Calculate the present value of a perpetuity — an infinite stream of fixed payments. Enter the periodic payment, discount rate, and optional growth rate to get the present value instantly. Switch between a zero-growth perpetuity and a growing perpetuity to see how different assumptions affect valuation.
Present Value of Perpetuity
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Effective Yield
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Annual Cash Flow
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Net Spread (Discount − Growth)
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A perpetuity is a financial instrument that pays a fixed (or steadily growing) cash flow at regular intervals forever — it never ends. Common real-world examples include UK government consols, preferred stocks, and certain endowment funds.
For a zero-growth perpetuity the formula is PV = D / R, where D is the periodic payment and R is the discount rate. For a growing perpetuity (Gordon Growth Model) the formula is PV = D / (R − G), where G is the constant growth rate. The growth rate must always be less than the discount rate.
A zero-growth perpetuity pays the exact same amount every period indefinitely. A growing perpetuity pays an amount that increases at a constant rate each period. Growing perpetuities are commonly used to value dividend-paying stocks using the Gordon Growth Model.
An annuity makes fixed payments for a defined, finite period of time (e.g. 20 years), while a perpetuity makes payments forever with no end date. Because a perpetuity extends infinitely, its present value is calculated with a simpler formula — no term-length variable is needed.
Even though payments last forever, the time value of money causes each successive payment to be worth less and less in today's dollars. The sum of this infinite series converges to a finite number, which is why the simple PV = D / R formula works.
If the growth rate is equal to or greater than the discount rate, the growing perpetuity formula breaks down mathematically (division by zero or a negative denominator), and the present value would be infinite. In practice, the growth rate must always remain below the discount rate for the model to be valid.
Classic examples include UK government consols (bonds with no maturity), preferred shares that pay fixed dividends indefinitely, university endowments designed to fund scholarships forever, and certain land lease agreements. The Gordon Growth Model used in stock valuation also treats dividend streams as growing perpetuities.
The present value of a perpetuity is inversely related to the discount rate — as the discount rate rises, the present value falls, and vice versa. This is why bond and preferred stock prices drop when interest rates increase.