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Float can be a difficult concept to get your mind around. After reading a good explanation, almost everyone can understand the basic economic idea of float, but a full understanding is sometimes elusive when you actually want to figure out its actual quantitative value. I've been thinking about that very issue, and in doing so I thought I'd create some tables which describe how much Berkshire's float would be worth under different scenarios. By different scenarios, I mean different assumptions about the future levels of the key drivers that contribute to the value of float.
The value of float is straightforward, and Buffett's definition has been posted many times on this board.
To begin with, float is money we hold but don't own. In an insurance operation, float arises because premiums are received before losses are paid, an interval that sometimes extends over many years. During that time, the insurer invests the money. This pleasant activity typically carries with it a downside: The premiums that an insurer takes in usually do not cover the losses and expenses it eventually must pay. That leaves it running an "underwriting loss," which is the cost of float. An insurance business has value if its cost of float over time is less than the cost the company would otherwise incur to obtain funds. But the business is a lemon if its cost of float is higher than market rates for money.
In short, float is cheap capital. That is, it's the ability to use money at a cost less than you'd normally have to pay (e.g. interest on a loan), and less than the return you can earn on that money. Of course, it's possible to generate "float" that actually costs you more than other sources of capital, but a better description of that circumstance would be "high interest loan," since the word float really connotes some benefit to the recipient. If float has zero cost, it is the equivalent of an interest free loan. An example of zero cost float in the traditional business world is accounts payable, where companies can delay payment for 3090 days without paying interest (although contracts generally provide a discount for early payment, such that it may not be fair to really view this an economically zero cost).
To value float, then, you can identify five primary value drivers: (1) The cost of the float; (2) The current amount of the float; (3) The expected growth of the float; (4) The expected return on the float proceeds; and (5) Your required return on investment. I know these five drivers may seem unusual, or even redundant, but I'll explain why they are not in a minute. First, a quick example.
Take the simplest case where an insurance company generates float at zero cost. This means that the expected, average combined ratio is 100, i.e., it is breaking even on its insurance operations considering operating costs and claim payments owed. Say that the current $1 million dollar float is not expected to grow in the future, but likewise is not expected to shrink. Thus, every year into perpetuity, your $1 million interest free loan is being replaced with a new $1 million interest free loan, which you hypothetically use to pay off your old loan (in the form of insurance claims). Let's also assume that the float is guaranteed, and that you expect to earn typical riskadjusted returns on the proceeds. How much is this float worth, meaning, how much should you pay for the rights to it?
Well, we know that if the float was guaranteed  that there was no risk that it would shrink or grow more expensive  we could value it pretty easily. The float could be said to be worth book value: $1 million. The right to use $1 million forever at zero risk is equivalent to having cash of $1 million.
Here is how the example meshes with the five drivers mentioned above. The cost of the float (1), 0%, is straightforward, as is the initial amount (2) of $1 million. The expected growth in float (3) is 0%. The expect return on float proceeds (4) is slightly more complicated. The reason valuation models value cash on hand and free cash flow at face value is because the models assume that the business will earn "normal" returns on that capital, and thus it is worth the same as any other dollar of cash. That was the assumption in this case. Why might you vary that assumption? Well, you might vary it if you believed the float could be reinvested to earn excess returns, like if you had the greatest investor of all time overseeing it. The fifth driver of the value of float, your required return on investment (5), is also a little unclear.
At first, it may seem like because float is zero cost, your required return should be 0%. But that's a mistaken approach. The question of what it costs to get the float has already been answered; now you want to know how much you should pay for this admittedly cheap capital. If a company was given $1 million for free, it would have come at zero cost to the company, but you, as an investor, would still only value that money at exactly $1 million and not infinity, because you still require a return on your investment. The easiest way to look at factor 5 is this: This is your annual return if you buy the float at the computed value. So in paying $1 million for the above float, you'd earn a 6% risk free annual return on investment. One thing, then, that sticks out about this example is that it assumes that the stable float is risk free. That is an aggressive assumption, since even the most stable insurance business has more risk in maintaining its float amount and combined ratio than the risk of the government defaulting on its long term debt obligations.
