How to Use This Calculator
- 1
Enter the Periodic Payment
Input the fixed payment amount received each period. The period must match the discount rate (e.g., annual payment with annual rate, or monthly payment with monthly rate).
- 2
Specify the Discount Rate
Provide the interest or discount rate per period, as a percentage, used to value future cash flows.
- 3
Select the Payment Type
Choose between an Ordinary Perpetuity (payments at end of period) or Immediate Perpetuity (payments at beginning of period).
- 4
Review your results
Examine the Present Value, Immediate/Ordinary PV comparison, Break-Even Period, and Growing Perpetuity PV cards. The Perpetuity Insights panel shows rate sensitivity, ordinary vs immediate difference, and growing perpetuity cost.
Example Calculation
An investor wants to calculate the present value of an ordinary perpetuity that pays $1,000 per period indefinitely at a 5% discount rate.
Periodic Payment ($)
$1,000
Discount Rate (%)
5
Payment Type
Ordinary Perpetuity (End of Period)
Results
Present Value
$20,000
Immediate PV
$21,000
Break-Even
20 payments
Growing Perpetuity PV
$40,000
Insights card shows rate sensitivity (PV ranges from $16,667 at 6% to $25,000 at 4%), and growing perpetuity costs 2.
Tips
Rate Sensitivity Is Extreme
A small rate change has a large impact. Dropping from 5% to 4% increases PV from $20,000 to $25,000 — a 25% increase for just 1 percentage point. Always verify your discount rate assumption carefully.
Ordinary vs. Immediate Difference
An immediate perpetuity is always worth exactly one extra payment more than ordinary. At 5%, an immediate perpetuity paying $1,000 is worth $21,000 vs $20,000 for ordinary — the $1,000 difference is the first payment received today.
Inflation Makes Perpetuities Much More Expensive
A growing perpetuity (payments increasing at 2.5% inflation) costs $40,000 — double the $20,000 fixed perpetuity. If you need inflation-protected income forever, the required capital is substantially higher.
Use History to Compare Rates
Each calculation is saved automatically. Click the clock icon to recall previous scenarios and compare how different discount rates or payment amounts affect the present value.
The Perpetuity Present Value Calculator determines the current worth of an infinite stream of fixed payments.
At a 5% discount rate, a $1,000 periodic payment has a present value of $20,000 for an ordinary perpetuity or $21,000 for an immediate perpetuity.
If payments grow at 2.5% inflation, the required capital doubles to $40,000.
Perpetuities in Long-Term Financial Planning
While a true perpetuity — an endless stream of payments — is largely theoretical, the concept provides a useful benchmark for valuing long-term assets like preferred stocks or stable real estate income streams.
It's also applied in estimating terminal value in discounted cash flow (DCF) models, representing the value of a company's cash flows beyond the forecast period.
A typical dividend yield for blue-chip stocks ranges from 2-4% in 2026, which can be compared to the implied yield of a perpetuity to assess relative value.
The Perpetuity Valuation Formulas
The calculation of a perpetuity's present value is remarkably straightforward:
Ordinary Perpetuity (first payment at end of period):
PV = Payment / Rate
Immediate Perpetuity (first payment today):
PV = Payment x (1 + Rate) / Rate
Growing Perpetuity (payments grow at rate g):
PV = Payment / (Rate - g)
Where Payment is the fixed amount received each period, Rate is the periodic discount rate (as a decimal), and g is the constant growth rate (must be less than Rate).
Worked Example: Valuing a Perpetual Income Stream
Consider an investment that pays $1,000 indefinitely at the end of each period with a 5% discount rate.
Ordinary Perpetuity PV:
PV = $1,000 / 0.05 = $20,000Immediate Perpetuity PV:
PV = $1,000 x (1 + 0.05) / 0.05 = $1,050 / 0.05 = $21,000Difference:
$21,000 - $20,000 = $1,000— exactly one extra paymentBreak-Even:
$20,000 / $1,000 = 20 paymentsto recover the investmentGrowing Perpetuity (2.5% inflation):
PV = $1,000 / (0.05 - 0.025) = $1,000 / 0.025 = $40,000
An investor would pay $20,000 today to receive $1,000 at the end of every period forever.
If those payments need to grow with 2.5% inflation, the cost doubles to $40,000.
Rate Sensitivity and Terminal Value Applications
The perpetuity formula's extreme sensitivity to the discount rate makes it both powerful and dangerous in financial analysis.
In DCF terminal value calculations, the perpetuity growth model assumes cash flows grow at a constant rate forever:
Terminal Value = Final Year Cash Flow x (1 + g) / (WACC - g)
Where WACC is the weighted average cost of capital and g is the perpetual growth rate (typically 2-3%).
A small change in assumptions can dramatically alter valuations:
- At 5% discount / 2% growth: TV multiplier = 1/(0.05-0.02) = 33.3x
- At 5% discount / 3% growth: TV multiplier = 1/(0.05-0.03) = 50.0x
- At 4% discount / 2% growth: TV multiplier = 1/(0.04-0.02) = 50.0x
This sensitivity explains why analysts stress-test multiple discount rate and growth rate scenarios when using perpetuity-based valuations.
Frequently Asked Questions
What is a perpetuity and how is its present value calculated?
A perpetuity pays a fixed amount indefinitely. Its present value is PV = Payment / Rate. A perpetuity paying $1,000/year at 5% has a present value of $20,000, meaning $20,000 invested at 5% generates $1,000 per year forever.
What are real-world examples of perpetuities in 2025?
Preferred stock dividends, certain university endowment distributions, ground lease rental income, and some REIT distributions. While true mathematical perpetuities are rare, many income streams are long enough to be valued as perpetuities for practical purposes.
What is the difference between an ordinary perpetuity and an immediate perpetuity?
An ordinary perpetuity pays at the end of each period (PV = Payment / Rate). An immediate perpetuity pays at the beginning (PV = Payment / Rate x (1 + Rate)). The immediate perpetuity is always worth (1 + Rate) times the ordinary.
How do I use the perpetuity formula to value dividend-paying stocks?
Divide the annual dividend by your required return. A $3 dividend at 6% required return equals $50 per share. For growing dividends, use the Gordon Growth Model: Price = Dividend / (Required Return - Growth Rate).
