Principles of Managerial Finance

CHAPTER 4 Time Value of Money 169

6153.29

1000 PMT

N

CPT

FV

I

5

7

Solution

Input Function

Note: Switch calculator
to BEGIN mode.

Table Use Substituting i7% and n5 years into Equation 4.17, with the aid

of the appropriate interest factor from Table A–3, we get

FVIFA7%,5yrs(annuity due)FVIFA7%,5yrs(10.07)

5.7511.076.154

Then, substituting PMT$1,000 and FVIFA7%, 5 yrs (annuity due)6.154 into

Equation 4.14, we get a future value for the annuity due:

FVA 5 $1,0006.154$6,154

Calculator Use Before using your calculator to find the future value of an annu-

ity due, depending on the specific calculator, you must either switch it to BEGIN

mode or use the DUE key. Then, using the inputs shown at the left, you will find

the future value of the annuity due to be $6,153.29. (Note:Because we nearly

always assume end-of-period cash flows, be sure to switch your calculator back

toEND mode when you have completed your annuity-due calculations.)

Spreadsheet Use The future value of the annuity due also can be calculated as

shown on the following Excel spreadsheet.

Comparison of an Annuity Due

with an Ordinary Annuity Future Value

The future value of an annuity due is always greaterthan the future value of an

otherwise identical ordinary annuity. We can see this by comparing the future

values at the end of year 5 of Fran Abrams’s two annuities:

Ordinary annuity$5,750.74 Annuity due$6,153.29

Because the cash flow of the annuity due occurs at the beginning of the period

rather than at the end, its future value is greater. In the example, Fran would earn

about $400 more with the annuity due.

Finding the Present Value of an Annuity Due

We can also find the present value of an annuity due. This calculation can be eas-

ily performed by adjusting the ordinary annuity calculation. Because the cash

flows of an annuity due occur at the beginning rather than the end of the period,

to find their present value, each annuity due cash flow is discounted back one less

year than for an ordinary annuity. A simple conversion can be applied to use the

present value interest factors for an ordinary annuity (in Table A–4) with annu-

ities due.

PVIFAi,n(annuity due)PVIFAi,n(1i) (4.18)