Perpetuity Calculator – Present Value of Infinite Cash Flows
Calculate present value of infinite cash flows
Table of Contents
How to Use
- Select what you want to calculate (present value, payment, or rate)
- Enter the periodic payment amount
- Enter the discount rate (required rate of return)
- Optionally enter a growth rate for growing perpetuities
- Click calculate to see the result
What is a Perpetuity?
A perpetuity is a financial instrument that pays a fixed amount of money at regular intervals forever. While no investment truly lasts forever, perpetuities are useful for valuing assets with very long or indefinite cash flow streams.
The present value formula for a regular perpetuity is: PV = C / r, where C is the periodic payment and r is the discount rate. For a growing perpetuity: PV = C / (r - g), where g is the growth rate.
Types of Perpetuities
| Type | Description | Formula |
|---|---|---|
| Regular Perpetuity | Fixed payments forever | PV = C / r |
| Growing Perpetuity | Payments grow at rate g | PV = C / (r - g) |
| Perpetuity Due | Payments at start of period | PV = C / r × (1 + r) |
Real-World Applications
- Preferred stock valuation (fixed dividend payments)
- Consol bonds (British government bonds with no maturity)
- Real estate with stable rental income
- Endowment funds and scholarships
- Terminal value in DCF analysis
- Valuing companies with stable dividends
Frequently Asked Questions
- Why must the growth rate be less than the discount rate?
- If the growth rate equals or exceeds the discount rate, the present value would be infinite or negative, which is mathematically undefined. In practice, sustainable growth rates are typically lower than required returns.
- How is a perpetuity different from an annuity?
- An annuity has a fixed number of payments over a specific period, while a perpetuity theoretically continues forever. Annuities are more common in practice, but perpetuities are useful for valuing long-term investments.
- What discount rate should I use?
- Use a rate that reflects the risk of the cash flows. For low-risk investments like government bonds, use lower rates (3-5%). For stocks or riskier investments, use higher rates (8-15%). The rate should exceed expected inflation.
- Can I use this for stock valuation?
- Yes, the Gordon Growth Model for stock valuation is essentially a growing perpetuity formula. It values a stock as the next dividend divided by (required return - dividend growth rate).