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Geoff Gannon
Geoff Gannon

DCFs and Probabilities: How to Apply Them in Practice – Not Theory

Discounted cash flow calculations and probabilities are theoretical tools that rarely have direct application in a value investor's life. They are best used to simplify and rule out certain decisions

September 23, 2017 | About:

Value investors know that – as Buffett has said – the theoretically correct way to value a company is to project cash flows from now till Judgment Day and then discount those cash flows back to the present at an appropriate rate. They also know – more from hearing Munger talk than hearing Buffett talk – that the theoretically correct way to invest in stocks is by using probabilities. Applying the ideas of “Pascal and Fermat” as Munger would say. Theoretically, playing the probabilities is the right way to make bets. And, theoretically, the value of Coca-Cola (NYSE:KO) really is the sum of the company’s future cash flows discounted back to the present at an appropriate rate.

Buffett has simplified this by saying that Aesop was right – a bird in the hand is worth two in the bush. That’s discounting. If we knew one company is earning $1 per share now and another company is earning nothing now but will earn $1.50 a share in 2023 – we should be willing to pay more for the stock earning $1 now than the stock that will earn $2 in about six years. We can see this is true by taking $1.50 and then discounting it as if it became worth less each year we have to wait. If we have to wait 6 years, we are better off getting our $1 now. The simpler way for most investors to think about this is to simply pick a number – let’s say an 8% annual growth rate – and apply it to the $1 today. We can see that $1 compounded at just 8% a year will be a bit more than $1.50 in six years. This concept of discounting is more unwieldy than I’ve made it seem here. I made it seem like you’d get a choice between $1 today and then nothing forever after or nothing till six years from now at which point you get $1.50 just once.

Reality usually works more like this…

In Company A you get $1 today and then $1.05 next year and then maybe $1.10 the year after that and so on versus Company B that earns nothing for the next six years but then produces $1.50 a share in earnings and then continues to grow at a faster rate – say 10% a year instead of 5% – for many years to come. There are analysts who run discounted cash flow models using figures like the ones I just laid out. But, they’re impractical. And I don’t think you should use them. Charlie Munger (Trades, Portfolio) has said that Buffett talks about discounted cash flows – but he’s never seen Buffett do such a calculation. Buffett’s biographer, Alice Schroeder, claims that not only does Buffett not do discounted cash flow calculations – he doesn’t use models either. He just looks at tons and tons of historical financial information, knows what his hurdle rate is, and then does some back-of-the-envelope math to see if the business will clear his hurdle rate.

So, Buffett didn’t buy Coke using a DCF and neither should you. If you’re going to value a company like Coca-Cola, you can probably know whether it’s cheap, expensive, or somewhere in between just by knowing things like the EV/EBITDA is 5, 10, or 20 times. At 5 times it’s probably cheap. At 10 times it’s probably neither remarkably cheap nor remarkably expensive. And at 20 times EBITDA, it’s probably way too expensive for you to buy. You don’t need to do discounted cash flow calculations for good businesses. You know a normal business normally trades for about a P/E of 15 or 16. So, if you see a good business trading at a P/E of 8 – you buy it. If you see a good business trading at a P/E of 32 – you don’t buy it. And if you see a good business trading at a P/E of between 16 and 32 – well, it would take a lot of research and possibly some modeling (something we know Buffett doesn’t do) to know whether you should or shouldn’t buy such a stock.

So, DCFs aren’t necessary when buying good, predictable businesses like Coke. When are they necessary?

I can think of three situations where I did discounted cash flow calculations to prove an important point to myself. One was Progressive (NYSE:PGR). A couple years ago, I picked Progressive for a newsletter I was writing. I didn’t know a lot about self-driving cars. But I did know that Progressive’s loss frequency (not magnitude, just frequency) – along with the loss frequency of other auto insurers – had been dropping for some time. Why? I looked around for an answer, and the evidence said that auto accidents had been reduced in recent years by little automatic add-ons (things once done purely by humans but now partially done by computers in some situations) already in cars. Most drivers didn’t think their cars were doing any driving on their own. But there was already a noticeable increase in safety from adding some little features like sensing if you were about to change lanes into another car. I didn’t know when truly self-driving cars would become common place on the roads – or even if self-driving cars would ever outnumber human driven cars. But, in a worst case scenario, the auto insurance industry would eventually be made pretty much obsolete by self-driving cars.

