How the Perpetuity Calculator works
A perpetuity is a stream of equal (or steadily growing) cash flows that continues forever, with no maturity date. Because a dollar received further in the future is worth less today, the infinite stream of payments still has a finite present value as long as the discount rate exceeds the growth rate. This calculator applies the standard perpetuity valuation formula used in corporate finance and equity valuation.
The formula
For a payment C received at the end of the next period, a discount rate r per period, and a constant growth rate g per period, the present value of a growing perpetuity is:
PV = C / (r − g)
When there is no growth (g = 0), this reduces to the level (ordinary) perpetuity formula, PV = C / r. The formula is only valid when the discount rate is strictly greater than the growth rate — otherwise the payments do not shrink fast enough (after discounting) for the infinite sum to converge, and the present value is undefined.
Converting an annual rate to a payment period
You enter the discount rate and growth rate as annual percentages. If payments occur more often than once a year, the calculator converts each annual rate to the equivalent rate per payment period using (1 + annual rate)1/n − 1, where n is the number of payments per year. For annual payments (n = 1) the periodic rate equals the annual rate exactly.
Worked example
Take a payment of $1,000 due at the end of the year, an annual discount rate of 8%, an annual growth rate of 2%, and annual payments. The periodic discount rate and growth rate both equal the annual figures, so the present value is $1,000 / (0.08 − 0.02) = $1,000 / 0.06 ≈ $16,666.67. That single number represents the value today of every future payment in the growing, never-ending stream.
Real-world uses of the perpetuity formula
- Fixed-rate preferred stock: preferred shares that pay a constant dollar dividend with no maturity date are commonly valued as a level perpetuity, PV = dividend / required return.
- UK government consols: 19th and 20th century British government bonds known as consols paid a fixed coupon indefinitely and were textbook examples of a perpetuity.
- The Gordon Growth Model: equity analysts value a stock's terminal value, or a stock with a stable dividend growth rate, using the growing perpetuity formula PV = next dividend / (required return − growth rate).
- Real estate income capitalization: valuing a property as net operating income divided by a capitalization rate is mathematically the same level-perpetuity formula, PV = C / r.
What moves the present value most
The present value is most sensitive to the gap between the discount rate and the growth rate, not to either rate alone. As growth approaches the discount rate, the denominator shrinks toward zero and the present value rises sharply — small changes in that gap can double or triple the result. Always treat a perpetuity value as an estimate that depends heavily on the assumed long-run discount rate and growth rate, both of which are genuinely difficult to forecast decades into the future.