Context: Company X is evaluating two projects, Project Y and Project Z, which require initial investments of $50,000 each. The projected cash inflows are as follows:

Year	Project Y	Project Z
1	$20,000	$15,000
2	$18,000	$18,000
3	$16,000	$20,000
4	$10,000	$25,000

Requirements: a. Calculate the net present value (NPV) of each project if the discount rate is 10%. b. Determine the profitability index for each project. c. Calculate the payback period for each project. d. Analyze which project should be chosen based on NPV and profitability index if they are independent. e. Discuss the implications if the projects are mutually exclusive.