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      • CFA Institute members have access to the curriculum free of charge by downloading Refresher Readings, which are also eligible for Professional Learning (PL) credit. Members may also buy the print curriculum by ordering through Wiley or one of their retail partners.
      www.cfainstitute.org/en/programs/cfa/curriculum/print-version
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    • Net Present Value
    • Internal Rate of Return
    • Graphical Illustration
    • Npv and IRR Comparison
    • Multiple IRR and No IRR Problem
    • Shortcomings of IRR

    The net present value (NPV) of a project is the potential change in wealth resulting from the project after accounting for the time value of money. The NPV for a project with one investment outlay made at the start of the project is defined as the present value of the future after-tax cash flows minus the investment outlay. Where: = After-tax cash ...

    The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of all cash flows from a particular project equal to zero. For a project with one initial outlay, the IRR is the discount rate that makes the present value of the future after-tax cash flows equal to the investment outlay. The IRR solves the equation: It l...

    The NPV Profile is a graphical illustration of a project’s NPV graphed as a function of various discount rates. The NPV values are graphed on the vertical or y-axis, while the discount rates are graphed on the horizontal or x-axis. 1. The graph crosses the y-axis (vertical axis) when the discount rate = 0%; and 1. The graph crosses the x-axis (hori...

    For independent, conventional projects, the decision rules for the NPV and IRR will both draw the same conclusion on whether to invest or not. However, in the case of two mutually exclusive projects, sometimes the decision rules will draw different conclusions. For example, project X might have a larger NPV than project Y, but project Y might have ...

    It is quite possible, although rare, for a project to have more than one IRR or no IRR at all. Multiple IRRs, however, cannot occur for conventional projects which have outlay followed by cash inflows, but they may occur for non-conventional projects which have cash flows which change signs (negative, positive) more than once during the project’s l...

    As seen, there are some problems associated with the IRR method: 1. The method assumes that all proceeds from a project are immediately reinvested in projects offering a rate of return equal to the IRR – this is very difficult in practice. 1. It gives different rankings when the projects under comparison have different scales. 1. Sometimes, the met...

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