Principles of Managerial Finance

174 PART 2 Important Financial Concepts

0 1 2 3 4 5

End of Year

$400

366.80

673.60

386.00

283.20

195.00

$1,904.60

$

Present Value

$800 $500 $400 $300

Time line for present
value of a mixed
stream (end-of-year
cash flows, discounted
at 9% over the corre-
sponding number of
years)

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.

EXAMPLE Frey Company, a shoe manufacturer, has been offered an opportunity to receive

the following mixed stream of cash flows over the next 5 years:

If the firm must earn at least 9% on its investments, what is the most it should

pay for this opportunity? This situation is depicted on the following time line:

End of year Cash flow

1 $400

2 800

3 500

4 400

5 300

Table Use To solve this problem, determine the present value of each cash flow

discounted at 9% for the appropriate number of years. The sum of these individ-

ual values is the present value of the total stream. The present value interest fac-

tors required are those shown in Table A–2. Table 4.4 presents the calculations

needed to find the present value of the cash flow stream, which turns out to be

$1,904.60.

Calculator Use You can use a calculator to find the present value of each indi-

vidual cash flow, as demonstrated earlier (page 161), and then sum the present

values, to get the present value of the stream. However, most financial calculators

have a function that allows you to punch in all cash flows,specify the discount

rate, and then directly calculate the present value of the entire cash flow stream.

Because calculators provide solutions more precise than those based on rounded