In what follows, we simplify our discussion by assuming that the future
benefits from a piece of capital equipment are known with certainty. This
allows us to develop the central insights about present value and the
interest rate without dealing with complications arising from uncertainty.
The Present Value of a Single Future
Sum
To begin our analysis, consider a very simple setting in which the piece of
capital equipment produces an MRP only in one future period. Since most
physical capital is durable and thus generates a stream of benefits, this
assumption is quite unrealistic, but it is only our starting point. In our first
example, the MRP occurs one period from now. In the second, the MRP
occurs several periods from now.
One Period in the Future
How much would a firm be prepared to pay now to purchase a capital
good that produces an MRP of $100 in one year’s time, after which time
the capital good will be useless? One way to answer this question is to ask
a somewhat opposite question: How much would the firm have to lend
now in order to be repaid $100 a year from now? Suppose for the
moment that the interest rate is 5 percent per year. If we use PV to stand
for this unknown amount, we can write Thus,
. This tells us that the present value of $100
receivable in one year’s time is $95.24 when the interest rate is 5 percent.
PV ×(1.05)=$100.
PV =$ 100 /1.05=$95.24