Perpetuity
Calculate the present value of a perpetuity with constant or growing payments. Free tool for valuing preferred stock, consol bonds, and endowment income streams.
About This Calculator
The Perpetuity Calculator helps investors, financial analysts, and students calculate the present value of an infinite stream of payments. A perpetuity is a type of annuity that continues indefinitely — making it essential for valuing preferred stocks, consol bonds, endowment funds, and real estate with perpetual rental income.
The calculator uses the standard perpetuity formula PV = D / R, where D is the periodic payment and R is the discount rate. For growing perpetuities (where payments increase at a constant rate), the formula extends to PV = D / (R - G), with G representing the growth rate. The growth rate must always be less than the discount rate for the present value to be finite and meaningful.
Regional Notes
India: Preferred shares issued by Indian companies and perpetual bonds (AT-1 bonds) issued by banks are valued using perpetuity formulas. The Post Office Monthly Income Scheme offers regular income but has a fixed 5-year maturity rather than being perpetual. Indian investors often use a discount rate between 7-10% for equity valuation.
United States: Preferred stocks on US exchanges pay fixed dividends and are a common real-world perpetuity. The Gordon Growth Model (dividend discount model) is widely used by US analysts for stock valuation. The Federal Reserve's interest rate decisions significantly influence the discount rates used in perpetuity calculations.
United Kingdom: Consols (Consolidated Annuities) were British government bonds that paid interest indefinitely — first issued in the 18th century and fully redeemed in 2015. The UK's Bank Rate influences discount rates for perpetuity valuation. UK investors commonly use perpetuity formulas for valuing ground rents and leasehold properties.
Frequently Asked Questions
What is a perpetuity?
A perpetuity is a stream of regular, fixed payments that continues indefinitely. In finance, it is an annuity that has no end date. Examples include preferred stock dividends, consol bonds, and endowment fund payments. The present value of a perpetuity is calculated as the periodic payment divided by the discount rate.
How do you calculate the present value of a perpetuity?
The present value of a standard perpetuity is calculated using the formula PV = D / R, where D is the periodic payment (dividend) and R is the discount rate. For a growing perpetuity, the formula is PV = D / (R - G), where G is the growth rate of payments. The growth rate must be less than the discount rate for the formula to be valid.
What is a growing perpetuity?
A growing perpetuity is a series of periodic payments that increase at a constant rate indefinitely. Unlike a standard perpetuity where payments remain fixed, a growing perpetuity's payments grow each period by a specified growth rate. The present value is higher than a standard perpetuity because future payments are larger. The formula is PV = D / (R - G).
What are real-world examples of perpetuities?
Real-world perpetuity examples include preferred stocks that pay fixed dividends indefinitely, consol bonds issued by the UK government (redeemed in 2015), endowment funds that make annual grants forever, and real estate properties valued based on perpetual rental income. In India, the Post Office Monthly Income Scheme offers regular payments but has a fixed maturity rather than being perpetual.
How does the discount rate affect perpetuity value?
The discount rate has an inverse relationship with the present value of a perpetuity. A higher discount rate results in a lower present value because future payments are discounted more heavily. Conversely, a lower discount rate increases the present value. For example, a $100 annual payment at a 5% discount rate is worth $2,000, but at a 10% rate it is worth only $1,000.
What is the difference between an annuity and a perpetuity?
An annuity is a series of fixed payments made at equal intervals for a specified period of time, such as 10 or 30 years. A perpetuity is a type of annuity where payments continue forever with no end date. While annuities have a finite present value calculation that includes a terminal date, perpetuities assume infinite payments whose present value converges to a finite amount.
Can the growth rate be higher than the discount rate in a growing perpetuity?
No, in a growing perpetuity the growth rate must be less than the discount rate. If the growth rate equals or exceeds the discount rate, the present value becomes infinite, making the formula invalid. This condition ensures that each subsequent payment's present value is less than the previous one, allowing the sum to converge to a finite value.
How is perpetuity valuation used in stock investing?
Perpetuity valuation is commonly used for preferred stocks, which pay a fixed dividend with no maturity date. The Gordon Growth Model, a type of growing perpetuity formula, is used to value common stocks by assuming dividends grow at a constant rate. In India, preferred shares issued by companies and perpetual bonds by banks are valued using perpetuity formulas.