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Author: hsifyllej Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: of 18386  
Subject: Ben Graham's Equation Date: 10/31/2001 3:16 PM
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Today's Rule Maker column is about Graham's equation: http://www.fool.com/portfolios/rulemaker/2001/rulemaker011031.htm I quoute:

In The Intelligent Investor, Graham laid out an equation that was designed to help people value a growth company. The equation goes like this:
P = ProjEPS * (8.5 + (2*G)) * (4.4/AAA yield)


I would strongly recommend against using this equation which is little more useful than the PEG ratio. Like the PEG=1 rule it's ad hoc and doesn't account for risk and book value, two key components of valuation. Graham is from a time when the world looked a lot different than today. In the context of valuation you might say that in Graham's time the earth was thought to be flat. There's been a revolution in the field of valuation since which brings us to another quote from today's Rule Maker article:

I started today with Graham's equation, but we can't stop there. Discounted cash flow analysis is out there, along with other concepts such as "real options" that we need to consider.

You can start and stop with discounted cash flow analysis, or any other variant of the dividend-discount model, which is the correct way to value stocks. Real options are often abused here and elsewhere as a residual value generator, i.e. if a company is overvalued relative to formal valuation analysis but we are in love with the company it must have real option value making up for the difference and more.

Datasnooper.
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Author: dlbuffy Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16496 of 18386
Subject: Re: Ben Graham's Equation Date: 10/31/2001 3:32 PM
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Like the PEG=1 rule it's ad hoc and doesn't account for risk and book value, two key components of valuation.

My first thought when reading the article was "What about Book Value?" I have been involved with stocks that had a lower share price than the current book value. (One of which as since climbed back over the book value after I took my loss...:^(

How would we work Book Value into choosing stocks in this market low?

Thanks
Buffy

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Author: TMFBogey Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16497 of 18386
Subject: Re: Ben Graham's Equation Date: 10/31/2001 4:14 PM
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<<it's ad hoc and doesn't account for risk >>

Snoop,

I think "strongly recommending against this equation" is a little strong. It's certainly not going to hurt for people to investigate it for themselves and understand the underpinnings of it. I'm with you, though, it is not the be all and end all.

<<You can start and stop with discounted cash flow analysis>>

Hello Mr. Pot, I'm Mr. Kettle. ;) That sounds an awful lot like "the world is flat."

I was talking with Bill Mann today and we were discussing discounted cash flow analsysis. The problem with DCF, in my mind, is that with so many proponents of it, everyone is looking at it. It's not like a company's intrinsic value is the great unknown to people who follow DCF religiously.

The real problem is that the risk you assume has little or nothing to do with running a solid DCF because truly undervalued companies by traditional DCF standards are ONLY undervalued because there is doubt amongst market participants as to whether the future cash flows can remain in tact.

Philip Morris is a perfect case in point. By all traditional DCF measures, it's been dirt cheap for some time now, and especially last year. The real risk that you took was whether those cash flows would remain in tact. That's where the risk is assumed, at least for most large companies that are widely followed.

I challenge you to show me a single company that's trading at a significant discount to future cash flows where the predictability or even stability of those cash flows isn't in doubt.

While DCF needs to be in the holster, it too is not the be all and end all.

My 2 cents,

Bogey

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Author: Morris Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16499 of 18386
Subject: Re: Ben Graham's Equation Date: 10/31/2001 4:46 PM
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For what it's worth...

I tried the equation on American Express (AXP) using a projected EPS of $2.12 and a long-term growth rate of 13.07%. If the equation (and my numbers) are ok AXP should sell for $51.70. It doesn't.

So I thank the MF staff for starting to look at valuation, and agree with them that this equation doesn't seem like the final answer.

Morris

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Author: howardroark Big red star, 1000 posts Top Favorite Fools Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16500 of 18386
Subject: Re: Ben Graham's Equation Date: 10/31/2001 4:47 PM
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I challenge you to show me a single company that's trading at a significant discount to future cash flows where the predictability or even stability of those cash flows isn't in doubt.

Your argument seems to assume a proposition that I question. Namely, that models derive validity by differing from methodologies used by the market. Why would you think that is so? I can create numerous, ad hoc models which will easily provide valuations that differ significantly from market valuations, even given the same forecasts of future company fundamentals. For example, I can simply say that a company is worth the present value of its risk adjusted future cash flows times three. This would satisfy your implicit criteria of creating methodologically-based discrepancies, but of course add no validity to my attempt to value the business. In contrast, I'd argue that the valuation method should be judged by its empirical accuracy, and certainly not by whether it creates buying opportunities by virtue of its own methodology. In fact, I'd argue that the only valid criticism to DCF or any other valuation methodology is that it doesn't robustly model value. So when you say...

The real problem is that the risk you assume has little or nothing to do with running a solid DCF because truly undervalued companies by traditional DCF standards are ONLY undervalued because there is doubt amongst market participants as to whether the future cash flows can remain in tact.

..I am mystified, because I would identify this as the precise goal of a valuation model. That is, firms differ in expected value not because value is as value does, but because the expected future fundamentals of those firms vary. To say that a shortcoming of DCF is that it values all firms the same except for the differences in their expected future results is the ultimate compliment to a valuation model!

Of course, it is possible to argue, as some Real Options proponents do, that DCF is not the empirically superior way to value all firms at all times. Perhaps even a Graham proponent could attempt to argue this point on the basis that, in practice, his method eliminates the human tendency to be overly precise when using theoretically accurate models (a rather weak argument in this case, if you ask me). But the goal should not be for the model, itself to create value or to differ from the market, but rather that it best reflect value.

Philip Morris is a perfect case in point. By all traditional DCF measures, it's been dirt cheap for some time now, and especially last year. The real risk that you took was whether those cash flows would remain in tact. That's where the risk is assumed, at least for most large companies that are widely followed.

It's a myth that there are traditional DCF measures. There are some who would tag MO's cost of equity capital as extremely high due to litigation concerns, which itself could easily explain a DCF value equivalent to recent trading prices. Atlernatively or jointly, a model could simply predict lower future cash flows according to litigation-related predictions, and also create a much lower value. DCF does not mean the past equals the future. DCF means the present equals best expectations.




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Author: hsifyllej Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16501 of 18386
Subject: Re: Ben Graham's Equation Date: 10/31/2001 4:52 PM
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I think "strongly recommending against this equation" is a little strong.

I used the word "strongly" to make it, well, strong. I can make it stronger if you wish but wont make it weaker. Here you go: I extremely strongly demand that you don't consider this equation.

It's certainly not going to hurt for people to investigate it for themselves and understand the underpinnings of it.

In order to be able to understand why you don't want to use the equation you need to first understand valuation. If you understand valuation there's no need to understand that equation so you can start and stop with variants of the dividend-discount model (DDM).

I was talking with Bill Mann today and we were discussing discounted cash flow analsysis. The problem with DCF, in my mind, is that with so many proponents of it, everyone is looking at it.

This I can't understand. We know how to value stocks. Period. Stocks are valued by the DDM of which DCF is one variant. Everyone is looking at it because it is a correct method to value stocks. This I can't understand is a problem.

It's not like a company's intrinsic value is the great unknown to people who follow DCF religiously

Sure it is because different investors valuing the same company using DCF will come up with different intrinsic values as result of different assumptions. People using other variants of the DDM will come up with yet different values. To become a successful value investor you need superior skills in applying DDM variants, not to be looking for alternative approaches such as Graham's equation.

The real problem is that the risk you assume has little or nothing to do with running a solid DCF because truly undervalued companies by traditional DCF standards are ONLY undervalued because there is doubt amongst market participants as to whether the future cash flows can remain in tact.

