Perpetuity Calculator
Find the present value of a perpetual cash flow.
For a growing perpetuity; must be below the discount rate
Results update as you type.
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How it works
A perpetuity is a stream of identical cash flows that continues forever, and despite the payments never ending, its present value is a finite, calculable number. This perpetuity calculator returns that value by dividing the periodic payment by the discount rate, and it also handles a growing perpetuity, where each payment increases by a constant rate, by subtracting the growth rate from the discount rate in the denominator. The idea seems counter-intuitive at first, but because money received far in the future is worth very little today, the discounted value of an infinite series settles on a finite total. Perpetuities appear in real finance more often than you might expect: certain government bonds called consols paid interest indefinitely, preferred shares with fixed dividends behave like perpetuities, and the terminal value in a discounted cash flow valuation is frequently modelled as a growing perpetuity representing all cash flows beyond the forecast horizon. The growing version, known as the Gordon growth model when applied to dividends, is a staple of equity valuation. A crucial condition is that the growth rate must be below the discount rate; otherwise the value would be infinite and the formula breaks down. Enter the payment, discount rate, and optional growth rate to value the stream.
PV = payment / (r − g)
A perpetuity pays a fixed amount forever, and its present value is the payment divided by the discount rate, because although the payments never stop, each one is worth less than the last after discounting, and the infinite series converges to a finite sum. For a growing perpetuity, the denominator becomes the discount rate minus the growth rate, which only produces a sensible finite value when the discount rate exceeds the growth rate.
Source:Time value of money (perpetuity formula)
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Worked example
How to use this calculator
- 1
Enter your values
Enter payment per period and discount rate.
- 2
Adjust the options
Adjust growth rate (optional) if they apply — sensible defaults are already set.
- 3
Read your result
Present value updates instantly as you type — no button to press.
Frequently asked questions
What is a perpetuity?
A perpetuity is a series of equal cash payments that continues indefinitely with no end date. Although the payments never stop, the present value is finite because each future payment is discounted more heavily than the one before it, and the resulting infinite series converges. Real examples include consol bonds and fixed-dividend preferred shares, which pay the same amount forever.
How can something paid forever have a finite value?
Because of the time value of money, a payment received far in the future is worth almost nothing in today's terms. When you discount an endless stream of payments, the discounted amounts shrink toward zero fast enough that their total converges on a finite sum. Dividing the payment by the discount rate captures exactly this limit, giving a concrete present value.
What is a growing perpetuity?
A growing perpetuity is one whose payments increase by a constant percentage each period rather than staying level. Its present value is the first payment divided by the discount rate minus the growth rate. This model, known as the Gordon growth model when applied to dividends, is widely used to value stocks and to estimate the terminal value in discounted cash flow analysis.
Why must the growth rate be below the discount rate?
If the growth rate equalled or exceeded the discount rate, the payments would grow at least as fast as they are discounted, so the series would not converge and the present value would be infinite, which is meaningless. The formula only produces a sensible finite value when the discount rate is strictly greater than the growth rate, reflecting that no cash flow can sustainably grow faster than the required return forever.
Where are perpetuities used in valuation?
Perpetuities underpin the terminal value in discounted cash flow models, where all cash flows beyond the explicit forecast are captured as a growing perpetuity. They also value preferred stock and any fixed, indefinite income stream. Because the terminal value often makes up most of a company's estimated worth, the perpetuity assumptions about growth and discount rate strongly influence the final valuation.