If projects are mutually exclusive, only one project can be chosen. The internal
ID: 2798150 • Letter: I
Question
If projects are mutually exclusive, only one project can be chosen. The internal rate of return (IRR) and the net present value (NPV) methods will not always choose the same project. If the crossover rate on the NPV profile is below the horizontal axis, the methods will agree. Projects Y and z are mutually exclusive projects. Their cash flows and NPV profiles are shown as follows. NPV (Dollars) $200 Year Project Y Project z 0 -$1,500 -$1,500 1 $200 $900 2 $400 $600 $600 $300 4 $1,000 $200 Project Y Project Z . If the weighted average cost of capital (WACC) for each project is 14%, do the NPV and IRR methods agree or conflict? O The methods conflict. O The methods agree. -2001 0 2 4 6 8 10 12 14 16 18 20 COST OF CAPITAL (Percent)Explanation / Answer
If the cross rate on the NPV profile is below the horizontal axis, the method will sometime agree.
Because, We need to choose only one project from the two mutually exclusive projects. The IRR and NPV methods always will not choose the same project due to timing and size of the project.
The correct option is the methods agree.
Explanation:
The main conflict between NPV and IRR methods are timing and size differences between mutually exclusive projectss.
Here, we can see that the project Y’s cash ows occur late in the project's life ($1,500 / $2,200 = 68.18% occurring in the last two years), whereas the bulk of project Z’s cash ows occur relatively early in the project’s life ($1,500/ $2,000 = 75.0% occurring in the rst two years).
Thus, Project Y has greater undiscounted cash ows, but most of its cash ows occur further into the future.
Based on the required rate of return ,If return increases then project Y’s NPV decreases at a far greater rate than project Z’s NPV.
Cash flows
PV of cash flows
Year
Project Y
Project Z
Discounting factor at 14%
Project Y
Project Z
0
-1500
-1500
1
-1500
-1500
1
200
900
0.877192982
175.438596
789.4736842
2
400
600
0.769467528
307.787011
461.6805171
3
600
300
0.674971516
404.98291
202.4914549
4
1000
200
0.592080277
592.080277
118.4160555
-19.711205
72.06171163
At a required rate of retum of 14%, project Z has a higher NPV because its NPV prole is higher than project Y's NPV prole. Therefore, NPV method would choose project Z over project Y.
When comes to IRR for project Y it is 13% and for project Z it is 17%.
Therefore, the NPV and IRR methods agree with each other.
A key to resolving this conict is the assumed reinvestment rate. The NPV calculation implicitly assumes that intermediate cash ows are reinvested at the required rate of return , and the IRR calculation assumes that the rate at which cash ows can be reinvested is the internal rate of return (IRR).
As a result, when evaluating mutually exclusive projects, the NPV method is usually the better decision criterion.
Cash flows
PV of cash flows
Year
Project Y
Project Z
Discounting factor at 14%
Project Y
Project Z
0
-1500
-1500
1
-1500
-1500
1
200
900
0.877192982
175.438596
789.4736842
2
400
600
0.769467528
307.787011
461.6805171
3
600
300
0.674971516
404.98291
202.4914549
4
1000
200
0.592080277
592.080277
118.4160555
-19.711205
72.06171163
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