Fundamentals of Financial Management (Concise 6th Edition)

138 Part 2 Fundamental Concepts in Financial Management

5-9 PRESENT VALUE OF AN ORDINARY ANNUIT Y

The present value of an annuity, PVAN, can be found using the step-by-step, for-

mula, calculator, or spreadsheet method. Look back at Table 5-3. To! nd the FV of

the annuity, we compounded the deposits. To! nd the PV, we discount them,

dividing each payment by (1 + I). The step-by-step procedure is diagrammed as

follows:

Periods (^0) 5% 1 2
Payments

3

!$100 !$100 !$100

$ 95.24

$ 90.70

$ 86.38

$272.32= Present value of the annuity (PVAN)

Equation 5-5 expresses the step-by-step procedure in a formula. The bracketed

form of the equation can be used with a scienti! c calculator, and it is helpful if the

annuity extends out for a number of years:

PVAN! PMT/(1 " I)^1 " PMT/(1 " I)^2 "... " PMT/(1 " I)N

5-5! PMT #

1 # ___(1 "^1 I)N

__I (^) $
! $100 $ [1 # 1/(1.05)^3 ]/0.05! $272.32
Calculators are programmed to solve Equation 5-5; so we merely input the vari-
ables and press the PV key, making sure the calculator is set to End Mode. The cal-
culator setup follows for both an ordinary annuity and an annuity due. Note
that the PV of the annuity due is larger because each payment is discounted
back one less year. Note too that you can! nd the PV of the ordinary annuity
and then multiply by (1 # I)! 1.05, getting $272.32(1.05)! $285.94, the PV of
the annuity due.
N I/YR PV PMT FV
–100 0 End Mode
(Ordinary
Annuity)
3 5
272.32
N I/YR PV PMT FV
–100 0 Begin Mode
(Annuity
Due)
3 5
285.94
PVAN
The present value of an
annuity of N periods.
PVAN
The present value of an
annuity of N periods.