In the above example, I assumed that there was no risk to maintaining a stable float, and thus it was the same as having the cash already on hand. Another way to say this is that I discounted the cash flows expected to be earned on the float at the risk free rate. Mathematically, you would apply the perpetuity formula and say that $1 million would earn risk free returns equal to the risk free cost of capital (say 6%). Thus, you would receive annual interest of $60,000 from the float into perpetuity, which you would discount back to today at 6%. $60K / .06 = $1 million.
Looking at these assumptions in terms of Berkshire's float, you can see how differing the assumption would affect the value of the float to an outside investor. As of June 30, 2001, policyholder float was $30.8 billion. If we simply adhered to the assumptions in the example above, then, the float could be easily valued at $30.8 billion, which incidentally is the reasonable approach that Elias takes in computing the float's fair value in his valuation of Berkshire. You can also vary these assumptions and estimate the value of Berkshire float under each scenario.
Here are some tables outlining hypothetical scenarios, with the value of the float in each instance being the $ figure listed in the tables. In all cases, the current amount of float is $30.8 billion. A negative cost of float is a projection that Berkshire generates a Combined ratio below 100, and actually earns money annually on insurance operations.
These first tables assume that Berkshire's expected return on float is only normal (risk adjusted average return), that our required return on investment is 8%, and that the risk free rate is 6%. (note that this means $1 of expect float will be worth less than face, because it is risky and thus not quite as good as cash). Float value is in billions.
Float Growth
Cost of Float 0% 2% 4% 6%
6% $ 0 $ 0 $ 0 $ 0
4% $ 7.7 $10.47 $16.02 $ 32.65
2% $15.4 $20.94 $32.03 $ 65.30
0% $23.1 $31.42 $48.05 $ 97.94
2% $30.8 $41.89 $64.06 $130.59
4% $38.5 $52.36 $80.08 $163.24
On important thing to keep in mind is that this float growth assumes that there is no additional expense required to grow float. As in normal cash flow situations, if float growth requires capital expenditures or is acquired by the purchase of insurance companies, then those costs must be factored in to reduced the value of overall float.
Now I'll alter the assumptions a bit and focus on the return on float and required rate of return. This table assumes that Buffett can earn annual excess returns of 4%, meaning he can generate 4% per year more than the average investor taking on similar risk. For those who could give a flip about the risk adjusted notion, this model can be seen to assume that Buffett will earn 4% better than the benchmark return, be it the S&P or VTSMX or the Treasury Rate or whatever. In this case, that will be 10% a year, because my risk free rate is 6%. I'll keep the required return at 8%. Here is how the table would change.
Float Growth
Cost of Float 0% 2% 4% 6%
6% $15.4 $20.94 $ 32.03 $ 65.30
4% $23.1 $31.42 $ 48.05 $ 97.94
2% $30.8 $41.89 $ 64.06 $130.59
0% $38.5 $52.36 $ 80.08 $163.24
2% $46.2 $62.83 $ 96.10 $195.89
4% $53.9 $73.30 $112.11 $228.54
Keep in mind that at some point the logic embedded in this model must end  Buffett can't perpetually reinvest 100% of his cash flows or float and earn excess returns, or he would eventually eat up the entire economy; not that that's entirely out of the question for Buffett.
Finally, here's one assuming that Buffett only earns 2% better than the benchmark on float proceeds, an 8% risk free return.
Float Growth
Cost of Float 0% 2% 4% 6%
6% $ 7.7 $10.47 $ 16.02 $ 32.65
4% $15.4 $20.94 $ 32.03 $ 65.30
2% $23.1 $31.42 $ 48.05 $ 97.94
0% $30.8 $41.89 $ 64.06 $130.59
2% $38.5 $52.36 $ 80.08 $163.24
4% $46.2 $62.83 $ 96.10 $195.89
Keep in mind that these numbers represent the value of the float given these assumption. In valuing Berkshire, it is an error to add the value of the float to cash/investments because that double counts float. This is just of a way of valuing the float in isolation, under various assumptions.
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