Human drivers do not – as a group – get better with time. Drivers today are as prone to error as drivers in the 1950s were. Society may convince these drivers to stop drinking or to wear seatbelts or to use back-up cameras or whatever else. But human error doesn’t get any lower over time. There’s always a new batch of inexperienced drivers entering the driving population each year. Computers are different. Even if computers started out as accident prone – or even much more accident prone than humans – they could, over the next decade or two continually improve their safety record. They could learn in a way human drivers – as a group – never can. I believed that only two things could ever kill Progressive (or GEICO). The company could make bad underwriting decisions on its own. This almost killed GEICO 40 years ago. Or, human drivers could be replaced by self-driving cars and insurance laws could change to require car owners to carry less coverage or even not to have any coverage at all.

How could I quantify this risk? It was a catastrophic possibility for the company. When you face a risk of catastrophic loss like that, do you just eliminate the company from consideration?

I didn’t think that made sense here. I can’t expect most companies to be safe and sound 15 or more years out based only on what I know today. Organizations change. I may be able to look five years into the future and see a lack of change. But most industries will face very tough competitive threats I haven’t yet imagined within, say, the next 15-30 years. Well, self-driving cars may take 15-30 years to become so prevalent they make obsolete the business model of auto insurers. And that’s if that ever happens. It’s not a certainty. But, what did I think I knew for certain?

I thought it was unlikely there would be much impact on Progressive’s results for about 15 years. I did a little research into how long a safety feature has taken in the past to go from being adopted on one new model by one new car maker to the point where most new cars have the feature. It’s several years. And then, you have to add to this how long it takes most people to buy a new car. And then, you’d have to – in this case – consider how long it might take laws to change, insurers to reduce rates as they saw changes in losses, and so forth. Overall, it seemed likely that if Progressive was going to be harmed by self-driving cars – most of that harm would come in about 2029 or beyond (I wrote this report sometime in 2014).

Here’s how I estimated the minimal haircut a self-driving-car-filled future would do to Progressive’s intrinsic value today:

“…the end of car insurance would likely be some point 15 to 30 years after the successful introduction of driverless cars. The vast majority of net present value in a stock comes from returns generated within the first 30 years. Even if driverless cars are successfully introduced in the U.S. soon – and that is a completely speculative assumption – it is very likely that auto insurance will persist as a legal requirement for car owners for at least the next 15 to 30 years. So, even if the eventual adoption of driverless cars is a certainty – the durability of car insurers as a long-term investment is still sufficient to generate good returns for today’s investors. The shift to a driverless society is far enough in the future to justify an investment in Progressive right now.”

Let’s say the S&P 500 could return 6% a year for the next 15 years, but Progressive was expected (at its 2014 price) to return 11% a year for 15 years. The cost of forgoing 5% a year in expected return for 15 years is high. In fact, you should prefer to buy $1 today that grows at 11% a year for 15 years over buying something worth $2 right now that will only grow 6% a year. Progressive had a bright 15-year future. But I couldn’t see beyond that.

However, a DCF proved that Progressive was – at about $27 a share when I wrote that report – cheap enough to make up for the possibility of a disastrous future in years 16 and beyond. Of course, you’d have to constantly re-evaluate holding Progressive as you got closer to potential catastrophe.

Today, Progressive is much less attractive as a stock because it costs 75% more than when I wrote about the stock and it has gone from being something like 15 years from potential catastrophe to now only 12 years from potential catastrophe. Obviously, those are just rough guesses. What I’m saying is that the stock’s a lot more expensive and, in addition, the likelihood of a future filled with driverless cars is now closer. I wouldn’t buy Progressive today because of this combination of higher price and shorter bright future. I can’t see any better beyond the late 2020s today than I could back then. And I can see the stock price is 75% higher. So Progressive is a worse bet today than it was in 2014.

