IRR is the discount rate at which the NPV of the project is zero. If the IRR is less than the cost of capital, the project’s NPV will be negative, even though IRR is positive. Thus, both statements 3 and 4 are correct.
If the NPV and IRR methods give conflicting decisions for mutually exclusive projects, the project with greatest positive NPV should be selected. A project cannot have positive NPV if its IRR is less than the cost of capital. Thus, statements 1 and 2 are incorrect.