Novak Company is considering the purchase of a new machine. The invoice price of the machine is $$137,000,$ freight charges are estimated to be $$3,400,$ and installation costs are expected to be $$5,600.$ The salvage value of the new equipment is expected to be zero after a useful life of $4$ years. Existing equipment could be retained and used for an additional $4$ years if the company does not purchase a new machine. At that time, the equipment's salvage value would be zero. If the company purchases the new machine now, it would have to scrap the existing machine. Novak's accountant, Edward Lee, has accumulated the following data regarding annual sales and expenses with and without the new machine: Calculate the annual rate of return for the new machine. $1.$ Without the new machine, Novak can sell $11,200$ units of product annually at a per$-$unit selling price of $$100.$ With the new machine the number of units produced and sold would increase by $25\%,$ and the selling price would remain the same. $2.$ The new machine is faster than the old machine, and it is more efficient in its use of materials. With the old machine, the gorss profit rate is $28\mathrm{.}50\%$ of sales, whereas the rate will be $30\%$ of sales with the new machine. $3.$ Annual selling expenses are $$179,000$ with the current equipment. Because the new equipment would produce a greater number of units to be sold, annual selling expenses are expected to increase by $10\%$ if it is purchased. $4.$ Annual administrative expenses are expected to be $$112,000$ with the old machine, and $$125,000$ with the new machine. $5.$ The current book value of existing machine is $$45,000.$ Novak uses straight$-$line depreciation. $6.$ Novak management has a required rate of return of $15\%$ on its investments and a payback period of no more than $3$ years. $($Round calculations in percentages to $2$ decimal places and final answer to $1$ decimal places$)$

$1)$ Calculate the annual rate of return for the new machine.

$2)$ Compute the cash pay back period for the new machine

$3)$ Compute the net present value of the new machine