I don't agree with thus. The risk you assume has everything to do with running a solid DCF. The more uncertainty about future cash flows, i.e. the higher risk, the lower intrinsic value and thus the less likely it is that the company is undervalued. Evaluating risk is a key component of DCF, as important as getting the expected cash flows right.

Philip Morris is a perfect case in point. By all traditional DCF measures, it's been dirt cheap for some time now, and especially last year.

That's not clear to me because traditional DCF measures should take the substantial risk of tobacco companies these days into account. Whether a correct DCF will render Philip Morris undervalued remains to be seen.

The real risk that you took was whether those cash flows would remain in tact. That's where the risk is assumed, at least for most large companies that are widely followed.

It sounds like you don't consider risk to be a part of the DCF but it is. If you ignore risk and discount Philip Morris' expected extractable cash flows at a bond rate clearly it looks undervalued. However, you haven't performed a proper DCF analysis because you didn't increase your discount rate to account for risk.

I challenge you to show me a single company that's trading at a significant discount to future cash flows where the predictability or even stability of those cash flows isn't in doubt.

Again, you need to understand that risk-adjustment is part of the DCF. Let me turn the table and challenge you to find a single company trading at a significant discount to a DCF valuation where the predictability or even stability of those cash flows is in doubt.

While DCF needs to be in the holster, it too is not the be all and end all.

As the equivalent of the DDM, DCF is all and end all.

Datasnooper.


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Author: jwedgwood One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16502 of 18386
Subject: Re: Ben Graham's Equation Date: 10/31/2001 6:43 PM
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Hi Bogey,

Do you agree that the intrinsic value of a share of stock is the future free cash flows attributable to that share of stock, discounted back to the present at some appropriate rate?

In my experience that's a pretty well agreed on definition of intrinsic value. If you have another definition I'd love to hear it.

If you agree that this is the case, then I guess the question is whether your goal is to invest in companies at a price below your best estimate of intrinsic value with the expectation that the price will rise eventually to reflect your estimate.

If you think this is the right way to invest, then I'm just mystified by this statement:

The problem with DCF, in my mind, is that with so many proponents of it, everyone is looking at it. It's not like a company's intrinsic value is the great unknown to people who follow DCF religiously.

If the companies intrinsic value is known, and it's less than the stock price, then why not buy the stock? (Assuming a suitable margin of safety.) If the stock price is above intrinsic value, then it seems strange to curse the messenger (DCF) and to search for some other approach to investing.

I mean, you're either investing to take advantage of discrepancies between your estimate of intrinsic value and the market price, or you're not. If you're not, then the column on Graham seems a bit out of place. If you are, then how can you argue that DCF isn't the right path to estimating an intrinsic value?

As Snoop and Howard pointed out, there are huge variations in intrinsic value that are dictated by the assumptions of any DCF analysis. Your goal is to do a better job at it than others.

I think that having shortcuts to make a quick assessment of whether a stock might be trading below intrinsic value is very useful, and perhaps you can argue that this formula is one. But it seems pretty important to then follow up on a shortcut with more due diligence, and in my mind that means DCF.

Just my two cents.

-john

ps: I can't offer a citation, but I could swear that Graham's formula was his attempt to estimate the PE that an investor might expect to see for a solid growing company, and was not actually a shortcut to intrinsic value.


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Author: zarley00 Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16503 of 18386
Subject: Re: Ben Graham's Equation Date: 10/31/2001 8:35 PM
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As Snoop and Howard pointed out, there are huge variations in intrinsic value that are dictated by the assumptions of any DCF analysis. Your goal is to do a better job at it than others.


Amen brother!

I can't offer a citation, but I could swear that Graham's formula was his attempt to estimate the PE that an investor might expect to see for a solid growing company, and was not actually a shortcut to intrinsic value.


I would have sworn the same thing, but when I took out my copy of The Intelligent Investor I found this on page 158 (Chapter 11):

Value = Current (Normal) Earnings X (8.5 plus twice the expected annual growth rate)

Some thoughts:
- No comment about PE (looking at per share value)
- Normal earnings were defined as an average of three years earnings, not just the last year's
- No comment about the risk free rates, which makes me think TMF may have gotten their formula from another source, or I'm missing something.
- Further on he comments about expected growth rates. Interestingly he's looking at growth around 7-8% as extended term rates of growth. Much lower than what most here would deem acceptable. Also making the 19% used in the RM article today seem outlandish.

One final point. I like to look at a range of future growth rates to see the resulting range of potential intrinsic values. Perhaps this would be instructive with the example of Pfizer. I think if you bring those expected growth rates down to more reasonable levels, for a company the size of Pfizer, you'll get a better estimate of its possible value.

Zarley


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Author: thedumbox Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16504 of 18386
Subject: Re: Ben Graham's Equation Date: 10/31/2001 10:22 PM
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Snoop & Howard --

Are you saying that (a) the Graham formula is not, in itself, a substitute for a proper DCF analysis, or (b) it's a tool that is so fundamentally wrong-headed as to be useless for any purpose? I've used it for a few years as a method of getting a first rough cut at stocks that look interesting, and I've had reasonably good results with it -- stocks that look expensive under the Graham formula seem to look expensive when you run the numbers, although I've found the reverse isn't as true. If your answer is (b), can you suggest a better quick-and-dirty formula for making a first cut? Thanks.

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Author: hsifyllej Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16505 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 3:01 AM
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Are you saying that (a) the Graham formula is not, in itself, a substitute for a proper DCF analysis, or (b) it's a tool that is so fundamentally wrong-headed as to be useless for any purpose?

Definitely (a), not quite (b) but almost. The formula is increasing in projected EPS, growth, and decreasing in interest rates like a proper DCF analysis typically is. Therefore, there will be some correlation between Graham's measure and DCA valuations, which may explain your next comment:

I've used it for a few years as a method of getting a first rough cut at stocks that look interesting, and I've had reasonably good results with it -- stocks that look expensive under the Graham formula seem to look expensive when you run the numbers

Unfortunately the functional form is ad hoc and excludes key information on risk and book value making it so imperfect that I'm leaning towards (b) because value investing has to rely on more solid ground.

If your answer is (b), can you suggest a better quick-and-dirty formula for making a first cut?

I don't really perform valuation analyses often. I like residual income based valuation because it's based on raw earnings figures unlike DCF, while being the equivalent of DCF and the dividend-discount model under clean surplus***. Residual income is defined as:
Residual income = current year earnings minus required return times beginning year shareholders equity
If residual income is zero the company didn't create economic value. As required return I could use the CAPM (risk free interest rate plus beta times expected market return in excess of the risk free rate) or something else. The value of a company is then the net present value (computed using a risk-adjusted discount rate equal to the required return) of expected future residual incomes plus current book value. A company that's expected to generate zero future residual incomes, or economic values, should be worth only book value. Empirical research suggests that residual incomes typically are mean reverting towards zero. If residual incomes are expected to be constant over time (more agressive than for the typical firm) firm value is simply:
Value = current book + current residual income / discount rate.
That's my favorite quick-and-dirty formula. Here's an example for Nokia: http://boards.fool.com/Message.asp?mid=15015553. Here's one for LUV: http://boards.fool.com/Message.asp?mid=15196586. To be more precise I need to predict future residual income.

*** Clean surplus means that the change in book value equals earnings minus dividends paid. This is not a bad assumption for most US firms. Berkshire Hathaway is an important example of non clean surplus because, among other things, certain investments (such as KO) are included at market value in book on an annual basis while only appearing in earnings at time of liquidation: http://boards.fool.com/Message.asp?mid=15897935

Datasnooper.

