Present value of an annuity

The present value of an annuity is the current worth of a series of future cash flows, where the cash flows can be comprised of cash inflows, cash outflows, or both. The current worth of those cash flows is based on a discount rate selected by the user, such as a targeted return on investment or the current market interest rate (i.e., the interest rate at which you could obtain financing on the open market). The resulting present value can be used to place a price on the annuity that the user is willing to pay. This concept is used for the pricing of investment instruments, payouts on life insurance, and also for estimating the amount to pay for an acquisition (based on its projected cash flows).

If the discount rate is set to zero, this means the user is indifferent to the passage of time on cash flows. In reality, there is always a discount rate, since it is always more valuable to have the use of cash immediately, rather than on a delayed basis.  By receiving cash immediately, you can invest it and receive an additional return. If the projected cash flows associated with an annuity appear to be unusually risky, you might apply a high discount rate to those cash flows. The net effect of a higher discount rate is a lower present value, which would make you less likely to invest in an annuity; or, you would pay less for it.

Present Value of an Annuity Formula

The formula for the present value of an ordinary annuity (where annuity payments are made at the end of each period) is:

Periodic cash payment x ([1-(1+Interest rate)]Number of payments) / Interest rate

The calculation is available as a predetermined function on an electronic spreadsheet. Also, the discount rate is available on annuity tables. For example, an investor is presented with the option to buy an annuity that pays \$10,000 at the end of each year for four years. The investor selects a discount rate of 7%, which results in the following calculation of the present value of this annuity:

\$10,000*([1-(1+0.07)]-4/0.07= \$33,872

Based on this calculation, the investor determines that receiving \$33,872 immediately has the same value as receiving \$10,000 per year for four years.

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