PV of Perpetuity Due
Present value of infinite beginning-of-period payments with periodic compounding.
When to use: Use for monthly or quarterly perpetual payments due at the start of each period.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | Value of perpetuity due | $ |
| PMT | Payment | Periodic payment | $ |
| k | Interest Rate | Nominal annual rate | % |
| m | Periods/Year | Compounding frequency | integer |
Real-Life Examples
Example 1: Monthly Perpetuity Due
$1,000/month paid at start forever. Annual rate 6%.
Given
Step-by-Step
The monthly perpetuity due is worth $201,000.
Example 2: Quarterly Lease Forever
$5,000/quarter at start of quarter forever. Rate 8%.
Given
Step-by-Step
The perpetual quarterly lease due is worth $255,000.
Frequently Asked Questions
Add the first monthly payment to the ordinary monthly perpetuity value. The formula is PMT + PMT/(k/m). The first payment is received immediately, and all future monthly payments are valued as an ordinary perpetuity.
The perpetuity due is worth exactly one additional monthly payment more than the ordinary perpetuity. With a $1,000/month payment at 6%, the perpetuity due is worth $201,000 vs. $200,000 for the ordinary version.
If rent is collected at the start of each month and expected to continue indefinitely, the perpetuity due formula gives the property's value. The immediate first rent payment plus the present value of all future rents equals the total value.