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.