© 2000 John Petroff 

4)- Mutually exclusive projects of different size

 

The general rule is that NPV assures wealth maximization. But, when one project is larger than another, and it has the larger NPV, it is necessary to inquire if the cash flow difference between the projects is put to good use. The question arises only in the context of mutually exclusive projects, and only when it is the larger project that has the larger NPV. When projects are not mutually exclusive, naturally, all projects with positive NPV are chosen. Yet, projects that are not initially mutually exclusive can become such when capital rationing is present. The general analysis of capital rationing is undertaken next. Here, we look at the specific issue of how to handle all cases of choosing between mutually exclusive projects that have
different sizes. Several methods come to mind:
a)- bringing both projects to same size
b)- calculating NPV on the difference between the two projects
c)- using PI
Bringing both projects to the same size, while mathematically appealing but complicated, is only appropriate if duplicating the smaller project is actually possible. Calculating NPV on the difference is straightforward and implies that if the difference is worth accepting that implies that the larger project is superior. Some textbooks recommend using PI, but it will be shown below that PI does not give the correct solution.

To illustrate the methods of analysis we take project 1 and project 2. They are not mutually exclusive in the description of the case, but they may be as a result of capital rationing. In Table T-10.6, the intranet project has a higher IRR and PI, but the conveyor project has a higher NPV. In Table T-10.9 below the difference between annual cash flows is calculated and shown in the third column.

Table T-10.9

Comparison of projects (1 and 2) of different size 
. Conveyor Intranet Difference
. 1 2 =1-2

Beta

 0.8 0.9 0.8

Discount rate

 0.092 0.096 0.092
IRR 10% 13% 10%
PI

 1.05

 1.21

 1.02
NPV $67.09 $34.30 $28.42
ANVP $3.35 $2.45 $1.42
2000 -1450 -180 -1270
2001 250 30 220
2002 200 30 170
2003 200 30 170
2004 200 30 170
2005 200 30 170
2006 200 30 170
2007 200 30 170
2008 200 30 170
2009 200 30 170
2010 100 30 70
2011 100 30 70
2012 100 30 70
2013 100 30 70
2014 100 - 100
2215 100 - 100
2016 100 - 100
2017 100 - 100
2018 100 - 100
2019 100 - 100

This difference can be thought of as a separate additional third project that allows a comparison of the first two. The projects have different lives, but using the annualized NPV is not necessary because we only need to determine if we should accept undertaking the difference. Table T-10.9 shows that the difference has a positive NPV and annualized NPV. This implies that this third project should be chosen, which is tantamount to choosing project 1.

By contrast, to the conclusion above, Table T-10.10 below uses the same presentation to compare projects 1 and 8.

Table T-10.10

 Comparison of projects (1 and 8) with different size
. Conveyor New prod1 Difference
. 1 8 =1-8
Beta 0.8 1.9 0.8
Discount rate 0.092 0.136 0.092
IRR 11% 16% 8%
NPV $109.02 $47.76 ($54.31)
ANVP $5.45 $6.82 ($2.72)
2000 -1450 -500 -950
2001 300 5 295
2002 200 15 185
2003 200 50 150
2004 200 100 100
2005 200 400 -200
2006 200 500 -300
2007 200 - 200
2008 200 - 200
2009 200 - 200
2010 100 - 100
2011 100 - 100
2012 100 - 100
2013 100 - 100
2014 100 - 100
2215 100 - 100
2016 100 - 100
2017 100 - 100
2018 100 - 100
2019 100 - 100

 

As can be seen in Table T-10.10, the difference produces a negative NPV, which means that it should not be accepted. This means that is project 1 not superior to project 8.

See review questions Q-10E4.1 through Q-10E4.3.

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