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Question:

# A company prepares a chart with the net present value (NPV) profiles for two mutually exclusive projects with equal lives of five years. Project Jones and Project Smith have the same initial cash outflow and total undiscounted cash inflows, but 75% of the cash inflows for Project Jones occur in years 1 and 2, while 75% of the cash inflows for Project Smith occur in years 4 and 5. Which of the following statements is most accurate regarding these projects?

A There is a range of discount rates in which the optimal decision is to reject both projects.
explanation

If the total undiscounted cash flows from two projects arc equal, their NPV profiles intersect the vertical axis at the same value. The NPV profile will have a steeper slope for Project Smith, which has more of its cash inflows occurring later in its life, and therefore the IRR of Project Smith (its intersection with the horizontal axis) must be less than the IRR of Project Jones. The NPV for Project Jones will be greater at any rate of discount, and Project Jones will be preferred over the entire range. However, if the discount rate applied to the cash flows is greater than the IRR of Project Jones, both projects will have negative NPVs and the company should reject both of them.