Perpetuity Calculator
Evaluate an infinite stream of continuous cash flows. Perfect for assessing preferred dividends, endowments, and perpetual bonds.
Choose the variable to solve for
How often payments are made
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What Is the Perpetuity Calculator?
A perpetuity is a stream of equal cash flows that continues forever. Our Perpetuity Calculator computes the present value of such infinite payment streams, a fundamental concept in finance used for valuation of preferred stocks, real estate, and endowment funds.
The formula is elegantly simple: PV = PMT / r, where PMT is the periodic payment and r is the discount rate. For example, receiving 50,000 every year forever with a 5% discount rate gives a present value of 10,00,000.
Investors valuing preferred stocks, real estate professionals using capitalization rates, and finance students learning time value of money concepts will benefit from this calculator.
How to Use This Calculator
Enter the periodic payment amount
The fixed cash flow you receive or pay at each interval.
Set the discount rate
The rate used to discount future cash flows to their present value. Higher rates reduce present value.
Choose the payment frequency
Select annual, semi-annual, quarterly, or monthly payment periods.
Optionally select growing perpetuity
If payments grow at a constant rate each period, toggle the growing perpetuity option.
View the present value
The calculator shows the present value of the infinite cash flow stream.
Real-World Example
Meet Anita. She is evaluating a preferred stock that pays 1,20,000 in dividends every year indefinitely. She wants to know what this stock is worth today if she expects an 8% return.
Using the Perpetuity Calculator:
Annual Payment
1,20,000
Discount Rate
8%
Payment Frequency
Annual
Present Value
15,00,000
Growing (4%) PV
30,00,000
Anita finds that the stock is worth 15,00,000 based on a simple perpetuity. If dividends grow at 4% annually, the value doubles to 30,00,000. This helps her decide whether the current market price is fair.
The Mathematics Behind Perpetuity Valuation
A perpetuity values an infinite stream of equal cash flows. For growing perpetuities, the growth rate is subtracted from the discount rate:
Frequently Asked Questions
Preferred stocks that pay fixed dividends indefinitely, perpetual bonds, and endowment funds that preserve principal while spending earnings are common perpetuities.
A growing perpetuity assumes payments increase by a fixed percentage each period. Its present value is PV = PMT / (r - g) where g is the growth rate, provided r > g.
The perpetuity formula is used in the Gordon Growth Model to value stocks and in the capitalization rate method for real estate valuation.
If r = g, the formula breaks down because the present value becomes infinite. In practice, this indicates an unsustainable situation where payments grow faster than the discount rate, which cannot continue indefinitely.
More frequent payments increase the present value slightly. For monthly payments, use the monthly discount rate. For example, 10,000 monthly with 8% annual rate gives a PV of 15,00,000, same as 1,20,000 annually.
Using PV = PMT / r, with 7% annual discount rate, monthly rate = 0.07/12 = 0.005833, PV = 10,000 / 0.005833 = approximately Rs 17,14,286. So Rs 10,000 monthly forever is worth about Rs 17.14 lakhs today at a 7% discount rate.
Real estate uses the capitalization rate approach: Property Value = Net Operating Income / Cap Rate. A property generating Rs 6,00,000 annual rent with an 8% cap rate is valued at Rs 75,00,000. This assumes rental income continues indefinitely like a perpetuity.
The Gordon Growth Model values stocks as growing perpetuities: Stock Value = D1 / (r - g). For a stock with Rs 50 expected dividend, 12% required return, and 6% growth, value = 50 / (0.12 - 0.06) = Rs 833. This is widely used for dividend stocks.
Perpetuity values are very sensitive to interest rates. When rates rise, present value falls sharply. A Rs 1,00,000 annual perpetuity is worth Rs 12,50,000 at 8% but only Rs 10,00,000 at 10%. This explains why bond prices fall when central banks raise rates.
A growing perpetuity uses PV = PMT / (r - g), where r > g. For Rs 50,000 growing at 4% with 10% discount: PV = 50,000 / (0.10 - 0.04) = Rs 8,33,333. A regular perpetuity at the same rate: PV = 50,000 / 0.10 = Rs 5,00,000. The growing version is 67% higher.
Key Takeaways
Perpetuity values infinite equal cash flows in today's money.
Present value decreases as discount rate increases.
Growing perpetuity formula is essential for stock valuation.
Used in preferred stock, real estate, and endowment valuation.
The Gordon Growth Model uses perpetuity principles.
Why This Matters
The perpetuity concept is the foundation of modern valuation theory. Understanding it unlocks the ability to price any asset that generates ongoing cash flows.
This calculator is for educational and planning purposes. Consult a qualified professional for personalized advice.