Graham Osborn

When you think about it, Berkshire is now buying the only higher-earning nonfinancial company than itself. There isn’t much left to buy in the public markets - regardless of what the market does - that can really make a dent. I guess they could buy some Aramco. They might by some Google sooner or later. But for really big companies, public or private, the number of candidates looks pretty slim.

Sitting up in the nosebleed section waiting for the movie. Happy posting everyone!

We’re making this the “AirBnb of Omaha” thread :) Hope you all had a good flight in!

Yes, you are right that this approach chops off the tail of the DCF. I would argue this is the best approach for the investor concerned with establishing a margin of safety in his valuation. As a practical matter, all too often the projected growth rate proves over-favorable, in which case even the calculations presented here may be high. Just look at Microsoft circa 2000. Prudent investing is not about determining a single correct value for a business, but rather about establishing a "price ceiling" below which a profit is high probable. I have seen more overvaluation atrocities perpetrated by the "terminal value crowd" than any other. For me, 10 years is the limit - and only in very special cases. I will leave the theoreticians to debate 20- and 30-year projections. As your broker will tell you, even a theoretician can receive a margin call - and when he does I'll be happy to buy his shares as he debates projections vs practicalities :) Peter Lynch didn't use the PEG because it was theoretically accurate - he used it because it worked. I think this method illustrates that the PEG is actually pretty darn useful between PE's of 15-25. I think the modified curve extends this utility.

I did a little calculation yesterday I think provides a reasonably practical solution to this problem. I assumed that the price one is willing to pay for a business is the next 10 years' worth of unrestricted earnings. This only works for simple-capitalization businesses (in other cases EV/ FCF would be more accurate). You can see how the PEG agrees pretty well with this result for businesses growing around 20%, but becomes inaccurate for lower or higher growth rates. There was a debate on an earlier thread about the obvious limitations of the PEG, and I think this helps resolve that debate. For a business where you can't establish some boundaries on probable FCF for the next 5-10 years, PE's are largely worthless unless they are ridiculously low. PEG_vs_10-year_earnings_calculator.xlsx

A big couple weeks coming up with Sohn, Fairfax, and Berkshire meetings! Thought I'd start a thread for discussion of Sohn ideas and presenters this year. Some of the perennials have been further ravaged over the past year. Cash is the ultimate hedge - but it's hard to justify 2/20 on a "cash" fund lol.

That's an interest point. If you count just what is in the insurance businesses I guess the equity is 258B (cash and investments) - 114B (float) - X (other liabilities)? I'm also not sure what you would pick for the cost of equity.

It seems like cost of float and float growth are related under Buffett's definition, although I agree that it would be much more desirable for them not to be. I assumed in the model that each policyholder will ultimately collect exactly what they pay in, which would make for a combined ratio of 100%, ignoring operating costs and inflation, on a per-policy basis. I agree with your definition of "cost of float" as better than Buffett's - but coming up with an actual formula is difficult for an insurer that is not in steady-state. You have to somehow link together the premiums collected for a book of business with the claims that book ultimately generates. In a heterogeneous policy pool (e.g. auto claims, supercat, etc) the average-time-to-claim would vary dramatically so you would have to segment those books somehow also. I'm a bit confused on your 3rd point - wouldn't a CR < 100% by definition be an underwriting gain? The converse wouldn't be true - you could have CR > 100% and have an underwriting gain but operating costs out of control. To the broader point though, you're right that underwriting can be profitable or unprofitable, and highly profitable underwriting would counteract the premium growth variable. But unless underwriting quality varies dramatically, the simulation seems to suggest that there would be situations where premium growth would be the dominant variable using Buffett's formula. Buffett has this kind of schizoid thing going on where he talks about how long-tail business will by definition feel artificially profitable for many years - and that tendency just worsens when the ratio of fresh/ seasoned business is high (effectively you partly reset the clock each year). But in the next paragraph he typically goes on to say that their cost of capital is lower than the government's - even though the cost of debt is fixed upfront and can only go down from today's levels due to inflation (it wasn't always like that, but he's been saying this since the mid-90s when rates were already on the decline). With float, the cost of capital rises with inflation because you don't get to fix your cost of capital upfront the way the government does (talking about seasoned vs newly issued bonds). I think Buffett got an artificial sense of the attractiveness of float since rates have generally fallen between 1980-present, similar to how he said in the late 90s that stocks were not overvalued if interest rates remained low. I think this perception could change dramatically over the next 40 years. I still think the premium growth factor is more important than the inflation factor under most circumstances, but inflation looks like a second secular factor that could work against Berkshire's model (or Fairfax for that matter).

