Inflation and Internal rate of return: Difference between pages

From ACT Wiki
(Difference between pages)
Jump to navigationJump to search
imported>Doug Williamson
(Add link.)
 
imported>Doug Williamson
(Remove surplus wording.)
 
Line 1: Line 1:
1.  
(IRR).  


The rate at which prices are rising.


Usually measured in the UK by the Consumer Prices Index (CPI).
== Definitions of internal rate of return (IRR) ==


IRR is a percentage summary of the cash flows of a project, for example, an IRR of 10%.


2.  
The IRR summarises the timing, as well as the amounts, of the cashflows.


A situation in which prices generally are rising. 


This is the usual situation in most developed economies at most times.
For an investor, the IRR of an investment proposal represents their expected rate of [[return]] on their investment in the project.


Contrasted with the less usual situation of Deflation, when prices generally are falling. However, for example, measured by the [[CPI]], UK inflation was negative in both September and October 2015.
A greater IRR is normally more attractive for an investor.




===Points to note===
The IRR is driven by the expected future cash flows from the project.


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 the questions of "What prices?" and "What does generally mean?"


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.
The IRR of a set of cash flows is:


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?
:the [[cost of capital]] which,  


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.
:when applied to discount all of the cash flows,


And how do we find out prices - read a catalogue, go to the village shop, look online, etc.?
:including any initial investment outflow at Time 0,


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.
:results in a [[net present value]] (NPV) of 0.


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.
<span style="color:#4B0082">'''Example 1: IRR'''</span>


Surveys of the prices in each year are hard too and raise a lot of the same questions as discussed above.
A project requires an investment today of $100m, with $110m being receivable one year from now.


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


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.  
[[PV]] of Time 0 outflow $100m
 
= $(100m)
 
 
PV of Time 1 inflow $110m
 
= $110m x 1.10<sup>-1</sup>
 
= $100m
 
 
NPV = - $100m + $100m
 
= '''$0'''.
 
 
If the project had been funded by borrowing all the required money at the IRR of 10%, there would have been exactly the right amount of profit from the project to repay the borrowing and interest, with neither a deficit nor a surplus.
 
This is another way to define the IRR.
 
 
== Project decision making with IRR ==
 
 
Target or required IRRs are set based on the investor's [[weighted average cost of capital]], appropriately adjusted for the risk of the proposal under review.
 
In very 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).
 
 
== 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.
 
 
<span style="color:#4B0082">'''Example 2: Straight line interpolation'''</span>
 
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.
 


== See also ==
== See also ==
* [[Consumer Prices Index]]
* [[Effective interest rate]]
* [[Cost-push inflation]]
* [[Hurdle rate]]
* [[Crawling peg system]]
* [[IBR]]
* [[Deflation]]
* [[Implied rate of interest]]
* [[Demand-pull inflation]]
* [[Interpolation]]
* [[Inflation risk]]
* [[IRI]]
* [[Real]]
* [[Iteration]]
* [[Stagflation]]
* [[Linear interpolation]]
* [[Transmission mechanism]]
* [[Market yield]]
* [[Treasury inflation-indexed securities]]
* [[Net present value]]
* [[Present value]]
* [[Return on investment]]
* [[Shareholder value]]
* [[Weighted average cost of capital]]
* [[Yield to maturity]]
 
[[Category:Investment]]
[[Category:Cash_management]]

Revision as of 16:38, 26 February 2019

(IRR).


Definitions of internal rate of return (IRR)

IRR is a percentage summary of the cash flows of a project, for example, an IRR of 10%.

The IRR summarises the timing, as well as the amounts, of the cashflows.


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

A greater IRR is normally more attractive for an investor.


The IRR is driven by the expected future cash flows from the project.


The IRR 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 0.


Example 1: IRR

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.


If the project had been funded by borrowing all the required money at the IRR of 10%, there would have been exactly the right amount of profit from the project to repay the borrowing and interest, with neither a deficit nor a surplus.

This is another way to define the IRR.


Project decision making with IRR

Target or required IRRs are set based on the investor's weighted average cost of capital, appropriately adjusted for the risk of the proposal under review.

In very 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).


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: Straight line interpolation

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.


See also

Retrieved from ‘https://wiki.treasurers.org/w/index.php?title=Inflation&oldid=27970’