Principles of Managerial Finance

CHAPTER 4 Time Value of Money 167

9. A mathematical expression that can be applied to calculate the present value interest factor for an ordinary annu-
   ity more efficiently is
   PVIFAi,n 1   (4.15a)
   The use of this expression is especially attractive in the absence of the appropriate financial tables and of any finan-
   cial calculator or personal computer and spreadsheet.

^1

(1i)n

^1

i

2794.90

700 PMT

N

CPT

PV

I

5

8

Solution

Input Function

present value interest factor
for an ordinary annuity
The multiplier used to calculate
the present value of an ordinary
annuityat a specified discount
rate over a given period of time.

factors (in Table A–2) for the appropriate number of years at the given discount

rate. The formula for the present value interest factor for an ordinary annuity

with cash flows that are discounted at ipercent for nperiods, PVIFAi,n, is^9

PVIFAi,n

n

t 1

(4.15)

This factor is the multiplier used to calculate the present value of an ordinary

annuity at a specified discount rate over a given period of time.

By letting PVAnequal the present value of an n-year ordinary annuity,letting

PMTequal the amount to be received annually at the endof each year, and let-

ting PVIFAi,nrepresent the appropriate present value interest factor for a one-

dollar ordinary annuity discounted ati percent forn years,we can express the

relationship among these variables as

PVAnPMT(PVIFAi,n) (4.16)

The following example illustrates this calculation using a table, a calculator, and

a spreadsheet.

EXAMPLE Braden Company, as we have noted, wants to find the present value of a 5-year

ordinary annuity of $700, assuming an 8% opportunity cost.

Table Use The present value interest factor for an ordinary annuity at 8% for

5 years (PVIFA8%,5yrs), found in Table A–4, is 3.993. If we use Equation 4.16,

$700 annuity3.993 results in a present value of $2,795.10.

Calculator Use Using the calculator’s inputs shown at the left, you will find the

present value of the ordinary annuity to be $2,794.90. The value obtained with

the calculator is more accurate than those found using the equation or the table.

Spreadsheet Use The present value of the ordinary annuity also can be calcu-

lated as shown on the following Excel spreadsheet.

1



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