Thursday, March 7, 2013

Value of Investments per Share (Berkshire Hathaway)

So I explained in my most recent post (Buffett Letter 2012) on Berkshire Hathaway (BRK) why investments per share is not worth investment per share to me.  I know this makes no sense to many, and even Buffett would say it makes no sense.  Cash is worth what it's worth.  No more, no less.

I don't have a problem with that, really.  But I just have another way to look at it, so I thought I'd clarify a little bit more.  Someone posted a comment that I should value investments at market value, and I responded there but then realized I should make my response a full post.  I know there have been debates about this all over the internet for years.

So anyway, here are my thoughts.

Investments are Often Worth Market Value
First of all, investments are worth their market value if they are realizable.  If it can be distributed to shareholders in some way (spin-off, liquidated and cash distributed etc.) without disrupting the business operations, then I believe you can value it at market (less taxes or whatever adjustments that need to be made).

On the other hand, if the investments are part of a business, like in an insurance company, then this is not freely distributable, and therefore it may not be worth market value (not to mention that float becomes an obligation on liquidation).

To keep things really simple, I'll talk about a hypothetical insurance company instead of plugging in the real figures for BRK.  I am going to make up all of these figures so bear with me.

Hypothetical Insurance Company:  Berkaway Hathshire
First of all, let's assume that this amazing insurance company, Berkaway, has an incredible underwriting staff that always breaks even (at least) in the underwriting operations.  Let's say that it's pretty much a sure thing that the cost of float will be free.

Second, let's assume that the investment leverage is 2.5x (much higher than BRK), and this company invests it's float in only fixed income securities.   After-tax return on fixed income securities these days come to around 2% (Don't argue! Let's just say it is true).

Let's also say that the shareholders equity of Berkaway is $1 million.

So here are the figures:

Shareholders equity:        $ 1 million
Float:                                $ 1.5 million
Investments:                     $ 2.5 million (2.5x investment leverage)
Net earnings:                    $ 50,000
ROE:                                 5%

This is what Berkaway looks like.  You see that the ROE comes to 5% despite 2.5x investment leverage.

Now, this is what we are arguing about:  What is the value of this insurance company?

If you believe that an insurance company with zero cost float is worth the investments it owns, then you are saying that Berkaway is worth $2.5 million.

OK.  No problem.  That's one way to look at it.

Some say that the investments is worth market value because that is what you can get if you sell it.  But does the $2.5 million really represent liquidation value?  Let's see what happens if you sold all the investments, paid back the float and distributed the rest to shareholders.  What do you get?  Exactly.  You get $1 million, not $2.5 million.  In liquidation, the float becomes an obligation even if it's as good as equity in a going concern.   That's the paradox of this situation (like trying to catch your own thumb); float is as good as equity and investments are worth market value, but if investments are worth market value in liquidation, then float is not equity anymore).

Equity Investor
Here is how an equity investor might look at it.  I don't want to get into theoretical stuff too much, but let's just say that the cost of equity is 10%.  In other words, when investors invest in stocks, they typically want to earn around 10%. 

If that is the case, then Berkaway is clearly not worth $2.5 million.

As is common in valuing financial companies, the usual way to look at this (and I admit the usual way is not always the right way) is that if a financial company can't earn 10% ROE, then it's not worth book value, and if it can earn more than 10%, then it's worth more than book value.

Buffett Agrees with This
So before we dismiss this notion that firms that earn an ROE below 10% isn't worth book value as being silly, let's think about what Warrren Buffett himself just said on CNBC the other day.

In talking about banks, someone asked him about the cheap banks; banks that trade for less than tangible book.  Wells Fargo trades above book value.  Buffett said that book value doesn't matter in valuing banks, it's the earnings that count.  Now, that sounds odd coming from Buffett who advocates ROE as an important measure of capital efficiency or management competence.

What I realize now when he said that is that he just means that looking at P/B ratios is not that meaningful in evaluating banks.

He clarified that by saying that if a bank can earn return on tangible assets above 1.0%, then it can trade above tangible book value.  If it can't earn 1.0% on tangible assets, then it is worth less than tangible book value.  Banks like Citigroup have ROA below 1% so isn't worth more than tangible book.

By the way, I think Buffett uses 10x leverage for a typical bank, so 1% ROA translates into 10% ROE.

So he is saying the same thing I am saying about financials:  If a financial can earn an ROE above 10%, it is worth more than book, and if it can't, then it's worth less than book.

