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LOS e: Explain the NPV profile, compare and contrast the NPV and IRR methods when evaluating independent and mutually exclusive projects, and describe the problems associated with each of the evaluation methods.

If the calculated net present value (NPV) is negative, which of the following must be CORRECT. The discount rate used is:

A)	less than the internal rate of return (IRR).

B)	greater than the internal rate of return (IRR).

C)	equal to the internal rate of return (IRR).

When the NPV = 0, this means the discount rate used is equal to the IRR. If a discount rate is used that is higher than the IRR, the NPV will be negative. Conversely, if a discount rate is used that is lower than the IRR, the NPV will be positive.

A)	one should accept all independent projects with positive NPVs.

B)	the NPV profile's intersection with the vertical y-axis identifies the project's internal rate of return.

C)	one should accept all mutually exclusive projects with positive NPVs.

Where the NPV intersects the vertical y-axis you have the value of the cash inflows less the cash outflows, assuming an absence of money having a time value (i.e., the discount rate is zero). Where the NPV intersects the horizontal x-axis you have the project’s internal rate of return. At this cost of financing, the cash inflows and cash outflows offset each other. The NPV profile is a tool that graphically plots the project’s NPV as calculated using different discount rates. Assuming an appropriate discount rate, one should accept all projects with positive net present values, if the projects are independent. If projects are mutually exclusive select the one with the higher NPV at any given level of the cost of capital.

The NPV profile is a graphical representation of the change in net present value relative to a change in the:

As discount rates change the net present values change. The NPV profile is a graphic illustration of how sensitive net present values are to different discount rates. By comparison, every project has a single internal rate of return and payback period because the values are determined solely by the investment’s expected cash flows.

Which of the following statements about the internal rate of return (IRR) and net present value (NPV) is least accurate?

A)	The discount rate that causes the project's NPV to be equal to zero is the project's IRR.

B)	The IRR is the discount rate that equates the present value of the cash inflows with the present value of the outflows.

C)	For mutually exclusive projects, if the NPV rankings and the IRR rankings give conflicting signals, you should select the project with the higher IRR.

The NPV method is always preferred over the IRR, because the NPV method assumes cash flows are reinvested at the cost of capital. Conversely, the IRR assumes cash flows can be reinvested at the IRR. The IRR is not an actual market rate.

Which of the following is the most appropriate decision rule for mutually exclusive projects?

A)	Accept the project with the highest net present value, subject to the condition that its net present value is greater than zero.

B)	Accept both projects if their internal rates of return exceed the firm’s hurdle rate.

C)	If the net present value method and the internal rate of return method give conflicting signals, select the project with the highest internal rate of return.

Which of the following statements about independent projects is least accurate?

A)	If the internal rate of return is less than the cost of capital, reject the project.

B)	The net present value indicates how much the value of the firm will change if the project is accepted.

C)	The internal rate of return and net present value methods can yield different accept/reject decisions for independent projects.

For independent projects the IRR and NPV give the same accept/reject decision. For mutually exclusive projects the IRR and NPV techniques can yield different accept/reject decisions.

Which of the following statements regarding the net present value (NPV) and internal rate of return (IRR) is least accurate?

A)	For independent projects, the internal rate of return IRR and the NPV methods always yield the same accept/reject decisions.

B)	For mutually exclusive projects, you must accept the project with the highest NPV regardless of the sign of the NPV calculation.

C)	The NPV tells how much the value of the firm will increase if you accept the project.

The underlying cause of ranking conflicts between the net present value (NPV) and internal rate of return (IRR) methods is the underlying assumption related to the:

The IRR method assumes all future cash flows can be reinvested at the IRR. This may not be feasible because the IRR is not based on market rates. The NPV method uses the weighted average cost of capital (WACC) as the appropriate discount rate.

A)	The IRR can be positive even if the NPV is negative.

B)	When the IRR is equal to the cost of capital, the NPV equals zero.

C)	The NPV will be positive if the IRR is less than the cost of capital.

This statement should read, "The NPV will be positive if the IRR is greater than the cost of capital. The other statements are correct. The IRR can be positive (>0), but less than the cost of capital, thus resulting in a negative NPV. One definition of the IRR is the rate of return for which the NPV of a project is zero.

Which of the following statements about the internal rate of return (IRR) for a project with the following cash flow pattern is CORRECT?

A)	No IRRs can be calculated.

B)	It has a single IRR of approximately 38%.

C)	It has two IRRs of approximately 38% and 260%.

The number of IRRs equals the number of changes in the sign of the cash flow. In this case, from negative to positive and then back to negative. Although 38% seems appropriate, one should not automatically discount the value of 260%.

Check answers by calculation:

10,000 ÷ 1.38 - 10,000 ÷ 1.38² = 1995.38

And:

10,000 ÷ 3.6 - 10,000 ÷ 3.6² = 2006.17

Both discount rates give NPVs of approximately zero and thus, are IRRs.

If a project has a negative cash flow during its life or at the end of its life, the project most likely has:

A)	a negative internal rate of return.

B)	more than one internal rate of return.

C)	multiple net present values.

Projects with unconventional cash flows (where the sign of the cash flow changes from minus to plus to back to minus) will have multiple internal rates of return. However, one will still be able to calculate a single net present value for the cash flow pattern.

Which of the following statements regarding the internal rate of return (IRR) is most accurate? The IRR:

A)	can lead to multiple IRR rates if the cash flows extend past the payback period.

B)	and the net present value (NPV) method lead to the same accept/reject decision for independent projects.

C)	assumes that the reinvestment rate of the cash flows is the cost of capital.

NPV and IRR lead to the same decision for independent projects, not necessarily for mutually exclusive projects. IRR assumes that cash flows are reinvested at the IRR rate. IRR does not ignore time value of money (the payback period does), and the investor may find multiple IRRs if there are sign changes after time zero (i.e., negative cash flows after time zero).