Question

6. Understanding the NPV profile

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 W and X are mutually exclusive projects. Their cash flows and NPV profiles are shown as follows.

Year	Project W	Project X
0	–$1,000	–$1,500
1	$200	$350
2	$350	$500
3	$400	$600
4	$600	$750

  

If the weighted average cost of capital (WACC) for each project is 10%, do the NPV and IRR methods agree or conflict?

The methods conflict.

The methods agree.

A key to resolving this conflict is the assumed reinvestment rate. The NPV calculation implicitly assumes that intermediate cash flows are reinvested at the   , and the IRR calculation assumes that the rate at which cash flows can be reinvested is the   .

As a result, when evaluating mutually exclusive projects, the    is usually the better decision criterion.

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Answer 1

If the crossover rate on the NPV profile is below the horizontal axis, the methods will always agree.

The NPV =PV of inflows -Initial outflow

The NPV can be computed using the excel function=NPV()

The IRR can be computed using the excel function=IRR()

The NPV of Project W can be computed using the formula=NPV(10%,B3:B6)+B2 we get NPV as $181.41

The NPV of Project X can be computed using the formula=NPV(10%,C3:C6)+C2 we get NPV as $194.45

The IRR of Project W can be computed using the formula=IRR(B2:B6) we get IRR as 16.85%

The IRR of Project X can be computed using the formula=IRR(C2:C6) we get IRR as 15.17%

From the aforementioned values we can see that the NPV and IRR methods conflict

A key to resolving this conflict is the assumed reinvestment rate. The NPV calculation implicitly assumes that intermediate cash flows are reinvested at the WACC(or cost of capital) , and the IRR calculation assumes that the rate at which cash flows can be reinvested is the IRR.

As a result, when evaluating mutually exclusive projects, the NPV(Net Present Value)    is usually the better decision criterion.