Perpetuity
1.
A series of cash flows modelled to carry on for an infinite amount of time in the future.
2. Fixed perpetuity
A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter.
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
3. Growing perpetuity
A growing perpetuity is an infinite series of cash flows, modelled to grow by a constant proportionate amount every period.
For a growing perpetuity, the present value formula is modified to take account of the constant periodic growth rate, 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.
