Perpetuity Calculator

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Table of Contents

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What is Perpetuity Calculator?

A perpetuity is a stream of periodic cash payments assumed to continue indefinitely. This calculator estimates the present value of that stream from the next payment, a discount rate and a constant growth rate. It can illustrate textbook examples involving endowments, preferred dividends or other long-lived cash-flow assumptions.

The answer is a model value, not a market quote or a promise that payments will continue. Real securities can carry credit, liquidity, tax and timing risks that three inputs cannot capture. Treat the result as a starting point for analysis and compare it with the actual terms of the asset or obligation.

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How to Use This Calculator

  1. Enter the payment expected one period from now in the Dividend field and choose its currency label.
  2. Enter the discount rate and expected constant growth rate as percentages for the same period. For annual payments, both must be annual rates.
  3. Make sure the discount rate is greater than the growth rate, then select Calculate.

The page changes each percentage to a decimal and divides the entered payment by the difference between the two rates. Enter zero for growth to value a level payment. A positive growth assumption raises the estimate because later payments are larger; a negative growth assumption represents a stream that shrinks at a steady percentage.

The currency selector labels the answer only. It does not look up exchange rates or convert the payment.

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Formula Used

Growing perpetuity: PV = C₁ / (r − g). For a level perpetuity, g = 0, so PV = C / r. The discount rate r must be greater than the growth rate g, and all three inputs must use the same payment period.
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Variables Explained

InputMeaningHow to enter it
DividendCash payment expected at the end of the next periodNonnegative amount in the selected currency
Discount rateRequired return used to translate future cash flows into present valuePercentage per payment period
Growth rateConstant change assumed for every later paymentPercentage on the same time basis as r
PVModeled value todayShown in the chosen currency label

The entered cash amount should be the next payment, commonly written C₁. If the amount available is the payment just made, grow it one period first before using the growing formula.

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Worked Example

Assume the next annual payment is USD 120, the annual discount rate is 8 percent and payments are expected to grow by 2 percent each year. Convert the rates to decimals: 0.08 and 0.02. Their difference is 0.06. Dividing 120 by 0.06 gives a present value of USD 2,000.

As a reasonableness check, set growth to zero while keeping the 8 percent discount rate. The level-payment value would be 120 ÷ 0.08 = USD 1,500. The higher growing value reflects the assumption that payments rise forever, which is a strong assumption and deserves careful review.

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Why Use This Calculator?

The result is the present value implied by the entered assumptions. It does not say what an asset must trade for, and it does not include a separate sale price. Small changes in the gap between discount and growth rates can cause large valuation changes. In the example, changing growth from 2 percent to 3 percent narrows the denominator from 6 to 5 percentage points and raises the result to USD 2,400.

Review a range of plausible rates rather than relying on one point estimate. A permanently high growth rate may be hard to sustain, especially when it approaches broad economic growth. Inflation should also be handled consistently: pair nominal cash flows with a nominal discount rate, or real cash flows with a real rate.

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Common Mistakes

    Never use a discount rate equal to or below the growth rate in this standard formula; the finite result no longer has the intended meaning. Avoid mixing monthly payments with annual rates, entering 0.08 when the field expects 8 percent, or using a payment that already includes several periods.

    Do not interpret the currency menu as conversion. Selecting EUR after entering a USD payment simply changes the label. Finally, do not overlook payment timing: the formula assumes the first cash flow arrives one period from today. A payment due immediately must be handled separately.

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Frequently Asked Questions

Can the growth rate be zero?

Yes. Zero growth changes the expression to the level-perpetuity formula, so the payment is divided by the discount rate alone.

Why must the discount rate exceed growth?

The usual infinite-series derivation converges only under that relationship. As the gap approaches zero, the estimate becomes extremely sensitive and grows without bound.

Should the dividend be the last payment or the next one?

Use the next expected payment for the growing-perpetuity form. If you have the payment just made, apply one period of assumed growth first.

Can I mix an annual discount rate with monthly payments?

No. Convert the rate and growth assumption to the payment period, or convert the payments to an annual basis. Every input needs a consistent timeline.

Does this estimate include a future selling price?

No. It values an assumed infinite stream directly. A finite holding-period model with a later sale price is a different calculation.

Is the displayed amount a fair market price?

It is an assumption-driven estimate. Market price can differ because of risk, taxes, liquidity, changing expectations and features absent from this simple model.

How should I choose a discount rate?

The appropriate required return depends on risk and context. Use documented assumptions, consider alternative rates and seek qualified financial guidance for an actual decision.

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Sources & References

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