Inflation and Internal rate of return: Difference between pages

From ACT Wiki
(Difference between pages)
Jump to navigationJump to search
imported>Doug Williamson
m (Categorise.)
 
imported>Doug Williamson
(Make 10% more visible and note that initial investment is a cash outflow.)
 
Line 1: Line 1:
1.  
(IRR).  


The rate at which prices are rising.


Usually measured in the UK by the Consumer Prices Index (CPI).
== Definition of IRR ==


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 outflow at Time 0) results in a Net Present Value ([[NPV]]) of NIL.


2.  
For an investor, the IRR of an investment proposal therefore represents their expected rate of [[return]] on their investment in the project.


A situation in which prices generally are rising. 


This is the usual situation in most developed economies at most times. 
'''Example 1'''


Contrasted with the less usual situation of Deflation, when prices generally are falling. However, very low - and negative - inflation has been more common in recent years.  For example, measured by the [[CPI]], UK inflation was negative in both September and October 2015.
A project requires an investment today of $100m, with $110m being receivable one year from now.


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


===Points to note===


We have taken inflation and deflation above as changes in "prices" or "prices generally" as if they have a clear meaning. But they raise the questions of "What prices?" and "What does generally mean?"
[[PV]] of Time 0 outflow $100m


Since the term was first used "inflations" have proliferated. Retail price inflation, consumer price inflation, services inflation, government sector inflation, health sector inflation, asset price inflation (house prices, vintage cars, industrial assets, etc.), wage inflation, and so on.
= $(100m)


And once we know what we are interested in, we need to define it more closely. What exact set of goods or services or assets precisely are we looking at? For each member of the set, how much weight do we give it in the basket - how do we weigh cream cakes against toothpaste? And if we include a device or a machine or a house, which precise type, model or design, and where bought?


And what if our selected type is no longer made, or even the whole product ceases to be relevant? For example in Europe, households no longer launder with wash-boards and mangles (relatively cheap, though requiring much manual labour) but with washing machines (relatively expensive, but with much less manual labour required). And bars of laundry soap have been replaced by "clever" detergents? Or consider a mega-byte memory - that industrial good that fitted on the back of a truck and was used only by the largest companies and governments against the litter of USB memory sticks in drawers in developed-country houses at the start of the 21st century. Adjusting for this effect is called hedonic adjustment - but any two people are likely to value changes differently: it has huge amounts of subjectivity.
PV of Time 1 inflow $110m


And how do we find out prices - read a catalogue, go to the village shop, look online, etc.?
= $110m x 1.10<sup>-1</sup>


So always have great suspicion of any calculated inflation index and ask yourself if it is the index best suited for what you have in mind - and don't apply it where it may be positively misleading.
= $100m


And the most general measure of inflation in an economy - the implied GDP deflator - doesn't that include everything and so is most relevant to its society as a whole at the time? Well, it makes an effort, but it has its own problems. It is the (percentage) difference between nominal and real growth - this year's GDP ([[Gross domestic product]]) at actual prices and this year's GDP at last year's prices. But estimating GDP is very hard, different methods producing different results.


Even what one should try to include in GDP is disputable. For example, if you employ a care-worker to look after a sick or infirm family member, the service provision is part of GDP. If one of the family does it, it is not. And what about the [[black economy]]? If you pay the just discussed care-worker in cash and don't tell the tax man, will that be included? So, for example, internationally in the early 21st century, GDP estimates are being changed to include the "value" of prostitution and illegal drug use as the discussion moves on.
NPV = - $100m + $100m


Surveys of the prices in each year are hard too and raise a lot of the same questions as discussed above.
= '''$0'''.


We are dividing an uncertain numerator by an uncertain denominator. So while the implied GDP deflator may be the best "general inflation" measure we have readily available, it should still be treated circumspectly.


Added to which, if we don't quite know what inflation is, we certainly have little idea of what the underlying causes of inflation are, though there are a lot of theories. The choice of underlying cause assumed in any article, speech or policy decision being perhaps as much an exercise in politics and wishful thinking as in economics.


For these reasons it is normally better to undertake forecasting in money terms, rather than in 'real' (inflation-adjusted) terms.  
== 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 2'''
 
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 ==
* [[Consumer Prices Index]]
* [[CertFMM]]
* [[Cost-push inflation]]
* [[Effective interest rate]]
* [[Crawling peg system]]
* [[Hurdle rate]]
* [[Deflation]]
* [[Implied rate of interest]]
* [[Demand-pull inflation]]
* [[Interpolation]]
* [[Financial stability]]
* [[Iteration]]
* [[Hyperinflation]]
* [[Linear interpolation]]
* [[Inflation risk]]
* [[Market yield]]
* [[Nominal]]
* [[Net present value]]
* [[Real]]
* [[Present value]]
* [[Recession]]
* [[Shareholder value]]
* [[Reflation]]
* [[Yield to maturity]]
* [[Stagflation]]
* [[Trade union policy]]
* [[Transmission mechanism]]
* [[Treasury inflation-indexed securities]]
* [[Underlying]]
 
[[Category:Financial_risk_management]]

Revision as of 22:01, 8 April 2015

(IRR).


Definition of IRR

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 outflow 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.


Example 1

A project requires an investment today of $100m, with $110m being receivable one year from now.

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


PV of Time 0 outflow $100m

= $(100m)


PV of Time 1 inflow $110m

= $110m x 1.10-1

= $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 2

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

Retrieved from ‘https://wiki.treasurers.org/w/index.php?title=Inflation&oldid=27947’