Growing Perpetuity Calculator

A growing perpetuity is a cash flow that arrives every year without end and rises by the same percentage each time. Its present value is the first-year cash flow divided by the gap between the discount rate and the growth rate. At the default 8% discount rate against 3% growth that gap is 0.05, so the value is the first-year figure divided by 0.05, or twenty times that figure whatever it happens to be. The division only converges while growth stays below the discount rate.

What moves the number most

Only the spread between the two rates reaches the denominator, so a 1 percentage point fall in the discount rate and a 1 percentage point rise in the growth rate land on exactly the same answer: both take the spread from 5 points to 4, and the multiple from 20 times the first-year cash flow to 25 times. The two directions are not mirror images. Measured from the same five-point starting spread, taking a point off raises the value by 25% while putting a point on lowers it by 16.67%, because value scales as one divided by the spread rather than with the spread itself.

In proportional terms the three levers have closed forms, and not one of them depends on the size of the cash flow. A 1% change in the first-year cash flow moves the value by exactly 1%. A 1% rise in the discount rate lowers the value by the discount rate divided by the spread, and a 1% rise in the growth rate raises it by the growth rate divided by the spread. At an 8% discount rate against 3% growth those ratios come to 1.60 and 0.60, against measured moves of −1.5748% and +0.6036% once the step is taken discretely rather than as a gradient. Two consequences hold at every input vector: the discount rate is the strongest of the three levers whenever growth sits above zero, and growth passes cash flow once it climbs above half the discount rate.

How the formula gets there

The stream being valued is a cash flow at the end of year one, the same amount plus growth at the end of year two, and so on without end. Discounting each of those payments back to today gives an infinite sum, and because every term is a fixed multiple of the one before it, that sum is a geometric series. A geometric series converges only when the ratio between successive terms stays below one, which here means the growth rate has to sit below the discount rate. Where it does, the entire infinite sum collapses to a single division: the first payment over the difference between the two rates. Where it does not, the series has no finite total, which is why the calculator returns a message instead of a figure.

Two points about timing change how the result reads. The first cash flow is treated as arriving one year out rather than today, and the answer is a value in present-day terms. A payment already in hand is not part of the stream and belongs outside the calculation, added separately.

What this doesn't capture

The formula assumes cash flows grow at one constant rate forever and that the discount rate stays fixed, and neither holds cleanly in practice. The result is sensitive to the spread between the two rates: as growth approaches the discount rate, the value rises sharply. It also ignores the risk that the cash flows are cut or stop entirely, along with taxes and inflation beyond the stated growth rate. The number represents one steady-state scenario rather than a forecast.

Where to go next

The Perpetuity Value Calculator handles the same structure without growth, the Gordon Growth Model Calculator applies it to dividends specifically, and the Future Value Calculator runs a single amount forward instead of discounting a stream back.