Perpetuity

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Fixed perpetuities

A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever - ‘in perpetuity’.

Each cash flow is an equal fixed amount.

The present value of a fixed perpetuity is calculated - assuming a constant periodic cost of capital (r) for all periods from now to infinity - as:

Present Value = A1 x 1/r


where:

A1 = Time 1 cash flow

r = periodic cost of capital


Growing perpetuities

For a growing perpetuity, the present value formula is modified to take account of the constant periodic growth rate from one period in the future to infinity, as follows:

Present Value = A1 x 1 / (r - g)

where g = the periodic rate of growth of the cash flow.


The growing perpetuity concept is applied in many contexts.

For example, the Dividend growth model for share valuation.


See also