Table15-3 The Present Value of a Stream of Future Sums
In general, if is the MRP that occurs t years from now, if i is the
interest rate, and if the stream of MRPs lasts for N years, the present value
of the stream of MRPs is
Table 15-3 computes the present value of several streams of MRPs. It
confirms the relationships we observed earlier. First, other things being
equal, a higher interest rate leads to a lower present value. Second, for a
given interest rate, a larger MRP leads to a larger present value. But now
that we have a stream of MRPs that lasts for several periods, rather than
just a single period, we can add a third general result: The longer a
stream of MRPs lasts into the future, the greater is the present value.
The present value of a future stream of sums is negatively related to the
interest rate, positively related to the size of each payment, and
positively related to the length of time the stream continues. Part A
presents a given stream of MRPs over three years but considers two
different interest rates. The PV of the stream of MRPs is higher when the
interest rate is lower.
Part B uses only a single interest rate of 5 percent but considers two
different streams of MRPs. One is a stream of $300 that lasts for three
years; the other is a higher stream of $400 that also lasts for three years.
The stream with the higher MRPs has the higher present value.
Part C uses an interest rate of 5 percent and a constant stream of MRP
$500 per year. One stream lasts for two years, whereas the other lasts for
three years. The longer-lasting stream of MRPs has the higher present
value.
MRPtPV = M 1 R+Pi^1 + MRP^2 +⋯+
( 1 +i)^2MRPN
( 1 +i)N