Internal rate of return and Lender of last resort: Difference between pages

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(IRR).  
A concession given to a select number of financial institutions whereby their central bank agrees to provide them with funds if they should get into [[liquidity]] difficulties.


The primary purpose of the activity by the central bank is stability of the financial system as a whole.


== Definition of IRR ==
Secondarily, the purpose is stability of the particular institution affected.


The internal rate of return of a set of cash flows is the [[cost of capital]] which, when applied to discount all of the cash flows (including any initial investment flow at Time 0) results in a Net Present Value ([[NPV]]) of NIL.


For an investor, the IRR of an investment proposal therefore represents their expected rate of [[return]] on their investment in the project.
Central banks generally avoid risk taking behaviour.  


Accordingly, in principle, the central banks only lend against good security ([[collateral]]) and with a conservative [[haircut]].


'''Example'''
In practice, liquidity shortage may force a bank to seek to dispose of assets, even at significant losses that erode its capital.


A project requires an investment today of $100m, with $110m being receivable one year from now.
Eventually the central bank may lend against less-good collateral and with less than its desired haircut on collateral valuation - until it won't, when the game is over and the story becomes one of [[resolution]].


The IRR of this project is 10%, because that is the cost of capital which results in an NPV of $0, as follows:


Lender of last resort activity is more recently often referred to as emergency liquidity assistance.


[[PV]] of Time 0 outflow $100m
The European Central Bank's scheme is called Emergency Liquidity Assistance (ELA), for example.
 
= $(100m)
 
 
PV of Time 1 inflow $110m
 
= $110m x 1.1<sup>-1</sup>
 
= $100m
 
 
NPV = - $100m + $100m
 
= '''$0'''.
 
 
 
== Determining IRR ==
 
 
Unless the pattern of cash flows is very simple, it is normally only possible to determine IRR by trial and error (iterative) methods.
 
 
'''Example'''
 
Using straight line interpolation and the following data:
 
First estimated rate of return 5%, positive NPV = $+4m.
 
Second estimated rate of return 6%, negative NPV = $-4m.
 
The straight-line-interpolated estimated IRR is the mid-point between 5% and 6%.
 
This is '''5.5%'''.
 
 
Using iteration, the straight-line estimation process could then be repeated, using the value of 5.5% to recalculate the NPV, and so on.
 
The IRR function in Excel uses a similar trial and error method.
 
 
 
== IRR project analysis decision rule ==
 
 
In simple IRR project analysis the decision rule would be that:
 
(1) All opportunities with above the required IRR should be accepted.
 
(2) All other opportunities should be rejected.
 
 
However this assumes the unlimited availability of further capital with no increase in the cost of capital.
 
 
A more refined decision rule is that:
 
(1) All opportunities with IRRs BELOW the required IRR should still be REJECTED; while
 
(2) All other opportunities remain eligible for further consideration (rather than automatically being accepted).




== See also ==
== See also ==
* [[CertFMM]]
* [[Central bank]]
* [[Effective interest rate]]
* [[Hurdle rate]]
* [[Implied rate of interest]]
* [[Interpolation]]
* [[Iteration]]
* [[Linear interpolation]]
* [[Market yield]]
* [[Net present value]]
* [[Present value]]
* [[Shareholder value]]
* [[Yield to maturity]]

Revision as of 20:36, 3 June 2014

A concession given to a select number of financial institutions whereby their central bank agrees to provide them with funds if they should get into liquidity difficulties.

The primary purpose of the activity by the central bank is stability of the financial system as a whole.

Secondarily, the purpose is stability of the particular institution affected.


Central banks generally avoid risk taking behaviour.

Accordingly, in principle, the central banks only lend against good security (collateral) and with a conservative haircut.

In practice, liquidity shortage may force a bank to seek to dispose of assets, even at significant losses that erode its capital.

Eventually the central bank may lend against less-good collateral and with less than its desired haircut on collateral valuation - until it won't, when the game is over and the story becomes one of resolution.


Lender of last resort activity is more recently often referred to as emergency liquidity assistance.

The European Central Bank's scheme is called Emergency Liquidity Assistance (ELA), for example.


See also

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