Growing Perpetuity Calculator
A growing perpetuity is a payment that never ends and rises a little every year: a dividend that grows with the company, rent that climbs with inflation, a royalty stream with an annual escalator. This calculator turns that endless rising stream into one number in today’s dollars, refuses the classic mistake of letting growth outrun the discount rate, and shows a sensitivity grid so you can see exactly how fragile the answer is.
| Sensitivity: present value if r or g moves |
|---|
This is the Gordon growth model: it assumes the payment grows at exactly g forever and that your discount rate r stays constant. Real dividends get cut, real rents reset, and real discount rates move. Treat the answer as a valuation anchor for your assumptions, not a price the market owes you.
Quick Answer
Present value = D / (r − g), where D is the first-year payment, r is the discount rate, and g is the growth rate, with r strictly bigger than g. A $10 payment growing at 2% with an 8% discount rate is worth $10 / (0.08 − 0.02) = $166.67 today, and $180.00 if the first payment arrives immediately.
Key takeaways
- D is next period’s payment, not the last one paid. Entering last year’s dividend understates the value by a factor of (1 + g).
- The whole answer lives in the spread r − g. At a 6% spread $10 is worth $166.67; at a 2% spread it is worth $500.00.
- Growth at or above the discount rate has no finite value. This tool refuses those inputs; tools that print zero or a negative value for them are wrong.
- The sensitivity grid under every result is part of the answer. Quote it alongside the headline number.
- Quick Answer
- How the Growing Perpetuity Formula Works
- Worked Example, Verified Against the Tool
- Sensitivity: Small Inputs, Huge Swings
- The Trap This Tool Refuses to Fall Into
- Where a Growing Perpetuity Earns Its Keep
- What Competing Perpetuity Calculators Miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
How the Growing Perpetuity Formula Works
PV = D / (r − g). D is the payment received at the end of year 1, r is your required return as a decimal, and g is the constant annual growth rate as a decimal. The formula is the closed form of an infinite geometric series, the standard treatment in Aswath Damodaran’s dividend discount model notes for NYU Stern: year 1 pays D/(1+r), year 2 pays D(1+g)/(1+r)^2, and so on forever.
The series converges only when each year’s payment is worth less today than the one before it, which is exactly the condition r > g. If you tick the perpetuity due box, the first payment arrives now instead of at year-end and the formula becomes PV = D + D(1+g)/(r − g): the immediate payment at face value, plus an ordinary growing perpetuity that starts with the grown year-1 payment. For the worked example that is $10 + $10.20/0.06 = $180.00.
The D timing mistake that changes the answer
D is the payment one period from now. The most common error with this formula is feeding it the dividend just paid, D0, which understates value by exactly one year of growth. Textbook treatments grow the current figure once first: a $100 cash flow today at 2% growth is a $102 first-year payment, worth $102 / (0.10 − 0.02) = $1,275 at a 10% discount rate, not $1,250. If your starting figure is last year’s, multiply it by (1 + g) before you type it in.
Worked Example, Verified Against the Tool
A stock pays a $10 dividend at year-end, growing 2% per year forever. You require an 8% return. PV = $10 / (0.08 − 0.02) = $10 / 0.06 = $166.67. The tool shows exactly this, and the same figure sits in the middle of its sensitivity grid at r = 8%, g = 2%.
| Run | Inputs | Tool result |
|---|---|---|
| Worked example, year-end payment | D $10, r 8%, g 2% | $166.67 |
| Same stream, first payment now (due) | D $10, r 8%, g 2%, due ticked | $180.00 |
| No growth, for comparison | D $10, r 8%, g 0% | $125.00 |
| Declining stream | D $10, r 8%, g −2% | $100.00 |
| Near the cliff edge | D $10, r 9.9%, g 9.8% | $10,000.00 |
Without growth, the same dividend is worth $125.00, so the 2% growth assumption alone adds $41.67 of value. The due variant adds $13.33 more, because a year of discounting disappears from the first payment and every later payment shifts one year closer.
Sensitivity: Small Inputs, Huge Swings
The growing perpetuity is famously touchy: when r and g get close, the denominator shrinks and the answer explodes. This static grid uses the same $10 payment as the tool. The live grid under your result does the same thing around your own inputs, stepping r and g by 2 points each way.
| r across / g down | g = 0% | g = 2% | g = 4% |
|---|---|---|---|
| r = 6% | $166.67 | $250.00 | $500.00 |
| r = 8% | $125.00 | $166.67 | $250.00 |
| r = 10% | $100.00 | $125.00 | $166.67 |
Read it and the lesson is obvious: moving growth from 2% to 4% at r = 6% doubles the answer from $250 to $500. Two quirks of the live grid are worth knowing. It always shows the ordinary, year-end-payment values, even when you ticked perpetuity due, so use it to judge spread sensitivity rather than as a due-mode price list. And where a stepped growth rate goes negative, the grid prints a dash instead of a value, even though the main calculation accepts negative growth directly.
The Trap This Tool Refuses to Fall Into
Many online calculators accept any numbers you type. Enter growth of 10% with a discount rate of 8% and the unguarded ones divide anyway and print the negative number the raw arithmetic produces, which is nonsense: a stream that outgrows your discount rate has no finite value; it is not worth less than zero. This calculator blocks g ≥ r with a plain explanation instead of printing garbage. The honest answer to “what is it worth when growth beats the discount rate?” is “this model cannot say”, and the tool says so.
The same discipline caps how the model should be used for terminal value in a discounted cash flow: a perpetual growth rate is normally held at or below long-run nominal economic growth, a point Damodaran makes explicitly in his valuation chapter on dividend discount models, because no firm outgrows the economy forever. If your g only makes sense for the next five years, it does not belong in a perpetuity.
