Alpha Corp. has two investment opportunities. Project X will provide an initial outlay of $30,000 and is expected to generate the following cash flows:

• Year 1: $10,000
• Year 2: $15,000
• Year 3: $20,000

Project Y requires an initial investment of $50,000 and has the following projected cash flows:

• Year 1: $20,000
• Year 2: $25,000
• Year 3: $30,000
• Year 4: $35,000

Requirements:

1. Calculate the Net Present Value (NPV) of both projects if the discount rate is 10%.
2. Determine which project should be undertaken based on the NPV.
3. Compute the Internal Rate of Return (IRR) for both projects.
4. Discuss the sensitivity of the NPV to changes in the discount rate.