Perpetuity Calculator

Calculate the present value of a perpetuity - a stream of infinite cash flows. Perfect for valuing stocks, bonds, or any investment with indefinite payments.

Calculator Inputs

Annual payment amount

Required rate of return

Annual growth rate of payments (0 for regular perpetuity)

Results

  Values
Annual payment $100.00
Discount rate 5.00%
Growth rate 0.00%
Present value $2,000.00
Formula: PV = D / (r - g)

What is a Perpetuity?

A perpetuity is a type of annuity that receives an infinite amount of regular payments forever. It is a financial product or investment that guarantees to pay a fixed stream of payments indefinitely. Unlike a regular annuity, a perpetuity has no end date. The most common example of a perpetuity is preferred stock, which pays a fixed dividend indefinitely.

Perpetuity Formula

To calculate the present value of a regular perpetuity, you can use the formula:

PV = D / r

Where:

  • PV = Present Value
  • D = Annual Dividend/Payment
  • r = Discount Rate (as decimal)

Growing Perpetuity Formula

For a perpetuity with growing payments:

PV = D / (r - g)

Where:

  • PV = Present Value
  • D = Annual Dividend/Payment
  • r = Discount Rate (as decimal)
  • g = Growth Rate (as decimal)

Real-World Examples

  • Preferred Stock: Most preferred stocks have a fixed dividend rate that is paid out indefinitely.
  • Consols: British government bonds that pay interest forever.
  • Dividend Stocks:Stocks with a history of stable, growing dividend payments.
  • Real Estate:Rental properties can be considered a form of perpetuity if they can be rented out indefinitely.

Important Considerations

  • The growth rate must be lower than the discount rate
  • The model assumes that the payments will be made forever, which may not be realistic
  • Market conditions and company performance can impact the actual payments
  • UThis should be used as a starting point for valuation, not as the final answer