Which of the following statements is incorrect?
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A. B. C. D. E.Explanation
NPV is positive if IRR is greater than the cost of capital.
Let's go through each statement and determine which one is incorrect:
A. NPV can be negative if the IRR is positive. This statement is correct. NPV stands for Net Present Value, which is a measure of the profitability of an investment. It calculates the difference between the present value of cash inflows and the present value of cash outflows. If the cash inflows are less than the cash outflows, the NPV will be negative. The IRR (Internal Rate of Return) is the discount rate that makes the NPV of an investment equal to zero. It is possible for the IRR to be positive while the NPV is negative.
B. Assuming a project has normal cash flows, the NPV will be positive if the IRR is less than the cost of capital. This statement is correct. In general, if a project has normal cash flows (an initial cash outflow followed by positive cash inflows), the NPV will be positive if the IRR is less than the cost of capital. The cost of capital represents the required rate of return for an investment, taking into account the risk and opportunity cost of capital. If the IRR is lower than the cost of capital, it means the project's return is not sufficient to meet the required rate of return, and therefore the NPV will be positive.
C. If IRR = k (the cost of capital), then NPV = 0. This statement is correct. When the IRR of an investment is equal to the cost of capital (k), the NPV will be zero. This implies that the present value of cash inflows equals the present value of cash outflows, resulting in no net gain or loss.
D. If the multiple IRR problem does not exist, any independent project acceptable by the NPV method will also be acceptable by the IRR method. This statement is correct. The multiple IRR problem occurs when a project has unconventional cash flow patterns, such as both positive and negative cash flows or multiple sign changes in cash flows. In such cases, the IRR method may yield multiple IRRs or no real IRR at all. However, if the multiple IRR problem does not exist, meaning the cash flows are conventional and the IRR is unique, any independent project that is acceptable by the NPV method will also be acceptable by the IRR method.
E. The NPV method is not affected by the multiple IRR problem. This statement is incorrect. The NPV method is affected by the multiple IRR problem. As mentioned earlier, the multiple IRR problem occurs when a project has unconventional cash flow patterns. In such cases, the IRR method may yield multiple IRRs or no real IRR at all, which can lead to difficulties in decision-making. On the other hand, the NPV method is not affected by this problem and remains a reliable measure for evaluating investment opportunities.
Therefore, the incorrect statement is E. The NPV method is affected by the multiple IRR problem.