XYZ Corporation has three potential projects with the following details:

• Project Alpha
  • Cost of Capital: 7%
  • Initial Investment: $200,000
  • Cash Inflow Year 1: $80,000
  • Cash Inflow Year 2: $90,000
  • Cash Inflow Year 3: $100,000
  • Scrap Value at Year 3: $10,000
• Project Beta
  • Cost of Capital: 10%
  • Initial Investment: $180,000
  • Cash Inflow Year 1: $70,000
  • Cash Inflow Year 2: $80,000
  • Cash Inflow Year 3: $110,000
  • Scrap Value at Year 3: $5,000
• Project Gamma
  • Cost of Capital: 12%
  • Initial Investment: $150,000
  • Cash Inflow Year 1: $60,000
  • Cash Inflow Year 2: $70,000
  • Cash Inflow Year 3: $80,000

Tasks:

1. Determine the payback period for each project.
2. Calculate the NPV for each project.
3. Calculate the IRR for each project.
4. Assess the profitability index for each project.
5. Provide a recommendation on which project to choose.