The Present Value of a Stream of Future
Sums
Now consider the present value of a stream of payments that continues
for many periods into the future. As we said earlier, the future benefits
that a firm receives from a piece of capital equipment may not be
constant. Changes in market conditions, technology, or the quality of the
capital itself may result in different MRPs in different periods. For
example, one new lathe may generate a marginal revenue product equal
to $200 one year from now, $180 two years from now, and $210 in the
third year—before it wears out and ceases to generate any further
benefits.
How do we compute the present value of such an uneven stream of
MRPs? The answer is surprisingly simple. We just treat each future MRP
as a single MRP that occurs at some point in the future. We then apply
our earlier formula to each MRP and add them up. For example, suppose
the interest rate is 6 percent per year and the capital generates MRPs
equal to $200 in one year, $180 in two years, $210 in three years, and
nothing thereafter. The present value of this stream of MRPs is
PV = + +
= $188.68+$160.20+$176.32
= $525.20$ 200
1.06$ 180
(1.06)^2$ 210
(1.06)^3