# What is the Dow Worth?

Warren Buffett, the renowned value investor, is noted for his ability to respond to sellers of businesses "usually within five minutes" whether or not he is interested in buying that business (at a specified price, of course). He is interested if he can buy the business at a significant discount to its "true worth". The key, of course, is determining that thing called true worth, or as some call it, "intrinsic value".

I imagine Buffett uses a simple, but extremely powerful, formula that captures the essence of value. Using this valuation tool one can readily make an estimate of what the stock market, i.e. the Dow Jones Industrial Index ("the Dow"), is really worth.

Because the Dow Index (an agglomeration of 30 stocks) has a book value, earnings and an implied dividend it can be analyzed just like any individual stock.

Equity analysis requires a study of balance sheet items and income variables. Naturally, these numbers change each year, but they are also effected by inflation. Thus, it is necessary to "normalize" these variables in order to compare performance over time on an apples-to-apples basis. The mathematics is simple and logical.

The first step is to adjust the data for inflation. This reduces the reported numbers to constants which can then be properly compared from year to year. One of the things one notices is that, as time passes, the Dow Jones Industrial Index grows in "intrinsic value" by retaining that portion of its earnings which are not paid out as dividends. Earnings are the return on shareholders' equity, commonly called "book value".

Calculating intrinsic value is simplicity itself. Multiply **earnings times an appropriate multiple and you get intrinsic value**. That's it!

Well, that's not *quite* it. You might be wondering what the "appropriate multiple" part is all about. To find the answer, let's go through the valuation process step by step. The following is the essence, the very heart, of intrinsic value:

Book Value (**BV**) times Return on Equity (**RoE**) equals Earnings (**EPS**)

Then, Earnings times a Multiple equals Intrinsic Value (**IV**)

**B**ook **V**alue is a balance sheet item. While it is very stable and tends to grow steadily over time with retained earnings, it can shrink with operating losses or write-offs. It is a solid base on which to anchor the ensuing calculations.

**R**eturn **o**n **E**quity is the annual earnings generated by BV. ROE will fluctuate from year to year, so it is necessary to stabilize or "normalize" it by using a long term average figure - for example, the past ten years. In this way it is possible to reasonably estimate average returns on invested capital over a long time period. If there are write-offs to BV, it means that earnings in prior years were overstated and they have to be adjusted downwards. The effect is that the previously estimated ROE must be lowered accordingly.

The calculated Earnings will actually be the long term "average" earnings level. For the Dow Index this is equivalent to the "coupon", or interest rate, of a bond.

Because stock and bond investments compete for investor funds head to head in the marketplace, the equity Multiple (often referred to as the price to earnings multiple, or p/e ratio) is, *generally speaking*, a function of interest rates - long term corporate interest rates to be precise. The Multiple is simply the inverse the AAA corporate long bond yield. For example, if the long bond yield is 7%, then the appropriate multiple should be 100 divided by 7, or about 14.3 times. This Multiple can then be applied to the Dow Index.

Now that we have the pieces in place we are ready to calculate the intrinsic value of the Dow Jones Industrial Index. It looks like this:

Book Value of Dow, est. 2000 yr-end 1950

(times) Normalized Return on Equity: 14.0%

(equals) Normalized Earnings: 273

(times) Multiple (100/7%): 14.3

(equals) Intrinsic Value: 3904

Historically, the average ROE has been approximately two times the long term corporate AAA bond yield - this is a key relationship. In the above Intrinsic Value calculation you can change the ROE and the Multiplier to suit yourself, but make sure that your numbers conform to the 2-1 ratio.

Will 14% be an average ROE in future? Is 7% a "normal" or average corporate long bond rate? Just for fun, try a 10% ROE or an 8% bond yield. In a world of 8% bond yields, the ROE should be 16% and the price/earnings multiple the inverse of the bond yield (i.e. 100 divide by 8 = 12.5). It doesn't matter what assumption you make about either ROE or interest rates, if you apply the 2:1 ratio to its partner, the calculated intrinsic value will always be the same.

There are times when the 2:1 ratio gets seriously out of whack - in 1982 the ROE was 6.4% while the AAA corporate bond rate stood over 14%, a ratio of only .46 instead of 2. However, by 1988 things got back into line as the Dow's ROE was over 21% and the AAA corporate yield fell below 10%.

**Today the market is out of whack again - except this time recent estimates of ROE are in the 21% range and AAA corporate bonds are trading near a 7% yield.**

A study of a regression of the Dow's real prices shows a rising trend reflecting the fact that its inherent value increases over the long haul. Deviations form this trend identify, in retrospect, such undervaluations as the one which developed in the early 1980's and the overvaluation bubble of the late 1990's. While the regression line, which fluctuates as new data is incorporated, is not a proxy for intrinsic value, it does show clearly that market prices eventually revert to some long term "mean" or value.

In the long run, reversion to the mean is evident in many areas of the markets. Earnings, share prices, interest rates, currencies, commodities - they all fluctuate. As for the Dow, from this point forward, as the pendulum swings back to normal, one might reasonably expect either lower earnings or a rise in interest rates, possibly a combination of both.

From time to time wide differences between the Dow Index's intrinsic value and itsmarket price, or level, will develop resulting in serious mis-valuations. For those wishing to own stocks, these deviations from the norm should be seen either as investment opportunities or as signals to stand aside.

**So, when Warren Buffett eschews today's equity markets as generally overpriced, I suspect he has come up with values in line with the above calculation.**

John Di Tomasso

Di Tomasso Group Inc.

[email protected]