Where a Growing Perpetuity Earns Its Keep
Three jobs dominate. First, dividend stock valuation with the Gordon growth model, where this formula is the entire model. Second, terminal value in DCF analysis, where a growing perpetuity stands in for every year after the forecast period and routinely accounts for most of the total value, which is why its sensitivity matters so much. Third, income property and royalty streams with contractual escalators, where the growth rate is written into a lease rather than guessed.
For the dividend case, pair this page with the dividends calculator to get the payment stream itself, and sanity-check any growth assumption against the percent growth calculator and the business’s actual history. Annuity buyers comparing lifetime income products can cross-check the scale of the numbers against the lotto annuity calculator, which prices a finite stream instead of an endless one.
What Competing Perpetuity Calculators Miss
- Savvy Calculator growing perpetuity calculator: clean three-input tool with a worked example, but nothing on the page refuses g ≥ r: its own tips concede the formula “produces infinite or negative values” in that case, which leaves the bad output to the tool instead of blocking the input the way this one does.
- OnlyCalculators perpetuity calculator: the feature-richest rival, with reverse solving for payment, rate or growth and a benchmark table, but it bundles flat and growing perpetuities into one solver and never shows how violently the answer moves when the spread narrows.
- Ryan O’Connell annuity and perpetuity solver: strong all-in-one PV/FV tool from a CFA, aimed at students; the growing perpetuity is one mode among many, with no perpetuity-due handling and no refusal logic explained on the page.
- Wall Street Prep perpetuity guide: excellent teaching, including the grow-D0-once step most pages skip, but the calculator itself sits behind a course form, so there is no tool to run.
- Rows perpetuity calculator: tidy spreadsheet-style tool that explains convergence well, but offers no sensitivity view and no due mode.
- CalculatorSoup present value of annuity: rigorous formula coverage including continuous compounding, but the perpetuity is a limiting case inside an annuity page, not a tool built for the Gordon growth question.
- The gap this page fills: a dedicated growing-perpetuity tool with a due mode, a hard r > g refusal with the reason printed, a live sensitivity grid around your own inputs, and the D timing trap called out where users actually make it.
Frequently asked questions
PV = D / (r – g), where D is the first-period payment, r is the discount rate, and g is the constant growth rate, with r greater than g. It is the Gordon growth model used to value dividend stocks, and it is the closed form of an infinite discounted series.
Because the formula is an infinite series that only converges when each future payment is worth less today than the one before. If g reaches or passes r, the payments grow faster in present-value terms than they shrink, the total is infinite, and no finite number is correct. That is why this tool blocks those inputs instead of returning a fake answer.
A regular, flat perpetuity pays the same amount forever and is valued at PV = D / r. A growing perpetuity adds the growth rate: PV = D / (r – g). Set g = 0 in the growing formula and you get the flat one back. Growth always raises the present value, which is why a $10 payment at 8% is worth $125.00 flat and $166.67 growing at 2%.
It means the first payment arrives immediately instead of at the end of year 1. The value is the immediate payment plus a growing perpetuity on the grown year-1 payment: PV = D + D(1+g)/(r – g). For the worked example that gives $180.00 instead of $166.67. Use the checkbox for leases, annuities and any stream that pays up front.
Next year’s. The formula prices the payment due one period from now. If all you have is the payment just made, grow it once before entering it: next year = last year times (1 + g). Entering the old figure understates the value by a factor of (1 + g).
Yes. A negative g models a declining stream, and PV = D / (r – g) still works: a $10 payment shrinking 2% a year at an 8% discount rate is worth $100.00. One display quirk to expect: the tool’s workings line prints the rates as entered, so it reads 8% minus -2%, which is the arithmetic it actually performs.
Valuing dividend stocks with the Gordon growth model, estimating terminal value in a discounted cash flow, and pricing income streams with built-in escalators, such as rent under a lease with annual increases or royalties tied to a growing catalogue. In DCF work the terminal value from this formula often makes up most of the total valuation.
As far as you trust r and g, and no further. The formula is exact; the inputs are forecasts. When the spread is small the value swings violently: at D $10, r 9.9% and g 9.8%, the tool returns $10,000.00, and a tenth of a point either way roughly halves or doubles it. Read the sensitivity grid under your result before quoting the headline figure anywhere.
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References
- Damodaran, Aswath, NYU Stern School of Business. Dividend Discount Models (lecture notes). Accessed October 22, 2026.
- Damodaran, Aswath, NYU Stern School of Business. Investment Valuation, Chapter 13: Dividend Discount Models. Accessed October 22, 2026.
- Gordon, Myron J. Dividends, Earnings, and Stock Prices, The Review of Economics and Statistics, Vol. 41, No. 2 (1959), pp. 99-105. The original statement of the constant-growth valuation model this calculator implements. Accessed October 22, 2026.
- Federal Reserve Bank of St. Louis, FRED. Market Yield on U.S. Treasury Securities at 10-Year Constant Maturity (DGS10). Accessed October 22, 2026.
- U.S. Securities and Exchange Commission, Investor.gov. Compound Interest Calculator. Accessed October 22, 2026.
- U.S. Bureau of Economic Analysis. Gross Domestic Product. Accessed October 22, 2026.
- Board of Governors of the Federal Reserve System. Selected Interest Rates (Daily), H.15. Accessed October 22, 2026.
- Board of Governors of the Federal Reserve System. Federal Open Market Committee. Accessed October 22, 2026.
- Massachusetts Institute of Technology, OpenCourseWare. Finance Theory I (15.401). Accessed October 22, 2026.
- Yale University, Open Yale Courses. Financial Markets (ECON 252), Robert Shiller. Accessed October 22, 2026.