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Has the long-running bull market been a contemporary version of tulipmania? In explaining their new theory of stock valuation, the authors argue that in fact stock prices are much too low and are destined to rise dramatically in the coming years
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The P/E has a much more interesting history than the dividend yield. Firms tend to set their dividends at a level that they can comfortably maintain or increase every year—cutting dividends is a nasty business. Earnings, however, swing down sharply in recessions and up sharply in boom years. So although from 1890 to 1900 the average dividend yield for the market was around four percent just about every year, the P/E ranged from a low of 13 to a high of 27. Such wild P/E swings have been common. From 1916 to 1921 the average annual market P/E rose from six to 25, only to fall back around 11 the next year. During the Bush Administration the P/E swung wildly between 12 and 22.

Since the P/E is so volatile, it is harder to get a handle on a "reasonable" historical ratio. The average since the 1870s is about 14 (which is the same as an E/P of seven percent). In the late 1970s the P/E dipped below that, perhaps flashing a "buy" signal to market strategists. (Buying in the 1970s was a smart thing to do—but also very brave. The decade was the worst in modern times for the stock market, with the S&P falling by 13 percent after accounting for inflation. Even in the 1930s the S&P rose by 22 percent.) In the time since Ronald Reagan took office, the P/E has climbed from below 10 to between 25 and 30.

If you were adamant that the level of the late 1970s was the "correct" value for the P/E, as many analysts were, you would have stayed away from stocks through the greatest bull market in our history. Even if you took the longer-term view, and didn't bail out of stocks until the P/E climbed above its long-run average of 14, you would have sold out in the late 1980s and missed an octupling of your money.

Again, like the dividend yield, the P/E is a good sign to investors that an individual stock may be a bargain. But yields and P/Es do not indicate some kind of ceiling beyond which the market can't go. Consider Merck, the pharmaceutical house. From 1983 to 1998 its P/E averaged 19. But if investors had accepted that figure as a limit, they would have dumped their shares in early 1995. Over the past four years Merck has tripled in price. By June it was trading at a P/E of 32 and was still, according to our analysis, significantly undervalued. The stock has a dividend yield of 1.5 percent, and over the past five years its dividends have grown by an average of 13 percent.

A profound change has occurred in the attractiveness of stocks since the early 1980s, as investors have become more rational. The old "limits" of yields and P/Es do not apply anymore—if they ever did.

So the prime valuation measures that market analysts have traditionally used have been flashing "overvalued" signals for many years. For the market to return to historical valuation levels by these measures, declines of 50 to 75 percent would be necessary. Yet rather than waiting for the market to revert to the historical levels, we view the measures as woefully mistaken. What are they missing?

WE value stocks according to how much cash they put in your pocket. Stocks are less risky than bonds, so bonds should produce more cash. But let's be conservative and simply assume that stocks and bonds should produce the same amount of cash. In the past stocks produced more cash than bonds: stocks were too cheap. Are they still too cheap? To answer that question we need to construct a method to determine the flow of cash that stocks are likely to deliver. Then we need to put a present value on that flow—what it's worth today to own an asset that will give you, say, $50,000 over the next fifty years. The second part is easy; we can use a simple financial formula. The first part—estimating the cash flow—is a little tougher. Ultimately we want to be able to draw conclusions about the entire market, but let's start by looking at a single firm, Wells Fargo & Company.

Illustration by Christoph Nieman

With antecedents in the famous stagecoach line of the Old West, the San Francisco-based bank merged last year with Norwest Corporation, which had headquarters in Minneapolis and tentacles throughout the country. The new company kept the Wells Fargo name and became the seventh largest bank-holding company in the United States, with more than 2,800 conventional branches and 3,000 mini-branches inside retail stores in twenty-one states. It finished the year with $137 billion in deposits and $2 billion in after-tax profits. Wells Fargo also happens to be one of the better investments of Berkshire Hathaway, the holding company chaired by the superinvestor Warren Buffett. Berkshire owns 67 million shares of Wells, worth $2.9 billion—stock that originally cost Buffett just $392 million. Berkshire is the largest shareholder in the bank.

In April of this year a share of Wells Fargo stock cost $40 and paid an annual dividend of 75 cents, for a yield of 1.9 percent. If you had taken your $40 and put it in a long-term Treasury bond at that time, it would have paid you 5.5 percent interest, or $2.20 a year, for thirty years. The gap of $1.45 between the interest payment of $2.20 and the dividend payment of 75 cents seems very large. Can Wells Fargo really increase its dividends so much in the future that it will put more money in your pocket than the bond would?

The answer depends on how much the dividend grows. Let's look first at the past. Wells Fargo increased its dividend per share over the past five years at a rate of 16.5 percent annually, and over the past ten years at a rate of 14.5 percent. Those growth rates are solid, and Wells Fargo's story is not unusual. If Wells Fargo can sustain similar growth in the future, the dividend payments will become very big very fast. Growing at 16.5 percent a year, that 75-cent dividend will be $1.61 in five years, $3.45 in ten years, and $15.91 in twenty years. In thirty years it will rise to $73.26, whereas the payment from the Treasury bond will still be $2.20. In other words, in that thirtieth year the dividend payment to a Wells Fargo shareholder will be higher than the total of the bond's interest payments over thirty years—and almost twice as great as the bond's $40 principal.

