Perpetuity
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.
