Final answer:
The profitability index of project B is determined by calculating the present value of each future cash flow using the discount rate, summing these values to get the total PDV, and then dividing by the initial investment of $73.
Step-by-step explanation:
The profitability index (PI) of a project is a capital budgeting metric used to assess the attractiveness of an investment opportunity. It is calculated by dividing the present discounted value (PDV) of future cash flows of the project by the initial investment required. To calculate the PI for project B, we must first determine the present value of each future cash flow using the formula presented in Table C1, and then sum these up to find the total PDV of the project. After finding the PDV, we divide it by the initial cost of project B to get the PI.
Here's how we calculate each year's present value using the discount rate of 15%:
- Year 1: Present Value = $30 / (1 + 0.15)^1
- Year 2: Present Value = $30 / (1 + 0.15)^2
- Year 3: Present Value = $30 / (1 + 0.15)^3
- Year 4: Present Value = $30 / (1 + 0.15)^4
Add up all the present values for the different time periods to obtain the total PDV of project B. Finally, divide this total PDV by the initial investment of $73 to find the PI for project B:
Profitability Index = Total PDV of Future Cash Flows / Initial Investment
Calculating this for project B should provide a PI that is closest to one of the given options: 0.12, 12.04, 0.17, or 21.65.