Another way of saying that is that Buffett thinks the cost of equity for financial companies is around 10%  (But don't use that phrase, cost of equity, in front of Buffett!).

Back to Berkaway Hathshire
So, going back to Berkaway, the ROE in the above example would imply that it is only worth 50% of book value.  On a 5% ROE, you have to pay 50% of book to make a 10% return.   Book value of Berkaway was $1 million, so it's only actually worth $500,000 (at 50% of book).

So how does that compare to total investments?  Total investments are $2.5 million, so at $500,000, Berkaway is actually only worth 20% of total investments.

Other Insurance Companies
So if you still believe that BRK's investments per share are worth the total value, then why not look at other insurance companies?  I would imagine that other insurance companies are very cheap too using this metric (investments per share of Markel, for example, far exceeds it's share price).

The common argument (which is fair) is that BRK doesn't lose money in underwriting (unlike most other insurance companies).  In fact, it has earned $18 billion in the last ten years or some such thing.  I don't know if I would want to bake that into any valuation (opinion here differs, but I don't have a strong feeling either way.  I just sort of not include it.  All valuation measures to me are just ballpark things to think about, not concrete, absolute things).

But underwriting profits and losses can easily be incorporated in valuations.  If cost of float is positive for some companies, you can just deduct from the valuation of the company (if it tends to lose, on average, $1 billion a year, just knock off $10 billion from the valuation).  Conversely, if a company has a negative cost of float, then just capitalize that (if it tends to earn $1 billion in underwriting profits over time, then just add $10 billion to the valuation).

I don't think there is a need to value one insurance company at investments per share because they have a zero or negative cost of float, and then value every other insurance company on the planet at book value or according to ROE.

That sort of seems unreasonable to me.

So, either look at BRK like other insurance companies (using book value, ROE etc...) or look at the other insurance companies using investments per share (and then making adjustments for underwriting losses/cost of float etc.).

I don't think everything should be valued the same way, but in this case, I think it's reasonable as it's a pretty straightforward model we are talking about (ROE, P/B ratios etc...).

But anyway, this is just my opinion.  I'm just clarifying my thoughts on the subject.  I know that the opinions on this stuff differs dramatically and that's totally fine.



  1. I always find it interesting to read discussions (or arguments in many cases) regarding the fair value of Berkshire. Arguments invariably seem overly complex and almost always involve some magical P/B multiple that's based on interpreting Warren's words during interviews on CNBC, Fortune, BRK annual meetings, BRK annual letters, etc.

    Why argue over a P/B multiple? News flash -- Warren does NOT shake his Magic 8-Ball to determine the “right” P/B multiple. He’s translating his rough sum-of-the-parts valuation math into a number that the public can see in all of his financial reports. That’s why he says, “Fair value of Berkshire is MUCH higher than Book Value.”

    Here’s how I believe he comes to his fair value estimate. To me, it seems quite simple (lest we have any Charlie fans out there, “Simple… but not easy”):

    (1) Operating Businesses Earnings x “Appropriate” P/E Multiple [“appropriate” = defined by interest rates and his views on reasonable earnings growth rates for his businesses... 12-15x seem reasonable given the businesses he's assembled]

    (2) “Owner Earnings” from his Equity Investments x “Appropriate” P/E Multiple [he would say that the current market value of his stake in Coca-Cola may not represent intrinsic value, so you can’t just multiple # of shares x current market price... again, say 12-15x]

    (3) Fair Value of his Bond / Derivative / Commodity Investments [disclosure on these are often limited so this one’s tough]

    (4) $ of Current Berkshire Float x Long-Run Expected Return from S&P 500 + “a few percent” [this assumes BRK float continues to be zero-cost. It also assumes Warren is able to do “a few percent” above the S&P 500 return, which he has publicly stated is his goals since he’s now so large]

    That’s it.

    I haven’t studied the most recent balance sheet to determine how that fair value number translates to BRK’s current book equity value, but that’s the way I would go about it.

    P.S. Personally, I think Warren’s aim for the next 10 years will be to buy irreplaceable consumer franchises like Heinz and Mars so that BRK investors will not be as dependent upon (4) after he and Charlie have moved onto new things. So this "Magical P/B" multiple people love to talk about is going to keep going up long after Warren's gone, and you won't have Warren to tell you what it is then.