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Author: trojga Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16506 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 7:34 AM
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I'd be interested to see where they came up with this version of the formula. In my copy of Intelligent Investor it shows:

P = ProjEPS * (8.5 + (2*G))

Where did the adjustment for bond rate come from?

If you run Pfizer with the above you'll see the current price makes it OVERVALUED !

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Author: howardroark Big red star, 1000 posts Top Favorite Fools Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16509 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 12:57 PM
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Are you saying that (a) the Graham formula is not, in itself, a substitute for a proper DCF analysis, or (b) it's a tool that is so fundamentally wrong-headed as to be useless for any purpose? I've used it for a few years as a method of getting a first rough cut at stocks that look interesting, and I've had reasonably good results with it -- stocks that look expensive under the Graham formula seem to look expensive when you run the numbers, although I've found the reverse isn't as true. If your answer is (b), can you suggest a better quick-and-dirty formula for making a first cut? Thanks.

Well, for the record, I was really speaking to David's argument that DCF is of limited use because its methodology generally proscribes identifying undervalued companies, rather than Graham's formula itself, but (not surprisingly) I do have opinions on the issue.

I would absolutely agree with (a). I'd add that there's a fairly common tendency to take a sort of egalitarian approach to valuation, where every possible valuation model is viewed as just another "tool in the toolbox," with no single tool being inherently superior to any other. I think this is a big mistake, as a general proposition. Every tool is an attempt to quantify the definition of value. In some cases, such as EBO models versus DCF models, the tools are in fact (roughly)identical in accurately defining value, and thus it can be true that each is a tool that can be more or less useful depending on the situation, but neither is inherently superior. In others, there are clearly inferior short-cuts, such as P/E, Graham's Formula, PEG or Stable Excess Earnings models, which have other advantages such as ease and speed. This latter category of heuristics are sometimes reasonable but sometimes poor substitutes for quantifying the definition of value, and thus are rarely a good substitute for someone investing their hard earned money on a fundamental basis.

As for (b), I certainly wouldn't say that the formula is "useless for any purpose," though I would presonally use it. I think it helps to break down the formula in its constituent parts, and look at where it breaks from, or makes fixed assumptions about, the definition of value such that a user might be constrained. We know that almost all heuristics have these shortcomings, so it's important to make them explicit. The formula again, for convenience is the following:

P = EPS * (8.5 + 2g) * (4.4/AAA).

We can agree that a "correct" price generally equals EPS times the "correct" P/E (of course the "E" in PE is really EPS, such EPS cancels out and leaves you with PE. Thus, parantheticals in the formula can be characterized to mean this:

Correct PE: (8.5 + 2g) * (4.4/AAA).

I'd like to break the formula into its two implicit, constituent parts, which are also the two factors necessary to determine the "correct" (I put correct in quotes because I really mean correct given your forecasts and assumptions about the business) P/E in any valuation model, which are required return and expected growth. Start with required return. To control for this variable, I'm going to assume we have a no growth business (g = 0). For a no growth business, the formula can be restated as PE = 8.5*(4.4/AAA) (or, more concisely, PE = 37.4/AAA). We can compare that formula to the accurate formula for valuing a stream of inflows, which is the Gordon growth model: PE = 1 / Required Return.* Initially, it's pretty obvious that Graham's formula isn't actually much of a short-cut when it comes to zero growth companies, because it isn't really easier than the accurate model, except that it defines "required return" for you. Of course, if a heuristic isn't any easier than the most accurate model, it's not particularly useful. But it's still worth looking at the assumptions and method this part of the formula is employing to determine required return.

One way to view the formula is setting a universal required return of 11.76% (the reciprocal of an 8.5 PE), and then adjusting that return based on prevailing risk free rates. An immediate problem with this is that it prevents you from having a different required returns for different businesses, or, if you try to, you are forced to do it obliquely by using a larger margin or safety rather than expressly. Now, when the Risk Free rate is 4.4%, the formula assigns an equity risk premium of 7.36% with no distinction between companies, and arbitrary though not irrational number. But, if the Risk Free rate changes, the equity risk premium suddenly changes as well. For example, if long term bond rates rise to 8.8%, the "correct" P/E for a zero growth company under the formula is suddenly 4.25, a required return of 23.53% and suddenly an equity risk premium of 14.7%! That's an interest relation without much of a reasoned basis that I can see. Another way of saying this is that defining "required return," which most people agree is the risk free rate plus a risk premium (which also can be broken down into and equity premium plus a specific company premium), as 1/(37.4/AAA) is both importantly flawed and not particularly time reducing as compared simply expressly estimating your required return from the investment.

So with required return aside, the formula can be assessed as a heuristic for thumbnailing growth into a single metric. Clearly, growth cannot be accurately thumbnailed into a single metric unless it is constant into infinity, in which case the Gordon model is both the most accurate and quickest method to apply. But convenience is important, so the question whether Graham's growth model's convenience overcomes its assumption in a non-stable growth situation is important. The growth part of the formula, assuming the AAA yield is 4.4% to control for required return, is thus as follows:

PE = 8.5 + 2G.

This can be compared to another growth-based heuristic, the PEG formula, which sometimes posits that PE/G should equal 1, or:

PE = G.

Thus, Graham's version is theoretically much more optmistic than the PEG = 1 or PEG = 2 formula, except that Graham's threshold requirements (such as 7 to 10 year growth and a maximum PE of 2X AAA yield) strongly counterbalance that effect. We know that growth is an exponential phenomenon, not easily modeled by simple heuristics when unstable. We also know that the length of the growth period can be very important, but cannot easily be measured in a linear formula is it's not perpetual.

It's worth examining how the PE = 8.5 + 2.G compares to the "correct" answer, using varying asumptions about growth rates and time periods. Let's again control for Graham's required return issues and assume AAA =4.4 and required return is thus 11.76%. To further simplify, I'll assume that terminal growth is stable (zero) in all cases. Here is a chart showing the "correct" P/E, under a two stage DCF, that would emerge along a matrix of two variables: Growth rates (in %) and length of growth period (in years). I know that my growth period and growth rates may exceed Graham's caveats, but it's helpful to see how they apply to various scenarios (they don't exceed it as much as Pfizer's growth rate does).

3 5 7 9 11
4% 9.5 10.0 10.4 10.8 11.2
6% 10.0 10.8 11.6 12.3 12.9
8% 10.5 11.7 12.8 13.9 14.9
10% 11.0 12.6 14.2 15.7 17.2
12% 11.6 13.6 15.7 17.8 19.0

In those cases, Graham's formula would create the following PE ratios:

3 5 7 9 11
4% 16.5 16.5 16.5 16.5 16.5
6% 20.5 20.5 20.5 20.5 20.5
8% 24.5 24.5 24.5 24.5 24.5
10% 28.5 28.5 28.5 28.5 28.5
12% 32.5 32.5 32.5 32.5 32.5

Along with the absolute differences (which will change as assumption about terminal value change), it's also important to note the failure to distinguish appropriate between differing situations, such as differing growth rates and time periods. While there are many cases, especially if you start playing with the terminal growth rate, when Graham's formula will be a decent estimate, there are some striking examples of potential discontinuities.

So, to sum, I would say that it would be a needless exaggeration to call it "uttlerly worthless" and take more hubris than I have. In stable growth situations, however, I don't see any possible use, as its required return components is neither more simple nor close enough to accuracy to be of much use. In an unstable growth situation, I would personally (this is my answer to (c) rather keep simple one-page spreadsheet of appropriate P/Es under various two (or three, which we didn't even examine) stage DCF scenarios using differnt growth periods, rates, and required return, than subject even my quick and dirty valuation to large potential errors. But that's admittedly somewhat subjective subjective. I like to make my implicity assumptions as explicit as possible, if I can do it and still maintain convenience.

