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11ComparisonMethods2PDF.pdf-Centre for Management of Technology and
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When to Use ERR
ERR (approximate or precise) must be used when there
are mul8ple IRRs possible.
Usually, it is diﬃcult to predict when mul8ple IRRs
occur
Fortunately, most real life projects are structured in a
way that prevents mul8ple IRRs
Simple Investments
typically consist of several in (out)
ﬂows at the start and then several periods of out (in)
ﬂows.
No IRR diﬃcul8es for these projects
An approximate ERR will always provide a conserva8ve
answer because it is less than the real ERR and IRR
Nevertheless, it is desirable to compute the IRR
whenever possible and use an approximate ERR to
check the answer from a mul8ple root IRR calcula8on.

27

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28
IRR Comparisons
We have two types of situa8ons where IRR will
be used to compare projects
INDEPENDENT projects are when a ﬁrm/
government has a number of projects which
could be acceptable at the same 8me, but,
BUDGETS and MARR limit which ones to accept,
and more than one may be accepted
MUTUALLY EXCLUSIVE projects are those when
only ONE project can be accepted.
Clearly, investments which do not produce at
least MARR or exceed the available budget for
capital projects are not acceptable

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29
"Finding" MARR using IRR for
Independent Projects & Budget
In many cases, especially in large ﬁrms, the MARR is set at
corporate oﬃces and the budget may s8ll have cash leN aNer the
projects are selected
But equally, there may be projects leN aNer all the budget is used
up and this case, the last project accepted "deﬁnes" the de facto
MARR for the ﬁrm  aNer all, any other project must be be\er than
the last one accepted
We assume investment, not loan cash ﬂow pa\erns
rank the projects in their IRR order, but all must be >MARR (Corp)
calculate cumula8ve First Costs as projects are added to the list
keep comparing the above balance to the budget constraint
when you get to the end of the budget, you have found the MARR FOR
THAT SET OF PROJECTS ONLY.
Could use some op8misa8on technique (LP)
Major issue: all projects are not of the same risk!
Do not recommend this method!

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30
The Reﬁnery Case of MARR Selec8on
Assume MARR = 15% and Budget = \$1,000,000
The solu8on now as follows:
Start by adding the project with the largest IRR (Proj
A)
Con8nue un8l either MARR is reached or the last one
won't ﬁt the budget (B,C,D, etc.)
Juggle projects with IRR>MARR to ﬁt into money if any
leN over
Adjust scope of projects or budgets to ﬁt
use up cash
Use an LP solu8on aNer discarding the <MARR list

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