Perpetuity and Reputational risk: Difference between pages

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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.


For example, as a result of adverse publicity.


2. '''Fixed perpetuity'''


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.


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


==See also==
*[[Compliance risk]]
*[[Ethics]]
*[[Franchise viability risk]]
*[[Media risk]]
*[[Operational risk]]
*[[Working capital management]]


where:
[[Category:Financial_risk_management]]
 
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 ==
* [[Annuity]]
* [[Dividend growth model]]
* [[Growing annuity]]
* [[Growing perpetuity]]
* [[Irredeemable]]
* [[Perpetuity due]]
* [[Perpetuity factor]]
* [[Simple annuity]]
 
==Student article==
[[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.''
 
''Read this article to discover how to avoid the most common errors and add value for your organisation.''
 
[[Category:Corporate_finance]]
[[Category:Long_term_funding]]

Revision as of 09:29, 20 November 2019

1.

The risk of adverse consequences arising from a worsening of the reputation of a business.

For example, as a result of adverse publicity.


2.

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.


See also