Evaluate a project requiring an initial investment of $200,000 with expected cash inflows of $50,000 annually for 5 years. Use a discount rate of 10% to determine the profitability index (PI). Discuss what the PI indicates about the project's attractiveness and how it compares to other capital budgeting metrics like NPV and IRR. Calculate the NPV of the project and explain the relationship between PI and NPV. Analyze the advantages of using PI, particularly when dealing with capital rationing and comparing projects of different sizes. Consider the impact of varying discount rates on the PI and NPV, and explain how sensitivity analysis can help in understanding the risk associated with the project. Discuss the strategic implications of the PI for investment decision-making, particularly in a scenario where the company has limited capital resources and multiple competing projects.