How the Perpetuity Calculator Works
A perpetuity is a series of equal (or steadily growing) payments that continue forever. Despite the infinite time horizon, the present value is finite because payments far in the future are discounted to nearly zero.
This perpetuity calculator computes:
- Present Value of Perpetuity — the current worth of the infinite cash flow stream
- Perpetuity Type — whether it’s a level or growing perpetuity
- Cash Flow Value in Year 10 — the projected payment amount 10 years out
- Total Cash Received (First 10 Years) — cumulative payments over a decade
Perpetuity Formulas
Level Perpetuity
PV = C ÷ r
Growing Perpetuity (Gordon Growth Model)
PV = C ÷ (r − g)
Where: - C = Next period’s cash flow - r = Discount rate (as a decimal) - g = Growth rate (as a decimal)
Perpetuity Examples
Example 1: Level Perpetuity
| Variable | Value |
|---|---|
| Annual Cash Flow | $5,000 |
| Discount Rate | 8% |
| Growth Rate | 0% |
| Present Value | $62,500 |
Example 2: Growing Perpetuity
| Variable | Value |
|---|---|
| Annual Cash Flow | $5,000 |
| Discount Rate | 8% |
| Growth Rate | 3% |
| Present Value | $100,000 |
Who Benefits from the Perpetuity Calculator?
This perpetuity valuation calculator is designed for:
- Finance students learning time value of money concepts
- Investors valuing preferred stock or annuity-like assets
- Analysts applying the Gordon Growth Model to dividend-paying stocks
- Anyone evaluating an indefinite income stream
Frequently Asked Questions
What is a perpetuity?
A perpetuity is a stream of equal (or growing) cash flows that continues indefinitely, with no end date. Common examples include certain preferred stock dividends and some government bonds.
How do you calculate the present value of a perpetuity?
The present value of a level perpetuity is calculated by dividing the annual cash flow by the discount rate: PV = C ÷ r.
What is a growing perpetuity?
A growing perpetuity is a cash flow stream that increases at a constant rate each period. It’s valued using the Gordon Growth Model: PV = C ÷ (r − g), where g is the growth rate.
Why must the discount rate be greater than the growth rate?
If the growth rate equals or exceeds the discount rate, the present value formula produces an undefined or negative result, since the cash flows would grow faster than they’re being discounted.
Is my data stored anywhere?
No. All calculations run locally in your browser. No data is sent to any server.