Perpetuity
By Jude Wallis
A perpetuity is a level payment that continues without end. Its present value is the payment divided by the discount rate, provided the rate is above zero.
Keep reading
An endless stream having a finite value is the part that surprises people. Each payment is discounted harder than the one before, and the shrinking terms add up to a limit, so the sum settles rather than running away. One division replaces an infinite queue of discounting.
A growing perpetuity subtracts the growth rate from the discount rate in the denominator. That subtraction is where the arithmetic becomes delicate: as growth approaches the discount rate, the value runs off to a number no one should quote, which is why terminal value assumptions in a valuation get argued over so heavily.
A fixed run of payments is an annuity instead; see annuity present value. The perpetuity calculator is the division, present value is the underlying idea, and how the Gordon growth model works is the growing form applied to dividends.