Another stock where I applied a DCF was U.S. Lime & Minerals (NASDAQ:USLM). I was analyzing this stock a couple years ago and ran into a problem. Many resource-extraction businesses are valued on some multiple of EBITDA. Oil wells and copper mines and limestone quarries, however, all have different useful lives. If we look at the metric of “today’s production divided by the proven and probable reserves a company owns” we sometimes get a number like 15 years of production left, and we sometimes get a number like 50 years of production left. Applying a 51% probability to the “probable” reserves at U.S. Lime and adding that to the proven reserves gave me a figure that said USLM had about 50 more years of production left than other extractive companies often do. That means USLM could produce pretty much indefinitely without ever having to buy more lime deposits. A company like Exxon (NYSE:XOM) can’t do that. It needs to find or buy more oil somewhere or its production each year must decline. Without more cap-ex they will have a finite corporate lifespan. And by “finite” I don’t mean 50 years.

So what are 50 years' of limestone in the ground worth? We knew the exact tons involved here. So we could multiply the average price per ton of limestone times the deposits the company had. This would give us a ridiculously inflated value.


Because lime in the ground that is going to be sold at a rate of 2% a year is obviously worth less than the same weight of lime being sold to a paying customer today. So I did a DCF. I discounted the reserves of lime that USLM weren't going to be using in the near future. These lime deposits added a meaningful amount to my appraisal of the stock’s intrinsic value per share. But it added far less than the same amount of lime available for sale right now.

The most recent time I remember doing a DCF was for Howard Hughes (NYSE:HHC). Howard Hughes owns Master Planned Communities. Some of these MPCs own valuable residential land in places like Summerlin, Nevada. The company is going to sell this land to homebuilders at some point. When? Management gives estimates on how long it will take. So you can find the midpoint at which you’d expect abut half the land to be sold. And then you can ask yourself: How much inflation will there be in land prices between now and this future year? And, finally, you can discount this back to today.

For me, investing in something like Howard Hughes is difficult because of the discount rate used. A risk-free discount rate would be something like the 30-Year Treasury at about 3% to maybe 4% (if you expect rates to rise). Howard Hughes’ own required rate of return used inside the company would probably be something like 6% to maybe 8%. But then, my required rate of return as an investor is actually closer to 12% to 16%. That’s what I might be able to earn elsewhere over the next five to 10 years. Which rate is the correct discount rate?

To an interested buyer of the land (like a homebuilder), it’s the 6-8% rate. However, to someone like me – who is considering investing in Howard Hughes – it’s the 12% or higher rate of return I might be able to find in some other, higher-returning stock. Howard Hughes is limited to investing in land. But, I can buy stocks. If I can find stocks that will compound at higher rates than land will – then I have to heavily discount buying cheap land today versus buying a cheap stock today.

All of the valuations I came up with for the sum of the parts calculation I did for Howard Hughes used discounted values. I used something more like a 6% rate because I wanted to quickly decide whether I should eliminate the stock from consideration or keep looking. If I knew Howard Hughes didn’t look tremendously cheap with its undeveloped assets discounted at just 6% a year – then it was definitely not of interest to me (since I expect more than a 6% annual return). That test could let me kill the idea right there. I could move on to other stocks. So a DCF for Howard Hughes was a very useful “screening” tool.

This, in fact, is how you really use DCFs and probabilities in investing. You use them to quickly eliminate certain decisions. For example, I owned Weight Watchers (WTW) stock when it dropped to about $4 a share. There was a risk of bankruptcy. I got emails from people saying that if I was continuing to hold the stock – it must be because I believed the company would almost certainly not enter bankruptcy.

I said, “No. Even if I thought the stock was headed for bankruptcy, I’d still have to hold.” Why?

