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Determinant 1: The expected growth rate.
Most people
don’t recognize the implications of compound growth for
financial decisions. Albert Einstein once described compound
interest as the “greatest mathematical discovery of all time.”
It is often said that the Native American who sold Manhattan
Island in 1626 for $24 was rooked by the white man. In fact,
he may have been an extremely sharp salesman. Had he put
his $24 away at 6 percent interest, compounded
semiannually, it would now be worth more than $100 billion,
and with it his descendants could buy back much of the now
improved land. Such is the magic of compound growth!
Compounding is the process that makes 10 plus 10 equal
21 rather than 20. Suppose you invest $100 this year and
next year in an investment that produces a 10 percent annual
return. How much have you made by the end of year two? If
you answered 21 percent, then you deserve a gold star and a
trip to the head of the class.
The algebra is simple. Your $100 grows to $110 at the end
of year one. Next year, you also earn 10 percent on the $110
you start with, so you have $121 at the end of year two.
Thus, the total return over the two-year period is 21 percent.
The reason it works is that the interest you earn from your
original investment also earns interest. Carrying it out in year
three, you have $133.10. Compounding is powerful indeed.
A useful rule, called “the rule of 72,” gives you a shortcut
way to find out how long it will take to double your money.
Take the interest rate you earn and divide it into the number
72, and you get the number of years it will take to double
your money. For example, if the interest rate is 15 percent, it
takes a bit less than five years for your money to double (72
divided by 15 = 4.8 years). The implications of various
growth rates for the size of future dividends are shown in the
table below.
Growth
Rate of
Dividends
Present
Dividend
Dividend
in Five
Years
Dividend
in Ten
Years
Dividend in
Twenty-Five
Years
5%
$1.00
$1.28
$1.63
$3.39
15%
1.00
2.01
4.05
32.92
25%
1.00
3.05
9.31
264.70
The catch (and doesn’t there always have to be at least
one, if not twenty-two?) is that dividend growth does not go
on forever, for the simple reason that corporations have life
cycles similar to most living things. Consider the leading
corporations in the United States over a hundred years ago.
Such names as Eastern Buggy Whip Company, La Crosse and
Minnesota Steam Packet Company, Savannah and St. Paul
Steamboat Line, and Hazard Powder Company, the already
mature enterprises of the time, would have ranked high in a
Fortune top 500 list of that era. All are now deceased.
And even if the natural life cycle doesn’t get a company,
there’s always the fact that it gets harder and harder to grow
at the same percentage rate. A company earning $1 million
need increase its earnings by only $100,000 to achieve a 10
percent growth rate, whereas a company starting from a base
of $10 million in earnings needs $1 million in additional
earnings to produce the same record.
The nonsense of relying on very high long-term growth
rates is nicely illustrated by working with population
projections for the United States. If the populations of the
nation and of California continue to grow at their recent rates,
120 percent of the United States population will live in
California by the year 2045! Using similar kinds of
projections, one can estimate that at the same time 240
percent of the people in the country with venereal disease
will live in California. As one Californian put it on hearing
these forecasts, “Only the former projections make the latter
one seem at all plausible.”
Hazardous as projections may be, share prices must reflect
differences in growth prospects if any sense is to be made of
market valuations. Also, the probable length of the growth
phase is very important. If one company expects to enjoy a
rapid 20 percent growth rate for ten years, and another
growth company expects to sustain the same rate for only
five years, the former company is, other things being equal,
more valuable to the investor than the latter. The point is that
growth rates are general rather than gospel truths. And this
brings us to the first fundamental rule for evaluating
securities:
Rule 1:
A rational investor should be willing to pay a
higher price for a share the larger the growth rate of
dividends and earnings.
To this is added an important corollary:
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