A perpetuity pays a fixed amount forever. Its present value is surprisingly simple: the payment divided by the discount rate. The backbone of valuing preferred stock and endowments.
The example
$100 a year forever at a 5% rate.
| A | B | |
|---|---|---|
| 1 | Item | Value |
| 2 | Payment / yr | $100 |
| 3 | Rate | 5% |
| 4 | Present value | $2,000 |
The formula
The formula:
How it works
How it works:
- A perpetuity is an annuity with no end date.
- Its present value is simply
payment / rate— the infinite series collapses to this clean formula. - Used to value preferred stock (fixed dividend), endowments, and console bonds.
- A growing perpetuity (payment rising by g) is
C / (r − g).
Sustainable withdrawal: flip it — a balance B supports a forever-payment of B × r without ever depleting. That’s the perpetuity logic behind “live off the interest.”
Try it: interactive demo
Payment and rate.
Variations
Growing perpetuity
Payment grows at g:
Sustainable withdrawal
From a balance:
Preferred stock value
Dividend / yield:
Pitfalls & errors
Rate can’t be zero. Dividing by a zero rate is undefined — a perpetuity needs a positive discount rate.
Growth below rate. The growing formula requires g < r, or it’s nonsensical (infinite value).
“Forever” is an idealization. Real cash flows end; use it for very long or truly perpetual streams.
Practice workbook
Frequently asked questions
How do I value a perpetuity in Excel?
How do I value a growing perpetuity?
What's the sustainable forever-withdrawal from a balance?
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