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Perpetuities are a fundamental concept in finance, representing an infinite series of equal payments. Our Perpetuity calculator makes understanding and quantifying them straightforward. Simply provide the fixed payment amount received each period (like an annual dividend) and the required rate of return or discount rate. Our Perpetuity Calculator instantly reveals the Present Value– the total worth of all those future payments condensed into a single value today. This calculator is perfect for academic exercises, financial modeling, or getting a quick valuation for specific investment scenarios.
Calculate the present value of infinite cash flows with our perpetuity calculator. Our Perpetuity Calculator is perfect for investments, business valuations, and financial planning. It also handles both basic and growing perpetuities with precision.
Calculate the present worth of perpetual cash flows with just a few clicks
Account for growth rates to model increasing payment streams over time
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Learn the concepts behind perpetuities with comprehensive guides and examples
Featuring both zero-growth and growing perpetuity formulas, real-world applications like preferred stocks and real estate valuation, and expert investment insights.
Our perpetuity calculator helps you determine the present value of a stream of cash flows that continues forever. Whether you're evaluating an investment, understanding a financial concept, or valuing a business, this tool and guide will provide a clear and comprehensive understanding of perpetuities. Use our perpetuity calc to find results quickly!
This perpetuity calculator is designed to be user-friendly and provides accurate calculations for both basic perpetuities and growing perpetuities. By entering a few simple inputs, you can quickly determine the present value of infinite cash flows and make informed financial decisions.
A perpetuity is a financial concept where a constant stream of identical cash flows continues indefinitely, with no end date. Think of it as an annuity that never stops. While the total sum of the payments is infinite (because they go on forever), the present value of those payments is finite and can be calculated. This might seem counterintuitive, but it's a core principle of finance, based on the time value of money.
Perpetuity is a series of fixed payments made at equal intervals that continue forever, with the present value being finite despite the infinite timeline.
You might also hear perpetuities referred to as perpetual annuity or infinite annuity. This perpetual annuity calculator will help clarify and quantify these concepts, making it easier to understand the value of cash flows that continue indefinitely.
The time value of money states that a dollar received today is worth more than a dollar received in the future. This is because you can invest the dollar you have today and earn a return on it. Therefore, future cash flows need to be discounted to reflect their lower present value.
This concept is fundamental to understanding perpetuities. Because cash flows that occur far in the future have very little present value, we can calculate a finite value for an infinite stream of payments. The discount rate used in the calculation represents the required rate of return or the opportunity cost of capital.
Enter the dividend or payment amount (D) in the input field.
Enter the discount rate (R) as a percentage (e.g., 5 for 5%).
Optionally, enter the growth rate (G) as a percentage if the payments are expected to grow over time.
Click the 'Calculate' button to determine the present value of the perpetuity.
Review the results to see the present value of your perpetual cash flows.
Use the 'Ask AI to Explain' feature for a detailed analysis of your specific calculation.
This is the simplest case, where the payment remains constant forever.
PV = D / R
Example: If you receive $100 per year forever, and the discount rate is 5% (0.05), the present value is PV = $100 / 0.05 = $2,000.
This formula is used when the payment grows at a constant rate forever.
PV = D / (R - G)
Example: Suppose the current dividend is $100, the growth rate is 2% (0.02), and the discount rate is 5% (0.05). The present value would be: PV = $100 / (0.05 - 0.02) = $100 / 0.03 = $3,333.33.
Crucial Condition: The formula for a growing perpetuity only works if the growth rate (G) is less than the discount rate (R). If G is greater than or equal to R, the present value would be theoretically infinite, which is not economically meaningful. Our growing perpetuity calculator will alert you if this condition is not met.
While true perpetuities are rare in the strictest sense, several financial instruments and situations closely resemble perpetuities. Understanding these examples, or perpetuity in real life examples, helps solidify the concept:
Historically, the British government issued bonds called "Consols" that paid a fixed interest payment forever. These were a classic example of a true perpetuity (although they have since been redeemed).
The income stream from a well-maintained rental property can be modeled as a perpetuity. If you assume the property will continue to generate rental income indefinitely, you can use perpetuity calculations to estimate its value.
Some preferred stocks pay a fixed dividend payment indefinitely. This makes them very similar to perpetuities, although there's always a (small) risk the company could suspend the dividend.
Many universities and organizations have endowments that fund scholarships or grants in perpetuity. The principal of the endowment is invested, and the earnings are used to make regular payments, theoretically forever.
