PV of Growing Perpetuity Due
Present value of an infinite growing stream with payments at the beginning of each period.
When to use: Use when growing perpetual payments are made at the start of each period.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | Value of the growing perpetuity due | $ |
| PMT | First Payment | The first payment | $ |
| k | Interest Rate | Required return (must be > g) | % |
| g | Growth Rate | Constant growth rate | % |
Real-Life Examples
Example 1: Growing Endowment Due
An endowment pays $50,000 at start of year, growing 3%/year forever. Discount rate 7%.
Given
Step-by-Step
The growing endowment due is worth $1,337,500.
Example 2: Growing Dividend Due
A special dividend structure pays $4/share at start of year, growing 5% forever. Required return 12%.
Given
Step-by-Step
The stock with growing perpetuity due is worth $64.00 per share.
Frequently Asked Questions
Use it when valuing a stream of growing payments made at the beginning of each period that is expected to continue indefinitely. Examples include endowments with beginning-of-year disbursements that increase annually with inflation.
The growing perpetuity due value equals the ordinary growing perpetuity value multiplied by (1 + k). The first payment is received immediately and every subsequent growing payment arrives one period earlier.
While the ordinary growing perpetuity (Gordon Growth Model) is standard for stock valuation, the due version applies when dividends are paid at the start of the period. In practice, most dividend valuations use the ordinary version.