imported>Doug Williamson |
imported>Doug Williamson |
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| A series of cash flows modelled to carry on for an infinite amount of time in the future.
| | The risk of adverse consequences arising from a worsening of the reputation of a business. |
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| | For example, as a result of adverse publicity. |
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| 2. '''Fixed perpetuity'''
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| A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter.
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| Each cash flow is an equal fixed amount.
| | The risk of incurring costs, or limiting the flexibility of commercial actions, because of the need to protect the reputation of the business from damage. |
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| 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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| Present Value = A<sub>1</sub> x 1/r
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| | ==See also== |
| | *[[Compliance risk]] |
| | *[[Ethics]] |
| | *[[Franchise viability risk]] |
| | *[[Media risk]] |
| | *[[Operational risk]] |
| | *[[Working capital management]] |
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| where:
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| A<sub>1</sub> = Time 1 cash flow
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| r = periodic cost of capital
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| <span style="color:#4B0082">'''Example 1: Fixed perpetuity valuation'''</span>
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| Time 1 cash flow = $10m, continuing at the same amount each period thereafter in perpetuity.
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| Periodic cost of capital = 5%
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| The present value of the fixed perpetuity is:
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| = $10m x (1 / 0.05)
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| = $10m x 20
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| = $'''200'''m
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| 3. '''Growing perpetuity'''
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| A growing perpetuity is an infinite series of cash flows, modelled to grow by a constant proportionate amount every period.
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| For a growing perpetuity, the present value formula is modified to take account of the constant periodic growth rate, as follows:
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| Present Value = A<sub>1</sub> x 1 / (r - g)
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| where g = the periodic rate of growth of the cash flow.
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| <span style="color:#4B0082">'''Example 2: Growing perpetuity valuation'''</span>
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| Time 1 cash flow = $10m, growing by a constant percentage amount each period thereafter in perpetuity.
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| Periodic cost of capital = 5%.
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| Periodic growth rate = 2%
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| The present value of the growing perpetuity is:
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| = A<sub>1</sub> x 1 / (r - g)
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| = $10m x (1 / (0.05 - 0.02) )
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| = $10m x (1 / 0.03)
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| = $10m x 33.3
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| = $'''333'''m
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| The modest rate of growth in the cash flow has added substantially to the total present value.
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| 4. '''Declining perpetuity'''
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| Growth can be negative, in other words, decline.
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| For a declining perpetuity, the present value formula is the same as the growing perpetuity, but the growth rate (g) is entered as a negative number as follows:
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| <span style="color:#4B0082">'''Example 3: Declining perpetuity valuation'''</span>
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| Time 1 cash flow = $10m, declining by a constant percentage amount each period thereafter in perpetuity.
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| Periodic cost of capital = 5%.
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| Periodic growth rate = -(2)% negative = -0.02
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| The present value of the declining perpetuity is:
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| = A<sub>1</sub> x 1 / (r - g)
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| = $10m x (1 / (0.05 - -0.02) )
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| = $10m x (1 / 0.07)
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| = $10m x 14.3
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| = $'''143'''m
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| The small negative rate of growth in the cash flow has reduced the total present value very substantially.
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| The growing / declining perpetuity concept is applied in many contexts.
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| For example, the Dividend growth model for share valuation.
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| == See also ==
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| * [[Annuity]]
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| * [[Dividend growth model]]
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| * [[Growing annuity]]
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| * [[Growing perpetuity]]
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| * [[Irredeemable]]
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| * [[Perpetuity due]]
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| * [[Perpetuity factor]]
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| * [[Simple annuity]]
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| ==Student article==
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| [[Media:2013_10_Oct_-_The_real_deal.pdf| The real deal, The Treasurer]]
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| ''Real rates of corporate decline often lead to miscalculation, overpaying for acquisitions and disastrous losses.''
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| ''Read this article to discover how to avoid the most common errors and add value for your organisation.''
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| [[Category:Corporate_finance]]
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| [[Category:Long_term_funding]] | |