A company is considering two investment opportunities. Investment X requires an initial outlay of $50,000 and will generate cash flows of $15,000 per year for six years. Investment Y requires an initial outlay of $100,000 and will generate cash flows of $28,000 per year for eight years. The company's required rate of return is 10%.

a) Calculate the payback period for each investment.

b) Calculate the profitability index (PI) for each investment.

c) Using the discounted payback period method, which investment should the company choose? Show all calculations and provide a recommendation.