Principles of Managerial Finance

172 PART 2 Important Financial Concepts

$11,500 $14,000 $12,900 $16,000 $18,000

012345

$15,640.00

17,640.00

15,041.40

17,280.00

18,000.00

$83,601.40 Future Value

End of Year

mixed stream
A stream of unequal periodic
cash flows that reflect no partic-
ular pattern.

Time line for future
value of a mixed
stream (end-of-year
cash flows, com-
pounded at 8% to
the end of year 5)

LG4 4.4 Mixed Streams

Two basic types of cash flow streams are possible: the annuity and the mixed

stream. Whereas an annuity is a pattern of equal periodic cash flows, a mixed

streamis a stream of unequal periodic cash flows that reflect no particular pat-

tern. Financial managers frequently need to evaluate opportunities that are

expected to provide mixed streams of cash flows. Here we consider both the

future value and the present value of mixed streams.

Future Value of a Mixed Stream

Determining the future value of a mixed stream of cash flows is straightforward.

We determine the future value of each cash flow at the specified future date and

then add all the individual future values to find the total future value.

EXAMPLE Shrell Industries, a cabinet manufacturer, expects to receive the following mixed

stream of cash flows over the next 5 years from one of its small customers.

If Shrell expects to earn 8% on its investments, how much will it accumulate by

the end of year 5 if it immediately invests these cash flows when they are

received? This situation is depicted on the following time time:

End of year Cash flow

1 $11,500

2 14,000

3 12,900

4 16,000

5 18,000

Table Use To solve this problem, we determine the future value of each cash

flow compounded at 8% for the appropriate number of years. Note that the first

cash flow of $11,500, received at the end of year 1, will earn interest for 4 years

(end of year 1 through end of year 5); the second cash flow of $14,000, received at

the end of year 2, will earn interest for 3 years (end of year 2 through end of year

5); and so on. The sum of the individual end-of-year-5 future values is the future

value of the mixed cash flow stream. The future value interest factors required are