# Present Value (PV) of a growing perpetuity (Gordon Growth Model) calculator

LAST UPDATE: September 29th, 2019

### 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.

### 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. $\text{Present Value} = \frac{\text{Payment Amount}}{\text{Interest Rate} - \text{Payment Growth Rate}}$

Where:

• 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.

### Example

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? $\text{Present Value} = \frac{100}{0.022 - 0.005}$ $\text{Present Value} = \frac{100}{0.017}$ $\text{Present Value} = 5882.35$

### 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?

A perpetuity keeps the same payment through its entire existence. A growing perpetuity increases by a set amount each payment period.