Final answer:
The net present value (NPV) of the project with an investment cost of $900,000 and a profitability index of 0.2 is calculated to be negative $720,000, indicating the project is not currently profitable.
Step-by-step explanation:
The net present value (NPV) of a project can be determined by using its profitability index (PI). The profitability index is calculated by dividing the present value of future cash flows (PV) by the initial investment cost (C0). Since the profitability index provided is 0.2 and we have an investment cost of $900,000, we can rearrange the formula to solve for the net present value.
The formula for the profitability index is PI = PV / C0, which rearranges to PV = PI * C0. Plugging in the values, we get PV = 0.2 * $900,000, which equals $180,000. However, this $180,000 is the present value of the benefits (return), not the NPV. The NPV is calculated by subtracting the initial cost from the present value of benefits: NPV = PV - C0. Therefore, NPV = $180,000 - $900,000, which equals -$720,000.
Hence, the NPV of the project is negative $720,000, indicating that the project does not currently return the initial investment under these conditions, thus it may not be a profitable venture.