*For the purposes of this discussion, I'd like to assume equivalency of earnings and cash flow. The potential discrepancy can be an important issue unless in some cases, but I'm going to set it aside for the purposes of this post.








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Author: TMFBogey Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16510 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 4:04 PM
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Wow. I'm very impressed with the conversation over the past 24 hours and regret not jumping in sooner. Kudos to Snoop and HR (and others) for some solid thinking. When two of the smartest guys in the house are calling me on the carpet, I have to assume that I'm either wrong about something, or not effectively communicating. I'll entertain the latter for a moment, though I'm willing to accept the former.

A few issues:

1. On the value of Graham's equation - HowardRoark rightly points out that the equation is a shortcut. My guess, having never spoken to him personally, is that Graham offered it in an attempt to simplify the complex. Whether the endeavor of simplifying the complex is a good one or not is up to you. What I DO know for sure is that having this tool in your belt would have kept you away from companies like Cisco, Yahoo! and JDS Uniphase when they were going crazy. In that regard, it has its utility.

2. On the issue of DCF being problematic - I don't think I explained myself very well on this. Let me try again. I am a firm believer that the value of an investment is all of the future cash flows + the terminal value. In order to decide whether or not the investment is currently priced attractively, you apply a discount rate to those future cash flows and arrive at net present value. I'm in total agreement with that.

I also recognize that the person that picks the correct discount rate wins. I guess the problem I'm trying to get at is one of moral hazard, for lack of a better descriptor. By default, the higher your required rate of return (based on your assessment of the underlying stability and predictability of the cash flows), the less likely it is that you'll ever actually realize those cash flows, assuming you're able to acquire the asset.

The challenge is no longer focused on choosing an appropriate discount rate, but more on judging whether the firm's future cash flows are predictable or stable. Because those two are so intricately tied (choosing your discount rate and judging the stability/predictability of future cash flows), it makes it almost impossible to ever pull the trigger. Let me give a mythical example:

Let's say XYZ Corp is just an OK business with cash flows that used to be fairly predictable, but because of business conditions have now deteriorated somewhat. Because you recogniae that there is less stability, you require a higher rate of return. Let's assume the stock trades at $25. Let's assume that your DCF tells you that the stock needs to trade at $15 to allow for the higher required return you've built in.

Now, it's a two months later and the stock is at $15. Do you pull the trigger, or do you ask yourself, "did this get down to this price because the market is efficient, or because the cash flows are less stable than I thought?" Ooooh, wait, let me run those numbers again with new assumptions.

You see what I'm driving at? (Perhaps not). The real risk is not in assigning the proper discount rate, but in being able to assess the future cash flows which will allow you to assign the proper rate. In many ways it's a nose dive that you don't ever really come out of. And, it's one of the reasons that I like the fact that Buffett doesn't use a risk premium. He just uses the risk free rate and then requires that the asset trade at a significant discount to his valuation without the risk premium. Of course, the same problems remain, but they are numerically less complicated.

I feel like I'm talking in circles even though I don't intend to. Let me know your thoughts.

David



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Author: BizKiffer Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16511 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 4:47 PM
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I think I understand what you mean David, even though I am _way_ behind the understanding of most people that I have had the please to read posts from on this board after your article.

What I would agree to is that all formulas will have no importance whatsoever if you are not good at predicting the future. Also in this formula we are using the 5 year growth rate. Changing that between 15 and 20% will be a HUGE difference in the stock price. In whatever you do you will need to know a bit about the future and I think that these formulas will be very good at trying to find a bottom somewhere, or checking out if you worst-case prediction would be a buy now, but it will not help you predict the future.

There we might find Philip Fisher more usable.

Oliver aka BizKiffer

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Author: hsifyllej Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16512 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 4:59 PM
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There we might find Philip Fisher more usable.

Although I argued against Graham's formula it's infinitely better than a Fisher analysis. I remember seeing a 15 (?) point Fisher analysis by Mycroft*** some time ago on Nokia and found no attempt to measure whether the company was under- or overvalued. That's similar to the rule maker flaw. We might have reasons to like a company, but without translating that into a formal valuation we can't know whether it has a chance of being a good investment.

*** I don't know whether Fisher advocated some valuation steps also, but recommending a buy based on the 15 (?) point analysis I saw is meaningless.

Datasnooper.

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Author: BizKiffer Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16513 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 5:04 PM
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The biggest flaw in Mycrofts Fisher analysis was that the neglected the valuation and almost half of Fisher's book is on being careful to find stocks that are undervalued. I think we need a mix. Try to find company that have good value with some formulas. Try to find companies that meet the 15 Fisher points (or just a few or roughly) and go from there with looking deeper into valuation. Things like that. It is surely not as simple as using the 15 points and then buying. It is also not as simple as looking up some figures, putting them in a formula and then buying.

In short. It's not simple ;)

Oliver aka BizKiffer

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Author: hsifyllej Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16514 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 5:16 PM
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Things like that. It is surely not as simple as using the 15 points and then buying. It is also not as simple as looking up some figures, putting them in a formula and then buying.

You can use any method, such as the 15 points, or combination of methods to arrive at the key inputs to the valuation formula (expected cash flows and risk). I don't consider the 15 points useful for this purpose, but if you see a link then fine. From that point it's as simple as putting them into the formula and making a buy/sell decision based solely on the outcome. At that stage the 15 points can guide you no further. It's solely a matter of comparing DCF valuation to current market cap.

Datasnooper.

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Author: zarley00 Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16515 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 7:01 PM
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Just to put my own twist on Oliver's thoughts . . .

The use of Fisher's 15 points seems to me to be a great process for uncovering great companies and learning about the business. Having completed a thorough "Fisher Analysis" (for lack of a better term) will allow you to better understand and/or estimate the growth possibilities for a company. Meaning you will be better prepared to determine if 10%, 15% or 5% is a reasonable growth rate to expect from the company. Presumably, you would also be better prepared to evaluate current events and market action as it pertains to your investment, and thus be better able to make adjustments to your future cash flow estimates (which will determine your company's value).

In short, it provides a structure for learning about the company that will allow you to better estimate (or guess) the prospects for future growth -- allowing you to be more accurate in your calculations of present value.

Of course, having the patience to wait until a great company is unreasonably beaten down and trading below a reasonable estimate of its intrinsic value is essential (and probably the least learnable skill and investor needs to develop).

Zarley

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Author: pppgbr Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16516 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 8:03 PM
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Hello datasnooper.

You sound like someone who knows a lot about DCF.

Please would you comment on the effect of different discount rates on the bottom line?

Kind regards
pppgbr

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Author: howardroark Big red star, 1000 posts Top Favorite Fools Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16517 of 18386
Subject: Re: Ben Graham's Equation Date: 11/1/2001 8:07 PM
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Thanks for the clarification Bogey.

Let's say XYZ Corp is just an OK business with cash flows that used to be fairly predictable, but because of business conditions have now deteriorated somewhat. Because you recogniae that there is less stability, you require a higher rate of return. Let's assume the stock trades at $25. Let's assume that your DCF tells you that the stock needs to trade at $15 to allow for the higher required return you've built in.

Now, it's a two months later and the stock is at $15. Do you pull the trigger, or do you ask yourself, "did this get down to this price because the market is efficient, or because the cash flows are less stable than I thought?" Ooooh, wait, let me run those numbers again with new assumptions.


