What happens at a discount rate of zero?

The value is infinite, and the tool says so rather than showing a number. That is not a failure to compute: a payment that never stops and is never discounted really is worth an unbounded amount, and any finite figure would be a lie. It is also the clearest demonstration that the rate is doing all the work — remove it and the formula has nothing left to say.

Which rate should I use?

The return you would require to hold this stream instead of the next-best thing you could buy — which means it belongs to you and your alternatives, not to the asset. For a company's cash flows that is usually its cost of capital; for a personal decision it is what the money would otherwise earn. Because the answer moves a quarter for every point, it is worth computing the value at two or three rates and reading the spread rather than one figure.

One Point of Discount Rate Moves a Perpetuity by a Quarter

Published 9/21/2026 · 3 min read · Finance calculators

Camille Laurent — Finance writer at OneKitly

Tax · Personal finance

Checked against 2 sources

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In short

A perpetuity is a payment that never stops, and its present value is the payment divided by the discount rate — nothing more. A thousand a year at 5 % is 1,000 ÷ 0.05 = 20,000. The same thousand at 4 % is 25,000. One percentage point off the rate adds a quarter to the value, and the sensitivity gets worse as the rate falls: the same point between 2 % and 1 % doubles it. That is the whole lesson of the formula. The arithmetic is trivial and the answer is entirely hostage to a number nobody can observe — the rate at which you discount a stream you will never see the end of. Anyone quoting a perpetuity value without quoting the rate beside it has given you half a sentence.

A payment of 1,000 a year is worth 20,000 at a 5 % discount rate and 25,000 at 4 %. The formula is a single division, and that is exactly why the input matters more than the arithmetic.

Where a perpetuity actually turns up

Almost nothing pays forever, and yet the formula is everywhere — because it is the tail of a discounted cash-flow model. Past the years anyone is willing to forecast, the remaining value is usually collapsed into a single terminal figure, and that figure is a perpetuity. On a typical valuation it can be most of the total, which means most of the answer rests on the same one division shown above, with a rate somebody chose. Ground rents, some preference shares and a few perpetual bonds are the rare cases where the payment really does have no end date.

Growth changes the denominator, not the shape

If the payment grows at a steady rate, the divisor becomes the discount rate minus the growth rate. That single subtraction is where valuations go wrong: as growth approaches the discount rate the divisor approaches zero and the value approaches infinity, so a model with 5 % discounting and 4.5 % assumed growth values the same thousand at 200,000. It is not a rounding problem — it is the formula behaving exactly as written, on an assumption that a spreadsheet will never flag as absurd.

1,000 a year, at four discount rates
Discount rate	Present value
8 %	12,500
5 %	20,000
4 %	25,000
2 %	50,000

Worked with our own calculator

Perpetuity value calculator

Given

Payment per period: $1,000.00
Discount rate (%): 5

Result

Present value: $20,000.00

These figures are produced by the calculator below, not typed in by hand — they are recomputed whenever the tool changes.

Run it on your own figures →

Frequently asked questions

What happens at a discount rate of zero?: The value is infinite, and the tool says so rather than showing a number. That is not a failure to compute: a payment that never stops and is never discounted really is worth an unbounded amount, and any finite figure would be a lie. It is also the clearest demonstration that the rate is doing all the work — remove it and the formula has nothing left to say.
Which rate should I use?: The return you would require to hold this stream instead of the next-best thing you could buy — which means it belongs to you and your alternatives, not to the asset. For a company's cash flows that is usually its cost of capital; for a personal decision it is what the money would otherwise earn. Because the answer moves a quarter for every point, it is worth computing the value at two or three rates and reading the spread rather than one figure.

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