PRESENT VALUE OF AN ANNUITY
Consider a five-payment annuity, with payments of $500 at the end of each of the next five years.
a. If the appropriate discount rate is 4%, what is the present value of this annuity?
b. If the appropriate discount rate is 5%, what is the present value of this annuity?
a. Given:PMT =$500; i=4%;N=5. Solve for PV. PV =$2,225.91
b. Given: PMT =$500, i=4%,N =5. Solve for PV. PV=$2,164.74
Note: The higher the discount rate, the lower the present value of the annuity.
Equations (10.8) and (10.9) are the valuation—future and present value—formulas for an ordinary annuity. An ordinary annuity is therefore a special form of annuity, where the first cash flow occurs at the end of the first period.
F V=\sum_{t=0}^{N} C F(1+i)^{N-t}=C F \sum_{t=0}^{N}(1+i)^{N-t} (10.8)
P V=\sum_{t=0}^{N} \frac{C F}{(1+i)^{t}}=C F \sum_{t=0}^{N} \frac{1}{(1+i)^{t}} (10.9)
This annuity short-cut is built into financial calculators and spreadsheet functions. For example, in the case of the present value of the four-payment ordinary annuity of $2,000 at 5%:
| Hewlett-Packard 10B | Texas Instruments 83/84 | Microsoft Excel |
| 2000 PMT | N = 4 | =PV(.05,4,2000,0) |
| 4 N | I% = 5 | |
| 5 I/YR | PMT = 2000 | |
| PV | FV = 0 | |
| Place cursor at PV = and then SOLVE |