Shreyas Patel

# Buffett’s Buyback Math – why 120% of book value is the magic number for Berkshire

In 2012 Warren Buffett (Trades, Portfolio) indicated he would buy back Berkshire Hathaway stock up to 120% of its book value, but have you wondered why 120% is the right yardstick and not 110% or 130%? There have been a few posts explaining why 120% might sound reasonable premised on assumptions around estimated book growth and future multiples, however these arguments are unconvincing in my view.

I believe the "magic" 120% of book value is a simple back-of-the-envelope calculation which makes an adjustment for Berkshires capital structure. It requires no forecasts or assumptions to be made and is purely balance-sheet driven.

This adjustment relates to the insurance float that should economically be counted as book value but isn’t under the accounting rules. The “float-adjusted book value” therefore results in a conservatively understated valuation at a premium to reported book value. I believe this estimate is where Buffett has pinned his buyback threshold and the clue behind why lies in this quote:

“The value of our float is one reasona huge reasonwhy we believe Berkshire’s intrinsic business value substantially exceeds its book value.” (Buffett 2013)

So let’s work through the detail. It helps to consider Berkshire’s balance sheet in two parts being (i) the operating businesses and (ii) the insurance business.

We know that valuing the operating business at 100% of book value will underestimate intrinsic value given the significant earnings power and growth warrants an "economic goodwill" premium when trying to determine intrinsic value. However, the level above book value for which this is appropriate is highly subjective – so being deliberately conservative we assume 100% of book value for the operating businesses is the threshold for this part of Berkshire.

2.The Insurance business at >100% of book value – adjustment for float

We also now realise that 100% of book value for the insurance business is not an accurate value anchor given the treatment of float as a liability (it is counted as a deduction in determining net worth under accounting rules). Buffett is strongly opposed to the idea that float should be valued as a liability. Consider the following comments from Buffett and its implications for the valuation of float:

=> Float should not be considered a liability, but more like equity

“Though float is shown on our balance sheet as a liability, it has a value to Berkshire greater than an equal amount of net worth would have had”. (Buffett 1997)

=> A dollar of float has more value than a dollar of equity

“Since our float has cost us virtually nothing over the years, it has in effect served as equity. Of course, it differed from true equity in that it doesn’t belong to us. Nevertheless, let’s assume that instead of our having \$3.4 bn of float at the end of 1994, we had replaced it with \$3.4 bn of equity. Under this scenario, we would have owned no more assets than we did during 1995. We would, however, have had lower earnings because the cost of float was negative last year. That is our float threw off profits”. (Buffett 1995)

=> Float is worth more than its face value if it can grow.

“If I were offered \$7 bn for \$7 bn of float and did not have to pay tax on the gain but would thereafter have to stay out of the insurance business forever a perpetual non-compete in any kind of insurance would I accept that? The answer is no. That’s not because I’d rather have \$7 bn of float than \$7 bn of free money. It’s because I expect the \$7 bn to grow”. (Buffett 1996)

And so we conclude that a conservative (understated) value of float for Berkshire is at least equal to its face value as if it were equity. Therefore, adding back float to book value should result in a more appropriate book multiple anchor for the insurance business. Note, we also need to make an additional adjustment to exclude insurance goodwill since this is an intangible asset included in book value, but economically represents the cost to acquire the float which we are adding back.

Berkshire’s float adjusted book value is 120% of reported book value

So putting the above together, the float adjusted book value (FABV) for Berkshire can then be represented as:

• Reported book value of operating businesses at 100%
• Plus reported book value of insurance businesses at 100%
• Plus insurance float
• Less insurance goodwill

This simply breaks down to reported book value (BV) plus float less goodwill.

The table below highlights this book value adjustment going back to 2004. The analysis shows:

• Float-adjusted book value multiple has trended from 129% to 119% at 2Q-2014
• Float-adjusted book value multiple has averaged 121% since 2010 – this is likely why Buffett has chosen 120% as the magic buyback number

In light of the above trends, it is obvious that Buffet’s previous 110% threshold (before it was lifted to 120%) was way too low given the 120-130% historical range. As a final sense check, Buffett has said growth in book value tracks growth in intrinsic value. We should expect the float-adjusted book value to broadly track book value growth – and it does (BVPS growth at 10.4%pa versus FABVPS at 9.4%pa since 2004).

With BRK.A trading at \$196K (138% of book value) and only 16% above our understated \$169K float-based book value per share, the stock appears to have limited downside risk and could prove to be a reasonable risk/reward play.

Disclosure: I do not hold BRK.A at the time of writing.

Shreyas Patel
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Rdj1234 - 2 years ago    Report SPAM

Hi Shreyas,

Your hypothesis seems well researched, and is very thought provoking.

My own hypothesis was that it had to do with the long term, 20% growth of book value actually being equal to roe, one of his favorite metrics.

Roger

Shreyas Patel - 2 years ago    Report SPAM

Hi Roger,

Berkshire's book growth is alot slower than it used to be. Around 10%pa over the last decade versus 20%pa over the very long-term. Going forward you would expect it will be closer to the 10% mark.

In any case, I think if a business was retaining earnings and compounding at 20% you would be happy to pay well over 1.2x book, especially if all you want is a 15%pa return.

Cheers, Shreyas