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=
I $12,950
Since this project generates $1.31 for each dollar invested (i.e., its profitability index is greater than l),accept the
project.
8.4 MUTUALLY EXCLUSIVE INVESTMENTS
A project is said to be mutually exclusive if the acceptance of one project automatically excludes
the acceptance of one or more other projects. In the case where one must choose between mutually
exclusive investments, the NPV and IRR methods may result in contradictory indications. The
conditions under which contradictory rankings can occur are:
1. Projects that have different life expectancies.
2. Projects that have different sizes of investment.
3. Projects whose cash flows differ over time. For example, the cash flows of one project increase
over time, while those of another decrease.
The contradictions result from different assumptions with respect to the reinvestment rate on cash
flows from the projects.
1. The NPV method discounts all cash flows at the cost of capital, thus implicitly assuming that
these cash flows can be reinvested at this rate.
2. The IRR method implies a reinvestment rate at IRR.Thus, the implied reinvestment rate will
differ from project to project.
The NPV method generally gives correct ranking, since the cost of capital is a more realistic
reinvestment rate.
EXAMPLE 8.12 Assume the following:
Cash Flows
1 4
3
2
0 5
(loo) 120
A
B 201.14
(100)
Computing IRR and NPV at 10 percent gives the following different rankings:
NPV at 10%
IRR
A 9.01
20%
15%
B 24.90
The NPVs plotted against the appropriate discount rates form a graph called a NPV profile
(Fig. 81).
208 [CHAP. 8
CAPITAL BUDGETING (INCLUDING LEASING)
Fig. 81 NPV profile
At a discount rate larger than 14 percent, A has a higher NPV than B.Therefore, A should be
selected. At a discount rate less than 14 percent, B has the higher NPV than A, and thus should be
selected. The correct decision is to select the project with the higher NPV, since the NPV method
assumes a more realistic reinvestment rate, that is, the cost of capital.
8.5 THE MODIFIED INTERNAL RATE OF RETURN (MIRR)
When the IRR and NPV methods produce a contradictory ranking for mutual exclusive projects,
the modified IRR, or MIRR, overcomes the disadvantage of IRR.
The MIRR is defined as the discount rate which forces
I = PV of terminal (future) value compounded at the cost of capital
The MIRR forces cash flow reinvestment at the cost of capital rather than the project's own IRR, which
was the problem with the IRR.
1. MIRR avoids the problem of multiple IRRs.
2. Conflicts can still occur in ranking mutually exclusive projects with differing sizes. NPV should
again be used in such a case.
EXAMPLE 8.13 In Example 18.12, Project A's MIRR is:
First, compute the project's terminal value at a 10% cost of capital.
120 FVIFIO,, 12 X 1.4641 = 175.69
=
Next, find the IRR by setting:
100 = 175.69 PVIFM1RR.S
PVIF = 100/175.69 = 0.5692, which gives MIRR = about 12%
Now we see the consistent ranking from both the NPV and MIRR methods.
209
CHAP. 81 CAPITAL BUDGETING (INCLUDING LEASING)
8.6 COMPARING PROJECTS WITH UNEQUAL LIVES
A replacement decision typically involving two mutually exclusive projects. When these two
mutually exclusive projects have significantly different lives, an adjustment would be necessary. We
discuss two approaches: (1) the replacement chain (common life) approach and (2) the equivalent
annual annuity approach.
The Replacement Chain (Common Life) Approach
This procedure extends one, or both, projects until an equal life is achieved. For example, Project
A has a 6year life, while Project B has a 3year life. Under this approach, the projects would be extended
to a common life of 6 years. Project B would have an adjusted NPV equal to the NPVBplus the NPVB
discounted for 3 years at the projectâ€™s cost of capital. Then the project with the higher NPV would be
chosen.
EXAMPLE 8.14 Sims Industries, Inc. is considering two machines to replace an old machine. Machine A has a
life of 10 years, will cost $24,500, and will produce net cash savings of $4,800 per year. Machine B has an expected
life of 5 years, will cost $20,000, and will produce net cash savings in operating costs of $6,000 per year. The
companyâ€™s cost of capital is 14 percent. Project Aâ€™s NPV is
= PV  I = $4,800 PVIFA10,14 $24,500
NPVA
= $4,800(5.2161)  $24,500 = $25,037.28  $24,500
= $537.28
Project Bâ€™s extended time line can be set up as follows:
0 4 6 8 9
5
1 2 7
3 10
60 60
60
200 60 60 60 60 60 60 60 (in hundredths)
200

Adjusted NPVB = PV  I = $6,000 PVIFAIo,14 $20,000 PVIF5,14 $20,000 PVIF5,14 $20,000
 
= $6,000(5.2161)  $20,000(0.5194)  $20,000
= $31,296.60  $10,388.00  $20,000
= $908.60
Or, alternatively,
NPVB = PV  I = $6,000 PVIFAs.14  $20,000
= $6,000(3.4331)  $20,000
= $20,598.60  $20,000
= $598.60
Adjusted NPVB = NPVB + NPVB discounted for 5 years
= $598.60 + $598.60 PVIF5.14
= $598.60 + $598.60(0.5194)
= $598.60 + $310.91
= $909.51 (due to rounding errors)
CAPITAL BUDGETING (INCLUDING LEASING)
210 [CHAP. 8
The Equivalent Annual Annuity (EAA) Approach
It is often cumbersome to compare projects with different lives. For example, one project might have
a 4year life versus a 10year life for the other. This would require a replacement chain analysis over 20
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