βΎοΈ Perpetuity Calculator
What is a payment stream that never ends worth today?
Value today of the endless payment stream
Estimates for planning only, not financial advice.
A perpetuity pays forever, and its present value is almost embarrassingly simple: annual payment divided by the discount rate. Five thousand dollars a year forever at 6 percent is worth $83,333 today. If the payment grows, the value jumps: the same $5,000 growing 2 percent a year is worth $125,000. This little formula quietly powers terminal values, preferred stock pricing, and endowment spending rules.
How to Use This Calculator
Pick the flat tab for fixed payments like preferred dividends, or the growing tab for payments that rise each year, like a mature business's cash flow. Enter the first year's payment and your discount rate. The calculator returns the lump sum today that is economically identical to the endless stream.
Choose flat or growing. Growing fits businesses and rents; flat fits fixed dividends and ground rents.
Enter the annual payment and discount rate. For growing, add a sustainable long-run growth rate below the discount rate.
Read the present value. To value a finite stream instead, our present value calculator handles any term.
The Perpetuity Formula
The math works because distant payments shrink toward zero when discounted, so the infinite sum converges to a finite number. Most of the value sits in the early years: at 6 percent, the first 30 years of a flat perpetuity hold about 83 percent of its total value. Forever sounds infinite, but financially it is mostly the next few decades.
Worked Example
An endowment expects to pay out $5,000 a year. At a 6 percent discount rate, the flat perpetuity value is $5,000 divided by 0.06, which is $83,333. If payouts grow 2 percent annually to keep up with inflation, the value is $5,000 divided by 0.04, which is $125,000. The growth assumption alone adds $41,667 of value, which shows why terminal-value growth rates deserve more scrutiny than any other input in a valuation.
Reading Your Result
Small rate changes move the answer a lot. Dropping the discount rate from 6 to 5 percent lifts the flat perpetuity from $83,333 to $100,000, a 20 percent jump from one point of rate. That sensitivity is the whole story of asset prices in different rate environments, and it is why growth stocks soared when rates fell.
My rule: the growth rate in a growing perpetuity must be a forever rate, not a forecast rate. Nothing grows 8 percent forever; long-run growth cannot exceed long-run economic growth for long, or the business eventually becomes the economy. Cap it near inflation plus a point or two, and be deeply suspicious of any valuation where the terminal value is 80 percent of the total. That is not analysis, it is a growth-rate bet wearing a model's clothes. For multi-year finite projections feeding into that terminal value, our NPV calculator does the discounting.
Estimates for planning only, not financial advice.
Frequently Asked Questions
What is a perpetuity in finance?
A perpetuity is a stream of payments that continues forever at regular intervals. Its present value is the payment divided by the discount rate. Real examples include perpetual bonds, preferred stock dividends, and the terminal value of a business assumed to operate indefinitely.
What is the formula for present value of a perpetuity?
For fixed payments: PV = payment / discount rate. For payments growing at rate g: PV = payment / (discount rate - g). The growing version is the Gordon growth model, the workhorse of dividend and terminal-value valuation. At a 10 percent discount rate, a $100 perpetuity is worth $1,000; at 5 percent, it doubles to $2,000.
Why does an infinite stream have a finite value?
Because discounting shrinks distant payments toward zero. At 6 percent, a dollar paid in year 50 is worth about five cents today, and year 100 is worth a fraction of a cent. The infinite tail adds almost nothing, so the sum converges.
What is the difference between a perpetuity and an annuity?
An annuity pays for a fixed number of periods; a perpetuity pays forever. An annuity's present value formula includes a term that fades as periods grow, and in the limit of infinite periods it becomes exactly the perpetuity formula. A 30-year annuity at typical discount rates is already worth over 90 percent of the equivalent perpetuity.
When is the growing perpetuity formula used?
Most famously for terminal value in a DCF: the business's final forecast-year cash flow, grown one year at a sustainable rate, divided by (discount rate minus growth). It is also the Gordon model for valuing dividend-growing stocks. Damodaran's rule of thumb: set the terminal growth rate near the risk-free rate, never above it.
What growth rate is reasonable in a growing perpetuity?
A forever rate: near long-run inflation plus a little real growth, typically 2 to 4 percent nominal for a mature business. Anything higher implies the company eventually outgrows the economy, which is impossible in aggregate. Keep it humble. For high-growth firms, use a two-stage model: supernormal growth for years, then the humble perpetuity rate.
Why must growth stay below the discount rate?
If growth equaled or exceeded the discount rate, the formula gives infinity or a negative number, both meaningless. Economically, a business cannot permanently grow faster than the return investors demand without becoming infinitely valuable, which markets do not allow. A 1 percent change in the growth assumption can swing terminal value by 20 percent or more: sensitivity-test it.
What is a consol bond?
A perpetual bond with no maturity date that pays a fixed coupon forever, first issued by the British government in the 1700s. Consols are the textbook perpetuity: price equals coupon divided by yield. The UK redeemed its last consols in 2015.
How do endowments use perpetuity math?
An endowment spending 4 to 5 percent a year is implicitly treating its portfolio as a growing perpetuity: the spending rate must stay below expected returns minus inflation or the real principal shrinks. Perpetuity math sets the sustainable payout. Yale's endowment targets roughly 5 percent spending for the same mathematical reason.
Does the payment timing matter?
Yes. The standard formula assumes the first payment arrives one full period from now. If the first payment is immediate, add it: value equals the immediate payment plus the standard perpetuity value. Mixing the two up is a classic exam and modeling error.