Perpetuity Calculator
Calculate the present value of a perpetuity — infinite fixed or growing cash flows.
Covers dividend discount models, preferred stock, and annuity comparisons.
Perpetuity
A perpetuity is a series of equal cash flows that continue forever — no end date. Despite paying forever, it has a finite present value because future payments are discounted at an exponentially increasing rate.
Simple Perpetuity:
PV = C / r
| Variable | Meaning |
|---|---|
| C | Cash payment per period |
| r | Discount rate per period |
| PV | Present value today |
Growing Perpetuity (Gordon Growth Model):
PV = C / (r - g)
Where g = constant growth rate of payments. Only valid when r > g.
Examples:
- British consol bonds pay a fixed coupon forever: classic perpetuity
- Preferred stock with fixed dividends is often modeled as a perpetuity
- Real estate held forever: net operating income / cap rate
- Terminal value in DCF models often uses the Gordon Growth Model
The power of the discount rate:
| Discount Rate | Payment = $1,000/year PV |
|---|---|
| 2% | $50,000 |
| 5% | $20,000 |
| 8% | $12,500 |
| 10% | $10,000 |
A small change in discount rate dramatically changes present value — this is why interest rates have such a large impact on long-duration assets.
Why perpetuities matter: The Gordon Growth Model is used to value stable dividend-paying stocks:
P = D1 / (r - g)
Where D1 is next year’s dividend, r is required return, g is dividend growth rate.
Limitation: The model assumes constant growth forever — unrealistic for most businesses. Growth must be sustainable and below the discount rate. It works best for mature, stable dividend payers like utilities and consumer staples.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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