I more than understand this problem, but I would argue that this is a problem that is inherent to investing and not DCF. So inherent, in fact, that you can't avoid it by using another model. Ignore it, yes, but not avoid it. If a stock I'm watching drops below my mental buy price, I do (usually quickly) ask myself whether my vision of the company's future has changed due to intervening events, or whether I am still willing to invest at the annual return I used in my earlier valuation. How could you not? Admittedly, this is sometimes a very easy, informal process. You don't have recompute all that much (if at all) to determine that little fundamental has changed. And if something fundamental has changed, then I'd think you'd want to reassess. I couldn't take much comfort from a methodology that allowed me to avoid important questions by simplifying them out of the equation.

You see what I'm driving at? (Perhaps not). The real risk is not in assigning the proper discount rate, but in being able to assess the future cash flows which will allow you to assign the proper rate. In many ways it's a nose dive that you don't ever really come out of. And, it's one of the reasons that I like the fact that Buffett doesn't use a risk premium. He just uses the risk free rate and then requires that the asset trade at a significant discount to his valuation without the risk premium. Of course, the same problems remain, but they are numerically less complicated.

I agree that business valuation is hard, and that many aspects of it are terribly imprecise. And with imprecision comes the danger of being precisely wrong rather than approximately right. But in my way of seeing things, it is a myth that discounting cash flows requires a particular level of precision. DCF (or EBO) is only the most accurate template, and within it you can choose your own threshold of precision. But at least in those cases, you are doing what I would consider the most important methodological part of investment valuation: you are accurately making your assumptions explicit. Unless you have Buffett's onboard computer and intuitive ability to compare prospective future cash flows and expected returns without express quantification, you may run the risk of closing your eyes to the difficult problem that is endemic to investing: The market forces you to make very precise bets about the future by charging you a particular price, even though we don't have very precise understanding of risk or crystal balls.

That's not to say that there aren't situations where the value might seem to "scream out" at even us non-Buffett lowlifes, but those cases would also be "buy" situations if you used an accurate valuation model. If someone asked me how investors should look at valuation, I'd say it should be the way to make explicit the bet they would be making at a given price, by shedding light on exactly what business results are needed to create their required return. Any flawed heuristic is naturally going to confound that bet, so that you're betting on a game without knowing the point spread. And although I understand your feeling that DCF might force you out of the game by futilely trying to figure out if the spread should be 12 points or 12.1 points, there's nothing intrinsic in DCF that imposes that sort of precision on you. And DCF and the like gives you the ability to reverse engineer the current market price to see what return the market is offering according to your vision of the future, rather than relying on your intuition or a heuristic (BTW, I just saved you $20 w/ that last sentence, which is basically the contents of Maubousssin and Rappaport's recent book, Expectations Investing, from which I was personally hoping for more given my admiration of the authors).

In sum, I refuse to grant credence to any argument that might require that I close Excel for at least ten minutes, because then I might have to deal with the fact that I haven't had a jump shot in ten years (okay, ever), which would leave me with nothing to do during the extended sabbatical that's currently in front me. Off to the Yanks.

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Author: hsifyllej Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16519 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 12:54 AM
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Please would you comment on the effect of different discount rates on the bottom line?

Different discount rates can lead to drastically different valuations. Imagine as a simple example that a mature company is expected to grow earnings at a constant 5% per year indefinitely. At a 6% discount rate a Gordon growth model would value the company at 100x next years earnings, at a 10% discount rate 20x, and at a 15% discount rate 10x next years earnings. With such variation finding the right discount rate no less important than predicting future extractable cash flows.

Datasnooper.

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Author: LeBeancountiere Big red star, 1000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16521 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 1:29 AM
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Excellent commentary Howardroark!

Regarding Graham's Intrinsic Value formula: For the record, the following is a quote by Warren E. Buffett to Janet Lowe in January 1995 (see page 56, hard cover copy of the book, Value Investing Made Easy, by Janet Lowe):

"I never used formulas like that. I never thought Ben was at his best when he worked with formulas either."


LeBean :-)




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Author: zarley00 Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16526 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 10:29 AM
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Datasnooper,

What is your opinion of using CAPM for determining the appropriate discount rate? I've seen it presented as:

DR = R(f) + b * ( R(m) - R(f) )

where

DR = Discount Rate
R(f) = Risk-free Rate (10yr treasury for example)
R(m) = Market Rate of Return (return from total stock market)
b = Beta

For Pfizer this would mean

R(f) = 4.5%
R(m) = 10% (give or take)
b = .66 (taken from yahoo profile)

DR = 4.5+.66*(10-4.5)

DR = 8.13%

Zarley

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Author: CorpLaw Two stars, 250 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16527 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 11:12 AM
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I've been interested in the discussion of Graham because I've used the formula and hadn't heard any discussion of it here. The discussion certainly has given me a lot to think about.

FWIW, back at the beginning of the year I posted some stocks that looked over- and under-valued by the formula, if you used consensus analyst estimates of FY2001 earnings and future growth, as of January 1.

http://fireboards.fool.com/Message.asp?mid=14028671

Stocks the formula saw as overvalued are down 42% YTD. The stocks the formula saw as undervalued are down 9%. For the equivalent period QQQ is down 40% and SPY is down around 18%.

Obviously this is too small a sample and too short a time to mean much. Some have also argued that in a market collapse the high P/E stocks (which tend to be overvalued on the Graham formula) will obviously take bigger falls than low P/E stocks, which are already beaten down, so we should expect this kind of correlation, even if the formula is invalid.

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Author: dataznooper Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16533 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 12:29 PM
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What is your opinion of using CAPM for determining the appropriate discount rate?

If your portfolio is well diversified, for example if you hold 30 stocks, then the CAPM gives you a useful discount rate that reflects the contribution of risk to your portfolio. If your portfolio is not well diversified then you must either (1) get financial advise, (2) have a crystal ball, or (3) be a very gifted investor. No matter whether the reason is (1), (2), or (3) the CAPM will not yield discount rates that are reflective of your situation, even though they might be right for the market***. Under (1) you might want to automatically double CAPM discount rates or something like that. A David Gardner type-(2) investor could use the risk free interest rate, while the howardroark type-(3) investor may choose something in-between.

*** It's not clear from empirical evidence that the CAPM works well for the market. I might prefer to use factor models myself.

Datasnooper.

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Author: zarley00 Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16535 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 1:01 PM
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Well, since I am neither DG(2) or HR(3), that leaves seeking financial advice and doubling the CAPM discount rate.

Hmmm . . . how about if I use (a not-quite-arbitrary) 15% as my required rate of return for my discount rate. Since my personal stock selections are a relatively small portion of my total portfolio I might simply want to make a 15% annual return on my investment to account for the increased risk of personally selecting individual investments. This would be higher than the CAPM rate in many (dare I say most) cases and roughly 50% higher than the market rate.

As for factor models:
While you may be in a position to accurately determine the appropriate factors (and calculate their sensitivities) for individual assets, I must sadly admit that I am not. At first glance, the factors themselves may be infinite (or at least too numerous for me to handle) or even too difficult to measure (for me, the lay-person, anyway).

Perhaps you can provide a simple example.

Zarley

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Author: dataznooper Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16537 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 1:45 PM
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how about if I use (a not-quite-arbitrary) 15% as my required rate of return for my discount rate

Using the same discount rate for all stocks is similar to what LeBean did in another thread. There are two important unknowns in valuation, future cash flows and future risk, and they are equally important to me. By using the same discount rate for all stocks you are screening only on cash flows, which essentially is as wrong as assuming that all stocks have the same expected future growth rates but different discount rates, effectively screening only on discount rates. You need to evaluate the relative riskiness of stocks, using the same discount rate at any level for all stock you end up with a portfolio concentrated in high-risk stocks.

