Fundamentals of Financial Management (Concise 6th Edition)

144 Part 2 Fundamental Concepts in Financial Management

quickly and ef! ciently. First, you enter all of the cash " ows and the interest rate;

then the calculator or computer discounts each cash " ow to! nd its present value

and sums these PVs to produce the PV of the stream. You must enter the cash " ows

in the calculator’s “cash " ow register,” enter the interest rate, and then press

the NPV key to! nd the PV of the stream. NPV stands for “net present value.”

We cover the calculator mechanics in the tutorial, and we discuss the process in

more detail in Chapters 9 and 11, where we use the NPV calculation to analyze

stocks and proposed capital budgeting projects. If you don’t know how to do the

calculation with your calculator, it would be worthwhile to go to the tutorial or

your calculator manual, learn the steps, and make sure you can do this calculation.

Since you will have to learn to do it eventually, now is a good time to begin.

$ 89.29

$ 239.16

$ 213.53

$ 190.66

$ 283.71

$1,016.35 = PV of cash "ow stream = Value of the asset

Periods (^0) I = 12% 1 2 4
Cash "ows
PV of CFs

3 5

$0 $100 $300 $300 $300 $500

PV of an Uneven Cash Flow Stream

F I G U R E 5! 4

SEL

F^ TEST How could you use Equation 5-2 to! nd the PV of an uneven stream of cash

" ows?

What’s the present value of a 5-year ordinary annuity of $100 plus an addi-

tional $500 at the end of Year 5 if the interest rate is 6%? What is the PV if the

$100 payments occur in Years 1 through 10 and the $500 comes at the end of

Year 10? ($794.87; $1,015.21)

What’s the present value of the following uneven cash " ow stream: $0 at

Time 0, $100 in Year 1 (or at Time 1), $200 in Year 2, $0 in Year 3, and $400 in

Year 4 if the interest rate is 8%? ($558.07)

Would a typical common stock provide cash " ows more like an annuity or

more like an uneven cash " ow stream? Explain.

5-13 FUTURE VALUE OF AN UNEVEN CASH FLOW STREAM

We! nd the future value of uneven cash " ow streams by compounding rather than

discounting. Consider Cash Flow Stream 2 in the preceding section. We discounted

those cash " ows to! nd the PV, but we would compound them to! nd the FV.

Figure 5-5 illustrates the procedure for! nding the FV of the stream using the step-

by-step approach.