Optimized Perpetuity — Smart Financial Analysis
Calculate present value of perpetuities. Standard PV=C/r, growing PV=C/(r-g).
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A perpetuity is an infinite stream of equal cash flows. PV = C / r for a standard perpetuity. Growing perpetuity has payments that increase at rate g forever. Annuity has finite payments (N periods).
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Why: A perpetuity is an infinite stream of equal cash flows. PV = C/r, where C is the periodic payment and r is the discount rate. British consols and preferred stock are real-world ...
How: Enter Payment C ($), Discount Rate r (%), Growth Rate g (%) to get instant results. Try the preset examples to see how different scenarios affect the outcome, then adjust to match your situation.
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📋 Quick Examples — Click to Load
📊 PV vs Discount Rate
📈 Growth Impact (r=8%)
🍩 Type Comparison
📊 Application Discount Rates
Present Value
Standard perpetuity PV = $20,000.
For educational purposes only — not financial advice. Consult a qualified advisor before making decisions.
💡 Money Facts
Optimized Perpetuity analysis is used by millions of people worldwide to make better financial decisions.
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Globally, only 33% of adults are financially literate, making tools like this essential.
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A perpetuity pays a fixed amount forever. PV = C/r. Growing perpetuity: PV = C/(r−g). First UK consol issued 1751. US endowments manage $40B+ in perpetuity-like structures. Gordon Growth Model uses this for stock valuation.
Sources: CFA Institute, Brealey Myers Allen, Yale Endowment, Bank of England.
Key Takeaways
- • Standard: PV = C/r. Growing: PV = C/(r − g), g < r
- • Higher r → lower PV. Higher g (when g < r) → higher PV
- • Used for preferred stock, consols, DCF terminal value
- • Gordon Growth: P = D₁/(r − g)
Did You Know?
How Does Perpetuity Valuation Work?
Standard Perpetuity
PV = C/r. Sum of infinite geometric series: C/(1+r) + C/(1+r)² + ... = C/r.
Growing Perpetuity
PV = C/(r−g). Payments grow at g. Requires g < r for convergence.
Gordon Growth Model
Stock price P = D₁/(r−g). Treats dividends as growing perpetuity.
Expert Tips
Perpetuity vs Annuity
| Type | Formula | Payments |
|---|---|---|
| Perpetuity | PV = C/r | Infinite |
| Growing Perp | PV = C/(r−g) | Infinite, growing |
| Annuity | PV = C×[1−(1+r)^(−N)]/r | N periods |
Frequently Asked Questions
What is a perpetuity?
A perpetuity is an infinite stream of equal cash flows. PV = C/r, where C is the periodic payment and r is the discount rate. British consols and preferred stock are real-world examples.
What is the perpetuity formula?
PV = C / r for a standard perpetuity. For growing perpetuity: PV = C / (r − g), where g is the growth rate. Gordon Growth Model uses this for stock valuation.
What is growing perpetuity?
Growing perpetuity has payments that increase at rate g forever. PV = C / (r − g). Requirement: g < r. Used for DCF terminal value and dividend discount models.
Perpetuity vs annuity?
Annuity has finite payments (N periods). Perpetuity has infinite payments. Annuity PV = C × [1 − (1+r)^(−N)]/r. Perpetuity PV = C/r. As N→∞, annuity PV → perpetuity PV.
Real-world perpetuity examples?
UK consols (1751), preferred stock dividends, endowment funds, ground rents, certain royalty streams. Yale and Harvard endowments manage $40B+ in perpetuity-like structures.
Perpetuity in stock valuation?
Gordon Growth Model: P = D₁/(r − g), treating dividends as a growing perpetuity. Terminal value in DCF often uses perpetuity formula for cash flows beyond the forecast period.
Key Statistics
Official Data Sources
⚠️ Disclaimer: This calculator is for educational purposes only. Not financial advice. Consult a professional for investment decisions.
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