5.4 Mixed Streams

LG 4 5.4 Mixed Streams

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

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

A stream of unequal periodic

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

cash flows that reflect no

tern. Financial managers frequently need to evaluate opportunities that are

particular pattern.

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

CHAPTER 5

Time Value of Money

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 5.12 3 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.

End of year

Cash flow

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 line:

Time line for future value of a $15,645.62 mixed stream (end-of-year

17,635.97 cash flows, compounded at

15,046.56 8% to the end of year 5)

$83,608.15 Future Value

End of Year

Calculator Use You can use your calculator to find the future value of each individual cash flow, as demonstrated earlier (on page 167), and then sum the future values to get the future value of the stream. Unfortunately, unless you can program your calculator, most calculators lack a function that would allow you to input all of the cash flows, specify the interest rate, and directly calculate the future value of the entire cash flow stream. Had you used your calculator to find the individual cash flow future values and then summed them, the future value of Shrell Industries’ cash flow stream at the end of year 5 would have been $83,608.15.

Spreadsheet Use

A relatively simple way to use Excel to calculate the future value of a mixed stream is to use the Excel future value (FV) function discussed on page 167 combined with the net present value (NPV) function (which will be discussed on page 181). The trick is to use the NPV function to first find the present value of the mixed stream and then find the future of this present value

PART 2

Financial Tools

A B FUTURE VALUE OF A MIXED 1 STREAM 2 Interest rate, pct/year

8% Year-End Cash

3 Year

Flow 4 1 $11,500 5 2 $14,000 6 3 $12,900 7 4 $16,000 8 5 $18,000

9 Future value

Entry in Cell B9 is =–FV(B2,A8,0,NPV(B2,B4:B8)). The minus sign appears before FV to convert

the future value to a positive amount.

PRESENT VALUE OF A MIXED STREAM Finding the present value of a mixed stream of cash flows is similar to finding the

future value of a mixed stream. We determine the present value of each future amount and then add all the individual present values together to find the total present value.