Perpetuity: Difference between revisions
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imported>Doug Williamson m (Spacing 21/8/13) |
imported>Doug Williamson m (Expand to clarify that Time 1 means one period hence.) |
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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. | A perpetuity is similar to an annuity except that the fixed periodic cash flow which starts at the future Time 1 period hence 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: | 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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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: | For a growing perpetuity the present value formula is modified to take account of the constant periodic growth rate from Time 1 period hence to infinity as: | ||
Present Value = A<sub>1</sub> x 1/[r-g] | Present Value = A<sub>1</sub> x 1/[r-g] | ||
Revision as of 09:23, 12 July 2014
1.
A perpetuity is similar to an annuity except that the fixed periodic cash flow which starts at the future Time 1 period hence 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 period hence 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.
