Chapter 5 Time Value of Money 145The values of all! nancial assets—stocks, bonds, and business capital invest-
ments—are found as the present values of their expected future cash " ows. There-
fore, we need to calculate present values very often, far more often than future val-
ues. As a result, all! nancial calculators provide automated functions for! nding
PVs, but they generally do not provide automated FV functions. On the relatively
few occasions when we need to! nd the FV of an uneven cash " ow stream, we gen-
erally use the step-by-step procedure shown in Figure 5-5. That approach works for
all cash " ow streams, even those for which some cash " ows are zero or negative.
$ 500.00
$ 336.00
$ 376.32
$ 421.48
$ 157.35
$ 0.00
$1,791.15
Periods (^0) I = 12% 1 2 4
Cash "ows
3 5
$0 $100 $300 $300 $300 $500
FV of an Uneven Cash Flow Stream
F I G U R E 5! 5SELF^ TEST Why are we more likely to need to calculate the PV of cash " ow streams
than the FV of streams?
What is the future value of this cash " ow stream: $100 at the end of 1 year,
$150 due after 2 years, and $300 due after 3 years if the appropriate interest
rate is 15%? ($604.75)5-14 SOLVING FOR I WITH UNEVEN CASH FLOWS
8
Before! nancial calculators and spreadsheets existed, it was extremely dif" cult to
! nd I when the cash " ows were uneven. With spreadsheets and! nancial calcula-
tors, though, it’s relatively easy to! nd I. If you have an annuity plus a! nal lump
sum, you can input values for N, PV, PMT, and FV into the calculator’s TVM regis-
ters and then press the I/YR key. Here is the setup for Stream 1 from Section 5-12,
assuming we must pay $927.90 to buy the asset. The rate of return on the $927.90
investment is 12%.
N I/YR PV PMT FV5 –927.90 100 100012.00(^8) This section is relatively technical. It can be deferred at this point, but the calculations will be required in Chapter 11.