CFA CFA Level 1 NPV/IRR Generalities – Question

NPV/IRR Generalities – Question

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  • mbnmichael17
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    Can someone please translate this into English for me? Thanks!

    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) Project Smith has a higher internal rate of return than Project Jones.
    B) There is a range of discount rates in which the optimal decision is to reject both projects.
    C) There is a range of discount rates in which the company should choose Project Jones and a range in which it should choose Project Smith.
    Your answer: C was incorrect. The correct answer was B) There is a range of discount rates in which the optimal decision is to reject both projects.

    Here is the answer:

    If the total undiscounted cash flows from two projects are 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.

    mitch895
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    Hi there, the best way to approach this question is to scratch out the answers that we know are not correct.

    As project Smith has its cash flows happening later in life, we know that it is going to have a lower IRR than project Jones. This is because IRR assumes reinvestment of cash flows. Therefore we can rule out “A” as the correct answer.

    Second, looking at option B. Quite obviously there will be levels at which both projects will fail to justify their investment, and there will also be levels at which their return (whether measured by IRR or NPV) will justify making the investment. Also, as the projects are mutually exclusive, we can say that there will be times when neither project justifies their investment, and at other times we will only select one of the projects. Therefore answer “B” looks pretty good so far….

    But to confirm, let’s look at answer C: the trick here is to remember that the projects are mutually exclusive AND they have the same cash flows (just spread out at different times). Because of this we will always choose either to not invest (if the IRR

    mbnmichael17
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    Very helpful. It’s amazing that questions like these hinge on one detail, in this case the fact that the further out cash flows are that a project receives, the lower the IRR.

    bostonCFA2014
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    The key to this question (and not a minor detail conceptually) is the timing of the CF’s given a constant discount rate. Since we know these are mutually exclusive projects w/ the same cumulative CF’s, the project w/ earlier cash flows will always have a greater PV.

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