Principles of Managerial Finance

PV = $918.42

0 1 2 3 4 5 6 7 8

End of Year

FV 8 = $1,700

Time line for present
value of a single
amount ($1,700 future
amount, discounted at
8%, from the end of
8 years)

160 PART 2 Important Financial Concepts

present value interest factor
The multiplier used to calculate,
at a specified discount rate, the
present value of an amount to be
received in a future period.

The Equation for Present Value

The present value of a future amount can be found mathematically by solving

Equation 4.4 for PV.In other words, the present value, PV,of some future

amount, FVn,to be received nperiods from now, assuming an opportunity cost of

i,is calculated as follows:

PVFVn (4.9)

Note the similarity between this general equation for present value and the

equation in the preceding example (Equation 4.8). Let’s use this equation in an

example.

EXAMPLE Pam Valenti wishes to find the present value of $1,700 that will be received 8

years from now. Pam’s opportunity cost is 8%. Substituting FV 8 $1,700, n8,

and i0.08 into Equation 4.9 yields Equation 4.10:

PV$918.42 (4.10)

The following time line shows this analysis.

$1,700



1.851

$1,700



(10.08)^8

1



(1i)n

FVn



(1i)n

Using Computational Tools to Find Present Value

The present value calculation can be simplified by using a present value interest

factor.This factor is the multiplier used to calculate, at a specified discount rate,

the present value of an amount to be received in a future period. The present

value interest factor for the present value of $1 discounted at i percent for nperi-

ods is referred to as PVIFi,n.

Present value interest factorPVIFi,n (4.11)

Appendix Table A–2 presents present value interest factors for $1. By letting

PVIFi,nrepresent the appropriate factor, we can rewrite the general equation for

present value (Equation 4.9) as follows:

PVFVn(PVIFi,n) (4.12)

This expression indicates that to find the present value of an amount to be re-

ceived in a future period,n,we have merely to multiply the future amount,FVn,

by the appropriate present value interest factor.

1



(1i)n