Perpetuity Calculator - Present Value and Growth

A perpetuity calculator estimates the present value of a cash flow expected to continue indefinitely. Use it for preferred-stock dividends, long-lived rental income, endowment payouts, infrastructure concessions, or terminal-value checks when a recurring amount is treated as continuing without a set final payment date.

• • Investment valuation: Convert a recurring dividend, lease payment, royalty, or other long-run cash flow into a present value using a required return.
• • Terminal value checks: Test whether a final-year cash flow in a valuation model creates a reasonable continuing value.
• • Income property review: Translate a stabilized annual net income amount into a value estimate when a simple perpetual model is appropriate.
• • Classroom finance work: Check level and growing perpetuity examples while learning time value of money formulas.

A perpetuity is not a forecast that cash will literally arrive forever without risk. It is a simplifying model that compresses a very long stream of similar cash flows into one value today. The model is most useful when the cash flow is stable, the discount rate is defensible, and growth is modest.

Use the output as a valuation check, not as a buy or sell decision by itself. Small changes in the discount rate or growth rate can move the value sharply, especially when the two rates are close.

When the cash flow occurs once instead of recurring indefinitely, the present value calculator is the closer match.

The calculation uses the standard present-value relationship for a perpetual cash flow. Set growth to 0 for a level perpetuity.

• PV: present value today of the recurring cash flow stream.
• C1: cash flow expected at the next payment period.
• r: discount rate or required return for the same period as the cash flow.
• g: constant growth rate per period. For a level perpetuity, g equals 0.

For a level perpetuity, the growth rate is zero, so the formula becomes PV = C / r. For a growing perpetuity, the denominator is the discount-growth spread. That spread is the part of the required return left after allowing for constant growth.

The calculator also displays the value per dollar of next-period cash flow. A 5% spread creates a 20x multiple because 1 divided by 0.05 equals 20. A narrower spread creates a larger multiple, which is why growth assumptions deserve careful review.

According to University of Texas at San Antonio Department of Mathematics, the present value of a perpetuity is A divided by i, and a growing perpetuity uses A divided by i minus g when g is less than i.

If you already know the current value and future cash flow, the discount rate calculator can help solve the rate side of the valuation.

These terms explain what the calculator is measuring and why the same cash flow can produce very different values.

A perpetuity differs from an annuity because an annuity has a finite number of payments. If the cash flow stops after 10, 20, or 30 periods, use an annuity model instead of treating the stream as endless.

The formula assumes the next cash flow arrives one period from now. If a payment arrives immediately, handle that immediate amount separately before valuing the remaining future stream.

For cash flows with a fixed ending date, the annuity present value calculator uses the finite-payment approach instead.

Enter assumptions that use the same time period. Annual cash flow should pair with annual discount and growth rates.

1. 1 Enter the next cash flow: Use the next expected periodic amount, not a total over many years.
2. 2 Enter the discount rate: Use the required return for the asset, project, or classroom problem.
3. 3 Enter constant growth: Use 0 for a level perpetuity, a positive rate for steady growth, or a negative rate for decline.
4. 4 Check the spread: Confirm the discount-growth spread is positive and not unrealistically narrow.
5. 5 Read the value: Use the present value as a model output, then compare it with other valuation approaches.

If a preferred share pays $4 per year and the required return is 6%, enter 4, 6, and 0. The result is $66.67, which means the level payment is worth about 16.67 times the annual dividend under that rate assumption. If the market price is far above that value, review whether your discount rate is too high, whether the payment is expected to grow, or whether the share has rights not captured by this simple model.

The perpetuity calculator is useful when you need a quick valuation check while keeping the key assumption visible.

• • Shows rate sensitivity: The spread output makes it easier to see when the result depends on a very thin difference between discount and growth.
• • Handles level and growing cases: A single growth input covers both ordinary level perpetuities and constant-growth versions.
• • Supports model review: The value-per-dollar multiple helps spot terminal values that may be too aggressive for the assumptions.
• • Keeps units aligned: Cash flow, discount rate, and growth rate all need the same period, which reduces accidental monthly-versus-annual mixing.
• • Explains invalid assumptions: The calculator rejects growth rates that are equal to or above the discount rate because the formula stops producing a finite positive value.

The result can support a first-pass comparison between an asking price and an income stream. It can also help audit another model by revealing the perpetuity multiple implied by a terminal-value assumption.

For real investment decisions, pair the output with business risk, taxes, transaction costs, debt terms, and scenario analysis. The formula is precise, but the assumptions still carry judgment.

For stock dividends with a valuation workflow around share price, compare the result with the dividend discount model calculator.

Perpetuity values are most sensitive to assumptions that affect the denominator and the durability of the cash flow.

• • A perpetuity model can overstate value when a cash flow is unlikely to last for a very long time.
• • The formula does not include taxes, fees, default risk, reinvestment risk, or changing discount rates.
• • When the discount-growth spread is very small, tiny input changes can create very large value swings.

The most important check is whether the growth assumption can reasonably continue for the period implied by the model. Long-run growth above the required return is not compatible with a finite growing perpetuity value.

Use a separate scenario for each major assumption instead of relying on one output. Comparing a level case, a modest growth case, and a lower-growth case often reveals whether the valuation is driven by operations or by the terminal assumption.

According to NYU Stern School of Business, a perpetuity is a constant cash flow at regular intervals forever, and a growing perpetuity lasts forever only when the growth rate is less than the discount rate.

According to Kellogg School of Management, present value equals C divided by r for a perpetuity and C divided by r minus g for a constant-growth perpetuity.

When growth continues for a known number of periods, the growing annuity calculator avoids treating the stream as endless.