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Present Value Annuity

Assignment / Homework Help
An annuity is a series of equal annual cash flows. In general terms, the present value of an annuity may be expressed as follows:

PV An = A A A

+
+ ........
(1 + r)1 (1 + r)2 (1 + r)n
OR
PV An = A { ∑ n      1 / (1 + r)t }
         t = 1
Where
PV An = Present value of an annuity
A = annuity amount (even cash inflows)
r = discount rate and
n = number of years of annuity (the last year)

Example: Let us find out the present value of an annuity of $10,000 to be received in the next 4 years time, the discount rate being 10%.

Years Cash inflows PV factor at 10% PV of cash inflows
1 $10,000 0.9091 $9,091
2 $10,000 0.8264 $8,264
3 $10,000 0.7513 $7,513
4 $10,000 0.6830 $6,830
Total $31,698.00

Graphic Presentation of Time Line of Present value of Annuity

0 1 2 3 4
$ 10,000 $ 10,000 $ 10,000 $ 10,000 $ 10,000
 
$ 9,091
 
$ 8,264  
 
$ 7,513  
 
$ 6,830  
 
$ 31,698  (Total PV)

Alternatively, the PV of an annuity can also be calculated by the formula:

PV An = A [ { 1 - (1/ (1 + r))n } / r ]

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