imported>Doug Williamson |
imported>Doug Williamson |
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| 1. ''Valuation.''
| | This is a form of securities issuance that has no exact definition. |
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| A series of cash flows modelled to carry on for an infinite amount of time in the future.
| | It usually refers to an issue that has been designed for a specific set of investor needs at a particular time. |
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| | As such it is not expected to be traded in the secondary market and is not a 'public' issue. |
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| 2. ''Fixed perpetuity''
| | It is not normally expected to be listed on an exchange. |
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| A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter. | | A wide variety of securities under various names are private placements. In Germany, [[Schuldschein]] are a form of private placements, for example. |
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| Each cash flow is an equal fixed amount.
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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:
| | == ACT Website links == |
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| Present Value = A<sub>1</sub> x 1/r
| | [http://www.treasurers.org/blogs/ceo/201307 Colin Tyler's Blog 5 July 2013] |
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| | | [http://www.treasurers.org/node/8624 Developing a UK Private Placement market – report of the PP15+ working group] |
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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 == | | == See also == |
| * [[Annuity]] | | * [[Issue]] |
| * [[Discounted cash flow]] | | * [[Placement]] |
| * [[Dividend growth model]] | | * [[Rule 144A]] |
| * [[Growing annuity]] | | * [[Secondary market]] |
| * [[Growing perpetuity]] | | * [[Security]] |
| * [[Growing perpetuity factor]]
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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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| ==The Treasurer articles==
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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]]
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