Perpetuity Calculator (Present Value, Growing Perpetuity)
Enter the first payment, the discount rate and the growth rate to value a stream that never ends.
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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
Worked example
Using the default values shown in the calculator:
| First payment (one period from now) | $5000 |
|---|---|
| Discount rate per period | 8 % |
| Growth rate per period | 2 % |
| Amount available (to find a sustainable payment) | $100000 |
- 5,000 a year growing 2% at an 8% discount rate is worth $83,333.33 today.
- 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
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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.