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Perpetuity Present Value Calculator

Value a level or growing perpetuity — an infinite stream of periodic cash flows — using the Gordon growth model, PV = C / (r − g).

Present value
$2,000.00
Value multiple (years of cash flow)
20×

How it works

A perpetuity is a cash flow that repeats forever at a fixed interval. A level perpetuity — the same payment every period — has present value PV = C / r, where C is the periodic cash flow and r is the discount rate. This calculator generalizes that to a growing perpetuity via the Gordon growth model, PV = C / (r − g), where g is the rate the cash flow itself grows by each period; setting g to 0 collapses it back to the plain level-perpetuity formula.

The discount rate must be strictly greater than the growth rate. If cash flows grew as fast as, or faster than, the rate they're discounted at, the terms of the underlying infinite sum would stop shrinking and the total would never converge to a finite value — the calculator rejects that case explicitly rather than returning a meaningless or infinite number.

The value multiple, 1 / (r − g), is the same 'how many periods' worth of cash flow is this worth' shorthand investors quote as a P/E-style multiple — it's just the present value expressed as a multiple of one period's cash flow instead of in currency.

FAQ

What's a real-world example of a perpetuity?

The classic textbook example is a UK government consol bond, which historically paid a fixed coupon with no maturity date. More commonly today, the Gordon growth model version is used to estimate a stock's value from its expected dividend growth, or a company's terminal value at the end of a multi-year cash flow projection — both are 'value everything from here to infinity' shortcuts, not literal infinite-cash-flow instruments.

Why can't the growth rate be equal to or greater than the discount rate?

Because the formula is really the closed form of an infinite geometric series, C×(1+g)/(1+r) + C×(1+g)²/(1+r)² + ..., which only converges to a finite sum when each term is smaller than the last — that requires g to be strictly less than r. Once g reaches r, the terms stop shrinking, and past that point they grow without bound, so no finite present value exists.

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