Hi there, looking for some help. I've been studying the way Buffett calculates the cost of float in his letters, and it seems wrong to me. This is the formula he uses: "cost of float" = (underwriting profit or loss)/ (net loss reserves + loss adjustment reserves + funds held under reinsurance assumed - agents balances - prepaid acquisition costs - prepaid taxes - deferred charges applicable to assumed reinsurance) The problem is that what you are really interested in is the total cost of a policyholder relative to premiums paid by that policyholder. In the case of a "steady-state" insurer (one where premiums received and claims paid out are both relatively constant over time) you can calculate that cost on a population basis. I did a little simulation ("constant float") of what that would look like for a hypothetical group of policyholders that each pays in at the start of year 1 and makes a claim for the same amount at the start of year 5. As expected, this generates a constant level of float so long as inflows and outflows remain constant. Note that the cost of float is zero in steady-state - again as expected. Notice also that the float appears unusually cheap (so much so that you're getting paid to hold it) until the "tail" begins (the longer the tail, the longer the period of apparently low-cost float). Now the interesting case is where the insurer never reaches steady state because premiums grow each year ("diverging float"). This is the case at Berkshire. Note that in this case float is costless for as long as the premiums continue to grow. Notice this has nothing to do with the quality of the underlying underwriting and everything to do with an ever-increasing supply of fresh premiums that haven't yet hit tail. The final case is one of declining premium volume - a point that most aging insurers will reach sooner or later. In this case float appears very expensive for the entire period using Buffett's formula - although the underlying underwriting quality was identical. Hopefully you understand my concern now. The calculation Buffett does makes float look great even with poor underwriting so long as the premium growth continues. But there would conceivably come a point where - as premium growth inevitably slows - that poor underwriting would start to manifest as an increasing cost of float. And by the time Berkshire reached steady-state float, they'd be contending with extremely high-cost capital that they couldn't give back. I worry that catalysts could be reduced compounding in float and book in future years - a certainty. Buffett made some serious underwriting screwups in the 70s and I worry that this a uniquely long-tail diagnostic issue. Float is - after all - still leverage, and leverage always has a downside. cost_of_float.xlsx

Hi Vinod, good to hear from you as always. This sounds like a variant of the "terminal value" method - I am assuming you project the next 7 years cash flows manually. One thing that has often concerned me about the terminal value method (including the Gordon Growth Formula) is that it assumes stable company growth and interest rates. As the Coke example above illustrates, this can be used to establish some "worst case" valuations but could be problematic in terms of assigning an exact value to intrinsic value. My personal bias in valuations on "moaty" businesses is to sum up the discounted earnings over the next 10 years and ignore anything after (this thread is mainly concerned with simplified assumptions). Most analysts would have a cow over this method - but I prefer to systematically undervalue businesses. Any time terminal value accounts for more than 30% of the "manual" valuation you are building a lot of assumptions "in the cloud" IMO. Sincerely, Graham

I was playing around this morning with how this formula would apply to Buffett's purchase of Coke in 1987-88. The analysis highlights how the converging portion of the DDF can be highly important in cases where the growth rate is non-decaying and inflation is modest or declining. calculation_of_PE_for_Coke_in_1987.docx

Your post got me thinking and I logged out of my account. Interestingly, I can now view a number of articles without a paywall prompt. For example if you google "Seekingalpha + ticker" you can go straight to an article without getting the prompt to create an account. So maybe there are some workarounds. I guess I just won't log in anymore - lol. I've complained to the editors in the past about the plagiarism problem. If they ordered articles based on comment recency (as happens on COBAF) it wouldn't be an issue. As things are, the few good articles get buried in a sea of poor articles and never get re-promoted when anticipated price action materializes. The cereal-box authors have learned to capitalize on this by stealing content from the older articles and re-publishing it shortly after price action occurs.

