Perpetuity: What Is It and Can You Buy One?

Financial models sometimes assume that an asset keeps producing income with no scheduled stopping point. A perpetuity places a value on that assumption by recognizing that money expected far into the future contributes progressively less to what the income is worth now. The concept appears in several types of valuation analysis, particularly when estimating the long-term worth of an asset or business after near-term projections end.

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What Is a Perpetuity?

A perpetuity models recurring income without assigning a final payment date. Rather than adding every future payment together, the calculation reduces later amounts according to an assumed rate of return and expresses the entire series as a single current value.

For a level perpetuity, the basic formula is:

Present value = Annual cash flow ÷ Discount rate

The percentage used in the denominator represents the return demanded for committing money to the asset. Increasing that percentage reduces the calculated price because the future income must meet a higher return requirement.

Suppose an investment is expected to pay $10,000 each year indefinitely and an investor uses a 5% discount rate. The estimated present value would be:

$10,000 ÷ 0.05 = $200,000

Changing the discount rate can substantially change the result. At a 4% rate, the same $10,000 annual payment would have an estimated value of $250,000. At 6%, it would be about $166,667.

For a more concrete illustration, consider a piece of real estate, like an apartment. If you own the apartment and rent it out, you can hypothetically receive an infinite stream of rent payments. In other words, the rent from your apartment is a perpetuity.

In practice, of course, you probably won’t own that apartment for all of eternity – and the rent wouldn’t stay fixed. But if you wanted to calculate the apartment’s value based on its income, you could use the perpetuity formula.

Businesses can also be valued by separating near-term projections from a later period in which operations are assumed to settle into a more stable pattern. A perpetuity calculation can be applied to that later stage to estimate how much the remaining years contribute to the company’s valuation.

Growing Perpetuity

Not every long-term model assumes an unchanged payment. A growing perpetuity allows the modeled amount to rise by the same percentage from one period to the next. Analysts can use this structure when they believe a mature source of income will increase gradually rather than remain flat.

The standard formula for a growing perpetuity is:

Present value = Next period’s cash flow ÷ (Discount rate − Growth rate)

This calculation requires the assumed return to exceed the growth assumption. Otherwise, the denominator reaches zero or becomes negative and the standard valuation approach no longer produces a meaningful finite result.

For example, assume an investment is expected to pay $10,000 next year, with payments growing 2% annually thereafter. Using a 6% discount rate, its estimated present value would be:

$10,000 ÷ (0.06 − 0.02) = $250,000

The growth assumption can have a large effect on valuation because even a small change is applied indefinitely. Raising the assumed growth rate to 3%, with the other inputs unchanged, would increase the estimated value to about $333,333.

How Is a Perpetuity Different From an Annuity?

The distinction comes down to whether the valuation model places a boundary on the payments. A perpetuity does not specify a last one. An annuity, by comparison, is built around payments that continue under the terms of the arrangement, such as for a stated number of years or for a person’s lifetime.

An insurance annuity, for example, is a contract that can provide income in exchange for one or more premium payments. Depending on the contract, payments may last for a set number of years or for the annuitant’s lifetime. Some contracts can provide benefits for a surviving spouse or another specified period, but those features do not turn the annuity into a financial perpetuity.

This distinction also affects valuation. An annuity calculation accounts for a finite payment period, while a perpetuity formula assumes the modeled cash flows continue indefinitely.

Can You Buy a Perpetuity?

True perpetual securities have existed, but they are uncommon and should not be confused with ordinary bonds or lifetime annuities. Historically, governments and other issuers have sold debt without a conventional maturity date. The United Kingdom, for example, once had several undated government securities, including debt connected with financing from the First World War and earlier periods. The government redeemed its remaining undated gilts in 2015.

For most individual investors in 2026, perpetuity is more relevant as a financial model than as a product to purchase. Stocks can continue paying dividends without a predetermined ending date and some securities may have very long or potentially perpetual structures, but their payments are not necessarily guaranteed forever.

How to Use Perpetuity Calculations When Evaluating an Investment

Individual investors can use the calculation to test whether a price appears reasonable under different long-range assumptions. One approach is to estimate the recurring income first and then calculate the value several times using different required returns. This shows how sensitive the result is to changes in the assumptions rather than presenting one valuation as definitive.

Pay particular attention to the discount rate. Suppose an investment is expected to produce $5,000 annually without growth. At a 5% discount rate, the perpetuity formula produces a value of $100,000. Increasing the rate to 7% lowers the estimate to about $71,429. The investment itself has not changed, but the higher required return makes its future income worth less today.

For a model that includes growth, investors can run the same exercise with several conservative increases in future payments. Because the calculation extends the assumption indefinitely, relatively small adjustments can produce sizable differences in the resulting valuation. Keeping the growth estimate below the required return is also necessary for this version of the formula.

A perpetuity calculation should therefore be one part of an investment review rather than the sole reason to buy or sell an asset. Actual dividends, rents and business cash flows can decline or stop, while discount rates and growth expectations can change. A financial advisor can help assess how those assumptions fit with an investment’s risks and your broader portfolio.

Bottom Line

A perpetuity is most useful as a way to put a current price on income that a financial model assumes has no expiration date. Its estimated value changes with the required return and models that allow payments to rise also depend on the chosen growth assumption. Investors are more likely to encounter this technique in valuation work than as a conventional investment available for purchase.

Tips for Retirement Planning and Investing

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As pointed out in the article, though, the fixed payments of an annuity will depreciate in value over time. Some insurance companies compensate for this by adding what’s called an inflation rider. But it will come at additional cost.
The idea of regular cash flow for infinity is awfully nice. Pensions had the same idea, though they were only for a worker’s lifetime. Now the closest thing you can buy is an annuity from an insurance company. If you’re interested in one, there are many kinds to choose from. Make sure you know the differences before you buy.