Please show all steps and calculations. Answers without steps and calculations will not receive full points.

$(1)$ A firm is considering an expansion project that will last three years. The project requires an immediate purchase of a new equipment that costs $$300,000.$ The equipment will be fully depreciated using straight$-$line method over the next three years. The resale price of the equipment at the end of year three is estimated to be $$100,000.$ The project will generate annual sales of $$400,000$ and incur annual costs $($all costs except depreciation expense$)$ of $$200,000$ for each of the next three years. The project also requires an immediate investment of $$50,000$ in net working capital $($NWC$),$ which will be fully recovered in year $3.$ The corporate tax rate is $21\%.$

Calculate the Cash Flow from Assets $($Project Cash Flow$)$ for the project for years $0,1,2,$ and $3.$

$(2)$ For the project above in question $(1),$ calculate the payback period, the discounted payback period, the net present value, and the internal rate of return. Assume that the required rate of return is $20\%.$

$(3)-(4)$ Consider the following two projects A and B$.$ Assume that the appropriate discount rate for each project is $20\%.$

Year CF for Project A CF for Project B

$0$

$1$

$2$

$3-$ $$200$

$100$

$200$

$300-$ $$3,500$

$1,700$

$2,500$

$2,800$

$(3)$ If projects A and B are independent projects, which project$($s$)$ should you accept based on your best capital budgeting criteria? Please explain your rationale based on the NPV and IRR of each project.

$(4)$ If projects A and B are mutually exclusive projects, which project$($s$)$ should you accept based on your best capital budgeting criteria? Please explain your rationale based on the NPV and IRR of each project.