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Perpetuity Calculator

Calculate perpetuity present value (PV = PMT ÷ r). Supports growing, due, deferred perpetuities with payment frequency. Ideal for stocks and endowments.

Calculate Perpetuity Present Value

Perpetuity Type
Annual Payment
$

The fixed amount paid annually forever

Discount Rate
%

Annual interest rate (e.g., 5 for 5%)

Payment Frequency
Quick Rate Presets

Perpetuity Present Value

$200,000.00
Present Value

Calculation Details

Annual Payment
Fixed payment amount
$10,000.00
Discount Rate
Annual interest rate
5.00%
Formula Used
Present Value = Periodic Payment ÷ Periodic Rate
PV = PMT / r
Payment Frequency
Effective annual rate: 5.00%
Annual

Sensitivity Analysis

Rate ChangeDiscount RatePresent ValueChange %
-3pp2.00%$500,000150.0%
-2pp3.00%$333,333.3366.7%
-1pp4.00%$250,00025.0%
0pp5.00%$200,0000.0%
+1pp6.00%$166,666.67-16.7%
+2pp7.00%$142,857.14-28.6%
+3pp8.00%$125,000-37.5%

Shows how present value changes with different discount rates (±1-3 percentage points)

Common Perpetuity Applications

Investment Analysis

Dividend Stocks3-5%

Stable dividend-paying companies

  • • Utility companies
  • • REITs with long leases
Government Bonds2-4%

Low-risk perpetual bonds

  • • Consols (UK)
  • • Perpetual bonds
Real Estate4-8%

Long-term lease agreements

  • • Ground leases
  • • Commercial properties

Corporate Finance

Endowment Funds5-7%

University and foundation funds

  • • Educational institutions
  • • Charitable foundations
Pension Obligations6-8%

Defined benefit pension plans

  • • Corporate pensions
  • • Government pensions
Insurance4-6%

Annuity and life insurance

  • • Immediate annuities
  • • Life insurance policies

How to Calculate Perpetuity Present Value

Perpetuity Formula

Present Value = Annual Payment ÷ Discount Rate
PV = PMT ÷ r
References: Brealey, Myers & Allen "Principles of Corporate Finance" (12th Ed.), CFA Institute Level I Curriculum

Calculation Steps:

  1. 1
    Determine the annual payment amount
    Fixed cash flow received each year
  2. 2
    Select appropriate discount rate
    Risk-adjusted rate of return (as decimal)
  3. 3
    Apply the perpetuity formula
    Divide annual payment by discount rate

Important Considerations

⚠️ Financial Disclaimer

This calculator provides estimates for educational purposes. Consult financial professionals for investment advice.

📈 Interest Rate Risk

Present value is highly sensitive to discount rate changes

  • • Small rate changes = large value changes
  • • Consider interest rate trends
  • • Use conservative estimates
💰 Inflation Impact

Real vs nominal discount rates matter

  • • Use real rates for inflation-adjusted analysis
  • • Consider purchasing power erosion
  • • Historical inflation averages 2-3%
🏢 Business Risk

Perpetuities assume infinite payments

  • • Companies can fail or change policies
  • • Economic conditions change
  • • Use higher rates for riskier assets
⚖️ Tax Considerations

Tax implications affect net returns

  • • Consider after-tax discount rates
  • • Different tax treatment for different assets
  • • Consult tax professionals

Example Cases

Case 1: Dividend Stock Investment

Input Parameters: $5,000 annual dividend
Discount Rate: 5% (0.05)
Asset Type: Blue-chip dividend stock
Present Value: $100,000
Formula: $5,000 ÷ 0.05
Use Case: Stock valuation

Analysis: This stock would be worth $100,000 if it pays $5,000 annually forever at a 5% discount rate.

Case 2: Real Estate Ground Lease

Input Parameters: $12,000 annual rent
Discount Rate: 6% (0.06)
Asset Type: Commercial ground lease
Present Value: $200,000
Formula: $12,000 ÷ 0.06
Use Case: Property valuation

Analysis: The ground lease has a present value of $200,000 based on perpetual $12,000 annual payments.

Frequently Asked Questions

What is a perpetuity in finance?
A perpetuity pays a fixed amount at regular intervals forever and is used to value infinite cash flows.
What is the perpetuity present value formula?
PV = PMT ÷ r (ordinary perpetuity).
What is a growing perpetuity?
PV = CF₁ ÷ (r − g), r > g.
What is perpetuity due?
PV = PMT × (1 + 1/r), payments start immediately.
What is a deferred perpetuity?
PV = (PMT ÷ r) × (1+r)^(−n), payments start after n periods.

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