PV of Growing Perpetuity
Present value of an infinite stream of payments growing at rate g forever (Gordon Growth Model).
When to use: Use to value stocks with growing dividends or any cash flow expected to grow forever.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | Value of the growing perpetuity | $ |
| PMT | First Payment | The first payment (next period) | $ |
| k | Interest Rate | Required rate of return (must be > g) | % |
| g | Growth Rate | Constant growth rate of payments | % |
Real-Life Examples
Example 1: Stock Valuation (Gordon Model)
A stock will pay a $3 dividend next year, growing 4% forever. Required return is 10%.
Given
Step-by-Step
The stock is worth $50.00 per share based on the Gordon Growth Model.
Example 2: Rental Property
A property generates $30,000/year in net rent, growing 2%/year forever. Cap rate is 7%.
Given
Step-by-Step
The property is worth $600,000 based on growing perpetuity valuation.
Frequently Asked Questions
The Gordon Growth Model (also called the Dividend Discount Model) values a stock by dividing the next expected dividend by the difference between the required return and the dividend growth rate. It is one of the most widely used stock valuation formulas in finance.
If the growth rate equals or exceeds the discount rate, the present value would be infinite — the payments grow faster than they are discounted. In practice, this means the model only works when k > g, which is usually satisfied for stable companies.
Commercial real estate is often valued using cap rates, which are closely related to the growing perpetuity formula. Net operating income divided by (cap rate minus expected rent growth) estimates the property value, just as PMT/(k - g) values the cash flow stream.
It assumes a constant growth rate forever, which is unrealistic for most assets. It is most accurate for mature, stable companies or assets with predictable, modest growth. High-growth companies require multi-stage models that transition to a stable growth rate.