As for factor models:
Perhaps you can provide a simple example.


It's fairly easy to do. Perhaps I will write up an example at some time if there's interest.

Datasnooper.


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Author: zarley00 Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16538 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 2:18 PM
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There are two important unknowns in valuation, future cash flows and future risk. . .

I'm not sure what you mean by future risk. The risk, as I see it, is the error in my prediction of future cash flows. If I could accurately predict (via crystal ball) the future cash flows of an asset, I could then determine an appropriate price to pay for those cash flows by calculating thier present value, discounted using my desired rate of return. It is the fact that I cannot accurately predict the cash flows from a stock that creates the risk of investing. This is where the idea of "Margin of Safety" comes in. The better your ability to predict the future cash flows (via true understanding of the business in question), the smaller your MoS needs to be.

Are you saying there is more to it than that? Some additional risk that is being ignored? For example, the risk of nuclear war or some fundemental change that impacts the demand for a product (i.e., the development of the automobile putting buggy makers out of business). Changes in the markets' risk-aversion (impacting future interest rates)?

Zarley





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Author: LeBeancountiere Big red star, 1000 posts Feste Award Nominee! Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16539 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 2:24 PM
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"Using the same discount rate for all stocks is similar to what LeBean did in another thread."

Hey Datasnooper, surprise! My database does not have the same discount rate for every stock. Just ask Cheeze and Howardroark (they both have seen my software).

The companies in my database that also appear within the RM porfolio just happen to have a relatively low discount rate assigned to them.

Now Datasnooper, I remember you were posting on the Cheeze-O-Rama board not very long ago and taking a rather strong view in favor of EMH - as in, there are no speculative bubbles in the stock market. So here is my question, if you embrace strong form and semi-strong form EMH, believe that the market does not ever become inefficient, then why is it that you waste your time talking about securities analysis respecting individual stocks and stock valuation at all?

LeBean :-)

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Author: dataznooper Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16542 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 4:26 PM
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The risk, as I see it, is the error in my prediction of future cash flows.

That's right.

The better your ability to predict the future cash flows (via true understanding of the business in question), the smaller your MoS needs to be.

Exactly and that's why you can't use the same discount factor to price different stocks. Trust me, even if you understand a business to perfection, everything that happens in the future is beyond your control.

Are you saying there is more to it than that? Some additional risk that is being ignored? For example, the risk of nuclear war or some fundemental change that impacts the demand for a product

No all these factors contribute to your prediction errors and should already be incorporated into the risk you assess for the cash flows.

Datasnooper.


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Author: dataznooper Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16543 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 4:30 PM
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So here is my question, if you embrace strong form and semi-strong form EMH, believe that the market does not ever become inefficient, then why is it that you waste your time talking about securities analysis respecting individual stocks and stock valuation at all?

Good question. I'm hoping that some are interested in what I write, and that I learn something in the process.

Datasnooper.

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Author: zarley00 Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16544 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 4:55 PM
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Datasnooper, thanks for your responses. I think we're getting somewhere here.

Exactly and that's why you can't use the same discount factor to price different stocks.

I'm still not sure I agree with this. What I like to do is use my discount rate (required return), look at different growth scenarios and see what kind of range of values I get from them. For relatively unpredictable companies I will use a wider range of growth assumptions, and a narrower range for more predictable companies. I think this is effectively the same as changing my discount rate to suit the company.

No all these factors contribute to your prediction errors and should already be incorporated into the risk you assess for the cash flows.


Of course. I was reaching for straws there.

Zarley


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Author: FractalWalk Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16545 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 5:53 PM
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What I like to do is use my discount rate (required return), look at different growth scenarios and see what kind of range of values I get from them. I think this is effectively the same as changing my discount rate to suit the company.

You are correct in that it is basically the same thing. One way of doing this is to use simulation software like @Risk or Crystal Ball and estimate a range of future cash flows as distributions and then discount them at a risk free rate. So, instead of predicting cash flow X in Yr1, you might predict the cash flow as a normal distribution (as an example) with a mean of X and a variance of Y. By simulating your cash flows multiple times you get a range of PV's. That range is your measurement of risk, which substitutes for a higher discount rate. This sounds similar to what you are doing. But be very careful of two things.

1) By removing the risk factor from your discount rate you are inherently assuming that you capture it in your cash flows. This means that your cash flow assumptions cover all possibilities. So you need to make sure that your worst case truly is worst case. If you underestimate the possible range of cash flows, you are underestimating risk. Of course this problem is also inherent to DCF; what is the appropriate discount rate?

2) The mean of your resulting PV distribution is not risk adjusted as the risk is accounted for in the variance. Stating that you value the stock at X because the mean of your distribution is X would be misleading. If you have two normal distributions both with the exact same mean but with unequal variances, they would not have equal value to you (assuming risk-aversion).




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Author: thedumbox Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16548 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 6:36 PM
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Thanks to Howard, Dataznooper, and others for your responses. Howard, I'm still digesting yours. Znoop, I've tried to get your quick & dirty model to work, but either I'm doing it wrong or everything from MO to C to MSFT is wildly overvalued. The latter is possible, of course, but before I hold out for the $5.99 blue-light special on MO I thought I'd see if you could explain it again, preferably in very short words, with copious illustrations. Thanks again.

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Author: TMFBogey Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16549 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 6:46 PM
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Yo! Dumbox, check your mail. I sent you mail a few times.

Thanks,

Bogey

PS - Sorry for the OT.

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Author: dataznooper Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16550 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 7:30 PM
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Znoop, I've tried to get your quick & dirty model to work, but either I'm doing it wrong or everything from MO to C to MSFT is wildly overvalued.

The market, although it has suffered recently, is still richly valued compared to historical data. Therefore, I wouldn't be surprised if most well-known companies look expensive in a quick & dirty model.

MO

* End of FY 1999 equity: $15,305 million
* Discount rate (sorry for using the CAPM but it's quick and dirty no?): 7%
* Required earnings for FY 2000: 7% x $15,305 million = $994.825 million
* Actual FY 2000 earnings: $8,510 million
* Residual income for FY 2000: $8,510 million - $994.825 million = $7,515.175 million.
* End of FY 2000 equity: $15,005 million
* Stock value at end of FY 2000: $15,005 million + $7,515.175 million/7% = $130,623.0769 million

And then you have a cigar and start researching the company.

Datasnooper.






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Author: dataznooper Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16552 of 18386
Subject: Re: Ben Graham's Equation Date: 11/2/2001 7:55 PM
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I suggested the following quick and dirty formula:
Value = current book + current residual income / discount rate
If you prefer a slightly cleaner but still dirty formula you can assume that residual income grows (or shrinks) at a certain rate and get:
Value = current book + (1+growth) x current residual income / (discount rate-growth)
Datasnooper.


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Author: Chinwhisker Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16553 of 18386
Subject: Re: Ben Graham's Equation Date: 11/3/2001 12:31 AM
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What I like to do is use my discount rate (required return), look at different growth scenarios and see what kind of range of values I get from them. For relatively unpredictable companies I will use a wider range of growth assumptions, and a narrower range for more predictable companies. I think this is effectively the same as changing my discount rate to suit the company.

Zarley,

I've been trying to set up a spreadsheet to do the Intrinsic Value for the companies I already have done the DD on, and would only try to guess at a realistic price that would offer some opportunities for growth. This may should be titled as OT, but here's the thoughts i have so far;

Intrinsic Value Calculator

Residual value = intrinsic value per share (in 5 years discounted back to today) plus the 5 year discounted earnigs minus debt per share.

