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Most people agree that discount rates are driven by the risk-free rate of interest in effect from time to time, usually that available on U.S. government bonds that are deemed free of any default risk. This could range from the prevailing rate of about 3%, to the historical average of about 3.5%, to the present rate on inflation-protected government bonds of about 4%. Some people use bonds of shorter durations (such as 30 days instead of 30 years), but since equities are inherently long term (i.e., corporations have perpetual duration), it is probably better to use the long bond.

After settling on a risk-free rate, you then add a premium for your stock. The tendency is to look at the average rates of return on equities overall for long periods of time, which has been roughly 7%. That gives you an average risk premium of 3 to 3.5%, which must be tailored to the individual stock you are investigating. The rules of thumb mentioned above get you a long way here, though you should know that many try to be very precise about these matters.

Believers in the modern finance stories discussed earlier, for example, multiply the stock market risk premium by a stock's ß to come up with an appropriate discount rate.

All this disagreement and the examples we've just gone through show you that there is plenty of play in the valuation enterprise. Tiny variations in your assumptions take the bottom line in widely different directions and magnitudes. A 1% change in your guess about the market premium, for example, throws off an appropriate level for the S&P Index by about 200 points (and more if you also play around with your estimate of future earnings growth rates).

Your best approach remains artistic judgment rather than scientific precision. Phil Carret made it one of his investing commandments to "ignore mechanical formulas for valuing securities." 10 Sorry to disappoint you if you expected magical solutions and think you haven't gotten them. In a sense, though, magic is what you get.

Graham delivered the silver bullet of investing when he said the three most important words in investing philosophy are "margin of safety." Recognizing that it is essentially impossible to pinpoint the precise intrinsic value of a stock investing business and that the best you can do is compute reasonable ranges of value based on reasonable assumptions, Graham thought you should give yourself a break by making sure the price you pay is way lower than the low end of your valuation estimate.

Graham called the margin of safety the central concept of investment because its essential function is to render an accurate estimate of the future unnecessary. In using it, you need not stress or struggle over the precise way to define the "right" risk premium, earnings, or discount rate so long as you have a reasonable approx­imation of what makes sense. Its secondary function is to absorb the effect of error in your assumptions—and remember, even tiny errors cause huge effects—as well as the effect of plain bad luck.

Graham observed that most stock investing errors are made not so much by paying too high a price for high-quality stocks as by buying low-quality stocks during times of economic prosperity (much as in early 2000s America). Indeed, Graham repudiated a strategy that overemphasizes what the fashion plates of finance call growth stocks. If you can get the same margin of safety by carefully estimating the future of growth stocks, more power to you, but the danger is that growth stocks tend to be favorites and favoritism in stocks is mea­sured by high prices that steal safety margins.

Graham said the margin of safety principle ultimately served as the touchstone in distinguishing between investing and speculation. Those who deny the difference between price and value or fail to get a margin of safety take their seats at the roulette wheel. Place your bets!

CASH

The same judgment can be applied to the cash a company is expected to generate and pay to shareholders in the future. The cash dividend—based approach to valuation was championed by John Burr Williams, who argued as follows:

Earnings are only a means to an end, and the means should not be mistaken for the end. Therefore we must say that a stock derives its value from its dividends, not its earnings. In short, a stock is worth only what you can get out of it.

In saying that dividends, not earnings, determine value, we seem to be reversing the usual rule that is drilled into every beginner's head when he [or she] starts to trade in the market; namely, that earnings, not dividends, make prices. The apparent contradiction is easily explained, however, for we are discussing permanent investment, not speculative trading, and dividends for years to come, not income for the moment only.

Of course it is true that low earnings together with a high dividend for the time being should be looked at askance, but likewise it is true that these low earnings mean low dividends in the long run. On analysis, therefore, it will be seen that no contradiction really exists between our formula using dividends and the common precept regarding earnings. 12

Williams indicates that dividend discounting and earnings capitalization give the same answer (or range of answers) to the question of what a share of stock is worth.

This is the case because dividends are a subset of earnings. A corporation can deploy its earnings either by paying them out to shareholders as dividends or retaining them for reinvestment in the business. If the retained earnings generate a return equal to the cap rate, the value you get from capitalizing the earnings stream will be the same as the value you get from discounting the dividend stream.

Indeed, valuation by discounting dividends is analytically identical to the capitalization of earnings technique. An assumed divi­dend payment is divided by an assumed discount rate, just as an assumed earnings level was divided by an assumed cap rate. In each case, the questions are (1) What does the expected stream look like in terms of amount and growth? and (2) What is the risk that the amount and growth will not be realized?

The conceptual difference between the two techniques is that in discounting dividends you assume that the value of a share of stock is the present value of the expected dividend payments on it from now until doomsday. This makes sense because the value of the stock consists of the payment stream it yields while it is owned and when it is sold.

The only reason there will be a gain on sale is that some other investor wants to buy the payment stream, and so on. These investors may or may not be correct or even rational in that determi­nation, but it is precisely differences in valuation judgments that lead to such exchanges anyway. As a result, the value of a share of common stock resides solely in its expected stream of cash dividends.

Discounting dividends is just as difficult as capitalizing earnings because both require selecting a highly sensitive discount rate. For dividend discounting, many people try to minimize this difficulty by using the subject's weighted average cost of capital. But that is not a uniquely correct number, and calculating it requires just as much judgment as they are trying to escape.

Calculating the weighted average cost of a company's indebted­ness is relatively easy: It is the average interest rate on all long-term obligations weighted according to the various amounts of principal outstanding on each type of debt. Figuring out the cost of a com­pany's equity capital is far harder.

The cost of equity is usually defined by what the market expects the annualized return on the stock to be, combining price appreciation and dividend payout. But what are we really doing here? In determining a stock's value, we are trying to figure out what the return is going to be. If your key variable in that figuring is what the market expects, you are begging the question. You are assuming the answer rather than analyzing the question.

You are better off forming your own value judgment. There is no formula to tell you the answer, as these examples emphasize. Your only friend at that point is the Graham-Buffett margin of safety, not Mr. Stock Market (you may be fallible; we know Mr. Stock Market is).