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assumed reinvested at the IRR,Example,Consider the following project:,The internal rate of return for this project is about 19.44%.,If we graph NPV versus the discount rate, we can see the IRR as the xaxis intercept.,Consider the following three projects available to a firm:,Please calculate the internal rate of return for each project.,Example,Problems with IRR,Investing or Financing? Multiple IRRs The Scale Problem The Timing Problem,Independent and Mutually Exclusive Projects,Mutually Exclusive vs. Independent,Mutually Exclusive Projects: only ONE of several potential projects can be chosen RANK all alternatives, and select the best one. Independent Projects: accepting or rejecting one project does not affect the decision of the other projects Must exceed a MINIMUM acceptance criteria,Two General Problems Affecting Both Independent and Mutually Exclusive Projects,Problem1: Investing or Financing?,The NPV of project A is negatively related to the discount rate. The NPV of project B is positively related to the discount rate. Projects with more than one change of sign can have multiple rates of return.,Some conclusions of the example,Investing projects Accept if IRR is more than market (discount) rate Reject if IRR is less than market (discount) rate Financing projects Accept if IRR is less than market (discount) rate Reject if IRR is more than market (discount) rate Mixture projects Can have multiple IRRs Should use NPV rule or MIRR method,Modified IRR,Calculate the net present value of all cash outflows using the given discount rate. Calculate the net future value of all cash inflows using the given discount rate. Find the rate of return that equates the