    1. Hi,

      Thanks for commenting. I look at BRK many ways, but this post is not about the p/b of BRK itself, but just what the p/b might be for the insurance operation.

      This is part of the discussion on what the investments per share is actually worth to the owner.

      Otherwise, I would more or less agree with your approach, except for (4). BRK's float is mostly invested in cash and bonds so I wouldn't use S&P 500 returns on that.

      Anyway, thanks for reading.

  2. First, thanks for the critical thinking you present on this blog. Really good stuff. I recently became a MKL shareholder so spent some time thinking about the arguments you present here.

    Naturally, as you make clear, an insurance company is worth substantially less than investments per share in a liquidation scenario.

    One thing that I think should be added though: If the insurance co. is running as a going concern, and if you view things as a truly long term investor, then substantially all the benefits of ownership of these investments belong to a shareholder. Interest, dividends, capital appreciation -- they all flow through if the operation is being run in perpetuity.

    So, if you think about it in this manner, I think it's reasonable to think of investments/share as a proxy for value, albeit a more aggressive one. Anyway, thanks again for posting.

    1. Hi,

      Thanks for commenting. Yes, it is a proxy for value and an aggressive one. As a going concern, the 'package' of 'free' float and bonds is worth the cash flow it generates to the owner of this package, and if you use an equity discount rate you get the sort of valuation that Berkaway gets in the above example...

  3. Hi,
    here is something that really puzzles me. Why is Buffett willing to buy BRK at 1.2x BV if ROE is only 8-9%, i.e. BV is growing at 8-9%? He said that he believes that shareholders will benefit in a meaningful way by purchases at 1.2x BV. He even suggested that buying at 1.2x BV is like buying dollar bills for 80 cents, implying IV of 1.5x BV.

    1. My above post was just about the insurance operation, not all of BRK.

      As for getting IV up to 1.5x book, you know, you can easily get there just by changing your discount rate. For example, if you expect book value to grow 10%/year over time and you have a 5% discount rate, you can say fair value is 2x book.

      I don't think Buffett uses a 5% discount rate, but I suspect that's where we may differ on the valuation of BRK.

    2. //Hi,
      here is something that really puzzles me. Why is Buffett willing to buy BRK at 1.2x BV if ROE is only 8-9%, i.e. BV is growing at 8-9%? He said that he believes that shareholders will benefit in a meaningful way by purchases at 1.2x BV. He even suggested that buying at 1.2x BV is like buying dollar bills for 80 cents, implying IV of 1.5x BV.//

      This is because the book value of the subs (not the equity holdings minus deferred taxes) way understates their true economic value. Definitely true with the insurance companies like Geico & Ajit Jain all by himself, and also true with the Iscars, Marmons, & BNSFs of this world. He uses book value changes as a proxy for change in IV but insists that book value understates IV and over time it should understate it more and more as FASB rules fail to recognize the increased earnings power of the subs close to reality.

    3. "As for getting IV up to 1.5x book, you know, you can easily get there just by changing your discount rate. For example, if you expect book value to grow 10%/year over time and you have a 5% discount rate, you can say fair value is 2x book."

      Sure but why is Buffett willing to buy at 1.2x BV? I don't think BRK can grow BV at anything above 8-9% unless interest rates go up a lot and/or equity valuations come down a lot. Buying at 1.2x BV gives him a return of only 6.7-7.5%. That seems pretty darn low - especially compared to alternatives like buying more WFC.

    4. I don't think 6.7-7.5% would be considered low by Buffett or Munger, especially in this environment. But yes, compared to WFC, it's not as interesting. I mentioned in one of my WFC posts that it's no wonder that Buffett keeps buying WFC instead of BRK, even though liquidity has to do with it too (easy to buy lots of WFC, not so easy to buy a lot of BRK).

      Also, if you look at growth in book value as a sort of comprehensive EPS, then 15x p/e on a 10% growth in book value gets you to 1.5x book.

      So it's a good question. Why is 1.2x book such a great deal? If you agree with all sorts of IV estimates out there in the $180-190,000/share range, then it's obvious. If you don't agree with those estimates, then it's a mystery.

      (and yes, I understand See's Candies and GEICO is worth way more than book, but in aggregate, I had trouble getting valuation far above book value)

    5. As for why 1.2x book, this article provides some colour.

  4. "I don't think 6.7-7.5% would be considered low by Buffett or Munger, especially in this environment."

