Irving Fisher’s formula is Market Value ⴝ Current Dividend / (DR ⴚDividend Rate of Growth)
Let’s define each term in this formula. Market value, as we discussed, is the so-called fair, or correct, price of the stock or stocks as determined by this formula. Even if someone does not accept all the assumptions inherent in this formula, the market value gives a reasonable baseline against which to evaluate a stock’s price.
The current dividend is available for any stock by searching the Web. If the dividend is given as percent dividend or dividend yield, then just multiply that num- ber times the price of the stock and divide by 100 per- cent. The dividend for the S&P 500 is also given on many web sites; for example, http://www.indexarb.com/
dividendYieldSortedsp.html gives the dividend yield. As of November 2007, the S&P 500 dividend yield shown on this site is 1.73 percent, and the price of the S&P 500 is $1,520. So, to get the current dividend: ($1,520 * 1.73 percent)/100 percent ⫽$26.30.
The dividend rate of growth (DR) is the yield we expect from the stock market to make it an investment we would choose over a safe alternative investment, like Treasury bond yields. Between 1926 and 2000, the S&P 500 yield, including reinvested dividends, was 10.9 per- cent. Treasury yields in those same years averaged 5.6 percent. So the stock market earned 5.3 percent more than Treasury bonds. We will assume that this is the
Key Point
Irving Fisher determined that a company’s stock price, or a group of stocks’ price, is worth its future discounted dividend stream. This is the value of its future dividends in today’s dollars.
Irving Fisher Formula A numerical way to deter- mine a fair market value of a stock or the stock mar- ket in general
Market Value
The calculated fair price of a stock or stocks, a number that provides a reasonable baseline against which to evaluate a stock’s price
extra yield that investors demand from stocks to justify the added risks. Assuming that Treasury yields are cur- rently 5 percent, this would make our DR ⫽5.0 percent ⫹ 5.3 percent ⫽10.3 percent.
We saw from Figure 8.3 that S&P 500 dividends have historically grown at a uniform rate, which happens to be 4.2 percent per year. So in the formula, the divi- dend rate of growth is 4.2 percent, or 0.042.
Therefore:
Current dividend ⫽$26.30 DR ⫽0.103
Dividend rate of growth ⫽0.042
Plugging these into Irving Fisher’s formula:
Market value ⫽current dividend / (DR – dividend rate of growth)
Market value ⫽$26.30 / (0.103 – 0.042) Market value ⫽$431
Now, $431 is certainly less than the current S&P 500 price of $1,520. This formula gives about the same price discrepancy we found in Figure 8.2, when we visually compared the current price/dividend ratio to the historical ratio. In fact, to match the Irving Fisher market value of
$431, the stock market would have to drop 71.5 percent.
This may seem impossible, but between year-end 1928 to year-end 1932, the U.S. stock market dropped 72 percent. The Japanese stock market, from 1989 through 2003, also dropped 71 percent. And remember, the 71.5 percent drop that is indicated by Irving Fisher’s formula would merely take us back to a level where stock prices would be historically expected, notto a depres- sion level.
The Irving Fisher Formula and GE Stock Value
Although Irving Fisher designed his formula for individual stocks, its use is valid only if you assume that a company’s historical dividend growth will con- tinue. Let’s use the previous formula to check out the market value for GE.
Let’s first look at a graph of GE’s dividends (Figure 8.4) to see if they have been growing at a constant rate. We will graph the dividends logarithmically to see if the resultant plot is an upward-trending straight line, which would indicate a value growing at a constant rate.
Current Dividend The most recent share of profits received by a share- holder, usually stated on an annual basis
DR
The yield we expect from the stock mar- ket to make it an investment we would choose over a safer alterna- tive investment
If you look closely, you will see that the dividend growth was at one rate in the 1980s, then at a higher rate in the 1990s, with a return to a somewhat slower growth rate starting in 2001. In the actual data, the rate of growth in the 1980s was 9.5 percent, 13.5 percent in the 1990s, and 10 percent since then.
We will use 10 percent in our Fisher analysis. As we did for the analysis of the S&P 500, let’s assume that we want a DR of 10.3 percent.
Therefore:
Current (2006) dividend ⫽$1.03 DR ⫽0.103
Dividend rate of growth ⫽0.10
Plugging these into Irving Fisher’s formula:
Market value ⫽current dividend / (DR – dividend rate of growth)
0.01 1
0.1
Dividend $
Date
Feb-79 Feb-80 Feb-81 Feb-82 Feb-83 Feb-84 Feb-85 Feb-86 Feb-87 Feb-88 Feb-89 Feb-90 Feb-91 Feb-92 Feb-93 Feb-94 Feb-95 Feb-96 Feb-97 Feb-98 Feb-99 Feb-00 Feb-01 Feb-02 Feb-03 Feb-04 Feb-05 Feb-06 Feb-07
FIGURE 8.4 GE Quarterly Dividends, Plotted Logarithmically Source:Data from http://finance.yahoo.com/
Key Point
Although Irving Fisher designed his formula for individual stocks, its use is valid only if you assume that a company’s historical dividend growth will continue.
Market value ⫽$1.03 / (0.103 – 0.100) Market value ⫽$343
As stated earlier in the book, GE’s current price is $41.00 per share. This formula says that if you believethat GE can continue its 10 percent annual growth in dividends for the long term, the per-share market value of GE stock is $343!
However, as we saw in Chapter 1, recent GE sales have been going up 2.3 percent per year. As we noted earlier, GE has been great at postponing and reducing costs, but this alone will not enable them to continue with their 10 percent annual div- idend growth. If their sales continue to be slow and the delayed costs start to catch up, they may have to reduce their dividend growth rate to the 4.2 percent of the general market. Let’s see what GE is worth under that scenario.
Current (2006) dividend ⫽$1.03 DR ⫽0.103
Dividend rate of growth ⫽0.042
Plugging these into Irving Fisher’s formula:
Market value ⫽current dividend / (DR – dividend rate of growth) Market value ⫽$1.03 / (0.103 – 0.042)
Market value ⫽$16.89
So, if GE dividends stop growing at their unusually high rate, and they grow like the general market’s rate, GE would be worth $16.89 versus its cur- rent $41.00 per share. As you just saw, Irving Fisher’s formula works well for doing what-ifs, but it doesn’t always give you a definitive answer!
Key Point
Some understanding of how a company is generating profits and whether dividends are likely to change is needed to make an intelligent decision on whether buying shares in a company is a good investment.
So, investors must not look at only one thing when using tools like Irving Fisher’s formula. Some understanding of how a company is generating profits and whether dividends are likely to change is needed to make an intelligent decision on whether buying shares in a company is a good investment. Since dividends for the whole S&P 500 are more stable than they are for individual stocks, I value Irving Fisher’s formula more for the total market than for evalu- ating any one stock.
Summary
It is important to determine whether a stock or the market in general is over- priced, because, like anything else you buy, at some point the price is so high that it is no longer worth buying! Although money managers, stockbrokers, and many others say that you should ignore price; you should at least be aware of an investment’s price versus its historical price level before investing.