Present Value Annuity (PVA) Homework Help & Present Value Annuity (PVA) Tutoring
Present Value Annuity (PVA) Assignment Help, Tutor Help:
Present Value – Annuity
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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