Has anyone else noticed how all the articles except the most recent are now locked behind the PRO subscription? At first I thought it was some kind of sick joke, but it literally seems they are now expecting everyone to pay $75/ mo for access to virtually all their articles. I'm just curious, is there anyone out there who is going to pay that kind of money for a site where 90% of the articles are of dubious quality? But what is even more upsetting is how the site has now basically stolen content from authors who put in 10s or 100s of hours on pieces that are no longer creating value for those authors. The author compensation policies were always a joke, so presumably authors were writing in order to gain recognition or perhaps introduce some efficiency to the market (obviously there were some manipulators as well, but my sense was that these were in the minority). That's all gone now. Unless your portfolio is big enough that a $900/ year charge doesn't matter, SeekingAlpha has now declared that you don't deserve the same access to information that the big guys do. It would be like Gmail deciding to charge you $10/ month for access to your existing email. So.. fundamentally.. wrong.

Many have had phenomenal returns with a large portfolio. Lynch owned on the order of hundred(s) of stocks and he killed the index. So did Schloss. Even buffett had around 100 holdings in the 60's. I think concentration on half dozen stocks should absolutely be value plays. That is they should be sure bets on undervalued assets -- not earnings. True, but that's not what the OP was asking. He was asking about concentration limits - the max % you should allow for given position. For Buffett in the BPL days that was 40% (market/ assets vs cost/ assets). I don't believe he ever prescribed a rule for cost/ assets, but looking at Berkshire's insurance portfolio in the 70s it was definitely up there around 20% at times. For me max cost/ assets is 20%. To calculate the right level of diversification for you you need to estimate the average upside for an idea, the probability of that upside, and same two variables for the downside. Then you set the threshold probability of achieving the expectation, which for me is 95% (assuming the downside is acceptable). If you suck at picking stocks, you need more diversification. And if you are doing higher-uncertainty stuff like venture capital you need much more diversification - typically at least 80 investments for an investor with average selection ability. For me I say my target stock is a 10X over 10 years and I assume my probability of making that selection in any given case is around 20%. If you build in a margin of safety so your downside is 0.5X-1X, that math is pretty attractive over a 10-year period. The people with truly insane IRRs are the superangels with really good selection ability and cyclical tailwinds. I think Chris Sacca's IRR for lowercase was around 57%.

On thing to note in this example, as someone pointed out to me on another thread, is that G is actually partly a function of R. In other words, businesses with pricing power should growth faster when inflation is higher because they (ideally) just raise prices in proportion to rising costs. Businesses with high fixed assets and commodity products or price controls may not be able to do this and so inflation has a much greater impact on their value. Mathematically, in the expression: P/E > 2/(G+R)*ln(g0/r0)-1 you can see that a business that can increase prices with inflation will actually be PE-neutral (the convention in his equation is that G is decline per annum in growth, so we DECREASE the rate of decline): P/E > 2/[(G-d)+(R+d)]*ln(g0/r0) = 2/(G+R)*ln(g0/r0)-1 So businesses with pricing power tend to maintain their multiples better than businesses that don't.

