Perpetual Annuity Calculator
Estimate the present value of an income stream that continues forever. This tool supports both standard perpetuities and growing perpetuities.
A perpetual annuity, often called a perpetuity, is one of the most useful valuation concepts in finance. If you know the payment amount and the discount rate, you can estimate what that endless cash flow is worth today. This page explains how the formula works and when to use it.
What Is a Perpetual Annuity?
A perpetual annuity is a stream of equal payments that never ends. In practical terms, no real asset pays forever, but many investments can be modeled as a perpetuity over a long horizon. Examples include:
- Preferred stock paying a fixed dividend
- Endowment payouts designed to continue indefinitely
- Long-run business cash flow approximations in terminal value models
- Real estate income assumptions in simplified valuation models
Core Perpetuity Formula
For a standard perpetuity where the first payment arrives one period from now:
PV = C / r
Where:
- PV = present value
- C = payment per period
- r = discount rate per period (as a decimal)
If payments grow at a constant rate, use the growing perpetuity formula:
PV = C / (r - g)
Here, g is the growth rate. This formula is valid only when r > g.
Perpetuity Due Adjustment
If the first payment happens immediately (instead of one period from now), multiply by (1 + r):
PVdue = PVordinary × (1 + r)
How to Use This Calculator
- Enter your periodic payment amount.
- Enter the discount rate that reflects required return or opportunity cost.
- Enter growth rate if payments rise over time (otherwise leave at 0).
- Select payment timing: ordinary or due.
- Click Calculate to view the result and formula used.
Quick Example
Suppose an asset pays $10,000 per year forever, and your discount rate is 8%.
PV = 10,000 / 0.08 = 125,000
This means the income stream is worth about $125,000 today under those assumptions.
Common Mistakes to Avoid
- Using percentages directly in formulas (use decimals: 8% = 0.08).
- Mismatching periods (annual cash flows require annual rates).
- Setting growth rate equal to or above discount rate.
- Ignoring risk when selecting discount rate.
When This Model Works Best
This present value calculator is best for stable, long-term cash flow assumptions. For assets with changing payment schedules, finite time horizons, or high uncertainty, discounted cash flow models with explicit yearly projections are usually better.
Final Thoughts
A perpetuity calculator is simple, but extremely powerful. It helps you think clearly about how payment size, growth, and discount rate interact. Small changes in discount rate can materially change value, so always test multiple assumptions before making financial decisions.