Perpetuity Calculator
Calculate the present value of a perpetuity - an investment that pays a fixed amount forever. Perpetuities are used to value preferred stocks, perpetual bonds, and certain types of annuities.
Perpetuity Value Results
Perpetuity Analysis
Common Examples
Preferred Stock: Fixed dividend payments
Perpetual Bonds: No maturity date
Royalties: Ongoing payment streams
Note: True perpetuities are rare
Understanding Perpetuities
A perpetuity is a financial instrument that pays a fixed amount indefinitely. While true perpetuities are rare in practice, the concept is fundamental to finance and is used to value assets that have very long or indefinite payment streams.
Standard Perpetuity Formula
The present value of a standard perpetuity is:
PV = PMT ÷ r
Where: PMT = annual payment, r = discount rate
Growing Perpetuity Formula
For a growing perpetuity:
PV = PMT ÷ (r - g)
Where: PMT = first payment, r = discount rate, g = growth rate
Deferred Perpetuity Formula
For a deferred perpetuity:
PV = [PMT ÷ r] × (1 + r)^(-n)
Where: n = deferral period
Real-World Applications
- Preferred Stock Valuation: Fixed dividend payments continue indefinitely
- Perpetual Bond Valuation: No maturity date, infinite coupon payments
- Royalty Valuation: Ongoing royalty payments from intellectual property
- Real Estate: Ground leases with very long terms
- Pension Funds: Modeling infinite payment streams
- Dividend Discount Model: Terminal value in DCF analysis
Key Assumptions
- Infinite Life: Payments continue forever
- Constant Payments: Fixed amount (or fixed growth rate)
- Constant Discount Rate: Same rate applied to all periods
- No Default Risk: Payments are guaranteed
- Stable Economy: No major economic disruptions
Perpetuity vs. Annuity
| Aspect | Perpetuity | Annuity |
|---|---|---|
| Duration | Infinite | Finite |
| Present Value | PMT ÷ r | PMT × (1 - (1+r)^-n) ÷ r |
| Applications | Preferred stock, royalties | Loans, leases, pensions |
| Sensitivity | Highly sensitive to r | Less sensitive to r |
Terminal Value in DCF
Perpetuities are commonly used to calculate terminal value in discounted cash flow (DCF) analysis. The terminal value represents the value of all future cash flows beyond the explicit forecast period.
Terminal Value Formula:
TV = CF_(n+1) ÷ (r - g)
Where: CF_(n+1) = first year after forecast, r = discount rate, g = long-term growth
Limitations
- Realism: True perpetuities don't exist in practice
- Interest Rate Sensitivity: Small changes in discount rate have large effects
- Growth Assumptions: Perpetual growth may not be sustainable
- Inflation: Doesn't account for purchasing power changes
- Tax Considerations: Tax treatment may change over time
Choosing the Discount Rate
- Risk-Free Rate: For government-backed perpetuities
- Cost of Equity: For preferred stock valuation
- Cost of Debt: For perpetual bond valuation
- WACC: For corporate cash flow valuation
- Risk Premium: Add premium for uncertainty
Tip: Perpetuities are theoretical constructs used for valuation, but they provide valuable insights into long-term value. The key is selecting appropriate discount rates and growth rates that reflect the true risk and growth prospects of the cash flows being valued.