Perpetuity Calculator
Calculate the present value of a perpetuity, an infinite stream of equal cash flows paid at regular intervals. Useful for valuing preferred stock, endowments, and terminal values in DCF analysis.
This free online perpetuity calculator provides instant results with no signup required. All calculations run directly in your browser — your data is never sent to a server. Enter your values below and see results update in real time as you type. Perfect for everyday calculations, homework, or professional use.
The fixed payment received each year forever.
The required rate of return or discount rate as a percentage.
Annual growth rate of cash flows. Enter 0 for a flat perpetuity.
How to Use This Calculator
Enter your input values
Fill in all required input fields for the Perpetuity Calculator. Most fields include unit selectors so you can work in your preferred unit system — metric or imperial, whichever matches your problem.
Review your inputs
Double-check that all values are correct and that you have selected the right units for each field. Incorrect units are the most common source of calculation errors and can produce results that are off by factors of 2, 10, or more.
Read the results
The Perpetuity Calculator instantly computes the output and displays results with units clearly labeled. All calculations happen in your browser — no loading time and no data sent to a server.
Explore parameter sensitivity
Try adjusting individual input values to see how the output changes. This is a quick and effective way to develop intuition about how different parameters influence the result and to identify which inputs have the largest effect.
Formula Reference
Perpetuity Calculator Formula
See calculator inputs for the governing equation
Variables: All variables and their units are labeled in the calculator interface above. Input fields accept values in multiple unit systems — select your preferred unit from the dropdown next to each field.
When to Use This Calculator
- •Use the Perpetuity Calculator when comparing financial options side-by-side — such as different loan terms or investment returns — to make more informed decisions.
- •Use it to quickly estimate costs or returns before making purchasing, investment, or borrowing decisions.
- •Use it for financial education and planning to understand how compound interest, fees, or tax affects the real value of money over time.
- •Use it when building or reviewing a budget to verify that projections and calculations are mathematically correct.
About This Calculator
The Perpetuity Calculator is a free financial calculation tool designed to help individuals and businesses understand key financial concepts and estimate costs, returns, and loan parameters. Calculate the present value of a perpetuity, an infinite stream of equal cash flows paid at regular intervals. Useful for valuing preferred stock, endowments, and terminal values in DCF analysis. The calculations are based on standard financial mathematics formulas. Results are for informational and educational purposes only and should not be considered financial, investment, or tax advice. Consult a qualified financial professional before making financial decisions. All calculations are performed in your browser — no personal financial data is stored or transmitted.
About Perpetuity Calculator
The Perpetuity calculator determines the present value of an infinite series of cash flows. A flat perpetuity pays the same amount forever, while a growing perpetuity increases payments at a constant rate each year. This concept is fundamental in finance for valuing preferred stock dividends, charitable endowments, and calculating terminal values in discounted cash flow models. The Gordon Growth Model, a form of the growing perpetuity formula, is one of the most widely used methods for valuing dividend-paying stocks. Understanding perpetuities helps investors evaluate any asset that promises regular payments extending indefinitely into the future.
The Math Behind It
Formula Reference
Flat Perpetuity
PV = CF / r
Variables: CF = annual cash flow; r = discount rate (decimal)
Growing Perpetuity (Gordon Growth Model)
PV = CF / (r - g)
Variables: CF = first year cash flow; r = discount rate; g = growth rate (r > g)
Worked Examples
Example 1: Endowment fund
A university endowment needs to pay $500,000 per year in scholarships forever. The fund earns 5% annually.
The endowment needs $10 million to fund $500K in perpetual annual scholarships at a 5% return.
Example 2: Growing dividend stock valuation
A stock pays a $3 dividend next year, growing at 4% per year. Your required return is 9%.
The stock is worth $60 per share based on the Gordon Growth Model.
Common Mistakes & Tips
- !Setting the growth rate equal to or greater than the discount rate, which makes the formula produce infinity or a negative number, both of which are meaningless.
- !Using next year's cash flow when the formula calls for the current year's flow or vice versa, causing a one-period timing error.
- !Forgetting that perpetuity assumes constant growth forever, which rarely holds in reality for individual companies.
Related Concepts
Used in These Calculators
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Frequently Asked Questions
Do true perpetuities exist in the real world?
Very few assets pay literally forever. The closest examples are British consols (government bonds with no maturity date), some preferred stocks, and endowments. In practice, the perpetuity formula is used as an approximation for very long-lived cash flow streams.
How is the growing perpetuity related to stock valuation?
The Gordon Growth Model values a stock as next year's dividend divided by the difference between the required return and the dividend growth rate. It is a direct application of the growing perpetuity formula and works best for mature, stable dividend-paying companies.
What happens if the growth rate exceeds the discount rate?
The formula breaks down mathematically, producing a negative or infinite value. Economically, this would imply the asset has unlimited value, which is impossible. If g exceeds r, use a multi-stage model with different growth rates for different periods.