Perpetuity Calculator

Calculate present value, payment, or rate for standard and growing perpetuities

About the Perpetuity Calculator

A Perpetuity Calculator is a specialized financial tool used to determine the present value of a stream of cash flows that continue indefinitely. This concept is fundamental in valuation, particularly for financial instruments like preferred stocks, certain types of bonds known as consols, and established real estate investments where income is expected to persist forever. Investors use this tool to determine the fair price they should pay today for an unending stream of income, helping them compare different investment opportunities with infinite horizons.

The tool handles two primary types of calculations: standard perpetuities and growing perpetuities. In a standard perpetuity, the payment amount remains fixed for eternity. In a growing perpetuity, the payments increase over time at a constant rate, which is often used in Gordon Growth Model valuations for dividend-paying companies. By adjusting inputs for the initial payment, the required discount rate, and the anticipated growth rate, users can quickly find the intrinsic value of an asset or solve for the required rate of return if the price is already known.

Formula

PV = C / (r - g)

In the standard perpetuity formula, PV represents the Present Value, C is the Cash Flow per period, and r is the discount rate or required rate of return. If you are calculating a constant perpetuity with no growth, g is set to zero, simplifying the formula to PV = C / r.

When accounting for a growing perpetuity, g represents the constant periodic growth rate. All rates (r and g) must be expressed as decimals for the calculation to be accurate. The formula assumes the first payment occurs one full period from today.

Worked examples

Example 1: An investor is looking at a preferred stock that pays a fixed annual dividend of $10,000 forever, with a required return of 8%.

C = $10,000\nr = 0.08\ng = 0\nPV = 10,000 / 0.08\nPV = 125,000

Result: $125,000.00. This is the maximum an investor should pay for this stream of income to achieve an 8% return.

Example 2: A commercial real estate property generates $40,000 in annual rent. The rent is expected to grow by 3% every year, and the discount rate is 7%.

C = $40,000\nr = 0.07\ng = 0.03\nPV = 40,000 / (0.07 - 0.03)\nPV = 40,000 / 0.04\nPV = 1,000,000

Result: $1,000,000.00. The growth in payments significantly increases the present value compared to a flat payout.

Common use cases

Valuing preferred stock that pays a fixed dividend with no maturity date.
Determining the terminal value of a business in a Discounted Cash Flow (DCF) analysis.
Estimating the value of a permanent endowment fund for a university or non-profit.
Calculating the fair market value of a ground lease or a perpetual royalty stream.

Pitfalls and limitations

Applying the formula when the growth rate is greater than or equal to the discount rate, which creates an impossible valuation.
Failing to adjust annual interest rates to match the frequency of the cash flows (e.g., using an annual rate for quarterly payments).
Assuming the payout starts immediately; the standard formula calculates the value one period before the first payment occurs.
Using nominal interest rates instead of real rates when cash flows are adjusted for inflation.

Frequently asked questions

how is a perpetuity different from an annuity?

A perpetuity is a series of equal cash flows that continue forever, while an annuity has a fixed end date. Because the time horizon is infinite, we calculate the present value of a perpetuity by dividing the payment by the discount rate.

what is the formula for a growing perpetuity?

In a growing perpetuity, the cash flow increases by a fixed percentage (g) every period. To find the present value, you subtract the growth rate from the discount rate in the denominator (PV = P / (r - g)).

can growth rate be higher than discount rate in perpetuity?

If the growth rate equals or exceeds the discount rate, the formula results in a negative value or infinity, which is mathematically invalid for valuation. In real-world finance, a perpetual growth rate must be lower than the cost of capital to be sustainable.

what are real world examples of a perpetuity?

Consol bonds (issued by the UK government) and many types of preferred stock are classic examples. These assets pay a fixed dividend or interest payment indefinitely without a set maturity date.

does the perpetuity formula work for monthly payments?

Yes, you must ensure the discount rate and the payment frequency match. If payments are monthly, you must divide the annual interest rate by 12 to get the periodic rate before performing the calculation.