Calculate the present value of a perpetuity or growing perpetuity from a fixed periodic payment and a chosen discount rate.
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Time Value of Money
A perpetuity is a stream of equal cash flows that continues forever. This calculator computes the present value of both level perpetuities and growing perpetuities using the Gordon Growth Model.
A perpetuity pays a fixed amount each period indefinitely. While no financial instrument truly lasts forever, perpetuities are a useful theoretical model for valuing very long-lived cash flows like preferred stock dividends, endowment payouts, and certain real estate income streams.
A growing perpetuity adds a constant growth rate to each payment, making it useful for valuing assets whose income is expected to grow with inflation or earnings growth.
Present value is derived by summing the infinite geometric series of discounted cash flows.
PV = C / (r − g)
C = periodic payment, r = discount rate, g = growth rate (0 for level perpetuity). Requires r > g.
Payment of 10,000/year, 8% discount rate, 2% growth. PV = 10,000 / (0.08 − 0.02) = 166,667.
No real cash flow stream lasts forever. The formula is extremely sensitive to the discount rate and growth rate — small changes in either produce large swings in present value. The growth rate must be strictly less than the discount rate.
Frequently asked questions
The formula becomes undefined (division by zero). This implies infinite present value, which is economically impossible. The constraint r > g ensures the sum of discounted cash flows converges to a finite value.
Preferred stock valuation (fixed dividends), endowment spending rules, terminal value in DCF models (Gordon Growth terminal value), and certain perpetual bonds (consols).
Very sensitive. Changing the discount rate from 8% to 7% with 2% growth increases PV from 166,667 to 200,000 — a 20% increase from a 1 percentage point change. Always test a range of assumptions.
Yes. The growing perpetuity formula is the basis of the Gordon Growth terminal value: TV = FCF₁ / (WACC − g), where FCF₁ is the first cash flow after the explicit forecast period.
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