15.2 Present Value

Suppose a firm buys a piece of capital equipment and thereby obtains the
use of that equipment until it wears out. The capital equipment delivers a
flow of benefits over its lifetime—that is, it delivers some benefit every
year for many years. The financial benefit to the firm in any given year is
the marginal revenue product (MRP) of that unit of capital (recall from
Chapter 13 that the MRP is the extra revenue generated by that unit). A
given piece of capital may deliver different MRPs in different years—the
MRP may change because of changes in market conditions or simply
because the capital wears out slowly over time. In reality, the stream of
future MRPs is uncertain. No firm can know with certainty how its market
will evolve, how consumers will respond to the product, or even how
long the capital equipment will last.

How much would a firm be willing to pay today to purchase a piece of
capital equipment that will deliver a stream of benefits into the future? To
answer this question we introduce the concept of present value. The
present value of a future amount is the most that someone would be
prepared to pay today to get that amount in the future. The concept of
present value is used extensively in financial analysis as well as in the
analysis of economic policies, where costs and benefits occur at different
points in time.

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