Learn what a perpetuity is, how the core perpetuity formula works, and why perpetuities matter in valuation even though real-world cash flows rarely last forever.
A perpetuity is a stream of equal cash flows that continues indefinitely.
It is an idealized finance concept, but it is extremely useful in valuation because many long-duration assets can be approximated with perpetuity logic.
For a level perpetuity:
where:
\(PV\) is present value
\(C\) is the cash flow per period
\(r\) is the discount rate
If an asset pays $100 every year forever and the discount rate is 5%, then:
The cash flows never stop, but the distant payments contribute less and less to present value because they are heavily discounted.
That is the key intuition:
the stream is infinite
the present value can still be finite
provided the discount rate is positive and the assumptions remain mathematically stable.
If the cash flow grows at a constant rate \(g\), the common formula becomes:
where \(C_1\) is the next period’s cash flow.
This only works when:
If growth is assumed to exceed the discount rate forever, the formula breaks down.
Perpetuity logic appears in:
preferred-stock valuation
terminal value in discounted cash flow models
some endowment or trust analysis
long-duration infrastructure or franchise valuation
Even when cash flows are not literally infinite, perpetuity formulas can approximate the value of very long-lived streams.
Annuity pays for a fixed number of periods.
Perpetuity has no end date.
That one difference changes the formula completely.
Annuity: A finite series of equal payments rather than an infinite one.
Present Value: The core valuation framework used in perpetuity formulas.
Discount Rate: The denominator that drives perpetuity valuation.
Preferred Stock: A common example approximated using perpetuity logic.
Future Value: A related time-value concept often contrasted with present-value valuation.