But, of course, growth at 16.5 percent cannot go on forever; indeed, if a firm constantly grew faster than the economy overall, the firm would ultimately swallow the whole thing up. Sooner or later a company matures, and thereafter it just keeps up with the growth of the economy (if that). Yes, 16.5 percent is unrealistic, but if we are willing to make some assumptions about the company's growth in the future, we can predict the amount of cash the company will generate in dividends—and from that figure we can compute its proper value today.

Let's divide a company's life cycle into two stages: "adolescence" and "adulthood" (we won't try to analyze companies that are now fast-growing infants, like so many Internet companies). During adolescence a company grows at a rate higher than that of the economy as a whole. Once it becomes an adult, it grows at a rate that is a bit slower than that of the economy as a whole.

The value of a company's stock depends on its current dividend, together with how fast the company will grow during adolescence, how long adolescence will last, and how fast the company will grow during adulthood. (The best firms, like the best people, are those that keep their adolescent energy even as they reach an advanced age.)

Wells Fargo is hardly an adolescent, but a reinvigorated management and the merger with Norwest give it teenage vitality. So let's start by assuming that Wells will maintain the 16.5 percent growth rate of its dividends of the past five years for another five years. Then let's assume that it will abruptly mature and after that will grow at a rate about 0.5 percent slower than nominal GDP growth, or about 4.5 percent a year. Let's also assume that the prevailing Treasury-bond rate is 5.5 percent, as it was in the spring of this year. This rate is really not so vital, as we will see.

Under these assumptions we can easily total all the bank's future dividends and calculate what those dividends are worth today—their discounted present value. The answer is $128 a share. Let's call that our first estimate of the perfectly reasonable price, or PRP, for Wells Fargo. If last April the market had smartened up and correctly priced the stock immediately, the share price would have risen from $40 to $128. The P/E ratio, which at the time was 33, would have increased to 105.

But this is just one scenario. Let's try some others. If we assume that the company can stay adolescent for ten years instead of five—that is, maintain the 16.5 percent growth rate for a full decade before trailing off—then the PRP becomes $214.

On the other hand, slower growth can lower the numbers—although not enough to make the company look like a bad investment. Say that the company grows at a rate of only 14.5 percent during adolescence. If the high-growth period lasts five years before the company reverts to low-growth adulthood, the PRP is $117. If adolescence lasts ten years, the PRP is $181.

Now assume that the company's dividends in adulthood rise only with the level of inflation—say, 2.5 percent—rather than at a rate slightly below the rate of GDP growth. In that case, with a five-year adolescence at a growth rate of 16.5 percent the PRP is $42, with a ten-year adolescence $67.

Which is the most likely scenario? The choice is yours—which is why you should study the stock. Our guess would be a ten-year adolescence at a growth rate of 14.5 percent followed by a reversion to growth that is 0.5 percent slower than the GDP's. That would cause the price of Wells to quadruple, and the P/E to rise to 149.

Is Wells Fargo special? Not at all. The stock market universe is filled with companies that have stories at least as compelling.

A Value for the Whole Market

IN order to value the whole market, we need first to go back to the yardstick against which stock prices are measured: the U.S. Treasury bond, the main alternative for many investors who are thinking about buying stocks.

A bond is an IOU, a piece of paper indicating that the borrower promises to pay the lender back, with interest. The longest maturity of any Treasury bond you can buy today is thirty years. At the end of last year thirty-year Treasury bonds were paying interest of about five percent. In other words, if you lend the U.S. government $1,000, it will send you checks of $50 a year for the next thirty years, and then hand back the $1,000. In the past bonds with even longer maturities have been issued—by companies, not by the U.S. government. The Walt Disney Company, the Coca-Cola Company, and IBM have all sold 100-year bonds.

If you are considering a long-term bond, you are probably thinking more about how much interest it will pay than about the money you will get back thirty years from now. That is perfectly reasonable. A claim today on $1,000 in thirty years is not worth very much. By the time you get the $1,000, its purchasing power will be reduced significantly. At an inflation rate of 2.5 percent $1,000 loses more than half its value in thirty years and about nine tenths of its value in a hundred years.

A stock has no definite maturity, and certainly comes with no promise to repay your original investment down the road. Sure, if a company is bought out or dissolved, the shareholders might be paid off, but if the company is successful, that event could be decades, or even a century, away. General Electric, for example, traces its beginnings to the Edison Electric Light Company in 1878 and continues to increase its profits at a rapid clip. GE's earnings were $9 billion last year, up from $4 billion in 1993.

So one way to think of a stock is as a bond with a really, really long maturity. Although no stock will last forever, a strategy of keeping your funds in the market as a whole through a mutual fund could be sustained for quite a long time. Extending the maturity toward a far-off horizon actually makes our analysis easier, because we can ignore the repayment of your original investment and focus on the cash flow. That, after all, is the key question in investing: How much money goes into your pocket?

Now suppose the government decided to offer a bond that lasted forever—something called a perpetuity. If the interest rate on this bond were constant over time, it would be easy to price—just like current long-term Treasuries.

Let's say that the rate on comparable investments, such as insured bank certificates of deposit, is 10 percent. Then a bond that paid $1.00 a year forever would cost $10—because that is how much you would have to invest elsewhere to get the same cash flow. If the interest rate on comparable investments was five percent, the perpetuity that paid $1 a year forever would cost $20, because that is how much you'd have to invest elsewhere to get that dollar.

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