Perpetuity

A perpetuity is an annuity with no end date — a fixed cash payment received at regular intervals, forever. While a standard annuity pays for a set number of years, a perpetuity's payments continue indefinitely. Classic examples include certain preferred stocks, which pay a fixed dividend with no maturity date, and the British "consol" bonds historically issued with no redemption date.

Even though the payments are infinite, a perpetuity's value is not, because distant payments are worth less and less in today's terms. The present value formula is simple: PV = payment ÷ discount rate. A perpetuity paying $1,000 per year, discounted at 5%, is worth $1,000 ÷ 0.05 = $20,000. A growing perpetuity — where the payment increases at a constant rate g — is valued as PV = payment ÷ (r − g), which only works when the discount rate exceeds the growth rate; this is the logic behind the dividend growth model for valuing stocks.

Perpetuities matter because they anchor time value of money analysis. They show why an infinite payment stream has a finite price, and the perpetuity formula underlies real valuation tools: preferred stock pricing, terminal values in discounted cash flow models, and endowment spending rules all rest on it. In partnership and business contexts, "perpetuity" also describes an entity with no fixed end date — one reason limited partnerships, which typically have a stated end date, differ from corporations.

The CGMA Fundamentals of Business Economics (CIMA Certificate BA) syllabus tests perpetuity present value calculations alongside annuities and investment appraisal methods, while the Series 7 and Series 66 exams touch on the concept in the context of direct participation programs and limited partnerships, which — unlike corporations — generally do not exist in perpetuity.