please explain your answer using formula

Silicon Co. is a start-up company. It is now considering going ahead with one of the following projects next month. The details about the two mutually exclusive projects are as follows: Project A - The initial cost is $1,500,000. In return, the company forecast year-end cash inflow of $600,000 from year 1 to year 3. The cash flow will drop to $400,000 in year 4. Project B - The initial cost is $1,800,000. The company forecasts to receive $500,000, $550,000, $400,000 and $1,200,000 from year 1 to 4 respectively. Assume that the required yearly return of both projects are 5%. a) Calculate the payback period of the two projects. Given the target payback period is 3 years, which project should the company choose? Explain your answer. (4 marks) b) Calculate the discount payback period of the two projects. Given the target payback period is 4 years, which project should the company choose? Explain your answer. (6 marks) c) Calculate the NPV of the two projects. Which project should the company choose? Explain your answer. (6 marks) d) Based on your answers in parts (a)-(e), which project should the company choose? Explain, (3 marks) e) Instead of choosing one out of the two projects, Silicon Co. has just realized that they can implement projects A and B simultaneously if they install a new machine. The installation cost is $200,000. Explain whether Silicon Co. should install this new machine. (Hint: Justify your answer base on the NPV of the two projects.) (4 marks)