Perpetuity Calculator
Calculate present value of perpetual annuities and growing perpetuities
Calculate Perpetuity Value
Regular payment amount received each period
Required rate of return or cost of capital
Annual growth rate of payments (0% for regular perpetuity)
Perpetuity Results
Formula used: PV = D / R
Input values: Dividend: $0, Discount Rate: 0%, Growth Rate: 0%
Type: Standard perpetuity with fixed payments
Valuation Analysis
Example Calculations
Regular Perpetuity Example
Scenario: Bond paying $10 yearly dividend indefinitely
Dividend: $10 per year
Discount Rate: 5%
Growth Rate: 0% (regular perpetuity)
Calculation
PV = D / R
PV = $10 / 5%
PV = $200
Growing Perpetuity Example
Scenario: Stock with $10 dividend growing at 2% annually
Dividend: $10 per year
Discount Rate: 8%
Growth Rate: 2%
Calculation
PV = D / (R - G)
PV = $10 / (8% - 2%)
PV = $10 / 6%
PV = $166.67
Types of Perpetuities
Regular Perpetuity
Fixed payments forever
Formula: PV = D / R
Growing Perpetuity
Payments grow at constant rate
Formula: PV = D / (R - G)
Preferred Stock
Fixed dividend payments
Valued as perpetuity
Real-World Examples
UK Consols
Government bonds with no maturity date
Preferred Stocks
Fixed dividend payments to shareholders
Real Estate
Rental income streams
Endowments
University investment funds
Understanding Perpetuities
What is a Perpetuity?
A perpetuity is a financial instrument that provides a stream of equal payments continuing indefinitely. Despite infinite payments, it has a finite present value due to the time value of money - future payments are worth less than present payments.
Key Characteristics
- •Regular: Payments occur at fixed intervals
- •Fixed: Payment amount remains constant (unless growing)
- •Indefinite: Payments continue forever
- •Finite Value: Has calculable present value
Mathematical Formulas
Regular Perpetuity
PV = D / R
Where PV = Present Value, D = Dividend, R = Discount Rate
Growing Perpetuity
PV = D / (R - G)
Where G = Growth Rate (must be less than R)
Important: For growing perpetuities, the growth rate must be less than the discount rate, otherwise the value becomes infinite.
Time Value of Money
Present Value
Money received today is worth more than the same amount received in the future
Discount Rate
Reflects opportunity cost and risk of the investment
Infinite Payments
Despite being infinite, they have finite value due to discounting