CFA® Level 1: CFA® Level 1 - Mutually Exclusive Projects NPV Profiles

Which NPV Profile Corresponds to Each Project?

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Question

Your assistant has just completed an analysis of two mutually exclusive projects. You must now take her report to a board of directors meeting and present the alternatives for the board's consideration. To help you with your presentation, your assistant also constructed a graph with NPV profiles for the two projects.

However, she forgot to label the profiles, so you do not know which line applies to which project. Of the following statements regarding the profiles, which one is most reasonable?

Answers

A. If one of the projects has a NPV profile which crosses the X-axis twice, hence the project appears to have two IRRs, your assistant must have made a mistake.

B. If the two projects' NPV profiles cross once, in the upper left quadrant, at a discount rate of minus 10 percent, then there will probably not be a NPV versus IRR conflict, irrespective of the relative sizes of the two projects, in any meaningful, practical sense (that is, a conflict which will affect the actual investment decision).

C. If the two projects both have a single outlay at t = 0, followed by a series of positive cash inflows, and if their NPV profiles cross in the lower left quadrant, then one of the projects should be accepted. Both would be accepted if they were not mutually exclusive.

D. Whenever a conflict between NPV and IRR exist, then, if the two projects have the same initial cost, the one with the steeper NPV profile probably has less rapid cash flows. However, if they have identical cash flow patterns, then the one with the steeper profile probably has the lower initial cost.

E. If the two projects have the same investment cost, and if their NPV profiles cross once in the upper right quadrant, at a discount rate of 40 percent, this suggests that a NPV versus IRR conflict is not likely to exist.

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Explanations

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A. B. C. D. E.

A conflict will exist if the cost of capital is less than the crossover rate. In this case the cost of capital must be greater than minus 10 percent and, therefore, there will probably not be a NPV versus IRR conflict.

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