Pharoah Company is considering the purchase of a new machine. Its invoice price is $$102,000,$ freight charges are estimated to be $$2,500,$ and installation costs are expected to be $$4,200.$ 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. Pharoah's accountant, Lisa Hsung, has accumulated the following data regarding annual sales and expenses with and without the new machine.

Without the new machine, Pharoah can sell $8,400$ 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 $28\mathrm{.}5\%$ of sales, whereas the rate will be $30\%$ of sales with the new machine. $($Note: These gross profit rates do not include depreciation on the machines. For purposes of determining net income, treat depreciation expense as a separate line item.$)$

Annual selling expenses are $$134,000$ 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 $$84,000$ with the old machine, and $$94,000$ with the new machine.

The current book value of the existing machine is $$34,000.$ Pharoah uses straight$-$line depreciation.

Pharoah's management has a required rate of return of $15\%$ on its investment and a cash payback period of no more than $3$ years.