Bridgeport Pix currently uses a six$-$year$-$old molding machine to manufacture silver picture frames. The company paid $$105,000$ for the machine, which was state of the art at the time of purchase. Although the machine will likely last another ten years, it will need a $$8,000$ overhaul in four years. More important, it does not provide enough capacity to meet customer demand. The company currently produces and sells $15,000$ frames per year, generating a total contribution margin of $$102,000.$

Martson Molders currently sells a molding machine that will allow Bridgeport Pix to increase production and sales to $20,000$ frames per year. The machine, which has a ten$-$year life, sells for $$140,000$ and would cost $$15,000$ per year to operate. Bridgeport Pix's current machine costs only $$8,000$ per year to operate. If Bridgeport Pix purchases the new machine, the old machine could be sold at its book value of $$5,000.$ The new machine is expected to have a salvage value of $$20,000$ at the end of its ten$-$year life. Bridgeport Pix uses straight$-$line depreciation.

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$($a$)$

Calculate the new machine's net present value assuming a $16\%$ discount rate. $($For calculation purposes, use $4$ decimal places as displayed in the factor table provided and round final answer to $0$ decimal place, eg$.58,971.)$

Net present value $

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