CP

To find the PV of these cash flows withExcel,put the cursor on Cell B4, click the

function wizard, click Financial, scroll down to NPV, and click OK to get the dialog

box. Then enter B1 or 0.06 for Rate and the range of cells containing the cash flows,

C3
I3, for Value 1. Be very careful when entering the range of cash flows. With a fi-

nancial calculator, you begin by entering the time zero cash flow. WithExcel,you do

not include the time zero cash flow; instead, you begin with the Year 1 cash flow.

Now,whenyouclickOK,yougetthePVofthestream,$1,413.19.Notethatyouuse

the PV function if the cash flows (or payments) are constant, but the NPV function if

they are not constant. Note too that one of the advantages of spreadsheets over fi-

nancial calculators is that you can see the cash flows, which makes it easy to spot any

typing errors.

Future Value of an Uneven Cash Flow Stream

The future value of an uneven cash flow stream (sometimes called the terminal value)

is found by compounding each payment to the end of the stream and then summing

the future values:

(2-9)

a

n

t 1

CFt(1i)n
ta

n

t 1

CFt(FVIFi,n
t).

FVnCF 1 (1i)n
^1 CF 2 (1i)n
^2 CFn
 1 (1i)CFn

Uneven Cash Flow Streams 81

the abbreviation for “Net Present Value,” which is simply the net present value of a

series of positive and negative cash flows, including the cash flow at time zero.

Thesecondpointtonoteisthatannuitiescanbeenteredintothecashflowregister

more efficiently by using the Njkey.^7 In this illustration, you would enter CF 0 0,

CF 1 100,CF 2 200,Nj4(whichtellsthecalculatorthatthe200occurs4times),

CF 6 0,andCF 7 1000.ThenenterI6andpresstheNPVkey,and1,413.19willap-

pearinthedisplay.Also,notethatamountsenteredintothecashflowregisterremainin

theregisteruntiltheyarecleared.Thus,ifyouhadpreviouslyworkedaproblemwith

eightcashflows,andthenmovedtoaproblemwithonlyfourcashflows,thecalculator

wouldsimplyaddthecashflowsfromthesecondproblemtothoseofthefirstproblem.

Therefore,youmustbesuretoclearthecashflowregisterbeforestartinganewproblem.

Spreadsheets are especially useful for solving problems with uneven cash flows.

Just as with a financial calculator, you must enter the cash flows in the spreadsheet:

(^7) On some calculators, you are prompted to enter the number of times the cash flow occurs, and on still
other calculators, the procedures for inputting data, as we discuss next, may be different. You should consult
your calculator manual or our Technology Supplementto determine the appropriate steps for your specific cal-
culator.
ABCDEFGHI
1 Interest rate 0.06
2 Time 0123456 7
3 Cash flow 100 200 200 200 200 0 1,000
4 Present value 1,413.19

Time Value of Money 79