CalculatorFly

Valuing Infinite Cash Flows: The Perpetuity Calculator

A perpetuity is a financial concept representing an annuity that pays a fixed stream of cash flows for an infinite period. The Perpetuity Calculator helps you determine the present value (PV) of such an income stream, which is a core concept in finance for valuing assets like preferred stocks and certain types of real estate.

💵 How to Use the Calculator

1. Enter Cash Flow per Period (C): This is the fixed payment you receive at the end of each period (e.g., annually).
2. Enter Discount Rate (r) (%): This is the interest rate used to discount the future cash flows to their present value. It reflects the time value of money and the risk of the investment.
3. Growing Perpetuity (Optional): If the cash flows are expected to grow at a constant rate forever, toggle the "Growing Perpetuity?" switch on.
4. Enter Constant Growth Rate (g) (%): If you enabled the growing perpetuity option, enter the constant rate at which the cash flows are expected to grow each period. Note: The discount rate (r) must be greater than the growth rate (g).
5. Calculate: Click the "Calculate Present Value" button.

The calculator will display the present value of the perpetuity and show the step-by-step calculation.

The Formulas Behind Perpetuity

1. Level (Zero-Growth) Perpetuity

For a perpetuity where the cash flow (C) is constant, the formula for its present value (PV) is remarkably simple:

PV = C / r

Where C is the cash flow per period and r is the discount rate per period.

2. Growing Perpetuity

For a perpetuity where the cash flow grows at a constant rate (g), the formula is adjusted as follows (also known as the Gordon Growth Model):

PV = C / (r - g)

Here, g is the constant growth rate per period. A critical condition for this formula is that the discount rate r must be greater than the growth rate g.

💡 Frequently Asked Questions (FAQ)

What is the difference between a perpetuity and an annuity?

The main difference is the time frame. A perpetuity has infinite cash flows, continuing forever. An annuity has a specified, finite number of payments (e.g., a 30-year mortgage).

Where are perpetuities used in the real world?

They are used to value assets that are expected to produce income indefinitely, such as preferred stocks (which pay a fixed dividend forever), real estate with stable, long-term rental income, and certain types of bonds issued by governments (consols).