PV of Perpetuity
Present value of an infinite stream of equal end-of-period payments.
When to use: Use to value preferred stock dividends, endowments, or any payment stream expected to last forever.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| PV | Present Value | Value of the perpetuity today | $ |
| PMT | Payment | Periodic payment amount | $ |
| k | Interest Rate | Discount rate | % |
Real-Life Examples
Example 1: Preferred Stock
Preferred stock pays $5/share annually forever. Required return is 8%. What should you pay?
Given
Step-by-Step
The preferred stock is worth $62.50 per share.
Example 2: University Endowment
A university needs $100,000/year forever from an endowment. Earn 5% annually. How large must it be?
Given
Step-by-Step
The endowment must be $2,000,000 to generate $100,000/year indefinitely.
Frequently Asked Questions
A perpetuity is a stream of equal payments that continues forever. While nothing truly lasts forever, perpetuities are used to value long-lived assets like preferred stock, endowments, and some government bonds (such as British consols).
Because each future payment is worth less in present value terms due to discounting. The further into the future a payment is, the less it is worth today. The sum of all these discounted payments converges to a finite number: PMT/k.
Preferred stock pays a fixed dividend indefinitely, making it a perpetuity. Divide the annual dividend by the required rate of return to get the stock's fair value. For example, a $5 annual dividend at 8% required return gives a value of $62.50.
An endowment is a fund that provides income indefinitely. To find the endowment size needed, divide the desired annual payout by the expected return rate. For example, $100,000/year at 5% requires a $2,000,000 endowment.