P$4.(10$ points$)$ Suppose that an auto company is thinking of adding a new assembly line to its operations. You have just completed a $$500,000$ feasibility study and have found the following: Adding the new assembly line will result in $$5$ million dollars in new sales per year and will save $$10$ million per year in expenses. However, the assembly line will cost $$1$ million per year to operate. Suppose that the assembly line costs $$80$ million and uses some parts from a $($fully depreciated$)$ retired assembly line that could be sold elsewhere for $$3$ million. The assembly line will last for $8$ years and has a scrap value of $$20$ million. Finally, the project will require a constant level of $$2$ million working capital over its $8$ year life time. The discount rate is $10\%.$ There is no inflation.a$)$ Assume no taxes. What is the NPV of the project? Should they add the new assembly line? Support your recommendation with the necessary calculations.b$)$ Assume a tax rate of $20\%.$ Suppose that the firm uses straight line depreciation for tax purposes and that it will depreciate the assembly line toward zero over its $8$ year life. Recalculate the NPV$.$