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How to Value a Payment Stream That Never Ends
Manesh Jayawardhana
CIO & Co-founder
A stream of payments continuing forever has a finite value, which is counter-intuitive until you notice that payments far enough in the future are discounted almost to nothing.
The formula is one line. Its sensitivity to your assumptions is the thing worth understanding, because in a discounted cash flow model this calculation frequently produces most of the answer.
The formula
For a level perpetuity — the same payment forever:
PV = payment ÷ r
For a growing perpetuity — payments increasing at a constant rate:
PV = payment ÷ (r − g)
Where r is the discount rate and g the growth rate. 150,000 a year growing at 2%, discounted at 9%:
150,000 ÷ (0.09 − 0.02) = 2,142,857
The discount rate must exceed the growth rate. If g ≥ r the denominator is zero or negative and the value is infinite or meaningless — which correctly reflects that nothing grows faster than the discount rate forever.
Why it’s so sensitive
Look at the denominator: 0.07. It’s a small number produced by subtracting two larger ones, which means small changes in either input move it proportionally a great deal.
Raise growth from 2% to 4% and the denominator halves to 0.05. The value jumps from 2.14 million to 3 million — a 40% increase from a two-point assumption change.
Raise it to 6% and the denominator is 0.03: the value becomes 5 million, more than double the original, from an assumption most people would consider a modest adjustment.
| Growth | Denominator | Present value |
|---|---|---|
| 1% | 0.08 | 1,875,000 |
| 2% | 0.07 | 2,142,857 |
| 4% | 0.05 | 3,000,000 |
| 6% | 0.03 | 5,000,000 |
Same payment, same discount rate, and the answer more than doubles across a range of growth assumptions that all sound reasonable in a meeting.
Where this matters most
Terminal value in a DCF. A discounted cash flow model projects explicit cash flows for five or ten years, then values everything after that as a perpetuity. That terminal value routinely accounts for the majority of the total valuation.
Which means the number that dominates the model is the one produced by the formula with the greatest sensitivity to assumptions — and it’s usually presented as a single figure.
Dividend valuation. The Gordon growth model is this formula applied to a dividend stream.
Perpetual instruments. Some bonds and preference shares genuinely pay indefinitely, where the level form applies directly.
Common mistakes to avoid
- Setting a growth rate near or above the discount rate, producing an absurd or infinite value.
- Assuming perpetual growth above long-run economic growth — nothing outgrows the economy forever.
- Presenting terminal value as a point estimate rather than a range.
- Using the payment already received rather than the one expected at the end of the first period.
- Forgetting that a terminal value dominating a DCF means the model is mostly an assumption, not a projection.
How to do it with Perpetuity Calculator
The Perpetuity Calculator computes both forms and makes the sensitivity visible.
- Enter the payment expected at the end of the first period.
- Set the discount rate, which must exceed the growth rate.
- Read the value, then change growth by one point and look at what happens.
- Present a range rather than a single figure.
Other valuation tools are in the tools directory.
Frequently asked questions
Why must the discount rate exceed the growth rate?
Because otherwise the denominator is zero or negative and the value is infinite or meaningless. A stream growing faster than the discount rate forever isn’t an assumption any real business supports.
Where is this used in practice?
Terminal value in a discounted cash flow model, valuing perpetual bonds, and pricing dividend streams under the Gordon growth model. In a DCF the terminal value often dominates the total.
How sensitive is the result?
Extremely. With rates close together the denominator is small, so a one-point change in growth can move the value by tens of percent. Always present a range.
Final thought
Run the calculation three times with three growth assumptions before quoting any of them. The spread is the honest answer; a single number is a decision disguised as a calculation.