Which of the following statements is false?
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A. B. C. D. E.D
If the IRR is less than the cost of capital, then taking on the project imposes a cost on current stockholders. If the cost of capital is greater than the IRR, the NPV will be negative.
Let's analyze each statement to determine which one is false:
A. When IRR = k (the cost of capital), NPV = 0. This statement is true. The internal rate of return (IRR) is the discount rate that makes the net present value (NPV) of an investment equal to zero. So, when the IRR is equal to the cost of capital (k), the NPV will be zero.
B. 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 true. The multiple IRR problem occurs when a project's cash flows have more than one sign change, resulting in multiple IRR values. However, if the multiple IRR problem does not exist, any project with a positive net present value (NPV) will also have a positive internal rate of return (IRR), and vice versa. In other words, if a project's NPV is positive, it means that the project's IRR is greater than the cost of capital, making it acceptable by both methods.
C. The IRR can be positive even if the NPV is negative. This statement is true. The internal rate of return (IRR) represents the discount rate at which the present value of cash inflows equals the present value of cash outflows. It is possible for the IRR to be positive even if the net present value (NPV) is negative. This situation arises when the cash outflows are relatively large in the earlier periods but are followed by significant cash inflows in the later periods. In such cases, the IRR may still be positive, indicating a potential return on investment, but the NPV may be negative because the present value of the cash outflows outweighs the present value of the cash inflows.
D. The NPV will be positive if the IRR is less than the cost of capital. This statement is true. The net present value (NPV) is positive when the internal rate of return (IRR) is greater than the cost of capital. If the IRR is less than the cost of capital, it implies that the project's cash flows are not generating returns sufficient to cover the required rate of return. Therefore, the NPV will be negative.
E. The NPV method is not affected by the multiple IRR problem. This statement is false. The multiple IRR problem can affect the NPV method. As mentioned earlier, the multiple IRR problem occurs when a project's cash flows have more than one sign change. This situation leads to multiple IRR values, making it challenging to determine the appropriate discount rate to use. The NPV method relies on a single discount rate, and in the presence of multiple IRRs, it becomes difficult to interpret and evaluate the project's profitability accurately.
Based on the analysis above, the false statement is:
E. The NPV method is not affected by the multiple IRR problem.