I made the same argument as you about DCF in the past. "DCF to is sort of like Hubble telescope - you turn it fraction of inch and you're in different galaxy" But I have changed my mind. Any valuation work you do is based on DCF with the exception of relative valuation or valuation of options. Let me explain. DCF does not mean you have to do spreadsheets. When you say a company is worth 10x earnings, you are doing a DCF valuation. The fact that you did not use a growth rate or discount rate or explicitly model cash flows, does not mean you are not making assumptions about these. You have just assumed away all these variables. You do not even know what you have assumed away. When you do DCF you are forced to think through these and it gives you a chance to make sure they are reasonable and consistent. If you are honest with yourself, this can make the valuation more robust. The fact that Buffett does not put this on paper should not mislead us into thinking we can do the same. He probably can model that in his head. Not so for most of us who have much less practice with DCF. I think it would be helpful for most of us to do a few hundreds of DCF valuations before resorting to shortcut of multiples. It would give one an idea of how cash flows, reinvestment rates, return on reinvested capital, dividends, buybacks, debt, etc impact business value. This is very hard to get an intuitive understanding of these without putting them on paper and looking at the results. These does not have to be complex. Actually these are much better if done by hand on paper at least for the first few. Vinod Hi Vinod, I agree with you probably more than you realize. I distinguish between the theory of DCF (which I agree with 100%) and the practice of DCF (which I think has serious shortcomings). Part of the reason I went through this exercise is to find a middle point between an all-stops-out DCF and the sort of ratios many of us use. The former incorporates all the variables but usually suffers from incorrect inputs. The latter is oversimplistic but, through its ease of calculation, enables the experienced investor to establish appropriateness in different situations. Buffett often says he can decide whether he wants to buy a company in 5 minutes, which means he's using pattern recognition as you say. I use probably 10-20 different ratios to value a stock. The most important are MC/ Cash, Price/ Tang book, Debt/ Equity (more risk means less value) EV/ Rev, EV/ EBITDA, EV/ FCF, Operating PE, PE, ROA, ROE, ROIC, revenue growth, tang book growth. But the most difficult thing is always figuring out how much value I should attribute to different levels of growth. I have used the PEG in the past because it produces numbers that pass my "whiff test" based on experience, at least for growth rates in the 10%-30% range. But I dislike the PEG because it's clearly a tool pulled out of thin air. It seems like the formula: P/ E > 2/(G+R)*ln(g0/r0)-1 provides a better estimate of the appropriate PE, so I plan to start using it rather than the PEG.

To drive that point home, here is a graph of the Google example showing the effect of the pace of annual interest rate increases on the calculated (minimum) fair value for the company. If you plug the formula illustrated into Desmos you can read the datapoints. In order for Google to reach a PE of 10 we would need to be adding about 1.5-2% per year to the current rates of 3%. So that would be a 1970s-type era. I wonder if people in the Depression were forecasting massive inflation to bail out the banks? Presentation1.pdf

Here's the corrected version. These functions for changes in growth and interest rates become pseudolinear so long as the rate of change is not too great. Again, I'm not bashing DCF/ DD theory - I'm just saying the practice is wrong. That's why people bother with PEGs or PEs at all. I wanted a tool that is better than the PEG, but is still simple enough that I don't have to bust out my spreadsheet to look at rate sensitivity on a growth stock. Part of the reason I'm doing this is I looked at Depression-era valuations (where the typical growth stocks sold for around 10X earnings) and asked myself - is that rational? And when you start playing around with the inputs in the formula you can see that it IS rational if growth is going way down or rates are going way up. I think understanding those dependencies in an intuitive way is valuable - it helps me quantify how low these stocks might fall with small changes in expected growth and interest rates. estimating_appropriate_PE_based_on_sustainable_growth_and_interest_rates.pdf

Just realized my math was messed up - in the generalized dividend discount model you have to multiply by the variable growth and interest rates for each individual cash flow. There's no generalized way to express a formula relating growth and interest rates unless you assume exponential rather than linear trajectories. Ugly math.

