Question

Calculate the profitability index for a project that costs 100,000 and will result in the following cashflows over a 5-year period: 5,000, 10,000, 15,000, 20,000, 25,000. Assume a discount rate of 5%.

Answer 1

To calculate the profitability index, present values of the future cash flows are determined using the discount rate and then summed. The sum of the present values is divided by the initial investment to find the profitability index, which in this case is 0.6329.

Step-by-step explanation:

The calculation of the profitability index (PI) requires finding the present value of future cash flows and comparing it to the initial investment. To do this, we use the formula for present value (PV) for each year's cash flow and then sum them up. The formula for PV is PV = Cash Flow / (1 + r)^t, where 'r' is the discount rate and 't' is the time period.

Calculating Present Value of Future Cash Flows

Year 1: PV = $5,000 / (1 + 0.05)^1 = $4,761.90

1. Year 2: PV = $10,000 / (1 + 0.05)^2 = $9,070.29
2. Year 3: PV = $15,000 / (1 + 0.05)^3 = $13,090.45
3. Year 4: PV = $20,000 / (1 + 0.05)^4 = $16,783.53
4. Year 5: PV = $25,000 / (1 + 0.05)^5 = $19,582.15

After calculating the present value of each year's cash flow, we add them up to find the total present value of the cash flows, which is: $4,761.90 + $9,070.29 + $13,090.45 + $16,783.53 + $19,582.15 = $63,288.32

Calculating the Profitability Index

Finally, to find the profitability index, we divide the total present value of future cash flows by the initial investment: PI = $63,288.32 / $100,000 = 0.6329. Since the PI is less than 1, it suggests that the project may not be a good investment under the given conditions.