Berkshire Hathaway Shareholder Meeting


I'm guessing one of the reasons these flawed ideas have remained popular for so long is simply because so many business executives and investors have been taught -- and continue to be taught -- this stuff in business school.

An investor can still decide to use a slightly higher discount rate than the U.S. Treasury rate in order to add a margin of safety. A higher rate may make sense if the investor views the current risk-free interest rate environment to be unusually low and unlikely to be sustainable. Buffett has said as much:

"We don't think we're any good at predicting interest rates. But in times of what seem like very low rates, we might use a little higher rate." - Warren Buffett at the 1996 Berkshire Hathaway Shareholder Meeting

Using a higher rate when somewhat less certain about the future stream of cash an asset will generate over time -- I say somewhat because there's a threshold of uncertainty about future cash flows above which no margin of safety will be sufficient -- can also make some sense. Buffett apparently even indicated that he does this on occasion at the 1994 shareholder meeting.***

"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." - Warren Buffett at the 1994 Berkshire Hathaway Shareholder Meeting

So there's more than one reasonable way to decide what the discount rate should be.

It's just that the higher discount rate need not be adjusted based upon beta, capital structure, or any similarly formulaic approach. The formulas may provide a false level of precision that likely means little if anything in terms of real risk and uncertainty.

My own preference is to have a "common yardstick" to compare investments at any point in time -- using, as a baseline only, likely long-term U.S. Treasury rates knowing that ultimately it is impossible to predict the inevitable and unknowable fluctuations -- then paying a price that provides enough margin of safety (i.e. something comfortably below my estimate of per share intrinsic value) based upon my best judgment of the specific risks and uncertainties of the investment.
(The yardstick to be used can be altered based on changes to likely future long-term U.S. Treasury rates, of course, but comparisons between alternatives at any point in time should be made with the same yardstick.)

In any case, it's likely unwise -- considering the range of interest rates over the past half century or so -- to assume prevailing interest rates will always remain low.

The process of estimating value is inherently and necessarily rather imprecise. It's highly unlikely that any two investors will come up with the same estimate of value. Some of the more formulaic approaches at least imply that precision can exist where it cannot.

Factors that are not easily quantifiable need to be considered carefully.

Eventually, an assessment of the risk and uncertainty should result in a go/no go decision. It should not result in the use of a higher discount rate to compensate for that risk and uncertainty.

At some point, no discount rate is high enough.

Buffett has said he does most calculations in his head and is wary of "false precision". As a result, with many investments, he doesn't rely on exact numbers. It's telling that Munger claims Buffett never actually does these calculations. It's also telling that Buffett agrees with him.

Charlie Munger (Berkshire Hathaway's vice chairman) said, "Warren talks about these discounted cash flows. I've never seen him do one."

"It's true," replied Buffett. "If (the value of a company) doesn't just scream out at you, it's too close." - from the 1996 shareholder meeting

No matter how one decides to calculate value it's best to keep it simple but meaningful. More importantly, accept that risk and uncertainty is not easily quantifiable.

The discount to estimated value should be quite large and obvious.

Sound qualitative judgments must be made.

Adam

Long BRKb

* I posted this fair value calculator on Tuesday. It's another convenient tool for calculating value that is, like all others, only as good as the assumptions used. The use of Treasury rates to calculate present value for stocks is not at all the widely accepted practice. The norm, more or less, would still be to add a risk premium into the equation. Well, unfortunately, risk just cannot be accounted for via a simple adjustment like this in my view. If only it were that straightforward.
** According to CAPM, expected return is supposed to come from multiplying beta by the difference between the expected return of the market and the risk free rate then adding that number to the risk free rate:

Ra = Rf + β(Rm-Rf)


Ra = Expected Return
Rf = Risk Free Rate
β = Beta of the Security
Rm = Expected Market Return

That, somehow, (well, if you buy this stuff) is supposed to produce the expected return on the asset. Well, at least that's the case when beta is actually available. Of course, in the real world -- for many investments -- there is no observable beta. In my experience this is, at best, mostly an interesting academic exercise. Usually, the discount rate that ends up being used is still a guess within a range depending on perceived risk. Ugh. It's simply calculated in a falsely precise manner. To me, it's a waste of time and energy. My preference is to just discount using the U.S. Treasury rate then separately make a judgment on investment specific risks and uncertainties.
*** The fact that Buffett may vary the discount rate based upon his level of certainty can possibly be a bit confusing, if not seemingly inconsistent, with his "common yardstick" and related comments. To me, he's still mostly saying a similar thing. That an investor can't account for risk simply by increasing the risk premium and there's no formulaic way to determine the right discount rate. A higher discount rate just creates some additional margin of safety when somewhat less certain. It's not a formulaic adjustment; it's instead, meant to be meaningful, rough, yet more or less subjective. It's also worth remembering that, unlike the shareholder letters, these are comments made on the fly at the shareholder meetings and may or may not be exact quotes. The comment from the 1994 meeting is still worth noting since it is not quite the same as comments he's made on the same subject at other times.
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