5 year earnings growth estimate = High estimate minus Low estimate divided by 3 plus Low estimate.

Discount rate for the first 5 years = No risk return (10 year T-Bill) + (BETA - 1) + Average equity risk premium (7.8%)

Additional adjustment to discount rate = { for any companys under 9 years of financial data = 9 - (number of years we have finacials for) * 0 .75}

Growth rate for infinity = 6% (average for the market, or for those with lower growth estimates but have been in business for 20 years or more, average growth may last longer, and for those with higher growth estimates but have been in business less years average growth may begin higher but not last as long before reaching zero growth, or going out of business)

Discount rate for infinity = No risk return (10 year T-Bill) + Average equity risk premium (7.8%)adjusted by 1% for companies with less than 3 years of financial data




These are just some thoughts on setting up a two stage intrinsic value calculator in a spreadsheet that would take only a five year first stage. The calculations are not that simple, but much more simple than others that I've read about. By setting this up in a spreadsheet, it would offer a simple means of calculating IV and considering more complex considerations without using a simple formula that may not consider all factors that may or not be relevant. Also, you would have the opportunity to simply adjust what doesn't fit the simpler mechanical calculations by changing what results you get in the speadsheet box results.

I'm not as advanced as most on this board, but feel that the intrinsic value should include such things as debt, BETA, and risk for companies that have not been in business a long as others, and reward for those that have a lower BETA.

I'm sure I may be way off base here, and welcome those who may tear my ideas apart.

Chin

note: The formula for the two stage IV from an article I don't have the link for - You can use FCF or EPS below;

Using Free Cash Flow to Determine Intrinsic Value

It would probably help if I first explained what is meant by intrinsic value. Intrinsic value is the present value of all future free cash flows (that is, all cash that could be taken out of the business over its lifetime).

I will try to explain this by analogy. Imagine that I offered you a box, telling you that in one year, it would spit out a dollar, and every year thereafter, it would spit out another dollar. What would you pay me for that box? Well, it would depend upon your choice of discount rate. If you put a $1 in an investment and expect to be able to get $1.25 out in a year, then what you are saying is that $1.25 next year is worth $1 to you now.
The discount rate you choose can be the return you require (that is the "official" definition, or it can be any reasonable number you would like to use. For example, some use the long bond yield, or the long bond yield plus an equity premium. Some calculate the cost of capital for each company (that's a whole other subject) and use that. But if you keep it simple, and use the same number across the board, you can compare values easily.

What is that box worth? To make this easy, I will use a discount rate of 10%. Here is how the calculation goes:
The present value of the dollar you would get in one year = $1.00/ (1 + 0.10) = $0.91

The present value of the dollar you would get in two years = $1.00/ (1 + 0.10)^2 = $0.83

The present value of the dollar you would get in three years = $1.00/ (1 + 0.10)^3 = $0.75

and so on. In other words, if you choose 10% as your discount rate (required rate of return), than a dollar next year is worth $0.91 to you today, a dollar two years from today is worth $0.83 to you today, and a dollar three years from today is worth $0.75 to you today. If you were to keep doing this calculation, and add up what each future dollar is worth today, you would get the intrinsic value of the box. BTW, the box is worth $10.
I will show you a short cut to getting this value, but first there are a couple of points of interest.

One, even though there is no growth here, the box has a value.

Two, if I gave you the opportunity to buy this box for only $5.00, you would buy it. But if I offered it to you for $15.00, you would not buy it (unless you were confident that some other person would be even crazier than you and would buy it for an even higher price). Note that the former approach guarantees you excess returns - for $5 you would get $10. If a company has rational management and the stock is priced below intrinsic value, you are not guaranteed excess returns, but you can be pretty sure of it. For you to make excess returns with the latter approach depends entirely upon the irrational behavior of somebody else.

Now I will tell you the short cut. The intrinsic value of a stream of free cash flow growing at a constant rate
RV = FCFn+1 / (k-g)
where RV is the residual (intrinsic) value, FCFn+1 is the FCF for next year, k is the discount rate, and g is the growth rate. The box has a free cash flow for next year of $1.00, the discount rate is 10% (0.10) and the growth rate is zero. Plug in the numbers, and you will see that it works.

Now the companies we are interested in are growing, so how do we value them? Actually, it works the same way. Imagine a company growing its free cash flow at 20% per year. If it just earned a dollar of free cash flow, then next year, it would earn $1.20. The year after, $1.44. Three years out, $1.73. If we use a 10% discount rate again, the first three years would be:

The present value of the money you would get in one year = $1.20/ (1 + 0.10) = $1.09

The present value of the dollar you would get in two years = $1.44/ (1 + 0.10)^2 = $1.19

The present value of the dollar you would get in three years = $1.73/ (1 + 0.10)^3 = $1.30
and so on.

You can easily set up to do this in a spreadsheet and go out as far as you like.
But of course even gorillas do not grow forever. At some time in the future even gorillas become slow growers. At that point you would need to calculate a residual value. Let's say that the hypothetical company I just described will grow its FCF at 20 per year for the next three years, but after that will only grow as fast as the average for the S&P 500, or about 6% per year (historical average). Its residual value (see the equation above) at the end of three years would be
$1.73 x 1.06 / (0.10-0.06) = $45.85
Now that is what that residual value will be worth after the third year - you still have to figure out what $45.85 is worth to you today. $45.85/(1+0.10)^4 = $31.32

So the intrinsic value of this company is $1.09 + $1.19 + $1.30 + $31.32 = $34.90.

(Note that even though this hypothetical company is going to grow at 20% for only three years, its intrinsic value is over 30 times its FCF for the next year.

Try taking the company you used for calculating free cash flow in Part 1, and make some assumptions on growth rate, choose your own discount rate, and calculate its intrinsic value.
Do it on paper, or do in in a spreadsheet, and you will find it is really quite easy.
You can have it grow at a high rate for a few years, a reduced rate for a few years, and then stop growing; you can adjust the number of years of high growth - go ahead, play with it. Of course you will never be able to know the "true" intrinsic value. But you can use this as a way of determining which company you are considering buying is the best value, and you can develop a feel for what stocks are truly priced too high even using optimist assumptions. It can be a good reality check.
I will stop here, not knowing whether any of this was even readable, much less useful, or just thread bloat.









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Author: kstoltz Two stars, 250 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16554 of 18386
Subject: Re: Ben Graham's Equation Date: 11/3/2001 1:39 PM
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Great comments so far, folks! And a great article, Bogey! I'm glad to see that the port is turning its attention towards the valuation subject.

Let me add the following into the mix: There is a inherent problem in using DCF valuation with Rule Maker companies. Rule Maker companies usually tend to run at a substantial premium to their intrinsic value. Rule Maker currently invests $500 a month into the various companies it holds, but based solely upon DCF, it may very well be that none of these companies are undervalued (and may not be for quite some time). I think it's crucial at this point to discuss when the Rule Maker intends to purchase more shares. Does dollar cost averaging even if a company is not undervalued according to DCF analysis make sense? Should the portfolio not focus on purchases every month, instead building a reserve of cash as it waits for a big pitch?

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Author: jwedgwood One star, 50 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16555 of 18386
Subject: Re: Ben Graham's Equation Date: 11/3/2001 1:56 PM
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Rule Maker currently invests $500 a month into the various companies it holds, but based solely upon DCF, it may very well be that none of these companies are undervalued (and may not be for quite some time).

If your investment strategy is to buy at a discount to intrinsic value and to sell at a premium to intrinsic value, then I'm not sure you should ever invest in a company which isn't selling below your estimates of intrinsic value.

