**Summary**: 1,25 price to book is a very reasonable price for Berkshire Hathaway stock. If you buy at that price point, you can expect a future return of roughly 12%. Buy A shares if the price dips under 1,4 PB = $182,816 x 1,4 = $255,942

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Below is a slightly simplified version of the explanation given by Warren Buffett in his Letter to Shareholders 2012; http://www.berkshirehathaway.com/letters/2012ltr.pdf see page 20.

"We’ll start by assuming that you are the owner of a business with $1.00 million of book value. The business earns 12% on tangible book value – $120,000 – and can reasonably expect to earn the same 12% on reinvested earnings. Furthermore, there are outsiders who always wish to buy into your business at 125% of net worth (in other words at a stock Price of 1.25x Book or 1.25 "PB"). Therefore, the quoted (or market) value of what you own is now $1.25 million. You leave all earnings in the company and sell 3.2% of your shares annually. Since the shares would be sold at 125% of book value, this approach would produce $40,000 of cash initially, a sum that would grow annually. Call this the “sell-off” approach. Under this “sell-off” scenario, the net worth of your company increases to $3,105,848 after ten years ($1 million compounded at 12%). Because you sell shares each year, your percentage ownership would have declined, and, after ten years, you would own 72.24% of the business. Even so, your share of the net worth of the company at that time would be $1 121 770. And, remember, every dollar of net worth (book value) attributable to you can be sold for $1.25. Therefore, the market value of your remaining shares would be $1 402 213. Voila! – you have both more cash to spend annually and more capital value.

**This calculation, of course, assumes that our hypothetical company can earn an average of 12% annually on net worth and that its shareholders can sell their shares for an average of 125% of book value. To that point, the S&P 500 earns considerably more than 12% on net worth and sells at a price far above 125% of that net worth.**__Both assumptions also seem reasonable for Berkshire, though certainly not assured.__(Keep remembering, open-market purchases of the stock take place at 125% of book value.)
Moreover, on the plus side, there also is a possibility that the assumptions will be exceeded. The sell-off method, unlike dividends, lets each shareholder make her own choice between cash receipts and capital build-up. One shareholder can elect to cash out, say, 60% of annual earnings while other shareholders elect 20% or nothing at all.

Let me end this math exercise – and I can hear you cheering as I put away the dentist drill – by using my own case to illustrate how a shareholder’s regular disposals of shares can be accompanied by an increased investment in his or her business. For the last seven years, I have annually given away about 4,25% of my Berkshire shares. Through this process, my original position of 712,497,000 B-equivalent shares (split-adjusted) has decreased to 528,525,623 shares. Clearly, my ownership percentage of the company has significantly decreased. Yet my investment in the business has actually increased: The book value of my current interest in Berkshire considerably exceeds the book value attributable to my holdings of seven years ago. (The actual figures are $28.2 billion for 2005 and $40.2 billion for 2012.) In other words, I now have far more money working for me at Berkshire even though my ownership of the company has materially decreased. It’s also true that my share of both Berkshire’s intrinsic business value and the company’s normal earning power is far greater than it was in 2005. Over time, I expect this accretion of value to continue – albeit in a decidedly irregular fashion – even as I now annually give away more than 4,25% of my shares (the increase has occurred because I’ve recently doubled my lifetime pledges to certain foundations).

At Berkshire we will stick with our no dividend, sell off policy as long as we believe our assumptions about the book-value buildup and the market-price premium seem reasonable. If the prospects for either factor change materially for the worse, we will reexamine our actions."

Below is a chart I have used for my own decisions on Berkshire Hathaway, when I wanted to sell around October 2016. I decided to wait and did some selling around January 2017. (The chart is in Euros and is based on only 7 unevenly distributed data sets across the years, but should get the point across.) The current Price / Book at Berkshire Hathaway is: $180/$122 = 1,48 which is higher than 1,25. (B shares is A shares divided by 1 500. Buy A shares if the price dips under 1,4 PB = $182,816 x 1,4 = $255,942 )

Comments, questions or E-mails welcome: ajbrenninkmeijer@gmail.com

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