Perpetuity Value Calculator
Value a stream of payments that lasts forever — a level or growing perpetuity — from its cash flow and discount rate.
How it works
Level: PV = C ÷ r · Growing (Gordon): PV = C ÷ (r − g), requires r > g
A perpetuity is a cash flow that continues forever, and its present value is finite because distant payments discount to almost nothing. A level perpetuity is simply the payment divided by the discount rate; a growing perpetuity divides by the rate minus the growth rate (the Gordon growth form). If growth ever equals or exceeds the discount rate the sum diverges, which is why that case has no finite value.
Worked example
A trust that pays $1,000 a year forever, discounted at 5%, is worth 1,000 ÷ 0.05 = $20,000. If instead the payment grew 2% a year, its value would be 1,000 ÷ (0.05 − 0.02) = $33,333 — the growth lifts every future payment and so raises today’s value.
Frequently asked questions
How can an endless stream have a finite value?
Each payment is discounted more heavily than the last, so the terms shrink geometrically. Their infinite sum converges to a finite number as long as the discount rate exceeds the growth rate.
What is a growing perpetuity used for?
It underpins the Gordon Growth Model for valuing stocks and the terminal value in discounted-cash-flow models, where cash flows are assumed to grow at a steady rate indefinitely.
Why must the discount rate exceed the growth rate?
If payments grow as fast as or faster than they are discounted, the terms no longer shrink and the total is infinite. The formula is only valid when r is strictly greater than g.
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Educational estimate, not investment advice.