EURIBOR and Perpetuity: Difference between pages

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''Reference rates.''
1. ''Valuation.''


(Euro Interbank Offered Rate).
A series of cash flows modelled to carry on for an infinite amount of time in the future.


Sponsored by the European Money Markets Institute ([https://www.emmi-benchmarks.eu/ EMMI]),  EURIBOR® is a formal benchmark or reference interest rate launched in 1998.


2. ''Fixed perpetuity.''


It estimates the all-in, simple interest rate (including credit premium and liquidity premium) at which euro denominated interbank term deposits for spot value (T+2) are offered within the euro-zone by one prime bank to another prime bank in the period before 10.45 [[CET]] each business morning.
A fixed perpetuity is a periodic cash flow starting one period in the future, then carrying on for ever thereafter.
EURIBOR is calculated for periods ranging from one day to one year. It is quoted to three decimal places and on an actual/360 day-count.


Each cash flow is an equal fixed amount.


Also written 'Euribor'.
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


EMMI continuously reviews the basis of EURIBOR, striving to improve it.


where:


:<span style="color:#4B0082">'''''Robust fallback language for EURIBOR'''''</span>
A<sub>1</sub> = Time 1 cash flow


:"... the working group on euro risk-free rates has been working extensively to identify best practices for contract robustness in contracts and financial instruments referencing EURIBOR.
r = periodic cost of capital


:Although EURIBOR is not scheduled to be discontinued, the development of more robust fallback language addressing the permanent discontinuation of EURIBOR can help to enhance legal certainty and reduce the risks stemming from the worst-case scenario and, at the same time, comply with the EU Benchmark Regulation (BMR), when applicable."


:''Recommendations by the working group on euro risk-free rates - European Central Bank - 11 May 2021 - p2''
<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%


'''Contributing rate estimates'''
The present value of the fixed perpetuity is:


Since 2013, a panel of banks contribute to the Euribor. The panel is made up of:
= $10m x (1 / 0.05)


* Banks from EU countries participating in the euro from the outset.
= $10m x 20
* Banks from EU countries not participating in the euro from the outset.
* Large international banks from non-EU countries but with important euro zone operations.


= $'''200'''m


The banks submit their estimate, to two decimal places, of the rate "at which euro interbank term deposits are being offered within the Eurozone by one prime bank to another at 11 am Brussels time" ("the best price between the best banks").


This is similar to the question for [[LIBOR]] contributing banks prior to reform of LIBOR in 1998 to improve accountability of contributing banks for the submitted rate.


EMMI publishes a [http://www.euribor-ebf.eu/assets/files/Euribor_code_conduct.pdf code of conduct] for contributing banks.
3. ''Growing perpetuity.''


A growing perpetuity is an infinite series of cash flows, modelled to grow by a constant proportionate amount every period.


'''Euribor calculation'''
For a growing perpetuity, the present value formula is modified to take account of the constant periodic growth rate, as follows:


In calculating the Euribor from the submitted rates, the highest and lowest 15% of submitted rates are ignored and the central 70% remaining is averaged and published to 3 decimal places.
Present Value = A<sub>1</sub> x 1 / (r - g)


Thomson Reuters is the screen service provider responsible for computing and also publishing Euribor.
where g = the periodic rate of growth of the cash flow.


The Euribor process is overseen by a [http://www.euribor-ebf.eu/euribor-org/steering-committee.html Steering Committee].
 
<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 ==
* [[Benchmark]]
* [[Annuity]]
* [[Benchmarks Regulation]] (BMR)
* [[Consol]]
* [[Bloomberg]]
* [[Discounted cash flow]]
* [[Contract]]
* [[Dividend growth model]]
* [[EONIA]]
* [[Growing annuity]]
* [[€STR]]
* [[Growing perpetuity]]
* [[Euro LIBOR]]
* [[Growing perpetuity factor]]
* [[European Central Bank]]
* [[Irredeemable]]
* [[European Money Markets Institute]]
* [[Perpetuity due]]
* [[Fallback]]
* [[Perpetuity factor]]
* [[Financial instrument]]
* [[Simple annuity]]
* [[InterBank Offered Rate]]
 
* [[LIBOR]]
 
* [[Panel]]
==The Treasurer articles==
* [[Panel bank]]
[[Media:2013_10_Oct_-_The_real_deal.pdf| The real deal, The Treasurer]]
* [[Reference rate]]
* [[Reuters]]
* [[Risk-free rates]]
* [[TIBOR]]


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


==External link==
''Read this article to discover how to avoid the most common errors, and add value for your organisation.''
*[https://www.ecb.europa.eu/pub/pdf/other/ecb.recommendationsEURIBORfallbacktriggereventsandESTR.202105~9e859b5aa7.en.pdf Recommendations by the working group on euro risk-free rates on EURIBOR fallback trigger events and €STR-based EURIBOR fallback rates - European Central Bank - 11 May 2021]


[[Category:Accounting,_tax_and_regulation]]
[[Category:Corporate_finance]]
[[Category:The_business_context]]
[[Category:Long_term_funding]]
[[Category:Manage_risks]]

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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