Thanks for the Einhorn paper. There is truth and untruth mixed in here.. 1) Most people intuitively realize that there is a correspondence between operating multiples and sustainable organic growth rates. Is it linear? Of course not, or a company with flat-line revenue and great cash flow would be worthless. The term “PEG” is unfortunate because it assumes the PE/ G term can be isolated, implying a linear relationship. But that doesn’t mean it isn’t a useful approximation when the assumptions are understood. It’s a bit too easy to rip the PEG without understanding that it does apply in special cases. I illustrated in the “proof” that it works fairly well when (1) interest rates are zero (2) interest rate velocity is zero (3) retained earnings growth falls off at around 1% per annum. Historically, the PEG was typically applied to high-growth companies where the interest-rate term was essentially negligible, meaning interest rates didn’t have to be zero at the time. As the other poster noted, the tech high-flyers of the late 90s often had both limited/ nonexistent retained earnings after buybacks plus unsustainable growth rates. That doesn’t make the dividend discount model wrong - it just means people plugged silly numbers into it. (2) Einhorn’s citation of the Gordon Growth Formula is both theoretically and practically irrelevant. Theoretically, GGF only applies when the growth rate is less than the long bond rate (otherwise the series would not converge). Most of us don’t waste our time evaluating a growth company that can’t even beat inflation. Practically, no company grows at any rate (including zero) forever, which is why the remainder term in most DCFs (which he lauds) produces systematic overvaluation of companies. (3) His “quality of growth” argument also misses the point. If you can’t say something positive about the reliability of retained earnings/ retained earnings growth for a business, you can’t value that business within a hemisphere by any means - DCF or otherwise. Only the balance sheet will (sometimes) save you there. As I practice it, the sustained growth rate is derived from the last 5 years’ (preferably more) compounded growth in retained earnings - assuming we have every reason to expect continuation of such growth in the future. You can count the number of businesses where that sort of characterization can be made on the head of a pin. (4) Einhorn suggests his gold standard of valuation is a DCF. I would be curious whether anyone has ever done a study showing that DCF valuations led to improved investment returns. In my experience, DCFs are riddled with assumptions (most notably the “magic” discount rate) that are at best wrong and at worst impossible to recognize by anyone except the author. While I’ve constructed DCFs in the past, I can’t think of a time I actually bought or sold a stock based on one. Buffett: “Spreadsheets never disappoint.” Buffett: “A good idea should hit you over the head with a baseball bat.” So I didn’t see anything in his analysis that accurately contradicts the inequality I presented. Again, the purpose is not to value a company but to establish in certain situations that a margin of safety may be quantitatively established. Since the mathematics of discounted dividends and discounted FCFs are structurally equivalent, the results are derived from assumptions shared by Einhorn. You’ll note that the changes to the formula generally result in a downward revision of acceptable valuations compared to the PEG result. For example, Google (which recently traded at 36X normative earnings) deserves a PE of about 18 based on the PEG rule. Using the rule outlined above with 18% growth, more normative 4% inflation, 1% growth decline per year, and 0.5% rate increase per year (aggressive perhaps), this would be: P/ E > (g-r)/(vg + vr) = (18-4)/(1+0.5) = 14/1.5 = 9X If you think 10-year AAA rates will stay closer to 3% with 0.5% growth decline and 0% rate increase, then: P/ E > (18-3)/(0.5+0) = 30X Bump up the rate increase 0.5%: P/ E > (18-3)/(0.5+0.5) = 15X Personally I’d be willing to start buying Google at 15-20X. 10X would be nice but probably won’t come unless growth slackens or inflation ramps up to the historic 4% annualized level (1956-2016). I continue buying a company growing at 20% last 5 years at about 7X earnings (which are pretty close to FCF): P/ E > (20-5)/(1+0.5) = 10X So I feel my margin of safety in this case is acceptable even if inflation goes wacko or the company starts slowing down. All approximate, but based on dividend discounting.

