Post New

I've been looking over the data for the period Dec '99 to Dec '24, and by my estimate IV/BV has increased quite smoothly from 1.35 to 1.60 over the period, with an r^2 of 0.99. These estimates are based on the weighing machine model, in which the stock price is plotted against BV over a long period of time, and the trendline at any point on the curve is taken as an estimate of IV.

Repurchase prices have been consistent with these estimates. For example, in March 2024 Buffett repurchased A-shares at 1.567x BV, and then on Sept 1, 2024 he issued shares to the Scott family at 1.565x BV as part of his purchase of their BHE shares. The recent $38 billion decline in the value of BHE, as inferred from Buffett's purchase prices of BHE in 2022 and 2044 (with no decline in the BV of BHE) should drop the IV/BV of Berkshire Hathaway shares from someone close to 1.60 to about 1.51 (Buffett's only explanation given for the decline in BHE's value was "Sometimes the value of a company declines.") However, I have to think that the 1.565x BV at which that Buffett issued B-shares to the Scott family is pretty close to his estimate of IV.

For the moment I'll stay with 1.56x BV as my best estimate of IV, while recognizing that no valuation method gives IV to better than about plus or minus 7% or so.

I don't follow what you're saying.

If you're assuming that the price is ultimately a pretty fair representation of value, the message from price in the last 25 years is that the fair book value per share has been falling, not rising, right?

For whatever it's worth, each quarter I look at book value, and also calculate intrinsic value using a fairly time consuming more sophisticated model. Over time one might reasonably expect some drift between the two, but I haven't seen any yet. If anything there is a very slight decrease in the implied fair P/B in the last decade, though I think that's mostly statistical noise - well within the error bars of both methods. There is no theoretically sound reason to expect P/B to remain a good yardstick of value, but to the best of my ability to determine, so far it's coincidentally as good as it always was and any given P/B number has about the same meaning as it has for a very long time. Emphasis on "so far".

Jim

"If you're assuming that the price is ultimately a pretty fair representation of value,..."

Yes, I am assuming that. A plot (log-log) of price versus BV since 1965 has an r^2 of 0.98. That alone doesn't necessarily imply that the trendline is a good estimate of IV. It could be consistently high or low. However when one looks at the points in time when the price has been above trend or below trend, it looks to be about right. For example the price is above trend in June 1998 and below trend in March 2000, above trend in Dec 2007 and below trend in Mar 2009, etc.

"...the message from price in the last 25 years is that the fair book value per share has been falling, not rising, right?"

No, it's been rising, although slowly, from 1.35 in Dec 1999 to 1.59 in Dec 2024. BV has risen by 10.4% annualized over the last 25 years, and IV/BV has risen 0.7%/year, annualized, for a total annualized rise in IV of 11.1%/year.

Here are a couple of points in time for which we can compare price, BV and estimated IV (in my case the trendline of the 1965-2025 plot of P vs BV) and see if we get similar numbers.

As of Dec 31, 1999, BVPS was $37,987 per A-share. The price was $56,100, and P/B was 1.48. The long term trendline of P versus book (my estimate of IV) was $51,456, and the long term trendline of P vs B (i.e., IV) to BV was 1.30.

As of Dec 31, 1024, BVPS was $451,507 per A-share. The price was $680,920, and P/B was 1.51 (As you say, very similar to Dec 1999). The long term trendline of P versus book (my estimate of IV) was $724,435, and the long term trendline of P vs B (i.e., IV) to BV was 1.59.

Please let me know how your estimates compare. Thank you.

"If you're assuming that the price is ultimately a pretty fair representation of value,..."
...

Yes, I am assuming that.

Sorry, I still don't understand your process.
P/B has been falling on trend since the 1990s, not rising. My usual P/B spreadsheet starts in Feb 1996, and the least-squares fit trend line is that the ratio has been falling 2.25 points per year--a whole lot. If you're assuming that market price is ultimately a good-enough proxy for value (not where I would start), it would seem that the conclusion is that intrinsic value as a multiple of book per share is very much lower than it used to be.

e.g.,
First five years of my table: average 1.996
Last five years: average 1.456

Even if you start after the end of the 1990s bubble when things got cheap in 2000, the message is similar:
Five years 2000-2004: average 1.711
Last five years: average 1.456

Or, breaking the data set in half:
1996-2010 average 1.726
2011-2025 average 1.392


True, there has been an upswing lately: the average in the last 18 months at 1.608 is higher than the previously established range. (Average post crunch 2008-2023 inclusive, 1.375).

