This is the third installment of a multi-part series covering the Berkshire Hathaway 2008 Annual Report and Warren Buffett’s letter to shareholders.  In this post, I will provide a valuation estimate for the insurance subsidiaries of Berkshire Hathaway.  Insurance has long been the largest driver of intrinsic value for Berkshire and I view it as the primary “engine” that will drive future growth.

The valuation of the insurance subsidiaries consists of two major components:  (1) Statutory surplus  and (2) Present value of future cash flows derived from investing policyholder “float”.   We will take a closer look at these two components.

Note:  Alice Schroeder wrote a research report for Paine Weber in 1999 that pioneered the use of the float based model.  Schroeder is also the author of Snowball, the latest biography of Warren Buffett.

Statutory Surplus

The combined shareholders’ equity, or statutory surplus, of Berkshire’s insurance subsidiaries was approximately $51 billion on December 31, 2008, which was down from $62 billion a year earlier.  This decline was attributed to declines in the value of Berkshire’s equity holdings over the course of 2008.  It should be noted that this $51 billion figure represents the value of several Berkshire holdings at relatively depressed prices, and prices have fallen further in 2009.  Nevertheless,  for purposes of establishing a value for the shareholders’ equity in the insurance subsidiaries at December 31, 2008, we will simply take the recorded value of statutory surplus at $51 billion.

Float

Policyholder float represents funds that have been paid to Berkshire in the form of premiums that have been reserved for payment of future claims.  On the balance sheet, float is recorded as a liability, and it certainly is a liability in the sense that it represents the best management estimate of what Berkshire will pay out in claims over the life of policies currently in force.  Float is one of the components of liabilities deducted from assets in the insurance subsidiaries in the computation of statutory surplus.  Given this fact, why am I looking at float at all in the calculation of Berkshire’s intrinsic value?

The primary reason to consider float is that, as a going concern, an insurance company is going to perpetually have some level of float on the books.  In the case of Berkshire, the overall level of float has grown dramatically over the past ten years.  The value of float is that Berkshire is able to use these funds for general investment purposes thereby earning returns on the money.  Float is only attractive if it can be obtained at low cost.  Cleary, if the cost of float exceeds the returns Berkshire can earn on the float, it would be destroying rather than enhancing intrinsic value.

It is necessary to calculate the present value of the investment returns Berkshire can expect to earn on the float within the insurance subsidiaries.  In order to make this assessment, we must determine three factors:

• Cost of Float. We must determine the anticipated cost of float in the future  to determine how much the use of these funds will cost Berkshire over time.
• Return on Float. We must determine the rate of return Berkshire can expect to earn on the float provided by the insurance subsidiaries.
• Growth of Float. We must determine how quickly float will grow in the future.

Cost of Float

Berkshire has an admirable long term record that provides significant credibility to Warren Buffett’s assertion that float should be cost free over long periods of time.  Buffett has actually gone further than this on Page 9 of the annual letter stating that he anticipates that Berkshire’s subsidiaries will generate underwriting profits over long periods of time.  Underwriting profits would indicate that the cost of float is better than cost free.

I have been following the cost of float at Berkshire for over a decade.  This link provides data for Berkshire’s four major insurance operations for the past ten years.   The following table provides a summary of the average cost of float for each of the four insurance operations for the entire ten year period, as well as for each five year period (1999 to 2003 and 2004 to 2008):

	Average Cost of Float
	1999-2008	2004-2008	1999-2003
General Re	3.6%	-1.0%	8.1%
GEICO	-8.5%	-15.6%	-3.5%
BH Reinsurance	-1.7%	-3.5%	0.0%
Other Primary	-5.7%	-7.1%	-4.3%

In this table, keep in mind that a negative figure indicates that the unit generated underwriting profits on average over the entire time frame.  One must note that there were specific years during this decade when individual units posted very large underwriting losses.  For example, 2001 was a terrible year for the insurance subsidiaries with a cost of float over 11%.  However, over long periods of time, Berkshire has proven to have the underwriting discipline needed to reject inadequately priced risk and to generate low cost or cost free float. Only General Re has failed to average zero or negative cost float and much of that is attributed to problems that Buffett inherited at General Re that have been largely fixed since 2004, as the figures demonstrate.

