Is MIRR as good as NPV for choosing between mutually exclusive projects? If two
projects are of equal size and have the same life, then NPV and MIRR will always lead
to the same decision. Thus, for any set of projects like our Projects S and L, if
NPVS NPVL, then MIRRSMIRRL, and the kinds of conflicts we encountered
between NPV and the regular IRR will not occur. Also, if the projects are of equal
size, but differ in lives, the MIRR will always lead to the same decision as the NPV if
the MIRRs are both calculated using as the terminal year the life of the longer project.
(Just fill in zeros for the shorter project’s missing cash flows.) However, if the projects
differ in size, then conflicts can still occur. For example, if we were choosing between
a large project and a small mutually exclusive one, then we might find NPVLNPVS,
but MIRRSMIRRL.
Our conclusion is that the MIRR is superior to the regular IRR as an indicator
o fa project’s “true” rate o freturn, or “expected long-term rate o freturn,” but the
NPV method is still the best way to choose among competing projects because it
provides the best indication o fhow much each project will add to the value o fthe firm.
Describe how the modified IRR (MIRR) is calculated.
What are the primary differences between the MIRR and the regular IRR?
What condition can cause the MIRR and NPV methods to produce conflicting
rankings?
Profitability Index
Another method used to evaluate projects is the profitability index (PI):
(7-3)
Here CFtrepresents the expected future cash flows, and CF 0 represents the initial cost.
The PI shows therelative profitability of any project, or the present value per dollar of
initial cost. The PI for Project S, based on a 10 percent cost of capital, is 1.079:
Thus, on a present value basis, Project S is expected to produce $1.079 for each $1 of
investment. Project L, with a PI of 1.049, should produce $1.049 for each dollar
invested.
A project is acceptable if its PI is greater than 1.0, and the higher the PI, the higher
the project’s ranking. Therefore, both S and L would be accepted by the PI criterion
if they were independent, and S would be ranked ahead of L if they were mutually
exclusive.
Mathematically, the NPV, IRR, MIRR, and PI methods will always lead to the
same accept/reject decisions for independentprojects: If a project’s NPV is positive, its
IRR and MIRR will always exceed r, and its PI will always be greater than 1.0. How-
ever, these methods can give conflicting rankings for mutually exclusiveprojects. This
point is discussed in more detail in the next section.
Explain how the PI is calculated. What does it measure?
PIS
$1,078.82
$1,000
1.079.
PI
PV of future cash flows
Initial cost
a
n
t 1
CFt
(1r)t
CF 0
.
276 CHAPTER 7 The Basics of Capital Budgeting: Evaluating Cash Flows
274 The Basics of Capital Budgeting: Evaluating Cash Flows