However 18 months is a pretty short time frame--I would not be in a hurry to call that the new norm. I suspect a lot more of that is generally rising prices in cap weight indexes, and a lot less in terms of calmly rational evaluation of what Berkshire is worth. Except perhaps in the sense of "better value than many other things out there"!

I think it is much more profitable to ignore price and look at a trend in real (after inflation) value per share, using whatever metric you prefer. Book, investments + multiple of earnings, multiple of (earnings + look-through earnings), multiple of multi-year growth in real book, etc. Minus whatever haircuts for debt and cyclical valuation levels you deem suitable. Price is great as one of the two inputs to find out whether something is cheap or expensive at a given time, but it isn't a good enough guide to value.

Jim

"Sorry, I still don't understand your process."

No, I'm sorry; I'm not explaining it well. The current price doesn't factor into the estimate of IV. The IV estimate is simply the long term trendline of P versus BV, at any point along the 60-year data series of P versus BV. Of course the trendline is actually price vs BV, not IV vs BV, but the assumption is that over the long term IV moves with BV, just as price does, and that the P versus BV trendline provides a reasonable estimate of the IV versus BV trendline.

John Kish estimated IV from Dec 1981 through Dec 2014. He calculated several IV's each year, which he labeled optimistic, conservative, etc., corresponding to the assumed discount rate applied. Each of the calculated IV sets, optimistic, conservative, etc. when plotted against BV tracked BV perfectly (r^2 = 1.0), but they were offset from one another. So which set was closest to actual IV. I postulated that if one used price as an imperfect proxy for IV, and plotted P vs BV, that that trendline might be closer to actual IV than the trendlines using Kish's various sets of assumptions. The P vs BV plot worked, with an r^2 of 0.98, so I used the P vs BV trendline as an estimate of IV.

As you point out, other valuation models also work well. A simple two-column model, as used by Tilson, gave an IV as of Dec '24 of $718K/A-share, as compared to the P vs BV model IV of $724K. I think that one of the best models is Buffett's highest P/BV paid in stock repurchases, and those P/BVs (highest repurchase price = 1.57x BV) are in agreement with the P vs BV trendline model (estimated IV = 1.59x BV). I have no doubt that your two and a half column model is one of the best models. My use of the P vs BV model (which I call the weighing machine model) was not to imply that that was the best model; it was only used because it gave a consistent set of IV estimates usable in a discussion of the trend in IV/BV.

Here are the IV/BV from the "weighing machine model." Again, the estimated IV is simply the trendline in the 60-year plot (log-log) of P vs BV (which has an r^2 of 0.98).

date, IV/BV
Dec '99, 1.35
Dec '04, 1.39
Dec '09, 1.43
Dec '14, 1.49
Dec '19, 1.55
Dec '24, 1.60

For comparison, the repurchase price paid in Mar, 2024 was 1.601x the BV at the start of the quarter and 1.567x the BV at the end of the quarter. Berkshire also issued B-shares on 9/1/24 at 1.565x the Sept 30 BV.

I'm sorry, I still can't understand what you are doing.

Your analysis suggests that intrinsic value was only 35% more than book value in 1999 (when market prices was around twice book value), and had risen over time as the market price became a lower and lower multiple of book. I just can't think of what you're doing with the data that leads you to this conclusion.
Can you explain the underlying principal as if to somebody stupid?

(as an aside, the buybacks at high P/B last year are known to be from a long time shareholder, so presumably have nothing to say about management's thoughts about fair value. The highest P/B paid for buybacks that were not from long time shareholders is, I believe, about 1.48 in Feb 2022)

Jim

Can you explain the underlying principal as if to somebody stupid?

Clearly I am indeed the stupid one, I meant principle.

Jim

Probably starts to look interesting sub 425 1.4x book. For me anyway.

Maybe showing the graphs will help. I uploaded a Word file with the graphs into a Google account so that I could share them. The axes got changed when I uploaded the graphs to Google, but the graphs are still correct.

https://docs.google.com/document/d/1jR1lLKl3p8j0Pn...

For the price versus BV graph I used the high and low price for the quarter in order deliberately to add scatter.

I made one correction to the graphs. When I first posted I used data through Mar '25, but out of laziness I used the equation of the trendline through Dec '22. With the equation corrected the IV/BV is 1.32 as of Dec '99 and 1.53 as of Dec '24. The P/B in Q4 '99 ranged from 1.37 to 1.76, ending the quarter at 1.48. The P/B in Q4 '24 ranged from 1.47 to 1.63, ending the quarter at 1.51.

