About the Perpetuity Calculator
A perpetuity pays the same amount forever. Its present value is finite anyway, because distant payments are discounted so heavily that they add almost nothing: PV = payment / discount rate. Allow the payment to grow at a steady rate and the denominator narrows to the gap between the two rates, giving PV = payment / (rate - growth), the Gordon growth model used for dividends and terminal values.
That gap does the heavy lifting, and it is where models go wrong. A discount rate of 8 percent with 2 percent growth gives a six point gap and a value of about 16.7 times the payment. Nudge growth to 6 percent and the gap collapses to two points, tripling the value. When growth meets or exceeds the discount rate the formula breaks entirely, so this page refuses the input rather than printing an infinite answer.
Real uses include valuing a preference share with a fixed dividend, pricing a consol style bond, and setting the terminal value at the end of a discounted cash flow forecast, where the terminal piece often carries most of the total. The timing switch handles the difference between an ordinary perpetuity, whose first payment arrives one period from now, and a perpetuity due, which pays today and is therefore worth one extra period of discounting. Keep the growth assumption below long run economic growth, because nothing outgrows the economy forever. For a fixed number of periods instead, the Future Value Calculator is the right tool.
How to use
- Enter the payment for one period, usually a year.
- Set the discount rate that reflects the risk of that payment.
- Add a growth rate if the payment rises over time, keeping it below the discount rate.
- Switch the timing to today if the first payment arrives immediately.
Common questions
- Why must growth stay below the discount rate?
- If payments grow at least as fast as they are discounted, each one contributes as much as the last and the sum has no finite limit.
- What is a sensible growth assumption?
- Something at or below long run nominal economic growth, often two to three percent. Anything higher implies the asset eventually swallows the economy.
- Where is a perpetuity used in practice?
- In dividend valuation, preference share pricing and the terminal value at the end of a discounted cash flow model.
- What is a perpetuity due?
- One where the first payment lands today rather than in a year, so its value is the ordinary figure multiplied by one plus the discount rate.