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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 вЂњhigh-

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margin, low volumeвЂќ strategy and a вЂњlow-margin, high-volumeвЂќ 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 вЂ“

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 вЂ“ 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. в˜ћ: 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 вЂ“ 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 вЂ“вЂ“ 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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