$1.$ XYZ Energy Inc is considering investing in a renewable energy project. The project requires an initial investment of $$5,000,000$ and is expected to generate the following cash flows over its lifetime:

Year $1$: $$1,000,000$ Year $2$: $$1,500,000$ Year $3$: $$2,000,000$ Year $4$: $$2,500,000$ Year $5$: $$3,000,000$

The company's cost of capital is $12\%.$

$1.$ Calculate the Net Present Value $($NPV$)$ for the renewable energy project.

$2.$ Use the Internal Rate of Return $($IRR$)$ and Profitability Index to complement the NPV analysis.

$3.$ Perform a sensitivity analysis to assess the project's robustness to changes in key assumptions, such as cash flow projections and discount rates.

$4.$ Provide a recommendation to XYZ Energy Inc on whether to proceed with the renewable energy project based on the comprehensive evaluation.