Final answer:
The profitability index cannot be calculated without specific cash flow data for each year and the discount rate. The question provided includes information unrelated to the calculation of a profitability index, such as investment opportunities with their probabilities and returns, which suggests there is an error in the question.
Step-by-step explanation:
The question is asking about the calculation of the profitability index of an investment project. The profitability index is a tool used in capital budgeting to determine the desirability of an investment. It is calculated by dividing the present value of future cash flows by the initial investment amount.
In order to calculate the profitability index, one needs information about the project's cash flows for each period, which includes years 0 through 4 in this case, and the required rate of return or discount rate. The example provided does not give enough information about the cash flows or the discount rate to calculate the profitability index. Instead, it discusses potential investments with associated probabilities and potential returns.
To respond directly to the question, we would need the specific cash flows for each year and the discount rate. Since those are not provided, and given that the question includes unrelated information about different investment opportunities with their probabilities and returns,
we can deduce that there might be an error or misunderstanding in the question. Therefore, it is not possible to provide an accurate profitability index for the investment in question without the necessary details.
As an educational note, the provided examples illustrate how to construct probability distribution functions (PDF) for different investment returns and calculate an expected rate of return for each investment. This involves a different process than calculating a profitability index.