If the project is a financing project, the decision rule for accepting the project is to accept the project when the IRR is less than the discount rate1.

For both independent and mutually projects, when the project's cash flows exhibit two or more changes of sign, the project has more than one IRR. In theory, a cash flow stream with M changes in sign can have up to M positive internal rates of return. In a case like this, the IRR does not make any sense. Because there is no good reason to use one IRR over the other, IRR simply cannot be used here. On the contrary, there is only one NPV for a project regardless of changes of sign in the project's cash flows1.

For mutually exclusive projects, the problem with IRR is that it ignores issues of scale, resulting in the acceptance of the wrong project if the IRR is used as a decision criterion. Project 1 may have a higher IRR but the investment is smaller. Another project, project 2, may have a lower IRR but the investment is bigger. The high percentage on project 1 is more than offset by the ability to earn at least a decent return on a much bigger investment under project 2. Therefore, project 2 should be accepted. However, if IRR is used as the decision criterion, project 1 with a higher IRR will be accepted and project 2 will be rejected. The NPV does not have the scale problem. Using NPV as the decision criterion will result in the right decision to accept project 2 with a higher NPV1.

For mutually exclusive project, another problem with IRR is that it ignores issues of timing, resulting in the acceptance of the wrong project if the IRR is used as a decision criterion. The cash flows of project 1 occur early, whereas the cash flows of 2 occur later. If we assume a high discount rate, we favour investment 1 because we are implicitly assuming that the early cash flow can be reinvested at that rate. Because most of investment 2's cash flows occur in later years, investment 2's value is relatively high with low discount rates. Using the IRR as the decision criterion may result in the wrong investment being selected. The investment with the higher IRR will be selected regardless of the discount rate used. Using NPV as the decision criterion will result in the right decision to accept the project with the higher NPV1.

In conclusion, NPV is theoretically superior to IRR. The strengths of NPV are that NPV uses cash flows instead of earnings, NPV uses all the cash flows of the project, and NPV discounts the cash flows properly. IRR has flaws that are not applicable to NPV. For both independent and mutually exclusive projects, the problem is that some projects have cash inflows followed by one or more outflows. The IRR rule is inverted here, that is, one should accept when the IRR is below the discount rate. Another problem is some projects have a number of changes of sign in their cash flows. Here, there are likely to be multiple internal rates of return. The practitioner must use NPV here. For
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