The notion of present value is crucial
to understanding the fundamentalists’ approach to stock valuation. It should
also be important to lottery players, mortgagors, and advertisers. That the
present value of money in the future is less than its nominal value explains why
a nominal $1,000,000 award for winning a lottery—say $50,000 per year at the end
of each of the next twenty years—is worth considerably less than $1,000,000. If
the interest rate is 10 percent annually, for example, the $1,000,000 has a
present value of only about $426,000. You can obtain this value from tables,
from financial calculators, or directly from the formulas above (supplemented by
a formula for the sum of a so-called geometric series).
The process of determining the present
value of future money is often referred to as “discounting.” Discounting is
important because, once you assume an interest rate, it allows you to compare
amounts of money received at different times. You can also use it to evaluate
the present or future value of an income stream—different amounts of money
coming into or going out of a bank or investment account on different dates. You
simply “slide” the amounts forward or backward in time by multiplying or
dividing by the appropriate power of (1 + r). This is done, for example, when
you need to figure out a payment sufficient to pay off a mortgage in a specified
amount of time or want to know how much to save each month to have sufficient
funds for a child’s college education when he or she turns
eighteen.
Discounting is also essential to
defining what is often called a stock’s fundamental value. The stock’s price,
say investing fundamentalists (fortunately not the sort who wish to impose their
moral certitudes on others), should be roughly equal to the discounted stream of
dividends you can expect to receive from holding onto it indefinitely. If the
stock does not pay dividends or if you plan on selling it and thereby realizing
capital gains, its price should be roughly equal to the discounted value of the
price you can reasonably expect to receive when you sell the stock plus the
discounted value of any dividends. It’s probably safe to say that most stock
prices are higher than this. During the 1990 boom years, investors were much
more concerned with capital gains than they were with dividends. To reverse this
trend, finance professor Jeremy Siegel, author of Stocks for
the Long Run, and two of his colleagues recently proposed eliminating the
corporate dividend tax and making dividends deductible.
The bottom line of bottom-line
investing is that you should pay for a stock an amount equal to (or no more
than) the present value of all future gains from it. Although this sounds very
hard-headed and far removed from psychological considerations, it is not. The
discounting of future dividends and the future stock price is dependent on your
estimate of future interest rates, dividend policies, and a host of other
uncertain quantities, and calling them fundamentals does not make them immune to
emotional and cognitive distortion. The tango of exuberance and despair can and
does affect estimates of stock’s fundamental value. As the economist Robert
Shiller has long argued quite persuasively, however, the fundamentals of a stock
don’t change nearly as much or as rapidly as its price.
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