Perpetuity Present Value Calculator

Enter your periodic payment amount, discount rate, and payment type to calculate the present value of an infinite cash flow stream — including growing perpetuity cost and break-even analysis.

Created by Luis GonzalezLast updated: June 15, 2026

How to Use This Calculator

1
Enter the Annual Payment
Input the fixed payment amount the perpetuity pays each year.
2
Set the Discount Rate
Enter the annual interest or discount rate as a percentage.
3
Select Payment Type
Choose ordinary perpetuity (end of period) or immediate perpetuity (beginning of period).
4
Review Results
View the present value for both types, required investment amount, yield, and break-even period.

Example Calculation

Valuing a preferred stock that pays a $2,000 annual dividend in perpetuity, using a 5% discount rate.

Payment

$2,000

Rate

Payment Type

Ordinary

Results

Present value of ordinary perpetuity

$40,000. Present value of immediate perpetuity: $42,000. Break-even period: 20 years. To generate $2,000/year forever at 5%, you need to invest exactly $40,000 today.

Tips

Use for Preferred Stock Valuation

Preferred stocks with fixed dividends are effectively perpetuities. Divide the annual dividend by your required return to estimate fair value.

Small Rate Changes Have Large Effects

Because PV = Payment / Rate, cutting the discount rate from 5% to 4% increases the present value by 25%. Always sensitivity-test your rate assumption.

Growing Perpetuities Need a Different Formula

If payments grow at rate g, use PV = Payment / (r - g). This is the Gordon Growth Model used for dividend stocks with expected growth.

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).

💡 To see how a consistent investment grows over time, which can eventually fund a perpetuity, check out our IRA Growth Calculator.

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 = $20,000
Immediate Perpetuity PV: PV = $1,000 x (1 + 0.05) / 0.05 = $1,050 / 0.05 = $21,000
Difference: $21,000 - $20,000 = $1,000 — exactly one extra payment
Break-Even: $20,000 / $1,000 = 20 payments to recover the investment
Growing 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.

💡 For a broader view of retirement income strategies including perpetual income streams, explore our Retirement Income Calculator with Annuities.

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).