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.

See also

• Annuity
• Dividend growth model
• Growing perpetuity
• Irredeemable
• Perpetuity due
• Perpetuity factor
• Simple annuity