Based on Berkshire’s track record, we will assume that Buffett’s prediction of zero cost float will materialize in the coming years over long periods of time (while understanding the fact that any particular year can show an underwriting loss).

Return on Float

The return on float is a somewhat subjective factor in this calculation.  One must keep in mind the fact that considerable reserves must be kept in relatively liquid assets in order to pay claims and historically significant holdings in treasury bonds have existed in the portfolio.  This is balanced by the fact that Warren Buffett has a superior record when it comes to selecting investments for the portfolio over long periods of time.  In prior years, my return on float estimate was much lower given the fact that overall market indices were at far higher levels.  Today, I am comfortable using a 7% return assumption and I believe this may well be exceeded from current depressed valuation levels.

Growth of Float

The final variable to consider is the growth rate of float in the future.  The rate of growth in float will directly contribute to additional funds that can be deployed by Berkshire.  If this growth in float is cost free, earnings on the growth in float will directly contribute to Berkshire’s profitability and our intrinsic value calculation.

Again, this is a subjective estimate, but we can look to the past to determine how float has grown over time.  The following table provides a summary of float growth over the past decade and this link provides more complete data:

	Average Annual Float Growth Rates
	1999-2008	1999-2003	2004-2008
GEICO	9.4%	9.0%	7.2%
General Re	3.3%	9.3%	-1.8%
BH Reinsurance	14.4%	17.3%	9.7%
Other Primary	27.9%	27.0%	22.2%
Total	8.7%	11.8%	4.9%

While past results do not necessarily indicate how much float will grow in future years, it provides some important context.  It clearly shows that float growth has declined (and even shrunk at General Re) over the past several years.  This is due to underwriting discipline.  Remember that float growth is only good if it is cost free (or very low cost)!  There is little point in growing float if that float costs more than Berkshire can earn on investments.  For purposes of this valuation model, I will assume that Berkshire can grow float at a 5% rate over a long period of time.  While this is close to the average annual rate over the past five years, I am actually basing the 5% figure on my estimate of long term growth in nominal GDP.  If insurance needs grow in line with GDP and Berkshire retains current market share, logically, over a long period of time, float should grow accordingly.

Float Valuation

Based on the discussion above, we have assumed long term averages of no cost float, return on float of 7%, and growth of float of 5%.  We are assuming that this pattern will roughly hold over the long term.  Therefore, we will use the growing perpetuity model to come up with the present value of the cash flow.  Assume year one cash flow of 7% of 2008 year end float of $58,488 million.  This would amount to year one cash flow of $4,094 million.  The growing perpetuity model results in the following calculation, assuming a 8% discount rate:

Present Value = Year One Cash Flow / (Discount Rate – Growth Rate)

Present Value = 4094 / (0.08 – 0.05) = $136,467 million

Please note that the calculation above is highly sensitive to the selection of the return assumption, the discount rate, and the growth rate.  For example, assuming a discount rate of 9% rather than 8% would result in the present value calculation of $102,350 million, a decrease of over $34,000 million!  This is why I have attempted to be conservative in my assumptions but clearly there is room for debate on the selection of each variable.

Insurance Subsidiary Valuation

Based on the model discussed in this post, we have a total insurance subsidiary valuation of roughly $188 Billion, or $121,350 per A share.  Please keep in mind that this is the valuation for only the insurance subsidiaries. Future posts in this series will estimate the value of the operating companies, Mid American, and the Finance units.  It is worth noting, however, that my valuation for just the insurance subsidiaries far exceeds that current quotation on Berkshire shares and I have used what I believe are conservative assumptions.