Perpetuities
Asset providing a fixed amount of cash flow
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A perpetuity is an asset that provides a periodic fixed amount of cash flow forever.
Endowments and trust funds, and long lived assets like oil wells or gas fields can be regarded as perpetuities.
The value of a perpetuity can be calculated as
PV = F / r (1)
where
PV = present value
F = F1 = F2 .. Fn = fixed amount of cash flow per period
r = discount rate of return (per time period)
Growing Perpetuity
If the cash flow grows in a constant rate the value of the perpetuity can be expressed as
PV = F / (r - g) (2)
where
g = growth rate of cash flow (per time period)
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