Perpetuity

1. A perpetuity is similar to an annuity except that the fixed periodic cash flow which starts at the future Time 1 then carries on for ever (‘in perpetuity’) rather than stopping after Time n.

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

2. For a growing perpetuity the present value formula is modified to take account of the constant periodic growth rate from Time 1 to infinity as:

Present Value = A₁ x 1/[r-g]

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

The growing perpetuity concept is applied by the Dividend growth model for share valuation.

See also

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