Introduction to Corporate Finance

3: The Time Value of Money

3-5 FUTURE VALUE OF CASH FLOW

STREAMS

Financial managers frequently need to evaluate streams of cash flows that occur in future periods. Though

this is mechanically more complicated than computing the future or present value of a single cash flow,

the same basic techniques apply.

Two types of cash flow streams are possible: the mixed stream and the annuity. A mixed stream is a

series of unequal cash flows reflecting no particular pattern. An annuity is a stream of equal periodic cash

flows over a stated period of time. Either of these cash flow patterns can represent inflows of returns

earned on investments or outflows of funds invested to earn future returns. Because certain shortcuts are

possible when evaluating an annuity, we discuss mixed streams and annuities separately.

3-5a FINDING THE FUTURE VALUE OF A MIXED STREAM

The future value of any stream of cash flows measured at the end of a specified year is merely the sum

of the future values of the individual cash flows at that year’s end. This future value is sometimes called

the terminal value. The following example demonstrates such a calculation.

mixed stream

A series of unequal cash flows

reflecting no particular pattern

annuity

A stream of equal periodic

cash flows over a stated

period of time

LO3.3

Assume that we want to determine the balance in an investment account earning 9% annual interest, given

the following five end-of-year deposits: $400 in year 1, $800 in year 2, $500 in year 3, $400 in year 4 and $300

in year 5. These cash flows appear on the time line at the top of Figure 3.7, which also depicts the future-

value calculation for this mixed stream of cash flows, followed by the financial calculator and spreadsheet

solutions.

Note that the first cash flow, which occurs at the end of year 1, earns interest for four years (end of year

1 to end of year 5). Similarly, the second cash flow, which occurs at the end of year 2, earns interest for three

years (end of year 2 to end of year 5), and so on. Summing the future values of the five deposits yields the total

future value of the mixed stream, which is $2,930.70.^4 The five deposits, which total $2,400 before interest,

have grown by nearly $531 at the end of five years as a result of the interest earned.

example

4 There is a $0.01 rounding difference between the future value given on the time line compared with the future-value calculation using a

calculator or spreadsheet.

CONCEPT REVIEW QUESTIONS 3-4

7 In the first example in this section (on p. 76), we saw that a $1,000 investment earning 8% would

triple in 14.3 years. Suppose the investment earns just 4%, half as much as originally anticipated. A

lower rate of return means that it will take more time for the investment to triple. Will it take exactly

twice as long (28.6 years) to triple, more than that, or less than that? Why?