Perpetuity Value Calculator

If growth equals or exceeds the discount rate the series does not converge and the present value becomes infinite or negative, which has no real-world meaning.

A level perpetuity pays the same amount forever, while a growing perpetuity increases each payment at a constant rate using the Gordon growth form.

A capitalization rate is the inverse of a perpetuity multiple. A property earning 100,000 dollars in net operating income at a 5 percent cap rate implies a value of 2,000,000 dollars, which is the same as the level perpetuity present value of income divided by rate.

An annuity pays for a fixed number of periods, then stops; a perpetuity pays the same (or a steadily growing) amount forever. The perpetuity formula is the limit of the annuity formula as the number of periods goes to infinity, which is why it collapses to the simple cash flow divided by the discount rate.

True never-ending payments are rare, but the math appears everywhere: the terminal value in a discounted-cash-flow valuation, a real estate cap-rate valuation, preferred stock with a fixed dividend, and old British consol bonds. Anytime you value a stream assumed to continue indefinitely, you are using a perpetuity.

Extremely. Because value equals cash flow divided by (rate minus growth), small changes in the denominator swing the answer sharply, especially when the rate and growth are close together. Moving the discount rate from 6 to 5 percent on a level perpetuity raises its value by 20 percent, so the inputs deserve careful scrutiny.