Perpetuities

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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  .. F_n  = 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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Related Topics

• Economics - Engineering economic concepts - cash flow diagrams, discount rate, internal rate of return - IRR, income taxes, inflation

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