Present Value of a Growing Perpetuity Calculator
Definition – What is a Present Value (PV) of a Growing Perpetuity?
The present value (PV) of a growing perpetuity is the value in today’s dollars of a series of payments that has no end and increases each compounding period. It uses a payment amount, rate of return, and payment growth rate to calculate the value of the payments in today’s dollars.
Formula – How is the Present Value of a Growing Perpetuity calculated?
The PV of a growing perpetuity is calculated through the Gordon Growth Model, a financial formula used with the time value of money.
Present Value = Payment Amount ÷ (Interest Rate – Payment Growth Rate)
- “Payment” is the payment each period.
- “Rate of Return” is a decimal rate of return per period (the calculator above uses a percentage). A return of 2.2% per period would be calculated in the formula as “0.022”.
- “Payment Growth Rate” is the amount the payment grows each period. In the formula, it is a decimal rate, while in our calculator it is a percentage.
The payment growth rate cannot exceed the rate of return, or else this model is meaningless.
We will receive a perpetuity of $100 each year. The interest rate at the moment is 2.2% compounded annually. The payment grows by 0.5% each compounding period. What is the present value of this perpetuity?
Present Value = 100 ÷ (0.022 – 0.005)
Present Value = 100 ÷ 0.017
Present Value = 5882.35
Present Value of a Growing Perpetuity Table
What is the difference between the present value of an annuity and a perpetuity?
The present value of an annuity is for a set number of payments. A perpetuity is for an unlimited number of payments.
What is the difference between a perpetuity and a growing perpetuity?
Sources and External Resources
- Wikipedia – Time Value of Money, Present Value, & Perpetuity – An overview of time value of money and the concept of present value and a perpetuity.
- The Street – What is Perpetuity and Why Does It Matter in 2019? – A discussion on why a perpetuity matters in 2019.
- University of Pittsburgh – Frederick P. Schlingemann – BUSFIN 1030 – Additional Notes & Examples on Time Value of Money – Summary calculations and a formula to calculate a growing perpetuity.