Zhang Company is considering the purchase of a new machine. Its invoice price is $200,000, freight charges are estimated to be $4,000, and installation costs are expected to be $6,000. Salvage value of the new machine is expected to be zero after a useful life of 4 years. Existing equipment could be retained and used for an additional 4 years if the new machine is not purchased. At that time, the salvage value of the equipment would be zero. If the new machine is purchased now, the existing machine would be scrapped. Zhangs accountant, Victor Wang, has accumulated the following data regarding annual sales and expenses with and without the new machine. Without the new machine, Zhang can sell 10,000 units of product annually at a per unit selling price of $100. If the new unit is purchased, the number of units produced and sold would increase by 25%, and the selling price would remain the same. The new machine is faster than the old machine, and it is more efficient in its usage of materials. With the old machine the gross profit rate will be 25% of sales, whereas the rate will be 35% of sales with the new machine. Annual selling expenses are $180,000 with the current equipment. Because the new equipment would produce a greater number of units to be sold, annual selling expenses are expected to increase by 10% if it is purchased. Annual administrative expenses are expected to be $100,000 with the old machine, and with the new machine the annual administrative expenses are expected to increase by 12%. The current book value of the existing machine is $20,000. Zhang uses straightline depreciation. Zhangs management has a required rate of return of 10% on its investment and a cash payback period of no more than 3 years.

Instructions Show your calculations with formulas for the following question a, b and c. a) Calculate the annual rate of return for the new machine. (Round to two decimals.) b) Compute the cash payback period for the new machine. (Round to two decimals.) c) Compute the net present value of the new machine. (Round to the nearest dollar.) d) Based on your analysis on question a, b, c, would you recommend that Mr. Zhang buy the machine? Why or why not? Stating your recommendations.(ignore Tex) answer is not on excel . please explain properly what is given and which formula is used.