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CHAPTER 6

PROJECT INTERACTIONS, SIDE COSTS AND SIDE BENEFITS
In much of our discussion so far, we have assessed projects independently of
other projects that the firm already has or might have in the future. Disney, for instance,
was able to look at the theme park investment and analyze whether it was a good or bad
investment. In reality, projects at most firms have interdependencies with and
consequences for other projects. Disney may be able to increase both movie and
merchandise revenues because of the new theme park in Bangkok and may face higher
advertising expenditures because of its Asia expansion.
In this chapter, we examine a number of scenarios in which the consideration of
one project affects other projects. We start with the most extreme case, where investing in
one project leads to the rejection of one or more other projects; this is the case when
firms have to choose between mutually exclusive investments. We then consider a less
extreme scenario, where a firm with constraints on how much capital it can raise
considers a new project. Accepting this project reduces the capital available for other
projects that the firm considers later in the period and thus can affect their acceptance;
this is the case of capital rationing.
Projects can create costs for existing investments by using shared resources or
excess capacity, and we consider these side costs next. Projects sometimes generate
benefits for other projects, and we analyze how to bring these benefits into the analysis.
In the final part of the chapter, we introduce the notion that projects often have options
embedded in them, and that ignoring these options can result in poor project decisions.

Mutually Exclusive Projects
Projects are mutually exclusive when only one of the set of projects can be
accepted by a firm. Projects may be mutually exclusive for different reasons. They may
each provide a way of getting a needed service, but any one of them is sufficient for the
service. The owner of a commercial building may be choosing among a number of
different air-conditioning or heating systems for a building. Or, projects may provide
alternative approaches to the future of a firm; a firm that has to choose between a “high-
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margin, low volume” strategy and a “low-margin, high-volume” strategy for a product
can choose only one of the two.
In choosing among mutually exclusive projects, we continue to use the same rules
we developed for analyzing independent projects. The firm should choose the project that
adds the most to its value. While this concept is relatively straightforward when the
projects are expected to generate cash flows for the same number of periods (have the
same project life), as you will see, it can become more complicated when the projects
have different lives.

Projects with Equal Lives
When comparing projects with the same lives, a business can make its decision in
one of two ways. It can compute the net present value of each project and choose the one
with the highest positive net present value (if the projects generate revenue) or the one
with the lowest negative net present value (if the projects minimize costs). Alternatively,
it can compute the differential cash flow between two projects and base its decision on
the net present value or the internal rate of return of the differential cash flow.

Comparing Net Present Values
The simplest way of choosing among mutually exclusive projects with equal lives
is to compute the net present values of the projects and choose the one with the highest
net present value. This decision rule is consistent with firm value maximization.

Illustration 6.1: Mutually Exclusive Cost Minimizing Projects with equal lives
Bookscape is choosing between alternative vendors who are offering phone
systems. Both systems have 5-year lives, and the appropriate cost of capital is 10% for
both projects. Figure 6.1 summarizes the expected cash outflows on the two investments:
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Figure 6.1: Cash Flows on Phone Systems
Vendor 1: Less Expensive System
-$ 8000 -$ 8000 -$ 8000 -$ 8000 -$ 8000
0 1 2 3 4 5


-$20,000
Vendor 2: More Expensive System
-$ 3000 -$ 3000 -$ 3000 -$ 3000 $ 3000
0 1 2 3 4 5


-$30,000
The more expensive system is also more efficient, resulting in lower annual costs. The
net present values of these two systems can be estimated as follows “
Net Present Value of Less Expensive System = - $20,000 - $8,000 [PV(A,10%,5 years)]
= - $50,326
Net Present Value of More Expensive System = - $30,000 - $3,000 [PV(A,10%,5 years)]
= - $41,372
The net present value of all costs is much lower with the second system making it the
better choice.

Differential Cash Flows
An alternative approach for choosing between two mutually exclusive projects is
to compute the difference in cash flows each period between the two investments being
compared. Thus, if A and B are mutually exclusive projects with estimated cash flows
over the same life time (n), the differential cash flows can be computed as shown in
Figure 6.2.
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Figure 6.2: Estimating Differential Cash Flows

