PV of Perpetuity
Present value of infinite periodic payments with m-period compounding.
When to use: Use for monthly or quarterly perpetual payment streams.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | Value of the perpetuity | $ |
| PMT | Payment | Periodic payment per period | $ |
| k | Interest Rate | Nominal annual rate | % |
| m | Periods/Year | Compounding frequency | integer |
Real-Life Examples
Example 1: Monthly Perpetuity
An investment pays $500/month forever. Annual rate is 6%. What is it worth?
Given
Step-by-Step
The monthly perpetuity is worth $100,000.
Example 2: Quarterly Perpetuity
An endowment generates $25,000/quarter forever at 8% annually.
Given
Step-by-Step
The quarterly perpetuity requires a $1,250,000 endowment.
Frequently Asked Questions
Divide the annual rate by the number of payments per year (m) to get the periodic rate, then divide the periodic payment by that rate. For example, $500/month at 6% annual gives $500 / (0.06/12) = $100,000.
A monthly perpetuity paying $500/month ($6,000/year) is worth more than an annual perpetuity paying $6,000/year at the same nominal rate. Monthly payments arrive sooner on average, increasing their present value.
Yes. If you expect rental income to continue indefinitely at a steady amount, the perpetuity formula gives a reasonable property valuation. Divide the periodic rental income by the appropriate periodic discount rate to estimate the property's value.