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For many years, the most common way to determine Berkshire Hathaway's (BRK.A) intrinsic value has been to simply take investments at their per share amount and then add in the value of the firm's operating businesses by capitalizing their pre-tax income per share. This methodology has been discussed many times before and I will not repeat it here, but there is clearly a good reason why this has been used. In his shareholder letters, Warren Buffett has regularly detailed the investment and pre-tax income per share figures in the sections designated to intrinsic value and has explicitly stated that they are important for it's determination. However, this method is rather simplistic and does a poor job factoring in the shifting nature of BRK's structure and it's use of float, as well as the relative value of other investment options, such as the S&P 500 or prevailing interest rates. Instead, I would like to propose an alternative method that is still reasonably simple, but I think more robust, and I will even take it from Buffett's own words.

Using Buffett's Investment Framework, as Discussed in 1977

Back in the spring of 1977, Buffett wrote an article for Fortune magazine titled "How Inflation Swindles the Equity Investor," which detailed his opinion of how inflation would affect American businesses and the valuation of their earnings. Before you continue, I recommend reading through the archived version of this article on the Fortune website. While it focuses specifically on how inflation adjusts the underlying variables that contribute to return on equity (ROE), it also provides a very unique framework for roughly guessing at future stock returns.

To determine these returns, one must consider stocks to be similar to a perpetual bond with ROE acting as a coupon on par, or book value (BV). The main difference is that stocks, instead of paying out the full coupon in cash that needs to be either consumed or reinvested by the bondholder, reinvest a portion of their coupon back into the company at par. On a market-wide level, the coupon proved to be reasonably stable over the thirty years prior to when the article was written, around 12%. Since 1990, however, the S&P 500 has averaged around 14%, the shift upward being the result of several factors that changed in favor of corporate profitability starting in 1980.

To determine the relative attractiveness of the market at any one time to bonds, one simply needs to price the index as though it were a high-grade corporate bond using prevailing interest rates. This intrinsic price to book value would obviously understate the true value, because of the benefit of reinvestment, but would provide a rough estimate of attractiveness across asset classes. The important point of this exercise is that it adjusts valuation for the inflationary and interest rate environment at the time of investment, and thereby shows that a P/BV of 2x, for example, is meaningless on its own without the knowledge of what the coupon rate is and what other investments yield. This is important for looking at historical P/BV of the market and making comparisons across wildly different interest rate, inflationary, and even ROE environments.

While this helps determine the relative attractiveness of the broader market versus other asset classes, it also helps indicate the relative value of an individual stock to the market. Simply stating that a stock is a good buy at a P/E of 10x because of its relation to the market P/E of 17x is not good enough, there needs to be a comparison of the underlying reinvestment rate of earnings retained and the amount of capital needed to produce them. In this way, we can come to a relative valuation of the S&P 500 and BRK, though the ROE for the latter will be determined from a somewhat unusual way.

What Is BRK's Normalized ROE?

Because BRK is a special company, we will obviously need a special way to determine it's true ROE. While it is possible at most companies to determine ROE by simply dividing net income by shareholders' equity, the accounting of BRK's investment portfolio results in net income understating the change in BV. For this reason, I think it is best to determine what the BV per share growth rate is likely to be over the coming years to determine a rough estimate of ROE.

Two things will determine BRK's BV growth: marketable security investments and operating income. This is convenient, because these are the exact two items that Buffett provides us with in his annual letters. But aren't I just getting back to the way the intrinsic value has been calculated in the past? No, instead of simply looking at the stated numbers, I'd like to look at the level of change for the two variables.

Click to enlarge.

Source: BRK 2012 Annual Report pg. 104.

The level of change is the most important part of the above figures because the investment per share is not all value for shareholders. These holdings are mostly funded by insurance float, but because of the incredibly low cost of this float, for many years most of the increase related to the market price of the underlying holdings have increased BV per share at a dollar for dollar rate. As the growth of insurance float is reduced, the growth in this investment per share figure will be attributable more toward actual market increases in the underlying securities than absolute increases in the amount of securities held. For this reason, and because Buffett himself can only look to companies of a certain size, it is hard to expect growth of investment per share to do much better than the market broadly. I personally don't think the market will do much better than 4%-5% over the next several years, based on its current valuation, and think it would be more than fair if we simply attached this growth rate to investment per share over the coming years. It should be noted, however, that I think it is quite likely that Buffett's holdings will beat the S&P 500, but to be conservative that is what I'll use.

Fortunately, operating income has done more of the heavy lifting in growing BV for shareholders in the last decade. From year-end 1990 to 2000, BV per share increased $35,830 with EPS, excluding realized investment gains, making up only $5,580 of that amount, or 15.5%. Now, from year-end 2000 to 2010, BV per share increased $55,011, but this time EPS contributed $42,655 of this amount, or a whopping 77%. This is a dramatic change in the underlying structure of BRK and it is one that must be accounted for. As shown in the 2012 annual letter, pre-tax earnings per share of non-insurance businesses grew at an annualized rate of 24.5% in the 1990s and 20.5% in the 2000s. Every year these earnings grow faster than broader BV growth, they become a larger contributor to ROE. If we look simply at EPS that excludes realized gains/losses from investments for the past decade, it has averaged a return on the whole of the firm's equity of about 8%.

