Investing & Retirement

Perpetuity Calculator (Present Value, Growing Perpetuity)

Enter the first payment, the discount rate and the growth rate to value a stream that never ends.

Your numbers

Symbol only: enter amounts in the currency you pick.
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Your results

Present value
Present value
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Without growth
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If the first payment is today
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First payment the available amount supports (growing)
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Perpetuity Calculator (Present Value, Growing Perpetuity) by TheCalcTools

How the Perpetuity Calculator (Present Value, Growing Perpetuity) works

A perpetuity pays forever. Its present value is the payment divided by the discount rate: PV = C ÷ r. If the payments grow at rate g, PV = C ÷ (r − g), the Gordon growth model used to value stocks from dividends.

The formula only works when r is greater than g. A first payment today (perpetuity due) is worth (1 + r) times more.

The formula

PV = C ÷ (r − g)

Worked example

Using the default values shown in the calculator:

First payment (one period from now)$5000
Discount rate per period8 %
Growth rate per period2 %
Amount available (to find a sustainable payment)$100000
  1. 5,000 a year growing 2% at an 8% discount rate is worth $83,333.33 today.
  2. With no growth it is worth $62,500.00.

Result:

Present value$83,333.33
Without growth$62,500.00
If the first payment is today$90,000.00
First payment the available amount supports (growing)$6,000.00

Frequently asked questions

Where are perpetuities used?

Valuing preferred shares, endowments, consols, and the terminal value in discounted cash flow models.

Sources and further reading

More in Investing & Retirement · All calculators

This calculator gives estimates for information only. It is not financial advice, and your lender's or provider's figures will govern. Rates, fees and rules vary. See our disclaimer.