Question

which of the following statements is correct?
if a project with normal cash flows has an irr greater than the wacc, the project must also have a positive npv.
if project a’s irr exceeds project b’s, then a must have the higher npv.
a project’s mirr can never exceed its irr.
if a project with normal cash flows has an irr less than the wacc, the project must have a positive npv.
if the npv is negative, the irr must also be negative.

Explanation:

• For the first statement: For a project with normal cash flows (initial outflow, subsequent inflows), the NPV profile is downward - sloping. The WACC is the discount rate used to calculate NPV. If IRR (Internal Rate of Return, the discount rate where NPV = 0) > WACC, then at the WACC (which is less than IRR), the NPV will be positive (since as the discount rate decreases from IRR to WACC, NPV increases from 0 to a positive value for normal cash - flow projects).
• For the second statement: IRR and NPV can give conflicting results, especially when projects are mutually exclusive and have different cash - flow patterns or scales. A project with a higher IRR may have a lower NPV if the cash - flow timing or the size of the cash flows differ. For example, a small project with a high IRR may have a lower NPV than a large project with a slightly lower IRR.
• For the third statement: For projects with non - normal cash flows (multiple sign changes in cash flows), the MIRR (Modified Internal Rate of Return) can exceed the IRR. Also, in some cases with normal cash flows, due to the reinvestment rate assumption (MIRR assumes reinvestment at WACC, IRR assumes reinvestment at IRR), MIRR can be higher than IRR.
• For the fourth statement: If IRR < WACC, then at the discount rate of WACC (which is higher than IRR), the NPV will be negative (since as the discount rate increases from IRR to WACC, NPV decreases from 0 to a negative value for normal cash - flow projects).
• For the fifth statement: A negative NPV means that the present value of inflows is less than the present value of outflows. The IRR is the rate at which NPV = 0. A negative NPV does not imply that IRR is negative. For example, if the WACC is 15% and the IRR is 10%, the NPV will be negative (because 10% < 15%), but the IRR (10%) is still positive.

Answer:

The correct statement is: If a project with normal cash flows has an IRR greater than the WACC, the project must also have a positive NPV.