Perpetuities
An asset providing a fixed cash flow.
A perpetuity is an asset that provides a never ending periodic fixed amount of cash flow.
Endowments and trust funds and long lived assets like oil wells or gas fields can be regarded as a perpetuity.
The value of a perpetuity can be calculated as
P = F1 / (1 + i) 1 + F2/ (1 + i)2+ F3 / (1 + i)3 + ...... + Fn / (1 + i) n
= F / i (1)
where
P = present value
F = F1 = F2.. Fn = the fixed amount of cash flow per period
i = discount rate of return (per time period)
Example - The Value of a Company and Net Income
A company is able to deliver a net income every year of 100 . Assuming that this is a perpetuity - a never ending income - the value of this cash flow (and the value of the company) with a discount rate of 10% (i = 0.10) can be calculated to
P = (100) / 0.10
= 1000
Growing Perpetuity
If a cash flow grows in a constant rate the value of the perpetuity can be expressed as
P = F / (i - g) (2)
where
g = growth rate of cash flow (per time period)
Example - The Value of a Growth Company and Net Income
A growth company is able to deliver a net income first year of 200 with a net income growth rate the next years of 3% (g = 0.03) . Assuming that this is a perpetuity - a never ending income - the value of this cash flow (and the value of the company) with a discount rate of 10% (i = 0.10) can be calculated to
P = (100) / (0.10 - 0.03)
= 1429
Perpetuity Value Calculator
Related Topics
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Economics
Engineering economics - cash flow diagrams, present value, discount rates, internal rates of return - IRR, income taxes, inflation.
