What is Perpetuity?

Perpetuity is a financial concept referring to a stream of equal cash flows or payments that continue indefinitely, with no predetermined end date. In other words, a perpetuity is an annuity that pays out forever, making it a useful theoretical tool in finance and valuation[1][2][3].

Key Features of Perpetuity

Provides continuous, fixed payments at regular intervals (e.g., annually).
Has no maturity date; payments are assumed to last forever.
Commonly used in financial models to estimate the present value of infinite cash flows, such as in company valuations or endowments.

Perpetuity Formula

The present value (PV) of a perpetuity is calculated using the formula:

PV = C / r

PV = Present Value of the perpetuity
C = Cash flow per period
r = Discount rate or interest rate

For a growing perpetuity (where payments grow at a constant rate g), the formula is:

PV = C / (r - g)

Examples of Perpetuity

British Consol Bonds: Historical government bonds that paid interest forever to the holder, until they were phased out in 2015[1][2].
Endowment Funds: Scholarships or charitable funds that pay out a fixed amount each year, funded by an investment whose principal is never touched[3].
Preferred Stock: Certain stocks pay fixed dividends indefinitely, assuming the company remains in business[5].

Why is Perpetuity Important?

Helps in valuing assets or businesses expected to generate cash flows indefinitely.
Forms the basis for calculating terminal value in discounted cash flow (DCF) models.
Illustrates the concept that an infinite series of payments can have a finite present value due to discounting[1][3].

Key Takeaways

A perpetuity is a theoretical financial instrument with no end date.
Its present value is calculated by dividing the payment amount by the discount rate.
While rare in practice, perpetuities are vital in financial theory and valuation.

Return to Perpetuity Calculator