finance

Perpetuity Calculator

A perpetuity is a financial instrument that pays a fixed stream of cash flows indefinitely into the future. Investors, financial analysts, and portfolio managers use perpetuity valuations to assess bonds, preferred stocks, and real estate investments. This calculator determines what those endless payments are worth in today's money by accounting for the time value of money and optional growth rates.

Last updated: May 10, 2026

Creators Arturo Barrantes, MSc Finance

Reviewers Tibor Pál and Małgorzata Koperska

837 people find this calculator helpful

Understanding Perpetuity

A perpetuity is a sequence of equal payments made at regular intervals with no defined end date. Unlike ordinary annuities, which terminate after a set period, perpetual cash flows continue forever. The defining characteristics are regularity (payments occur at fixed intervals), consistency (each payment is identical or grows at a constant rate), and indefiniteness (there is no maturity date).

The concept may sound unusual, but perpetuities exist throughout financial markets. While truly infinite payments are rare, many securities and assets behave as perpetuities for practical valuation purposes. The key insight is that future payments have diminishing present value because money received today is worth more than money received later—you can invest it, earn interest, or spend it immediately.

The Time Value of Money and Discounting

Money's value changes over time due to inflation and earning potential. A payment due in ten years is worth less today than an identical payment received immediately, because you lose years of potential investment returns. This principle is captured in the discount rate, which reflects how much you'd expect to earn annually if you invested the money elsewhere.

When calculating perpetuity, the discount rate acts as a bridge between future cash flows and today's value. Higher discount rates mean future payments are worth less in present-value terms. For example, at a 5% discount rate, a £100 annual payment is valued very differently than at a 10% discount rate. The further into the future a payment occurs, the smaller its contribution to today's value becomes—this is why perpetuities have a finite present value despite infinite payments.

Perpetuity Valuation Formula

The present value of a perpetuity is calculated by dividing the periodic payment by the discount rate. This formula assumes fixed payments with no growth:

PV = D ÷ R

For perpetuities with payments that grow at a constant rate each period:

PV = D ÷ (R − g)

PV — Present value of the perpetuity in today's money
D — Dividend or periodic payment amount
R — Discount rate expressed as a decimal (e.g., 0.05 for 5%)
g — Annual growth rate of payments, expressed as a decimal (0 for fixed payments)

Fixed vs. Growing Perpetuities

A fixed perpetuity pays the same amount indefinitely. If you receive £50 annually forever, the payment never changes. These are simpler to value but less common in practice because inflation typically erodes purchasing power.

A growing perpetuity increases each payment by a constant percentage rate. If dividends grow at 3% annually, next year's payment is 3% higher than this year's. This structure better reflects reality: companies typically raise dividends over time, and rents increase with inflation. The growth rate must be lower than the discount rate for the calculation to work—otherwise, value becomes infinite or negative, indicating an economically infeasible scenario.

Consider a £100 annual payment with an 8% discount rate: fixed perpetuity value is £1,250. If those payments grow at 2% annually instead, the value rises to approximately £1,667. Growth makes the perpetuity more valuable because it offsets the diminishing effect of discounting.

Practical Considerations

When valuing perpetuities, several real-world factors affect accuracy and applicability.

Growth rate cannot exceed discount rate — If growth equals or exceeds the discount rate, the formula breaks down mathematically. This reflects economic reality: sustainable growth in a perpetuity cannot outpace overall returns available in the market, or the investment would be infinitely valuable (or worthless). Always ensure your growth rate is realistically lower than your discount rate.
Few true perpetuities exist — Most investments described as perpetuities—preferred stocks, bonds, real estate—can be called, redeemed, or cease payment. Use perpetuity calculations as approximations for long-duration assets. Preferred stocks, for example, can be repurchased by the issuer; government bonds eventually mature. Perpetuity valuation works best for these assets when you expect payments to continue for decades.
Discount rate selection is critical — Small changes in discount rate dramatically alter perpetuity value. A 1% increase in rate can slash value by half. Your discount rate must reflect current market conditions, the asset's risk profile, and available alternative investments. Use the cost of equity or the weighted average cost of capital (WACC) for company-specific perpetuities.
Inflation and real vs. nominal rates — Decide whether payments and discount rates are in nominal (unadjusted) or real (inflation-adjusted) terms, then stay consistent. A 5% nominal discount rate includes expected inflation; a 2% real rate does not. Mixing them produces meaningless results. For long-term perpetuities, explicitly modeling inflation in growth assumptions is essential.

Frequently Asked Questions

What is the difference between a perpetuity and an annuity?

An annuity is a series of equal payments over a fixed period—say, 20 or 30 years. A perpetuity has no end date; payments continue indefinitely. Because annuities terminate, their present value depends on how long payments last. Perpetuities ignore time horizon and instead rely on the discount rate to determine value. From a valuation standpoint, a perpetuity is like an annuity stretched to infinity, which is why its value is finite but depends heavily on the discount rate chosen.

Can perpetuity value ever be negative?

No, perpetuity value cannot be negative in normal circumstances. However, the mathematical formula breaks down if the growth rate exceeds the discount rate, producing a nonsensical result. This reflects an economic impossibility: an asset cannot sustainably grow faster than the overall market return forever. If your calculation suggests negative or infinite value, re-examine your assumptions. The growth rate should represent realistic dividend increases or inflation; the discount rate should reflect the market's return expectations for that asset's risk level.

How do I choose an appropriate discount rate?

The discount rate represents the annual return you could earn on alternative investments of similar risk. For stocks, it often equals the cost of equity (calculated using the capital asset pricing model or other methods). For bonds, it reflects current market yields. For real estate, use the capitalization rate. Start by comparing perpetuity valuations to current market prices. If your perpetuity formula gives £1,000 but the asset trades at £1,500, your discount rate is too high. Conversely, if it values the asset at £500, your rate is too low. Market data and peer comparisons help calibrate the discount rate correctly.

Why does increasing the discount rate decrease perpetuity value?

A higher discount rate means future cash flows are worth less today. If you can earn 10% annually elsewhere, a stream of payments is less valuable than if you could only earn 3% elsewhere. The discount rate reflects opportunity cost: what you're giving up by not investing the money in the next-best alternative. As the discount rate rises, the present value of every future payment shrinks. This inverse relationship is why perpetuity value is highly sensitive to discount rate assumptions.

Are preferred stocks really perpetuities?

Preferred stocks behave like perpetuities in many respects: they pay fixed dividends indefinitely and have no maturity date. However, they carry risks true perpetuities don't. Companies can suspend dividend payments during financial distress, or buy back preferred shares, effectively ending the cash stream. Additionally, some preferred stocks are callable, meaning the issuer can redeem them early. For valuation purposes, analysts often treat stable preferred stocks as perpetuities, but apply a higher discount rate to account for default and call risk. This premium reflects the fact that preferred dividend payments, unlike true perpetuities, are not guaranteed.

How does inflation affect perpetuity calculations?

Inflation erodes the purchasing power of money. A £100 annual payment decades from now buys far less than £100 today. In perpetuity calculations, you must decide whether to use nominal (unadjusted) or real (inflation-adjusted) figures. If you use nominal discount rates, don't apply real growth rates, and vice versa. For long-duration perpetuities, explicitly modeling inflation in the growth rate—or using inflation-adjusted discount rates—ensures accuracy. A growing perpetuity with growth rate equal to expected inflation preserves real purchasing power, making it a more realistic model for assets like real estate or utilities.

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