Perpetuity: Difference between revisions
imported>Doug Williamson (Slight rewording to make description clearer) |
imported>Doug Williamson (Remove excessive referencing of annuities.) |
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===== Fixed perpetuities ===== | |||
A perpetuity is | 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: | 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: | ||
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where: | |||
A<sub>1</sub> = Time 1 cash flow | |||
Present Value = A<sub>1</sub> x 1/ | 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 = A<sub>1</sub> x 1 / (r - g) | |||
where g = the periodic rate of growth of the cash flow. | where g = the periodic rate of growth of the cash flow. | ||
The growing perpetuity concept is applied | |||
The growing perpetuity concept is applied in many contexts. | |||
For example, the Dividend growth model for share valuation. | |||
Revision as of 10:03, 31 May 2015
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.
