Final answer:
The profitability index will be bigger than one for a negative npv investment and less than one for a positive npv investment.
Step-by-step explanation:
The statement is true. The profitability index is a financial ratio that measures the value of an investment by comparing the present value of its cash inflows to the present value of its cash outflows. The profitability index of an investment can be calculated by dividing the present value of the cash inflows by the present value of the cash outflows.
If the NPV of an investment is positive, it means that the present value of the cash inflows is greater than the present value of the cash outflows, indicating a profitable investment. In this case, the profitability index will be larger than one, as the numerator (present value of cash inflows) is greater than the denominator (present value of cash outflows).
Conversely, if the NPV of an investment is negative, it means that the present value of the cash inflows is less than the present value of the cash outflows, indicating an unprofitable investment. In this case, the profitability index will be less than one, as the numerator (present value of cash inflows) is smaller than the denominator (present value of cash outflows).