What is the profitability index for the cash flows if the relevant discount rate is 24 percent?

To calculate the profitability index, you need to know the cash flows of the project. The profitability index is calculated as the present value of future cash flows divided by the initial investment.

Here are the steps to calculate the profitability index:

1. Identify the cash flows: You need to know the initial investment (which is usually a cash outflow or a negative cash flow) and the future cash flows (which are usually cash inflows or positive cash flows).

2. Calculate the present value of future cash flows: You discount the future cash flows back to the present using the discount rate. The formula to calculate the present value (PV) is:

   PV = CF / (1 + r)^n

   where:

   • CF is the cash flow in the future,
   • r is the discount rate (in this case, 24 percent or 0.24), and
   • n is the number of periods.

   You do this for each future cash flow and then sum them up.

3. Calculate the profitability index: Finally, you divide the present value of future cash flows by the absolute value of the initial investment. The formula is:

   Profitability Index = PV of future cash flows / |Initial Investment|

If the profitability index is greater than 1, the project may be a good investment. If it's less than 1, the project may not be a good investment.

Please note that this is a simplified explanation. In reality, the calculation could be more complex, depending on the specifics of the cash flows and the project.