Present Value of a Growing Perpetuity Formula

Formula

PV = Pmt / (i - g)
Variables used in the annuity formula
PV = Present Value
Pmt = Periodic payment
i = Discount rate
g = Growth rate

Use

The present value of growing perpetuity formula shows the value today of series of periodic payments which are growing or declining at a constant rate (g) each period. The payments are made at the end of each period, continue forever, and have a discount rate i is applied.

A growing perpetuity is sometimes referred to as an increasing perpetuity or graduated perpetuity.

The formula discounts the value of each payment back to its value at the start of period 1 (present value).

When using the formula, the discount rate (i) must be greater than the growth rate (g).

Present Value of a Growing Perpetuity Formula Example

If a payment of 6,000 is received at the end of period 1 and grows at a rate of 3% for each subsequent period and continues forever, and the discount rate is 6%, then the value of the payments today is given by the present value of a growing perpetuity formula as follows:

PV = Pmt / (i - g)
PV = 6,000 / (6% - 3%)
PV = 200,000

The present value of a growing perpetuity formula is one of many used in time value of money calculations, discover another at the links below.

Last modified July 16th, 2019 by Michael Brown

About the Author

Chartered accountant Michael Brown is the founder and CEO of Double Entry Bookkeeping. He has worked as an accountant and consultant for more than 25 years in all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.

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