Perpetuity Calculator

What Is a Perpetuity?

A perpetuity is a financial instrument that pays a fixed amount of money at regular intervals indefinitely. Unlike standard annuities or bonds that have a defined maturity date, a perpetuity has no end date. The most common real-world example is a consol bond, a type of government bond that pays interest forever with no principal repayment.

Because the payments continue forever, the present value of a perpetuity is not infinite. The further into the future a payment occurs, the less it is worth in today's terms due to the time value of money. The present value of a perpetuity is the sum of all those discounted future payments.

How the Present Value of a Perpetuity Is Calculated

The calculation relies on a straightforward formula derived from the sum of an infinite geometric series:

PV = PMT / r

Where:

• PV = Present value of the perpetuity
• PMT = Payment amount per period (the fixed cash flow)
• r = Discount rate per period (the required rate of return, expressed as a decimal)

This formula assumes that the first payment occurs one period from today. It also assumes that the discount rate remains constant over time. The result tells you the maximum amount you should pay today to receive those future payments, given your required rate of return.

How to Use This Calculator

1. Enter the payment amount — the fixed cash flow received each period.
2. Enter the discount rate — your required annual rate of return, expressed as a percentage (e.g., 5 for 5%).
3. The calculator will instantly compute the present value of the perpetuity.

No additional inputs are needed. The tool handles the conversion of the percentage rate to its decimal form automatically.

Understanding Your Results

The output is a single dollar amount representing the present value of the perpetuity. This figure is highly sensitive to the discount rate. A small change in the rate can produce a large change in the present value.

For example, a perpetuity paying $1,000 per year has a present value of:

• $20,000 at a 5% discount rate
• $10,000 at a 10% discount rate
• $40,000 at a 2.5% discount rate

This inverse relationship is critical. A lower discount rate implies a higher valuation because future payments are discounted less heavily. A higher discount rate implies a lower valuation.

Key Assumptions and Limitations

The standard perpetuity formula relies on several assumptions that may not hold in all real-world scenarios:

• Constant payments: The payment amount never changes. Growing perpetuities (where payments increase at a constant rate) require a modified formula: PV = PMT / (r - g), where g is the growth rate.
• Constant discount rate: The required rate of return is assumed to remain the same forever. In practice, interest rates and risk premiums change over time.
• First payment timing: The formula assumes the first payment occurs one period from today. If the first payment is immediate (a perpetuity due), the result is adjusted by multiplying by (1 + r).
• No default risk: The calculation assumes the payments will be made indefinitely without interruption. Real-world perpetuities carry issuer risk.

Practical Use Cases

The perpetuity concept is used in several areas of finance and valuation:

• Preferred stock valuation: Many preferred shares pay a fixed dividend indefinitely and are valued using the perpetuity formula.
• Real estate: A property generating stable, ongoing rental income can be valued as a perpetuity when the holding period is indefinite.
• Terminal value in DCF models: In discounted cash flow analysis, the terminal value often assumes a perpetuity growth rate to estimate the value of a business beyond the projection period.
• Endowment and trust funds: These are often structured to generate perpetual income streams, making the perpetuity formula relevant for valuation.