In 2012, Warren Buffett indicated he would buy back Berkshire Hathaway (NYSE:BRK.A) 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 attempts 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 Berkshire's capital structure. It requires no forecasts or assumptions to be made and is purely balance sheet driven.

This adjustment relates to the insurance float which 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 the following quote:

The value of our float is one reason-a huge reason-why we believe Berkshire's intrinsic business value substantially exceeds its book value. (Warren Buffett, 2013 BRK Annual Report)

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 businesses.

**1.** **The operating businesses at 100% of book value - no adjustments**

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 realize 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. (Warren Buffett, 1997 BRK Annual Report)

**=>****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 $3.4bn of float at the end of 1994, we had replaced it with $3.4bn 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. (Warren Buffett, 1995 BRK Annual Report)

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

If I were offered $7bn for $7bn 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 $7bn of float than $7bn of free money. It's because I expect the $7bn to grow. (Warren Buffett, 1996 Shareholders' meeting)

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 for Berkshire (FABV) 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*

(Image source: iinvestor)

In light of the above trends, it is obvious that Buffett'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: **The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it. The author has no business relationship with any company whose stock is mentioned in this article.