Hi folks, people always ask where the PEG comes from and what it means so I made an attempt to derive it from the dividend discount model. It's a heuristic proof at best, but it does produce results that seem to align with experience. I was frustrated for many years by my inability to reconcile the PEG ratio with the Gordon Growth Formula, but I came to realize that the formula is invalid for companies growing above the level of inflation for finite periods of time (which of course is the case for most companies of interest). Hopefully this is helpful to those of you who were as confused as I was. I think it also lends some theoretical clarity to the comments Buffett has made over the years about the effect of interest rates on the valuations of growth stocks. [DERIVATION ATTACHED] Limitations_of_the_PEG_ratio.pdf

Who's going to the annual meeting this year?

I certainly wouldn't disagree with that. I played with Canadian E&Ps (specifically TGA and BNKJF) a few years ago. I gradually came to realize that in a secular bear market in crude the fundamentals themselves would be seriously impaired. Cyclicals will do that, and some never come out. The crazy thing in the early 1930s was you had companies like Coke trading at similar valuations. I did a little simulation of what some popular blue chips today would look like at those same valuations: Symbol Name Price to Book Value PE Ratio (TTM) FMCC Federal Home Loan 0.0 18.2 MSFT Microsoft 1.7 12.0 GOOGL Alphabet 1.0 11.7 TCEHY Tencent Holdings 2.8 11.1 BABA Alibaba Group Holding 1.7 9.2 FB Facebook 1.4 6.5 WMT Walmart 0.8 5.3 BRK.B Berkshire Hathaway 0.3 5.2 XOM Exxon Mobil 0.4 4.9 CVX Chevron 0.3 4.7 INTC Intel 0.6 4.4 PG Procter & Gamble 0.8 4.3 UNH UnitedHealth Group 0.9 4.1 ORCL Oracle 0.7 4.1 CSCO Cisco Systems 0.6 4.1 RDS.A Royal Dutch Shell 0.3 4.0 BAC Bank of America 0.3 3.9 TSM Taiwan Semiconductor 0.9 3.9 JPM JPMorgan Chase 0.3 3.5 AAPL Apple 1.1 3.2 DIS Walt Disney 0.7 2.9 WFC Wells Fargo 0.3 2.8 RY.TO Royal Bank of Canada 0.4 2.6 TD.TO The Toronto-Dominion Bank 0.4 2.6 MO Altria Group 1.6 2.4 SNY Sanofi 0.3 2.1 CIHKY China Merchants Bank Co 0.3 2.1 CHTR Charter Communications 0.4 2.1 PFE Pfizer 0.7 1.9 TM Toyota Motor 0.2 1.9 UNP Union Pacific 0.8 1.9 SBRCY Sberbank of Russia 0.3 1.8 DDAIF Daimler 0.3 1.8 CMCSA Comcast 0.5 1.6 T AT&T 0.4 1.5 IDCBY Industrial And Comml Bank 0.2 1.5 CICHY China Construction Bank 0.2 1.4 VZ Verizon Communications 0.9 1.4 HMC Honda Motor Co 0.2 1.3 BACHY Bank Of China 0.1 1.3 BCMXY Bank of Communications 0.1 1.3 ACGBY Agricultural Bank China 0.2 1.3 OGZPY Gazprom 0.1 0.7 NGG National Grid 0.3 0.7 SVCBY Svenska Cellulosa 0.3 0.1 SWZNF SNB 0.0 0.0 CHL China Mobile 0.3 0.0 FNMA Fannie Mae 0.0 0.0 PNGAY Ping An Insurance (Group) 0.0 0.0 NSRGY Nestle 0.8 0.0 Imagine Facebook trading at less than 10X earnings. It's almost mind-bending. But then again, people were sitting on 70-90% portfolio losses, losing their jobs, losing their savings accounts, etc. Hard to mentally reconstruct the despondency of the country in that era..

Although the market valuations in 1929 were quite high, it's easy to forget that a lot of blue chips were trading at half book or less after the crash. Admittedly, some of these companies probably had a lot of goodwill in their book values from acquisitions during the boom times, but still: https://www.joshuakennon.com/a-look-at-some-major-stocks-during-the-bottom-of-the-1933-stock-market-crash/

Only that that's about the dumbest reason for buying Berkshire that I've ever heard.