If the RM companies appear over-valued, then the problem is either that they are over valued (in which case it doesn't make sense to invest more money at that price) or else the assumptions that you have made in your DCF analysis aren't correct.

When you say that they appear over-valued by a DCF analysis, what you are saying is that your assumptions about the future of the company make it appear that the company is not worth the current price quoted on the market. It seems to me that if this is the case, then the course of action is sort of obvious.

If you aren't using this investment approach, then I'm not sure what a calculation of intrinsic value has to offer you, but I'm not really much of a student of other approaches to investing.

-john


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Author: kstoltz Two stars, 250 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16556 of 18386
Subject: Re: Ben Graham's Equation Date: 11/3/2001 8:03 PM
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jwedgwood -

This is exactly my point. We're starting to discuss valuation methods, with a large number of people pointing at DCF analysis without recognizing that the Rule Maker, as it exists today, uses dollar cost averaging by making monthly purchases. I'm questioning whether monthly purchases are right for the Rule Maker, and whether or not it should only buy when valuation strategies say that a stock is fairly valued or undervalued. There are proponents for both sides of the equation: discounted cash flow analysis and dollar cost averaging. It's just something to keep in mind during the discussion.

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Author: 1poorguy Big funky green star, 20000 posts Top Recommended Fools Old School Fool CAPS All Star Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16557 of 18386
Subject: Re: Ben Graham's Equation Date: 11/3/2001 9:21 PM
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I'm questioning whether monthly purchases are right for the Rule Maker, and whether or not it should only buy when valuation strategies say that a stock is fairly valued or undervalued.

You raise an excellent point, IMHO. My feeling is that since the RM was set up as a DCA port, for the sake of consistency in the experiment (yeah, I know they've broken their rules numerous times), I think they should keep the DCA aspect intact. I would say, however, that part of their purchase decision should include valuation (since they always pick one of their holdings).

The other advantage of DCA is that is how many small investors do it also (I know I send money to my brokerage account when I can, and then, as often as not, buy more of something I currently hold).

Snoop and others on the RB board always defined 'risk' in terms of variation in stock price (which I never liked - to me risk is more about how likely a company is to go under and I lose my money, then the emotional rollercoaster of "the market"). I would think DCA would alleviate risk in any given equity given their definition.

1poorguy (enjoying the discussion, wish I had a better valuation tool than valuepro.net since they removed some functionality)

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Author: TMFBogey Big gold star, 5000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16558 of 18386
Subject: Re: Ben Graham's Equation Date: 11/3/2001 11:30 PM
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wish I had a better valuation tool than valuepro.net

1poorguy,

Take this in the spirit that it's intended, but how about using your own mind as a valuation tool? I think most people believe that understanding things like discounted cash flow and other methods of valuation are beyond them somehow and that they need someone else to do the work for them.

I believe very strongly that we can explain any valuation methodology in easy-to-understand terms, if given enough time. I won't say that you won't have to work diligently, but it's not like you can't understand things.

Excel, sec.gov, and grey matter.

Best,

Poirot

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Author: Chinwhisker Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16559 of 18386
Subject: Re: Ben Graham's Equation Date: 11/4/2001 12:29 AM
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If you aren't using this investment approach, then I'm not sure what a calculation of intrinsic value has to offer you, but I'm not really much of a student of other approaches to investing.

John,

You might find this approach interesting;

Buying at Good Prices

Part 1 - http://www.fool.com/dripport/2000/dripport001228.htm

Part 2 - http://www.fool.com/dripport/2001/dripport010124.htm

Part 3 - http://www.fool.com/dripport/2001/dripport010125.htm

I think the RM team is developing a strategy somewhat similar, but taking other factors into consideration. As they have stated a number of times, the RM strategy is a work in progress, and they learn with us as we go along. There's no doubt they've realized the importance of valuation, and looking at intrinsic value is just one of a number of things they may look at in considering their investment or reinvestment in the companies.

As they grow, so shall we. Huh?

Chin



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Author: mineralpoint One star, 50 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16560 of 18386
Subject: Re: Ben Graham's Equation Date: 11/4/2001 2:24 PM
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Thanks Chin.

I need to look at IV much more closer (and keep an open mind <BG>) but is is oh so hard to find the time for everything I want to do. As a result, I read and follow along quietly (aka lurk) and fall into my own biases. (Boy I must be getting old ... I used to give my dad a hardtime when he did this <g>)

Thanks for the links...

MP

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Author: Chinwhisker Big red star, 1000 posts Old School Fool Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16562 of 18386
Subject: Re: Ben Graham's Equation Date: 11/4/2001 10:49 PM
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MP,

(Boy I must be getting old ... I used to give my dad a hardtime when he did this <g>)

I know the feeling. Turning into my Dad too, but he gave me a lot of reasons to reconsider my positions I previously held. It's amazing how you find out too late, you don't really know everything afterall. Huh?

I hate to post this here, because I feel I might be undermining what TMFBogey is trying to accomplish, but Quicken has a IV Calcualator that IMHO uses a formula not anywhere near mine, but if you put in the same discount rate and growth rates, it comes out fairly close to what I do.

Either one you use accomplishes pretty much what it was designed to do, which is make you think about what the fair price for the companies you'll already be investing in might be. My mechanical mathematical formulas couldn't come close to what an investor might decide for himself by doing the DD on the companies, and that's what the RM strategey is all about. Huh?

but is is oh so hard to find the time for everything I want to do

I resemble that remark. :o) It is hard to get everything in that you want in a day's time, but we just need to remember our fathers managed fairly well without the urgency we place on everything today, and we may be better off becoming a little more like them. As we go along, everything will kinda falls in place if we let it. Sometimes slowing down actually off-sets the need for the fast pace we feel we need keep up with.

Everything will come with time. What you think?

BTW, did you see Pierre's post? Pierre, how you doing Bud? You're right, the GAAP does need to help us out a little on the financials for these companies. You have to dig a little to hard to uncover this. Huh?

Looks like TMF might already be on their case. You're doing right posting your concerns here. With our concern and support, maybe it'll be a few less years.

Chin


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Author: thedumbox Three stars, 500 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16563 of 18386
Subject: Re: Ben Graham's Equation Date: 11/5/2001 10:33 AM
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Stock value at end of FY 2000: $15,005 million + $7,515.175 million/7% = $130,623.0769 million

Thanks for the clarification. For some reason I kept getting the parentheses in the wrong places.

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Author: dataznooper Big red star, 1000 posts Add to my Favorite Fools Ignore this person (you won't see their posts anymore) Number: 16564 of 18386
Subject: Re: Ben Graham's Equation Date: 11/6/2001 1:25 AM
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I wrote:

* End of FY 1999 equity: $15,305 million
* Discount rate (sorry for using the CAPM but it's quick and dirty no?): 7%
* Required earnings for FY 2000: 7% x $15,305 million = $994.825 million
* Actual FY 2000 earnings: $8,510 million
* Residual income for FY 2000: $8,510 million - $994.825 million = $7,515.175 million.
* End of FY 2000 equity: $15,005 million
* Stock value at end of FY 2000: $15,005 million + $7,515.175 million/7% = $130,623.0769 million
but received an email correctly indicating that my calculations are wrong. Thanks for that! While I don't have my original spreadsheet here I suspect that that I used a discount of 6.5% instead of 7%, which nevertheless appeared as 7% because it was placed in an Excel cell with no decimals, although 6.5% was used in the actual calculations. With a beta of 0.25, a risk-free rate of 5%, and an equity premium of 6% we get a discount rate of 5%+0.25*6%=6.5%. In other words, substitute 6.5% for 7% in the example and it's correct. I apologize for that.

Datasnooper.

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