To value an infinite stream of cash flows (a perpetuity) that begins one year from today, you would divide the annual cash flow by the discount rate. But what if the perpetuity doesn’t begin until more than one year from now? This is called a delayed perpetuity.
For example, let’s say you are valuing an investment that will provide an infinite stream of $100 cash flows forever, but that those cash flows don’t begin until three years from today. Also assume that your discount rate is 5%. The first step to valuing this delayed perpetuity is to calculate the present value of a regular perpetuity:
PV of regular perpetuity = cash flow / discount rate = $100 / 0.05 = $2,000
The present value of the regular perpetuity is what the infinite stream of cash flows will be worth two years from now (it is two years and not three, because the formula for the present value of a regular perpetuity assumes the first cash flow occurs at the end of the first period). In this case, the infinite stream of cash flows will be worth $2,000 two years from now. The next step is to discount the $2,000 figure to the present value:
present value of delayed perpetuity = $2,000 / [(1 + r)^n] = $2,000 / (1.05^2) = $1,814.06
Here’s an alternative formula for calculating the value of a delayed perpetuity:
present value of delayed perpetuity = (cash flow / r) * (1 / [ ((1 + r)^n) ])
This formula yields the same value for the delayed perpetuity as the process we followed earlier:
present value of delayed perpetuity = (cash flow / r) * (1 / [ ((1 + r)^n) ])
present value of delayed perpetuity = ($100 / 0.05) * (1 / [1.05^2])
present value of delayed perpetuity = $1,814.06
0:00 Introduction
0:57 Example
2:18 Common mistake to avoid
3:00 Alternative formula
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