Friday, 12 July 2013

Valuation - The Discount Rate

While I said that this post would be my last about valuation for the time being, as I was halfway through writing it I realised I would only have space to talk about the discount rate here, lest this turn into a long boring essay (I'm afraid it has). So I promise that my next post will be the last. It will also be the last for a while, as I'll have my trial HSC tests coming up. Without further ado, here it is:

As I covered earlier, DCF valuations are quite sensitive to the cash flows that an investor projects. They are also very sensitive to the discount rate, or interest rate used, so getting both right is important to coming up with an intrinsic value. Unfortunately, I don't know what the proper discount rate to use is for each and every business so I can't come up with a proper intrinsic value, but that doesn't rule out the usefulness of DCF analysis for me. Let me explain...

Depending on who you listen to, experts will either tell you that the discount rate should be 'risk free rate' (due to their low perceived risk, long-term government bonds are usually taken as a proxy), or more commonly they'll say that the discount rate needs to incorporate a 'risk premium' on top of the risk free rate (to compensate investors for the extra risk in buying assets such as shares). Determining the risk free rate is quite easy - according to Bloomberg the yield on Australian government bonds for a 15 year maturity is currently around 4.2%. But the risk premium isn't so conveniently found through a Google search. 

In the 1960s, finance academics attempted to overcome this issue (not that they had Google) of the lack of an easily calculable discount rate, and came up with the capital asset pricing model, or CAPM for short. Basically, the CAPM's risk premium is the market premium (or equity premium in the case of stocks) multiplied by the beta of the asset. In my opinion, the first number is on shaky ground, while the second is downright useless for the purposes of valuation. I've read quite a few papers that attempt to estimate the equity premium - which is the excess return of the stock market over the risk free rate - from historical results and get the impression that it isn't as simple as it would seem. Depending on what timeframe you select, whether you use an arithmetic or geometric mean, and whether you include franking credits, Australia's equity risk premium seems to be anywhere from 2% to 7% (it also differs country to country). That's too large a range to be useful in accurately valuing stocks. Some argue that a forward looking equity premium is a better way to do it, but as with most forward looking estimates, they too are subject to wide variations. And others argue that it doesn't even exist at all (see here). 

But even if you look past the dubious nature of the equity premium, it is the inclusion of beta that really ruins the CAPM. Since not all stocks entail the same level of risk, the CAPM attempts to quantify the risk of a particular stock through its beta. You can find this number for any stock quite easily on most financial websites. Beta is calculated by measuring how volatile the share price of an individual stock is when compared to the stock market as a whole. A beta below 1 indicates a relatively steady share price in comparison to the market and thus is less risky, while a beta above 1 signals more volatility and more risk. 

As I explained in my earlier post, How Many Baskets? measuring the risk of a business through its share price volatility just doesn't make sense at all. Every successful value investor knows this is obvious, take Seth Klarman who wrote in his book Margin of Safety: 'I find it preposterous that a single number reflecting past price fluctuations could be thought to completely describe the risk in a security. Beta views risk solely from the perspective of market prices, failing to take into consideration specific business fundamentals or economic developments. The price level is also ignored, as if IBM selling at 50 dollars per share would not be a lower-risk investment than the same IBM at 100 dollars per share.' And he goes to point out more flaws about beta but I hope you can see that it is not a measure of business risk at all. The whole foundation of the CAPM is deeply flawed too, relying on plainly unrealistic assumptions from the efficient market hypothesis (EMH) - for example, that every investor is always rational and risk averse, taking into account all possible information available at the same time as everyone else. Any of the countless financial bubbles and crashes in human history indicate otherwise. 

And can you believe that three of the men that devised the CAPM won the Nobel Prize in Economics for it? Furthermore, the CAPM and EMH are still taught as financial theory in business schools all over the world today. I can see why this is so - when mathematically gifted people turn to the field of economics, they naturally want to come up with elegant, precise formulas just like physics but eventually get carried away with this ambition and end up neglecting reality. As a final potshot at the CAPM, James Montier, author of Behavioural Investing, has suggested that the CAPM be renamed CRAP for 'completely redundant asset pricing'. I wholeheartedly agree. 

After that long rant about the popular CAPM explaining why it should be laid to rest, it's about time I got around to how I approach the discount rate. For DCF valuations I currently use two methods in tandem:

1. I use a single discount rate across all stocks which very roughly incorporates the risk free rate and an estimate of the equity premium. If you were to only discount cash flows at the current risk free rate of 4.2%, just about every stock would seem grossly underpriced, so I justify using a higher rate by fuzzily thinking that the additional amount needed for reasonable valuations must be the equity premium. In the present low interest rate environment, I'd be inclined to use a discount rate around 9 or 10% (yes this is very arbitrary but it doesn't really matter as I'll explain). Of course, using the same discount rate across everything doesn't adjust for the different risk of each stock, so I attempt to incorporate this risk through my projections of the business' future - I use more conservative assumptions for businesses I deem to be risky. Getting a feel for this risk is something that must be learned through practice (and I am still very much learning) but things such the business model, competitive landscape, debt/equity ratio and historical profitability provide some insights. Beyond a certain level of risk, I'm unwilling to attempt a valuation. 