Well, I asked those people emailing me what price they would expect Weight Watchers shares to recover to if the company survived but never again regained its former glory. So, it survives but never thrives. And then, what if the company does regain its former profit making level? Most people said something like: “I don’t see how – if it survives at all – it would trade at less than $16 a share. And, if it got back to where it was, it’d have to be worth more than like $32 a share.” In other words, the stock would quadruple if it just avoided bankruptcy (partial recovery) and it would octuple if it got back to what it had once been making (full recovery).

Now, let’s quickly try to see if we can eliminate the idea of selling Weight Watchers at $4 a share. Let’s take an extreme position to settle the matter quickly. What if the odds of bankruptcy and a $0 stock price were 80%, the odds of partial recovery and a $16 stock price were 10%, and the odds of full recovery and a $32 stock price were 10%. In that case, you’d have $16 * 0.10 = $1.60 plus $32 * 0.10 = $3.20. So, $1.60 a share plus $3.20 a share equals $4.80 a share. We just used an approach that assumes an 80% chance of bankruptcy and no chance for the stock to ever rebound beyond $32 a share (as I write this, the stock has recovered to $43 a share).

That’s the practical use of probabilities. If I knew there was some chance the stock would be worth $0 and some chance the stock would be worth a lot more than $0 – how do I quantify that?

I just have to quickly say that even if the odds were 80% that bankruptcy would happen and 0% that anything beyond a $32 recovery would happen – you still wouldn’t have the math support the idea of you selling out at a $4 price. Doing some quick math like that would force you to face facts and hold on to a stock you believed might face bankruptcy because it was simply priced too cheap.

All calculations like this are arbitrary. You can lie to yourself mostly by picking the more flattering of: a 3-4% discount rate, a 6-8% discount rate, or a 12-6% discount rate for something like Howard Hughes or U.S. Lime’s currently unproductive (but still valuable) assets. And you can lie to yourself by plugging in probabilities that flatter Weight Watcher’s possible recovery.

How can you avoid falling victim to arbitrary assumptions?

To quickly cut through an otherwise complicated problem, you plug in extreme numbers that are within the realm of possibility but which are harsher on the stock than you would ever actually believe the situation to be. In the case of Weight Watchers, credit was not tight at that point in the financial cycle and the company probably had a Z-Score at or around 3 (1.81 to 2.99 is the “gray zone” between signaling near-term solvency versus near-term insolvency) and the F-Score was 4 (out of 9).

Those statistics on their own are not what you normally see in a company with anywhere near an 80% chance of bankruptcy and no chance of a full recovery in the stock price. So that was a very extreme assumption to make. But, that freed me up from having to do any other calculations at that point. I knew right then the stock was too cheap to sell. I had to hold till it recovered at least somewhat in price – even if I thought bankruptcy was probable. Logic dictated that course of action. And the logic used was probabilities.

If making an adjustment like using an 8% discount rate instead of a 6% discount rate or using a 55% chance of bankruptcy versus a 75% chance of bankruptcy changes the action you’re being told to take by this DCF or probability test – then just drop this approach. For a DCF to be useful it needs to give you the same answer at a bunch of different discount rates. The same is true of any probability test. If a change of 20% odds in your input gives you a different output in the sense of what decision to make – then, forget probabilities. They aren’t going to give you a clear answer in such cases. That’s because you’re never going to know the odds of bankruptcy within a positive or negative 20% margin of error. Nor are you going to know the correct discount rate for something within a positive or negative 2%. You can know if a probability is 20% or 80% and you can know if a discount rate should be 5% or 15%. Don’t fool yourself into thinking you can be much more precise than that.

Disclosures: None

Talk to Geoff about DCFs and Probabilities

About the author:

Geoff Gannon

Rating: 4.6/5 (8 votes)



Carol Nadon
Carol Nadon premium member - 1 year ago

" ... That’s because you’re never going to know the odds of bankruptcy within a positive or negative 20% margin of error. Nor are you going to know the correct discount rate for something within a positive or negative 2%. You can know if a probability is 20% or 80% and you can know if a discount rate should be 5% or 15%. Don’t fool yourself into thinking you can be much more precise than that."

Then, how to be counterintuitive with so much distortions. It's like playing darts with very low probabilities of getting near the bull's eyes.

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