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Present Value of Perpetuity Calculator
Present Value of Perpetuity Calculator
Payments grow over time
Toggle on for a growing perpetuity (e.g. dividends that rise each year)
Present Value
$16,666.67
Valuation Analysis
A flat payment of $1,000 every year forever is worth $16,666.67 today at a 6% discount rate. That is a 16.7x multiple of the annual payment — the lower the required return, the more a perpetual income stream is worth.
Valuing Income That Never Stops
A perpetuity is a stream of equal payments that continues forever, and its present value answers a question every income investor eventually faces: what should I pay today for a dollar a year that never runs out? While no real asset literally pays forever, the perpetuity model underpins how analysts value preferred stock, permanent ground leases, perpetual conservation easements, and — most importantly — mature dividend-paying companies, whose payouts are routinely treated as growing indefinitely. In US markets this framework shows up constantly. The Gordon Growth Model, the standard way to estimate a stock's fair value from its dividend, is nothing more than a growing perpetuity calculation. Endowments that pay universities forever, consols-style government bonds in finance textbooks, and even the terminal value in a discounted cash flow analysis all rely on dividing a cash flow by the spread between discount rate and growth rate. Mastering this simple valuation tool lets you sanity-check whether a yield is genuinely attractive or merely looks that way.
Behind the Formula: PV = CF / (r − g)
For a flat perpetuity, the present value equals the annual cash flow divided by the discount rate: PV = CF / r. For a growing perpetuity, the formula becomes PV = CF / (r − g), where g is the annual growth rate of payments. Both are derived by summing an infinite geometric series: each future payment is discounted back by (1 + r)^t and, because the payments grow by g, the series converges to the clean closed-form expression as long as r exceeds g. Three mechanics drive every result. First, value is extremely sensitive to the discount rate: at 6% a $1,000 stream is worth about $16,700, while at 4% it is worth $25,000 — same income, wildly different price. Second, growth assumptions swing value dramatically; adding 2% of growth to that same stream at a 6% discount rate more than doubles its value. Third, when the growth rate equals or exceeds the discount rate, the formula breaks down because the sum no longer converges — a built-in reminder that no income stream can outgrow the broader economy indefinitely.
Expert Insights
Your Discount Rate Is Your Required Return
Do not use a Treasury yield as the discount rate for a stock dividend unless you want a wildly inflated valuation. The discount rate should reflect the risk of the income stream: roughly risk-free plus an equity or credit premium. A $2 payment on a $100 stock implies a 2% yield; if you require 8%, the perpetuity math tells you the stock is worth only $25 of value per share on income alone.
Small Growth Inputs, Massive Value Swings
The r − g spread sits in the denominator, so a single percentage point of growth can double a valuation. Treat long-term growth assumptions with suspicion: a company growing dividends 4% annually is implicitly assumed to outgrow inflation forever. Most analysts cap perpetuity growth at long-run GDP or inflation, around 2-3% for the US economy, precisely to avoid absurd terminal values.
Perpetuities Price the Yield You Actually Receive
The inverse of this formula is the income yield: price divided into cash flow. If you paid $30,000 for a preferred stream of $1,800 a year, your yield is 6% — and if comparable risk-free instruments pay 5% with growth available elsewhere, the perpetuity lens shows whether you are being compensated for the credit risk you hold.
Actionable Tips
- 1
Benchmark Every Income Purchase Against Perpetuity Value
Before buying any dividend stock, preferred share, or income property, run the flat perpetuity value at your required return. If the asking price is several times the perpetuity value, the entire investment case rests on growth assumptions — make sure those assumptions are explicit and defensible.
- 2
Cap Growth at Long-Run Economic Growth
When valuing a growing stream, never set the growth rate above 3-4% for a perpetual assumption, no matter the company's recent history. Use this calculator to see how a 4% versus 2% growth input changes the price, and you will understand why professional valuation models clamp terminal growth.
- 3
Use It to Judge Payout Sustainability
Reverse-engineer the deal: divide the annual income by the price paid to get the implied yield, then compare it with the discount rate you personally require. If the implied yield is below your hurdle, the asset only makes sense if growth is realistic; if growth is doubtful, pass on the position.
Real-World Examples
Grace Values a Utility Dividend
Grace, a retiree in Phoenix, was offered shares of a utility paying $1.60 per share annually. Using a 6.5% required return for regulated utilities, the flat perpetuity formula valued the income at about $24.60 per share. The stock traded at $38, meaning roughly a third of its price depended on the company's 2% dividend growth continuing indefinitely — a bet Grace decided was reasonable.
Tom Checks a Preferred Stock Deal
Tom, an accountant in Charlotte, considered a preferred stock paying $1.25 a quarter with a $25 par value. A flat perpetuity at his 8% hurdle valued the stream at $62.50 across the four quarterly payments — but the bank's callable par was only $25. The perpetuity figure revealed the market price of $24.80 already priced in call risk, confirming the yield was compensation for reinvestment risk, not a free lunch.
The Alvarez Family Prices a Ground Lease
The Alvarez family in Sacramento was offered a ground lease paying $9,000 a year with 2% escalators. At their 7% required return, the growing perpetuity formula valued the lease at $180,000. The seller asked $210,000, so the family countered at $185,000 using their own valuation math and closed near their number.
Glossary of Terms
- Perpetuity
- A stream of cash payments that continues indefinitely with no end date, used as a valuation building block for income assets that are expected to pay forever.
- Discount Rate
- The annual return an investor requires to part with money today, reflecting both the time value of money and the risk of the future cash flows being valued.
- Gordon Growth Model
- A stock valuation formula that treats dividends as a growing perpetuity, estimating fair value by dividing next year's expected dividend by the required return minus the growth rate.
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Ivy Sinclair-Wren
Financial Chaos Analyst
Ivy Sinclair-Wren is a Financial Chaos Analyst covering investing, AI, wealth psychology, and the emotional consequences of opening finance apps during market crashes. Based in Melbourne, she specializes in demystifying the US tax code and helping users navigate the intersection of spreadsheet logic and human irrationality.