I think the best way to determine future growth of BV is to simply add these two returns together, 4% + 8%, to get 12%. I think this is a fair return to expect for BRK's BV per share, but would not argue against someone claiming 10% or 11% was a better estimate. This is clearly much lower than it has averaged over the last 40 years, but is a few percentage points higher than average growth per share during the last decade (10.9%). I think these additional points are deserved due to the increased importance of the operating businesses on value, and therefore a clearer picture of their true ROE as they get bigger. Obviously I cannot give this normalized return number with certainty, particularly without knowing the true underlying economics of every business within the BRK structure, but I think it would be hard to argue an amount much lower -- i.e., something below 10%, because I think Buffett would start paying a dividend if he didn't think retained earnings could grow at a higher rate.

How Does This Relate to the S&P 500?

Now that we have a sense for the BRK equity coupon, how much could we reasonably pay relative to par? Let's consider the investment alternatives. Currently, an investor that goes out to buy something in the market could get the following: the 10-year U.S. treasury yielding 2.75%, the FINRA/Bloomberg Investment Grade bond index yielding 3.65%, the FINRA/Bloomberg High Yield bond index yielding 5.82%, or the S&P 500 with an ROE that has averaged 14% and has paid out about 42% of this in dividends over the last decade, but currently trades at a price of 270% to par.

Interestingly, 270% of par may be a good deal relative to the other bond options. If a perpetual bond had a coupon of 14%, couldn't reinvest back into the business at rates higher than current yields, and traded to have a current yield of 4%, it would trade at around 345% of par. A current yield of 5% brings us in line with the current valuation, or 135bps higher than bonds from similar companies. This is, of course, a rough approximation, but useful nonetheless. If one makes the assumption that anything paid in cash needs to be reinvested, then it makes sense to compare current income versus future income in a reasonably similar way, though the ability to reinvest at the S&P 500 ROE is a very valuable component of stock market returns. Even if one assumes that the ROE will come back in line with the long-term historical average of 12%, it is still highly accretive.

So the S&P 500 has a coupon of 13%-14% on average, but pays out 40% of that in dividends, which cannot be reinvested at the same rate of return. Having backed into a yield of 5% to hit the current P/B valuation, let's apply that rate to the BRK equity coupon we discussed above. If BRK is a bond that has a coupon of 12% and was priced at a current yield of 5%, leaving aside the fact that 100% of that coupon is reinvested back into the business, we get a fair valuation of 240%. Applying this to BV per A-share at Q3 2013 of $128,624 gets us a fair value, relative to the current investment environment, of $308,700. With shares currently trading hands at $172,000, an investor today is provided with a margin of safety of 44% relative to a valuation comparable to other broad investment indices.

What do we learn from this? Despite its lower coupon rate, BRK's current price provides a compelling valuation relative to the stock market as a whole. In addition, an owner is getting the ability to reinvest the whole coupon back in at 12%, instead of an S&P 500 holder who has only 60% of the coupon (about 8% of par) reinvested at the 13%-14%. If your goal is to beat the market, a rise in interest rates broadly will affect the coupon valuation of both the S&P 500 and BRK reasonably equally, as these rates act as gravity for valuations across the spectrum. If an investor buys at a large enough discount to the fair value, a change of that value due to interest rates can be better insulated from permanent loss.

On a side note, we know Buffett has stated that at 120% of BV the price of BRK is too enticing for him not to buy back stock in the open market. This 120% equates perfectly to a 10% current yield, or a 15% pre-tax yield at current corporate tax rates, a figure that has been thrown around before as his previous investment hurdle rate. I find it unlikely that this is his hurdle rate any more, but given the option of receiving it on a company he knows better than any other, I think it would be hard for him to pass up.

Final Thoughts

You cannot change the investment environment that you operate in, you simply have to choose from the best options available at the time. In presenting this alternative way of valuing BRK, I am attempting to create a framework that is more robust in the way it accounts for other investment opportunities and interest rates at the time of investment. I am not using this article to try and sell BRK stock to you as a good investment simply because it is valued attractively relative to the S&P 500. Having said that, it seems clear that the owner of BRK will likely do better than the holder of the S&P 500 in the future, and I would say it provides a reasonable investment yardstick that all other investment purchases can be held against. Buffett and Munger have both discussed the opportunity cost in not buying more of your current best idea and I see no reason why an individual investor can't use BRK as their potential alternative use for funds. Feel free to adjust any of the assumptions up above to suit your own idea of the firm's intrinsic value; I've only given the estimates that I think are reasonable based on available information.

Note: Current and historical market data taken from Bloomberg terminal.

Source: An Alternative Approach To Calculating Berkshire Hathaway's Intrinsic Value