Perpetuity and Private placement: Difference between pages

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1. ''Valuation.''
This is a form of securities issuance that has no exact definition.


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.


As such it is not expected to be traded in the secondary market and is not a 'public' issue. 


2. ''Fixed perpetuity.''
It is not normally expected to be listed on an exchange.


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.
 
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 = A<sub>1</sub> x 1/r
 
 
where:
 
A<sub>1</sub> = Time 1 cash flow
 
r = periodic cost of capital
 
 
<span style="color:#4B0082">'''Example 1: Fixed perpetuity valuation'''</span>
 
Time 1 cash flow = $10m, continuing at the same amount each period thereafter in perpetuity.
 
Periodic cost of capital = 5%
 
The present value of the fixed perpetuity is:
 
= $10m x (1 / 0.05)
 
= $10m x 20
 
= $'''200'''m
 
 
 
3. ''Growing perpetuity.''
 
A growing perpetuity is an infinite series of cash flows, modelled to grow by a constant proportionate amount every period.
 
For a growing perpetuity, the present value formula is modified to take account of the constant periodic growth rate, as follows:
 
Present Value = A<sub>1</sub> x 1 / (r - g)
 
where g = the periodic rate of growth of the cash flow.
 
 
<span style="color:#4B0082">'''Example 2: Growing perpetuity valuation'''</span>
 
Time 1 cash flow = $10m, growing by a constant percentage amount each period thereafter in perpetuity.
 
Periodic cost of capital = 5%.
 
Periodic growth rate = 2%
 
 
The present value of the growing perpetuity is:
 
= A<sub>1</sub> x 1 / (r - g)
 
= $10m x (1 / (0.05 - 0.02) )
 
= $10m x (1 / 0.03)
 
= $10m x 33.3
 
= $'''333'''m
 
 
The modest rate of growth in the cash flow has added substantially to the total present value.
 
 
 
 
4. ''Declining perpetuity.''
 
Growth can be negative, in other words, decline.
 
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:
 
 
<span style="color:#4B0082">'''Example 3: Declining perpetuity valuation'''</span>
 
Time 1 cash flow = $10m, declining by a constant percentage amount each period thereafter in perpetuity.
 
Periodic cost of capital = 5%.
 
Periodic growth rate = -(2)% negative = -0.02
 
 
The present value of the declining perpetuity is:
 
= A<sub>1</sub> x 1 / (r - g)
 
= $10m x (1 / (0.05 - -0.02) )
 
= $10m x (1 / 0.07)
 
= $10m x 14.3
 
= $'''143'''m
 
 
The small negative rate of growth in the cash flow has reduced the total present value very substantially.
 
 
 
The growing / declining perpetuity concept is applied in many contexts.
 
For example, the Dividend growth model for share valuation.




== See also ==
== See also ==
* [[Annuity]]
* [[Issue]]
* [[Consol]]
* [[Placement]]
* [[Discounted cash flow]]
* [[Rule 144A]]
* [[Dividend growth model]]
* [[Secondary market]]
* [[Growing annuity]]
* [[Security]]
* [[Growing perpetuity]]
* [[Growing perpetuity factor]]
* [[Irredeemable]]
* [[Perpetuity due]]
* [[Perpetuity factor]]
* [[Simple annuity]]
 


==The Treasurer articles==
[[Media:2013_10_Oct_-_The_real_deal.pdf| The real deal, The Treasurer]]


''Real rates of corporate decline often lead to miscalculation, overpaying for acquisitions and disastrous losses.''
== ACT Website links ==


''Read this article to discover how to avoid the most common errors, and add value for your organisation.''
[http://www.treasurers.org/blogs/ceo/201307 Hot money just got hotter...then evaporated, Colin Tyler, 5 July 2013]


[[Category:Corporate_finance]]
[http://www.treasurers.org/node/8624 Developing a UK Private Placement market – report of the PP15+ working group]
[[Category:Long_term_funding]]

Revision as of 14:37, 1 October 2013

This is a form of securities issuance that has no exact definition.

It usually refers to an issue that has been designed for a specific set of investor needs at a particular time.

As such it is not expected to be traded in the secondary market and is not a 'public' issue.

It is not normally expected to be listed on an exchange.

A wide variety of securities under various names are private placements. In Germany, Schuldschein are a form of private placements, for example.


See also


ACT Website links

Hot money just got hotter...then evaporated, Colin Tyler, 5 July 2013

Developing a UK Private Placement market – report of the PP15+ working group