Although I don't pretend this approach produces a proper intrinsic value per se, it does provide a relative measure of value across stocks. Therefore, one can rank dozens of stocks on this 'relative' intrinsic value, and simply purchase the cheapest ones. This seems to be in accordance with what Warren Buffett reportedly said at the 1998 Berkshire Hathaway 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.' (Please note, as far as I know Buffett hasn't been very specific about discount rates and how he adjusts for risks in writing. Oral quotes such as the one above are often conflicting - some suggest he does actually adjust discount rates but I suspect he's been misquoted in some instances. If you'd like to see more comments from him about the discount rate, including the one I conveniently chose, check them out here.)

2. My second approach is to use a constant discount rate of 15% no matter what level interest rates are and purchase stocks whose share prices are below that estimated value. Since the discount rate is essentially the required return that an investor desires from investing in something, personally I would be satisfied with a 15% annual return over the long term. While the first method provides a relative measure of value, blindly following that would see me continuing to buy the 'cheapest' stocks even in an environment when stocks in general are extremely overvalued, as can happen from time to time. Hence, this second method provides an absolute benchmark of value - if nothing offers a prospective return of 15%, then the stock market is probably overvalued and it may be time to sit out for a while. 

In practice, it wouldn't make much difference if I exclusively used the second approach as both a relative and absolute measure of value. Raising the discount rate by a few percent doesn't change the relative attractiveness of a group of stocks dramatically (higher discount rates favour stocks with cash flows closer to the present and vice versa with lower discount rates), although it will result in dramatically lower intrinsic values. Likewise, I could probably get away with only using the first method and just employing some common sense to figure out when stocks are exceptionally overpriced. 

So in conclusion, by using a constant discount rate DCF analysis enables me to determine which stocks are the cheapest, without actually coming up with a true intrinsic value (although I'd love to be able to). In any case, my inability to decisively determine what the discount rate should be doesn't preclude other investors from doing so - I'm sure someone else has a more logical process. And whatever you do, remember that the CAPM is total crap!


  1. You're an excellent writer Chris -- keep up the good work. I'm paying attention even if no one else is :)

    I don't have much to add, frankly. As you read more (and invest more), you'll find that the best investors don't do DCF's -- it's simply too easy to delude yourself into justifying a price target with various growth rates, margins, capital intensity, discount rate, perpetuity growth, et. al. Buffett, Munger, Greenblatt, Price, Klarman, Russo, Burry, etc. -- none use it.

    Some people like to do DCF's to see what the current market price is implying, but frankly even that is GIGO ("garbage-in, garbage-out") to me.

    That said, if you get mileage out of it, more power to you. You've got to find the methodology that works best for you. I don't because I've burned myself before by letting the model do the thinking for me, which is always a terrible mistake.

    Btw, the easiest way for me to think about discount rates is this -- *what rate of return do you want to earn on your investment?"

    Steve Romick said something funny that struck me like a Eureka! moment recently -- he said, "I laugh when I hear people talk about "intrinsic value," because *your* intrinsic value may be higher than *mine* because you're using a lower investment return threshold." It's a good point! I'd never thought of discount rates or intrinsic values like that before, and of course he's right.

    Anyway, I use 15% for no other reason than that it's an roundish number and Buffett uses it too. If you can compound at that rate for 30 years, things will work out alright I think.

    1. Thanks TboneSam! You sound like a very knowledgable investor yourself, probably because I largely agree with what you said. In fact, you beat me to the punch - my post next week was going to discuss some of the very things you mentioned. I won't spoil everything yet, but in the end, I advocate using some plain old common sense to figure out whether something is undervalued or not.

      Nevertheless, I think that understanding how value is derived from DCF is helpful. I'm not sure whether all those investors you mention don't ever do DCFs, I know Buffett has said he can do a DCF calculation in his head (he's actually quite a mathematical wiz) but it's usually unnecessary when he finds the really good investment. For sure, you need to take care in avoiding the psychological pitfall of altering inputs to justify the price you want it to produce, but that's the reason why I don't look at the calculated value until I am happy with my assumptions. For a similar reason, I try to avoid looking at charts which can lead to anchoring on past prices or any number of subconscious influences.

      By the way, I quite like that insight from Steve Romick - never heard of him before, but I'm very interested now :)

  2. I wholeheartedly agree with you about Buffett -- people either think he's (i) a grandfatherly figure who just recites folksy investing stories, or (ii) a leach on the US Government bailouts. Of course neither are true. If you've read Snowball, the Lowenstein book, or his partnership letter you'd know Warren is every bit the savant as Michael Burry.

    I had never heard of Romick either until I read an interview he conducted with Columbia's Graham & Doddsville publication. All ~16 of their publications are worthy of deep study. Have fun... I sure did.