Perpetuity Calculator
Evaluate the present value of perpetual cash-flow streams with support for ordinary, growing, due, and deferred structures. Use this calculator to stress discount-rate assumptions, compare payment timing models, and build valuation context for dividend assets, endowments, and long-duration liability plans.
Editorial & Review Information
Reviewed on: 2026-02-28
Published on: 2025-09-19
Author: LumoCalculator Editorial Team
What we checked: We re-checked ordinary/growing/due/deferred perpetuity equations, frequency conversion handling, and boundary constraints (especially r-g spread) so valuation comparisons remain internally consistent with the listed public references.
Purpose and scope: This page is designed for valuation education and planning. It helps users compare perpetual-cash-flow structures, but it does not replace security analysis, capital-market judgment, or personalized investment advice.
How to use this review: Build base and stress discount-rate scenarios, test growth assumptions with clear r-g spread buffers, and treat the output as a screening estimate before full credit, liquidity, and legal-term review.
Financial Disclaimer
Results are simplified estimates based on constant-rate assumptions. Real-world outcomes can differ because discount rates change, growth is rarely stable forever, and asset-level risk factors such as credit quality, liquidity, covenant terms, and tax treatment are outside this model.
Use Scenarios
Dividend and preferred-share screening
Translate recurring distributions into a present-value estimate to compare valuation multiples across steady-income securities before deeper credit and cash-flow analysis.
Endowment and foundation planning
Estimate capital required to support perpetual annual spending, with optional growth assumptions to reflect inflation-linked distribution policies.
Deferred benefit valuation
Value obligations that begin in the future, such as deferred pensions or delayed concession cash flows, by discounting the perpetuity over a specified waiting period.
Formula Explanation
Ordinary perpetuity
PV = PMT / r
Use when equal payments arrive at period end forever. The discount rate captures both time value and risk.
Growing perpetuity
PV = CF1 / (r - g), where g < r
Apply when each payment grows at a constant rate. The spread between discount rate and growth rate is the key driver of valuation sensitivity.
Perpetuity due
PV due = PMT x (1 + r) / r
Use when payment starts immediately at the beginning of each period. Earlier timing increases present value relative to ordinary perpetuity.
Deferred perpetuity
PV0 = (PMT / r) / (1 + r)^n
First compute ordinary perpetuity at start date, then discount that value by the deferral window. This is common in delayed pension and concession models.
Example Cases
Case 1: Preferred stock baseline
Inputs: Annual payment $8,000, discount rate 5.00%, ordinary perpetuity, annual frequency.
Computed results: Present value $160,000.00, PV multiple 20.00x annual payment. Sensitivity: at 4.00% PV rises to $200,000.00 (+25.00%); at 6.00% PV falls to $133,333.33 (-16.67%).
Interpretation: A one-point rate move changes valuation materially, so this simple baseline is useful for screening but fragile without rate-risk context.
Decision hint: Pair this result with issuer credit spread and required-return scenarios before comparing against market price.
Case 2: Growing scholarship fund
Inputs: Year-1 payout $100,000, discount rate 6.00%, growth rate 2.00%, growing perpetuity, annual frequency.
Computed results: Present value $2,500,000.00, spread (r-g) 4.00%, PV multiple 25.00x year-1 payout. Sensitivity: at 5.00% discount PV is $3,333,333.33 (+33.33%); at 7.00% PV is $2,000,000.00 (-20.00%).
Interpretation: Valuation reacts strongly when discount-growth spread narrows, which is typical for endowment or policy spending models.
Decision hint: Stress test both discount and growth assumptions together, and avoid funding plans that only work under tight spreads.
Case 3: Deferred pension liability
Inputs: Annual payment $150,000, discount rate 7.00%, deferred perpetuity with 10-year delay, annual frequency.
Computed results: Present value today $1,089,319.91. Ordinary perpetuity at start date is about $2,142,857.14, so deferral retention is 50.83%. Sensitivity: at 6.00% PV is $1,395,986.94 (+28.15%); at 8.00% PV is $868,487.79 (-20.27%).
Interpretation: Deferral erodes value substantially even with unchanged benefit size, because all cash flows are shifted further into the future.
Decision hint: For pension and long-tail liabilities, test timing and discount assumptions jointly before final reserve sizing.
Boundary Conditions
Practical Workflow
- Define the cash-flow pattern first: fixed, growing, immediate-start due, or deferred-start.
- Select a base discount rate and at least two stress rates to capture valuation uncertainty.
- Validate that growth assumptions are sustainable and remain below discount rate over time.
- Compare outputs with alternative valuation approaches (multiples, DCF terminal assumptions).
- Finalize conclusions only after risk, tax, and legal-review checks outside this calculator.
Sources & References
- U.S. SEC Investor.gov - Investor Bulletin - Investor-education reference for long-term security analysis and risk framing.
- U.S. Securities and Exchange Commission - Investor Education - Regulatory investor-education context for valuation assumptions and disclosure literacy.
- FINRA Investor Resources - Broker-dealer investor-protection guidance used for boundary and risk disclaimers.
- Federal Reserve - Monetary Policy - Rate-environment reference supporting discount-rate scenario planning.