Perpetuity
Present value of an infinite constant cash flow.
Formula
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Example
A bond paying $50/year forever, discounted at 5%, is worth 50/0.05 = $1000.
How it works
A perpetuity is a stream of equal payments that continues forever, so its value today is just the discounted sum of all those future payments. Because each payment is one period farther away and gets discounted by the same rate, the total forms a converging geometric series, which collapses neatly to PV = C/r. The formula shows that a higher cash flow raises value linearly, while a higher discount rate lowers value sharply because distant payments matter less.
When to use it
Use this when valuing cash flows that are intended to continue indefinitely, such as certain preferred shares, endowments, or idealized long-run project payoffs. It is also useful as a building block in more advanced valuation problems where a finite stream is followed by a perpetual tail.
Worked example, step by step
Suppose an endowment will pay $18,000 every year forever, and the appropriate discount rate is 6%. PV = C / r PV = 18,000 / 0.06 PV = 300,000 So the present value of the perpetuity is $300,000.
Common mistakes to avoid
- Using the formula for payments that stop after a fixed number of periods
- Forgetting that the discount rate must be written as a decimal, not a percent
- Applying the formula when the first payment is delayed without adjusting for timing
Did You Know?
A perpetuity pays forever, yet has a finite value — Britain once issued such never-maturing bonds called consols.
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