Exchange and Perpetuity: Difference between pages

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1. ''Investment - trading.''
1. ''Valuation.''


A traditional exchange is an open and organised marketplace in which commodities, securities or other financial instruments are traded.
A series of cash flows modelled to carry on for an infinite amount of time in the future.


Examples include stock exchanges such as the London Stock Exchange.


2. ''Fixed perpetuity.''


2. ''Investment - trading - other intermediaries.''
A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter.


More broadly, any intermediary that facilitates a broad range of economic activities, and including intermediaries that may be less well-organised, and less secure for participants.
Each cash flow is an equal fixed amount.


For example, cryptoasset exchanges.
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


3. ''Foreign currency.''


Relating to transactions between different currencies.
where:


A<sub>1</sub> = Time 1 cash flow


4. ''Financial and commercial transactions.''
r = periodic cost of capital


Relating to a two-way flow of money or other value.


Contrasted with a one-way flow, such as a remittance.
<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 ==
* [[Commodity]]
* [[Annuity]]
* [[Cryptoasset exchange]]
* [[Consol]]
* [[Exchange controls]]
* [[Discounted cash flow]]
* [[Exchange creditors]]
* [[Dividend growth model]]
* [[Exchange-for-value system]]
* [[Growing annuity]]
* [[Exchange rate]]
* [[Growing perpetuity]]
* [[Exchange traded]]
* [[Growing perpetuity factor]]
* [[Exchange Traded Commodity]]
* [[Irredeemable]]
* [[Exchange-traded funds]]
* [[Perpetuity due]]
* [[Financial instrument]]
* [[Perpetuity factor]]
* [[Foreign currency]]
* [[Simple annuity]]
* [[Foreign exchange]]
 
* [[Intermediary]]
 
* [[Remittance]]
==The Treasurer articles==
* [[Security]]
[[Media:2013_10_Oct_-_The_real_deal.pdf| The real deal, The Treasurer]]
* [[Stock exchange]]
 
* [[World Federation of Exchanges]]
''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:The_business_context]]
[[Category:Corporate_finance]]
[[Category:Investment]]
[[Category:Long_term_funding]]
[[Category:Financial_products_and_markets]]

Latest revision as of 13:25, 12 June 2021

1. Valuation.

A series of cash flows modelled to carry on for an infinite amount of time in the future.


2. Fixed perpetuity.

A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter.

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 = A1 x 1/r


where:

A1 = Time 1 cash flow

r = periodic cost of capital


Example 1: Fixed perpetuity valuation

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

= $200m


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 = A1 x 1 / (r - g)

where g = the periodic rate of growth of the cash flow.


Example 2: Growing perpetuity valuation

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:

= A1 x 1 / (r - g)

= $10m x (1 / (0.05 - 0.02) )

= $10m x (1 / 0.03)

= $10m x 33.3

= $333m


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:


Example 3: Declining perpetuity valuation

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:

= A1 x 1 / (r - g)

= $10m x (1 / (0.05 - -0.02) )

= $10m x (1 / 0.07)

= $10m x 14.3

= $143m


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


The Treasurer articles

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.

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