Perpetuity Calculator
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In financial valuation, a Perpetuity is a continuous stream of identical cash flows that continues indefinitely with no end date. While infinite cash flows sound complex to value, time-value-of-money mathematics allows financial analysts to calculate the exact finite Present Value (PV) of a perpetuity in today’s dollars.
Our free Perpetuity Calculator allows corporate finance specialists, investors, and endowment managers to value infinite cash streams. Whether you are pricing preferred stock, valuing university trust endowments, or calculating terminal values in DCF models, this tool delivers instant valuation math.
How to Calculate Present Value of Perpetuity
1. Ordinary (Constant) Perpetuity Formula
Used when cash flows remain fixed forever (e.g., preferred stock dividends):
Present Value (PV) = C / r
- C: Fixed cash payment received every period.
- r: Discount rate / required rate of return (as a decimal).
2. Growing Perpetuity Formula
Used when cash flows grow at a constant annual percentage rate (g) forever (e.g., inflation-indexed endowment payouts):
Present Value (PV) = C / (r - g)
- g: Constant annual growth rate of cash flow (must be less than discount rate r).
Ordinary vs. Growing Perpetuity Comparison
| Annual Cash Flow (C) | Discount Rate (r) | Growth Rate (g) | Present Value (PV) |
|---|---|---|---|
| $50,000 / year | 6.0% | 0.0% (Ordinary) | $833,333 |
| $50,000 / year | 6.0% | 2.0% (Growing) | $1,250,000 |
Adding a modest 2.0% annual growth rate increases the present value of the cash stream by $416,667!
Step-by-Step Preferred Stock Example
Imagine an investor evaluating a preferred stock share issued by a major bank:
- Fixed Annual Preferred Dividend: $6.00 per share
- Required Discount Rate (Investor Hurdle Rate): 7.5% (0.075)
Let’s calculate the fair market Present Value:
PV = $6.00 / 0.075 = $80.00
The fair market value of the preferred stock share is $80.00 per share.
Frequently Asked Questions (FAQ)
Why does an infinite cash stream have a finite present value?
Because of the time value of money, cash received far into the future (e.g., Year 100) has a present value approaching zero. The sum of infinitely small discounted cash flows converges mathematically to a finite number.
What happens if growth rate (g) is equal to or greater than discount rate (r)?
In the growing perpetuity formula C / (r - g), if g ≥ r, the denominator becomes zero or negative, resulting in an undefined or mathematically infinite present value. In financial reality, a company’s cash flow growth rate cannot permanently exceed the overall economy’s discount rate.
What are real-world examples of perpetuities?
Real-world perpetuities include preferred stock dividends, UK government Consol bonds (historically), university endowment scholarships, and real estate ground lease agreements.