EURIBOR and Perpetuity: Difference between pages

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(Euro Interbank Offered Rate).
1. ''Valuation.''


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


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.
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.


2. ''Fixed perpetuity.''


Also written 'Euribor'.
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.


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


==Contributing rate estimates==


Since September 2013, the panel of banks contributing to Euribor is made up of 32 banks though it has been larger in the past.
where:


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").
A<sub>1</sub> = Time 1 cash flow


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.
r = periodic cost of capital


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


<span style="color:#4B0082">'''Example 1: Fixed perpetuity valuation'''</span>


==Euribor calculation==
Time 1 cash flow = $10m, continuing at the same amount each period thereafter in perpetuity.


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.
Periodic cost of capital = 5%


Thomson Reuters is the screen service provider responsible for computing and also publishing Euribor.
The present value of the fixed perpetuity is:


The Euribor process is overseen by a [http://www.euribor-ebf.eu/euribor-org/steering-committee.html Steering Committee].
= $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 ==
* [[Benchmark]]
* [[Annuity]]
* [[EONIA]]
* [[Consol]]
* [[Euro LIBOR]]
* [[Discounted cash flow]]
* [[European Money Markets Institute]]
* [[Dividend growth model]]
* [[InterBank Offered Rate]]
* [[Growing annuity]]
* [[LIBOR]]
* [[Growing perpetuity]]
* [[TIBOR]]
* [[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.''
 
''Read this article to discover how to avoid the most common errors, and add value for your organisation.''


[[Category:Manage_risks]]
[[Category:Corporate_finance]]
[[Category:Long_term_funding]]

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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