The terminal value calculation for a discounted cash flow model is often based on the concept of a growing perpetuity. This represents the value of a business beyond the explicit forecast period.
Let's consider an investment opportunity that promises to pay a constant annual dividend forever. The investor wants to determine how much they should pay for this investment today.
An investor is considering a preferred stock that pays an annual dividend of $50 per share, and this dividend is expected to continue indefinitely.
Present Value (PV) = Dividend (D) ÷ Discount Rate (R)
= $50 ÷ 0.08
= $625
The present value of $625 represents the theoretical fair value of the investment. This means that if the investor pays $625 today, and the investment pays $50 annually forever, the investor will earn exactly their required rate of return of 8%.
If the investment is available for less than $625, it would represent a good opportunity as the investor would earn more than their required 8% return. Conversely, if the price is higher than $625, the investor would be better off looking for alternative investments.
Using our Perpetuity Calculator, the investor quickly determined that the present value of the preferred stock with a $50 annual dividend and an 8% discount rate is $625. This calculation provides a clear benchmark for making an informed investment decision.
It's important to distinguish between a perpetuity and an annuity. While both involve regular payments, there are fundamental differences:
| Feature | Perpetuity | Annuity |
|---|---|---|
| Payment Duration | Infinite (forever) | Finite (fixed number of periods) |
| End Date | No end date | Defined end date |
| Present Value Formula | PV = D/R or PV = D/(R-G) | More complex formula based on payment periods |
| Typical Examples | Preferred stocks, consols, real estate | Mortgages, loans, retirement plans |
| Present Value | Finite despite infinite payments | Finite and generally less than perpetuity |
Our perpetuity calculator features a clean, user-friendly design that makes calculating present values simple for both financial experts and beginners.
Calculate both constant and growing perpetuities with ease. Our tool handles growth rates that model increasing cash flows over time.
Get personalized, detailed explanations of your calculations with our AI assistant, helping you understand the results in the context of your specific scenario.
Learn how to apply perpetuity calculations to practical scenarios like business valuation, real estate investments, and retirement planning.
Access comprehensive guides, examples, and explanations that help you understand the concept of perpetuity and its applications in finance.
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Q1. What is a perpetuity?
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A perpetuity is a financial concept that describes a stream of equal cash flows occurring at regular intervals that continues indefinitely. While the payments go on forever, the present value is finite due to the time value of money.
Q2. How do you calculate the present value of a perpetuity?
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For a constant perpetuity, the present value is calculated using the formula PV = D/R, where D is the periodic payment and R is the discount rate (expressed as a decimal). For a growing perpetuity, the formula is PV = D/(R-G), where G is the growth rate.
Q3. What's the difference between a perpetuity and an annuity?
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The main difference is the time horizon. A perpetuity continues indefinitely with no end date, while an annuity has a specific, finite number of payments. This leads to different formulas for calculating their present values.
Q4. Can the growth rate be higher than the discount rate in a growing perpetuity?
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No, in a growing perpetuity, the growth rate must be less than the discount rate (G < R). If the growth rate equals or exceeds the discount rate, the present value would theoretically be infinite, which is not economically meaningful.
Q5. What are real-world examples of perpetuities?
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Real-world examples that approximate perpetuities include preferred stocks with fixed dividends, rental income from real estate, certain government bonds like the historical British Consols, university endowments, and the terminal value in business valuations.
Q6. Why is the present value of a perpetuity finite despite infinite payments?
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Due to the time value of money, cash flows received far in the future have diminishing present values. When discounted back to the present, the sum of these infinite but diminishing values converges to a finite number.
Q7. How does the discount rate affect the present value of a perpetuity?
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The present value of a perpetuity is inversely related to the discount rate. A higher discount rate results in a lower present value, while a lower discount rate leads to a higher present value. This relationship is particularly sensitive in perpetuities.
Q8. What is a growing perpetuity?
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A growing perpetuity is a series of cash flows that not only continues indefinitely but also increases at a constant rate (G) each period. This growth rate is incorporated into the formula: PV = D/(R-G), where D is the initial payment.
Q9. How are perpetuities used in business valuation?
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In business valuation, particularly in discounted cash flow (DCF) models, perpetuities are often used to calculate the terminal value—representing the value of all cash flows beyond the explicit forecast period. This assumes the business will continue operating indefinitely.
Q10. Can I use the perpetuity calculator for retirement planning?
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Yes, the perpetuity calculator can be useful for certain aspects of retirement planning, especially when considering how to structure investments that provide regular income indefinitely, or when determining how much capital is needed to generate a specific perpetual income stream.