Free ToolNo signup required
Perpetuity Calculator
Calculate the present value of infinite cash flow streams — flat or growing.
Flat & Growing
Both perpetuity types supported
Sensitivity Table
See PV across different discount rates
Valuation Ready
Use for terminal value in DCF analysis
Calculate Perpetuity Value
Enter the periodic cash flow, discount rate, and optional growth rate.
What Is a Perpetuity and How Is It Valued?
Flat Perpetuity
PV = C / r
Example: £10,000 / 5% = £200,000
A constant cash flow forever. At a 5% discount rate, £10,000 per year forever is worth £200,000 today. Real-world examples include consol bonds (UK government perpetual bonds) and some preferred shares.
Growing Perpetuity
PV = C / (r - g)
Example: £10,000 / (5% - 2%) = £333,333
Cash flows grow at rate g forever. The Gordon Growth Model uses this for stock valuation. Growth increases the present value significantly — adding just 2% growth nearly doubles the value in this example.
Perpetuities in Investment Valuation
Terminal Value in DCF
In discounted cash flow analysis, the terminal value represents all cash flows beyond the explicit forecast period. It is calculated as a growing perpetuity and often accounts for 60-80% of total enterprise value. The growth rate should reflect long-term sustainable growth (typically 2-3%, not exceeding GDP growth).
Dividend Discount Model
The Gordon Growth Model values a stock as: Price = D1 / (r - g), where D1 is next year's dividend. This is a growing perpetuity. It works best for mature companies with stable, growing dividends. For a stock paying £2 dividends growing at 4% with a 10% required return: Price = £2 / (10% - 4%) = £33.33.
How to Use This Perpetuity Calculator
Enter Cash Flow
The periodic payment amount.
Set Rates
Discount rate and optional growth rate.
View Results
Present value, formula, and sensitivity table.
Key Considerations for Perpetuity Valuation
- Growth must be less than discount rate. The formula PV = C/(r-g) only works when g < r. In practice, long-term growth should not exceed the economy's sustainable growth rate.
- Small changes in rates have large effects. Changing the discount rate from 5% to 4% can increase the PV by 25%. The sensitivity table shows how dramatically values change with small rate adjustments.
- Real-world perpetuities are rare. True perpetuities (infinite life) barely exist. Most applications use the formula as an approximation for very long-lived cash flows where the precise end date doesn't materially affect the value.
- Use real rates for real cash flows. If the cash flow is in nominal terms, use a nominal discount rate. If in real (inflation-adjusted) terms, use a real discount rate. Mixing real and nominal leads to incorrect valuations.
Want deeper insights?
ARIA analyses your portfolio with institutional-grade metrics including DCF valuation and dividend analysis.
Create Free Account