According to this analysis IV was below BV from 1965 to about 1980, but IV/BV is now about 1.54.

There have been three, distinct periods of BV growth and IV growth since 1965: 1965-1981, 1981-1999 and 1999 to present. The same is true of the S&P 500 index (not shown).

I hope this helps.

"Your analysis suggests that intrinsic value was only 35% more than book value in 1999"

Yes, and with the trendline corrected only 32% more.

Here are a couple of other IV/BV estimates as of Dec '99:

Kish conservative (DCF model), 1.45
Kish more conservative (two-column model), 1.31
Weighing machine (P vs BV model), 1.32

Maybe someone here can add another model and IV/BV estimate for Dec '99, and for Dec '24.

"as an aside, the buybacks at high P/B last year are known to be from a long time shareholder, so presumably have nothing to say about management's thoughts about fair value."

OK, however in Sept '23 Berkshire repurchased shares at prices corresponding to 1.47x the beginning BV for the quarter and 1.51x the ending BV for the quarter. The weighing machine model gave an estimated IV/BV of 1.51 as of the end of Q3 2023. The model isn't perfect, but I think it provides reasonable estimates of IV, and ones that are consistent enough to use for estimating the upward trend in IV/BV over the last 60 years and the last 25 years. JMHO.

Kish conservative (DCF model), 1.45
Kish more conservative (two-column model), 1.31
Weighing machine (P vs BV model), 1.32

Well, the consensus of all market players at the time was that the correct answer was 2.0 : )

Most folks on the boards in the stretch 1999-2004 would probably have said a number for value would be around 1.55-1.60, doing a mental average of my memories. I used 1.6 in a spreadsheet last updated in March 2003. Mr Kish's "conservative" figures for 1996-2002 averaged 1.6005 times book. If I (or anyone else) thinks the fair multiple is a hair lower now, I think that's more because there has been a slowly rising appreciation that the high growth rates of the 1990s were gone for good, not because anything big changed in the economic prospects of the firm.

More to the point, I don't think the ratio of true intrinsic value to book value per share has changed since around 2000 (around the time that overvaluation in the stock portfolio wore off, a transient distortion to book per share), certainly within the error bars of either. Especially if you smooth or peak-to-date book-per-share. There is no reason the two shouldn't diverge, but they simply haven't yet.

The best case for the fair IV-to-book ratio rising over time is that buybacks done at a market price above book depress book value. If they are also done at below IV, then they add to IV while decreasing book, so the ratio shifts a little. This has definitely happened.

But...
There are other factors at play, and all those several moving parts both up and down have (so far) cancelled out very closely. For example, investments are clearly not worth a multiple of their carrying value, nor are recent acquisitions which are generally paid for and booked at around fair value. Capex within an existing operating division, other than a railroad, is on average worth more than what was spent on it, driving fair P/B up over time. But some units have had falling profitability, so they are not obviously rising in value at all. Consider the railroad: though things will no doubt turn up at some point, the net earnings in the last many years is not pretty: four quarters after tax earnings are running 18% below their *lowest* level in the stretch 2019-Q2 through 2022-Q4.

Using my own valuation method, it actually shows the "fair" (true intrinsic value) P/B has been falling a bit in the last 10-15 years. Maybe 7 points lower in the last 20 quarters (5 years) than it was in the 20 quarters ending 2017. But I think this is in large part a mix of transient factors and limitations to my valuation skills, so I wouldn't put too much faith in it. I basically assume that it's flat--fair P/B isn't changing--and certainly I see no evidence that fair P/B is rising.

Jim

"I basically assume that it's flat--fair P/B isn't changing--and certainly I see no evidence that fair P/B is rising."

Interesting. That's why we post... to see what other people think. Even I think that IV/BV has increased only little, about 0.6% per year, over the last 25 years, as compared to 10.4% per year for BV itself. Thank you, Jim, for your input, and for your patience.

Sincerely,
rrr13245

"But some units have had falling profitability, so they are not obviously rising in value at all. Consider the railroad: though things will no doubt turn up at some point, the net earnings in the last many years is not pretty: four quarters after tax earnings are running 18% below their *lowest* level in the stretch 2019-Q2 through 2022-Q4."

I worry about BHE, which Buffett says has decreased in value, while its BV has not.

Post New

Berkshire Hathaway FAQ

---

Contact Shrewd'm
Contact the developer of these message boards.