 ## Present value ­ discount

Sometimes we want to know the current value of a cash flow that will occur at some future date. Discrete or continuous discounting is the process for equating a future cash flow with its present value. The discount rate may be referred to as the opportunity cost of an investment or the investor's required rate of return.

Annuity

An annuity is a security that involves a series of equal payments made at regular time intervals. To derive the future value of an annuity, each payment is compounded for the remaining life of the security. A payment made at the end of the first year of a ten-year annuity is compounded for nine years, the second payment is compounded for eight years, etc. All compounded payments added together equal the future value.

Calculating the present value of an annuity is the reverse process of compounding. The payment due at the end of the tenth year is discounted over the ten year period, the ninth payment is discounted over nine years, etc. The present values of all payments added together equal the present value of the annuity.

Perpetuity

A perpetuity is a special type of annuity with an infinite number of payment periods. The future value of a perpetuity is infinite -- and of little consequence. The present value is easy to calculate and provides the investor with information to facilitate a comparison of investment prices.

The present and future values of investments with payments of uneven size or spacing also may be calculated by totaling the compounded or discounted values of the cash flows. You can see that the present / future value of an investment depends on the discount / interest rate, the number of payments, the length of time until maturity, and the amount of each cash flow. By manipulating these factors, we can discover the future value of an interest-bearing investment or the discounted present value of future cash flows.