    You may be right but considering the 6.6% return assumtion for the pension asset mix I still find this a pretty low hurdle.
    I guess in the end the most likely explanation is that Buffett has lowered his hurdle rate to 12% pre tax / ~8% after tax and that he expects BRK to grow BV at 9-10%.

  5. The degree of popularity of berkshire hathaway is so high that its not very likely that the shares will trade at a big discount to the assets held.

  6. Here’s the way I think about it. If you gave me $73B (Berkshire’s float) to invest, cost free, where I get to keep the profits, and I am an average investor who ought to be able to return 10% average over time, then the float is worth $73B, the discounted value of a stream of $7.3B annual cash flows. Now if you give me caveats, e.g. you have to keep $20B in cash yielding nothing, then that float will be worth less. My gut feeling is that the insurance operations ought to be worth book plus reduced value of the float.

    The other way I think of the $20B cash that he says he needs to keep is that it is working capital, directly analogous to a manufacturer having to keep some minimum level of inventory. Just like you would not discount cash flows and then add back on the value of his inventory while figuring the value of a manufacturer, you shouldn’t give Berkshire’s value the benefit of that piece of the float.

    You may even able to make an argument that since part of his investments are kept in short term bonds that do not return well, they should be discounted by some percentage. However, there is also an option value in these. Rates will increase and Buffett will find future deals.

    Lastly, the part of the float related to future taxes on unrealized gains should be clipped by some small percentage. There is at least some chance that some of these securities will be sold and the capital redeployed at some point in time.

    Just to keep it simple, I would discount the entire float by a third or perhaps even half.

  7. This is unrelated to this post, but have you looked into international banks at all? I'd be interested to hear your thoughts on the National Bank of Greece given it's cheapness. You don't venture into pure international holdings too much though, so not sure if it is out of your expertise and comfort.

    1. Hi,

      Yes, it's a comfort level thing. I do look globally now and then and don't mind owning ADRs which I do now and then.

      But especially for banks these days, it's really tough. People are not even comfortable with U.S. banks, but at least I know people who work at these institutions, I am or have been customers, read and listen to conference calls and all that so I have a great deal of comfort with the management/people at the U.S. banks (that I like, of course).

      I can't say the same for European or other banks; I have no idea about that.

      Thanks for reading.

  8. Nice post. Two key points

    1) Float is a liability. But present value of that liability is less than total float as claims will be paid in future.

    Berkshire's Insurance is like a bank where Float can be compared to deposits and Investments can be compared to loans; Infact it is better than a bank as cost of float is -ve, less operations are needed to run insurance company and better investments than loan.

    2) What investment yield can you make out of float and durability of float is the key. If I can make 10% per year on 70 Billion float. I will make 70 billion in Ten Year, 140 in 20 and if I can maintain this float for 100 years. I have fountain of weath

  9. What about this: To estimate the true value of a float, I take the quoted value of my current float, let's say 1000 mUSD on which I expect to earn on average 5% in the future, and I divide that by a discount rate (e.g. 10%) minus my expected growth rate of that float (let's say 3%) to get the value of that float:

    (1000 mUSD * 0,05) / (0,1-0,03) = 714 mUSD?


    1. Yes, that makes perfect sense. There is a float-based model of BRK valuation that has been popular in years past. The only problem, like anything else, is that the model is very sensitive to changes in assumption about float growth. Can float keep growing at 3%? Didn't Buffett say it shouldn't grow that much more if at all going forward?

      So yes, the thinking is correct, but the output will differ dramatically based on the assumptions you put in, which is true of any model, but this one is particularly sensitive to the float growth rate.

      I don't have any thoughts on what float growth at BRK will be going forward, but I would tend to want to assume no float growth for a conservative valuation.

  10. Excellent site really enjoying reading these posts.

    Question 1: Perhaps to calculate value of Investments we look at average income earned from Investments over past 4-5 years, then take a 10X multiple? (or perhaps 15X multiple since isn't investment income reported as after tax on the Income Sheet?). This seems to be similar to your basic description with 10X multiple.

    Question 2: Are there any remaining Liabilities per share we should subtract? I'm thinking of all non-debt Liabilities (debt being already accounted for by Interest Expense).

  11. KK, sorry for necro post but did you check out Munger's post DJCO q&a session? He talks a little about investments per share and BRK in response to a question about his expected performance of the operating subs going forward. Thought it was interesting.

    1. Hi, I just watched the video but don't remember comments about subs performance... I may have just missed it... what'd he say about it?


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