Project A

CF4,A .....
CF1,A CF2,A CF3,A CFn,A

CF0,A


Project B

CF1,B CF2,B CF3,B CF4,B .... CFn,B


CF0,B
Differential Cash Flow

CF... -
CF1,B - CF2,B - CF4,B - CFn,B -
3,B
CF1,A CF2,A CF3,A CF4,A CFn,A


CF0,B -
CF0,A
In computing the differential cash flows, the project with the larger initial investment
becomes the project against which the comparison is made. In practical terms, this means
that the Cash FlowB-A is computed if B has a higher initial investment than A, and the
Cash FlowA-B is computed if A has a higher initial investment than B. If we compare
more than two projects, we still compare one pair at a time, and the less attractive project
is dropped at each stage.
The differential cash flows can be used to compute the net present value and the
decision rule can be summarized as follows:
If NPVB-A > 0 : Project B is better than project A
NPVB-A< 0 : Project A is better than project B
Notice two points about the differential net present value. The first is that it provides the
same result as would have been obtained if the business had computed net present values
of the individual projects and then taken the difference between them.
NPVB-A = NPVB “ NPVA
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The second is that this approach works only when the two projects being compared have
the same risk level and discount rates, since only one discount rate can be used on the
differential cash flows. By contrast, computing project-specific net present allows for the
use of different discount rates on each project.
The differential cash flows can also be used to compute an internal rate of return,
which can guide us to select the better project.
If IRRB-A > Discount Rate : Project B is better than project A
IRRB-A< Discount Rate : Project A is better than project B
Again, this approach works only if the projects are of equivalent risk.


6.1. ˜: Mutually exclusive projects with different risk levels
When comparing mutually exclusive projects with different risk levels and discount rates,
what discount rate should we use to discount the differential cash flows?
a. The higher of the two discount rates
b. The lower of the two discount rates
c. An average of the two discount rates
d. None of the above
Explain your answer.

Illustration 6.2: Differential Cash Flows “ NPV and IRR
Consider again the phone systems analyzed in illustration 6.1. The differential
cash flows can be estimated as shown in Figure 6.3:
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Figure 6.3: Cash Flows on Phone Systems

Vendor 1: Less Expensive System

- $ 8000 - $ 8000 - $ 8000 - $ 8000 - $ 8000
0 1 2 3 4 5


-$20,000
Vendor 2: More Expensive System
- $ 3000 - $ 3000 - $ 3000 - $ 3000 - $ 3000
0 1 2 3 4 5


-$30,000
Differential Cash Flows: More Expensive - Less Expensive System
+ $ 5000 + $ 5000 + $ 5000 + $ 5000 + $ 5000
0 1 2 3 4 5


-$10,000

The more expensive system costs $10,000 more to install but saves Bookscape $5,000 a
year. Using the 10% discount rate, we estimate the net present value of the differential
cash flows as follows:
Net Present Value of Differential Cash Flows = - $10,000 + $5,000 [PV(A,10%,5 years)]
= + $8,954
This net present value is equal to the difference between the net present values of the
individual projects, and it indicates that the system that costs more up front is also the
better system from the viewpoint of net present value. The internal rate of return of the
differential cash flows is 41.04%, which is higher than the discount rate of 10%, once
again suggesting that the more expensive system is the better one, from a financial
standpoint.

Projects with Different Lives
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In many cases, firms have to choose among projects with different lives1. In doing
so, they can no longer rely solely on the net present value. This is so because, as a dollar
figure, the NPV is likely to be higher for longer term projects; the net present value of a
project with only 2 years of cash flows is likely to be lower than one with 30 years of
cash flows.
Assume that you are choosing between a 5-year and a 10-year project, with the
cash flows shown in Figure 6.4. A discount rate of 12% applies for each.
Figure 6.4: Cash Flows on Projects with Unequal Lives

Shorter Life Project

$400 $400 $400 $400 $400

3 5
4
1 2
0


-$1000
Longer Life Project
$350 $350 $350 $350 $350
$350 $350 $350 $350 $350
3 5
4
1 2 8
6 10
0 7 9


-$1500
The net present value of the first project is $442, while the net present value of the second
project is $478. On the basis on net present value alone, the second project is better, but
this analysis fails to factor in the additional net present value that could be made by the
firm from years 6 to 10 in the project with a 5-year life.
In comparing a project with a shorter life to one with a longer life, the firm must
consider that it will be able to invest again with the shorter term project. Two
conventional approaches - project replication and equivalent annuities ““ assume that
when the current project ends, the firm will be able to invest in the same project or a very
similar one.

Project Replication


1 See Emery (1982).
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One way of tackling the problem of different lives is to assume that projects can
be replicated until they have the same lives. Thus, instead of comparing a 5-year to a 10-
year project, we can find the net present value of investing in the 5-year project twice and
comparing it to the net present value of the 10-year project. Figure 6.5 presents the
resulting cashflows:
Figure 6.5: Cash Flows on Projects with Unequal Lives: Replicated with poorer project
Five-year Project: Replicated
$400 $400 $400 $400 $400 $400 $400 $400 $400 $400
3 5
4
1 2 8
6 10
0 7 9


-$1000 -$1000 (Replication)
Longer Life Project
$350 $350 $350 $350 $350

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