Perpetuity Value Calculator

Frequently Asked Questions

Why must the discount rate exceed the growth rate?

If growth equals or exceeds the discount rate the series does not converge and the present value becomes infinite or negative, which has no real-world meaning.

What is the difference between a level and growing perpetuity?

A level perpetuity pays the same amount forever, while a growing perpetuity increases each payment at a constant rate using the Gordon growth form.

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When Perpetuities Appear in Real Finance

While no investment literally pays forever, the perpetuity framework is widely used in practice as a simplifying approximation for very long-lived income streams.

Preferred Stock Valuation

Preferred shares that pay a fixed dividend with no maturity date are priced exactly like a level perpetuity. The fair value is simply the annual dividend divided by the investor's required yield on that security. When market yields rise, preferred stock prices fall by the same perpetuity logic.

Commercial Real Estate Cap Rates

A capitalization rate is the inverse of a perpetuity multiple. If a property generates $100,000 in net operating income and trades at a 5% cap rate, the implied value is $2,000,000 - identical to a perpetuity present value calculation. Sophisticated buyers model growth explicitly using the growing perpetuity form, setting g equal to expected long-run rent inflation.

Endowments, Consols, and Sovereign Wealth Funds

University endowments define a spending rule (typically 4-5% of assets per year) so that the principal is never consumed and distributions can continue indefinitely. UK government bonds called consols, first issued in the 18th century, were perpetual bonds with no maturity date. Sovereign wealth funds in Norway, Singapore, and Abu Dhabi model long-run distributions using a perpetuity-like framework to preserve real capital for future generations.

The Gordon Growth Model Connection

The Gordon Growth Model (GGM) is the growing perpetuity formula applied to stock dividends. If a company just paid a dividend D0, the expected next dividend is D1 = D0 × (1 + g), and the stock's fair value is D1 / (r - g). This is the single most widely used formula in equity valuation for mature, dividend-paying companies.

Why g Must Be Less Than r

If a company's dividend growth rate could permanently exceed the investor's required return, the implied stock price would be infinite. In practice, no company can grow faster than the overall economy indefinitely. Analysts typically cap the terminal growth rate at 2-3%, roughly in line with long-run nominal GDP growth, precisely to satisfy the r > g constraint.

Sensitivity to Small Changes in the Rate Gap

The perpetuity formula is highly nonlinear in (r - g). Suppose r = 8% and g = 5%, giving a denominator of 3%. A stock with D1 = $3.00 would be valued at $100. But if g rises to 6%, the denominator drops to 2% and the value jumps to $150 - a 50% change from a single percentage-point shift in g. This extreme sensitivity is why analysts treat terminal growth rate assumptions with great care and why small forecast errors produce large valuation swings.

Tips & FAQ

Is any real investment truly perpetual?

Practically speaking, no. Even the oldest companies eventually mature, merge, or fail. The perpetuity model is most accurate when the investment horizon is very long (20+ years) and cash flows are stable, because the present value of payments far in the future is so heavily discounted that they contribute little to today's price. For most practical purposes, a 30-year annuity and a perpetuity produce nearly identical present values at moderate discount rates.

What discount rate should I use?

The discount rate should reflect the risk of the cash flows you are valuing. For a safe preferred stock dividend, you might use the yield on similar preferred shares in the market. For a real estate property, the local cap rate for comparable assets is the benchmark. For a corporate stock using the DDM, most analysts use the cost of equity derived from the Capital Asset Pricing Model (CAPM): the risk-free rate plus the company's beta multiplied by the equity risk premium. Using a rate that is too low inflates the valuation; too high understates it.

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