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Page 26
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
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)
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.

Page 27

Page 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

Page 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
Could use some op8misa8on technique (LP)
Major issue: all projects are not of the same risk!
Do not recommend this method!

Page 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
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
Add adjustable con8ngency amounts to projects to
use up cash
Use an LP solu8on aNer discarding the <MARR list

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