Growing Perpetuity Calculator
Value a stream of payments that grows at a constant rate forever with the Gordon growth formula PV = C / (r − g).
How it works
PV = C / (r − g) · valid only when r > g · C = first payment one period from now
A growing perpetuity pays a cash flow that increases at a constant rate g every period, forever. Its present value is the first payment divided by the spread between the discount rate and the growth rate. This Gordon growth formula underpins the dividend discount model for stocks and terminal-value estimates in discounted-cash-flow analysis; it only converges when the discount rate exceeds the growth rate.
Worked example
A payment of $100 next period, growing 3% a year forever, discounted at 8%: PV = 100 / (0.08 − 0.03) = 100 / 0.05 = $2,000. Had the payments not grown, the level perpetuity would be worth only 100 / 0.08 = $1,250.
Sources: Perpetuity — Wikipedia
Frequently asked questions
Why must the discount rate exceed the growth rate?
If growth matched or beat the discount rate, later payments would not shrink in present-value terms and the infinite sum would diverge. The formula only produces a finite value when r > g, which is why this calculator requires it.
Where is the growing-perpetuity formula used?
It is the heart of the Gordon dividend growth model for valuing stocks and of the terminal-value step in DCF valuations, where cash flows after the forecast horizon are assumed to grow at a steady long-run rate.
Is the first payment today or next period?
The standard formula assumes the first payment arrives one period from now. If a payment is due today as well, add it separately to the present value the formula produces.
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Educational financial-math tool, not investment or financial advice.