As a financial analyst for Greenwood Corporation, you have been assigned to assess the viability of two potential projects, Project Alpha and Project Beta. Both projects have an expected lifespan of $5$ years and will involve initial capital expenditures, changes in net working capital, and operational revenues and costs. Your task is to calculate the Net Present Value $($NPV$)$ and Profitability Index $($PI$)$ for each project and provide a recommendation. You are also required to explain under what circumstances the PI should be preferred over the NPV for project selection.

Project Financials:

$$ Project Alpha:

$$ Initial Capital Expenditure $($CapEx$)$: $$400,000$

$$ Annual Revenue: $$200,000$

$$ Annual Operational Cost $($excluding depreciation$)$: $$100,000$

$$ Inventory Changes: $+$$$20,000$ in Year $0,$ fully recoverable in Year $5$

$$ Accounts Receivable Changes: $+$$$10,000$ in Year $0,$ fully recoverable in Year $5$

$$ Accounts Payable Changes: $+$$$5,000$ in Year $0,$ fully repayable in Year $5$

$$ Project Beta:

$$ Initial Capital Expenditure $($CapEx$)$: $$600,000$

$$ Annual Revenue: $$300,000$

$$ Annual Operational Cost $($excluding depreciation$)$: $$150,000$

$$ Inventory Changes: $+$$$30,000$ in Year $0,$ fully recoverable in Year $5$

$$ Accounts Receivable Changes: $+$$$15,000$ in Year $0,$ fully recoverable in Year $5$

$$ Accounts Payable Changes: $+$$$10,000$ in Year $0,$ fully repayable in Year $5$

The Weighted Average Cost of Capital $($WACC$)$ for Greenwood Corporation is $7\mathrm{.}3\%$

Part A: Cash Flow Estimation and Project Evaluation

$1.$ Estimate the annual cash flows for each project, considering operational cash flows, depreciation $($straight$-$line$),$ and changes in net working capital.

$2.$ Calculate the NPV and PI for each project using the WACC $.$ Please give detailed excel explaination

$3.$ Calculate the IRR of each project.

$4.$ Provide a recommendation on which project to choose based on NPV and PI criteria.

$5.$ Explain under what circumstances the PI decision rule should be used over the NPV rule.

Part B:

$$ Present your recommendation in a brief recommendation, you must explain your analysis and decision$-$making process:

$$ State and justify all assumptions made during your analysis.

$$ Discuss the implications of your findings and the rationale behind your project recommendation and the choice of measure NPV or PI$.$

$$ Could we rank the project using the IRR? Why$/$Whynot$?$

$$ Discuss how would your analysis change if Project alpha has a lifespan of $5$ years, but project beta has a lifespan of six years? $($No data analysis needed here$)$

Thank you