Perpetuity Calculator
Calculate the present value of perpetual cash flows with constant or growing payments
Growth rate must be less than discount rate
Yield Rate
%
Annual return
Cash Flow
Per period
Payback Period
yrs
To recover principal
Formula Breakdown
PV = C / r
PV = / %
PV =
PV = C / (r - g)
PV = / (% - %)
PV =
r = C / PV
r = /
r = %
Rate Risk Assessment
Understanding Perpetuities
Regular Perpetuity
- Constant payments forever
- Simple formula: PV = C / r
- Examples: Consol bonds, preferred stock
Growing Perpetuity
- Payments grow at constant rate
- Formula: PV = C / (r - g)
- Examples: Dividend stocks, real estate
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About Perpetuity Calculator
What is a Perpetuity?
A perpetuity is a financial instrument that pays a constant stream of cash flows indefinitely, with no end date. While truly infinite payments are theoretical, perpetuities are useful for valuing assets with very long or indefinite lifespans.
Types of Perpetuities
Regular (Constant) Perpetuity
Payments remain the same forever. Examples include:
- Preferred stock dividends
- Consol bonds (UK government bonds)
- Endowment funds
Growing Perpetuity
Payments grow at a constant rate forever. Examples include:
- Dividend stocks with consistent growth
- Real estate with annual rent increases
- Business valuations with steady growth
Perpetuity Formulas
Present Value of Regular Perpetuity
PV = C / r
Where:
- PV = Present Value
- C = Annual cash flow (payment)
- r = Discount rate (required rate of return)
Present Value of Growing Perpetuity
PV = C / (r - g)
Where:
- PV = Present Value
- C = Cash flow in the first period
- r = Discount rate
- g = Growth rate (must be less than r)
Key Concepts
| Concept | Description |
|---|---|
| Discount Rate | The required rate of return for the investment |
| Growth Rate | Annual rate at which payments increase |
| Cash Flow | Regular payment amount |
| Present Value | Today's value of all future payments |
When to Use Perpetuity Valuation
- Stock Valuation: Gordon Growth Model uses perpetuity for dividend stocks
- Real Estate: Valuing properties with perpetual income streams
- Business Valuation: Terminal value in DCF analysis
- Endowments: Pricing perpetual funds and trusts
- Preferred Stock: Valuing fixed dividend payments
Important Considerations
- For growing perpetuity, the discount rate (r) must be greater than the growth rate (g)
- If g ≥ r, the present value would be infinite (not realistic)
- Perpetuity calculations assume payments continue forever
- Real-world applications often use finite projections
Example Calculations
| Scenario | Payment | Rate | Growth | Present Value |
|---|---|---|---|---|
| Consol Bond | $100 | 5% | 0% | $2,000 |
| Dividend Stock | $50 | 10% | 3% | $714.29 |
| Rental Property | $12,000 | 8% | 2% | $200,000 |
Note: Perpetuity calculations are theoretical and assume constant conditions. Real investments are subject to market changes and finite lifespans.