XYZ Manufacturing is currently using an outdated lathe to produce custom metal components. The lathe has $6$ years of remaining life. If retained, the lathe will have depreciation expenses of $$500$ for $5$ years and $$250$ for the sixth year. Its current book value is $$2,800,$ and it can be sold on an online marketplace for $$3,200$ at this time. If the old lathe is not replaced, it can be sold for $$600$ at the end of its useful life.

$xYZ$ is contemplating the purchase of the Precision Lathe $5000,$ a state$-$of$-$the$-$art machine, which costs $$10,000$ and has an estimated useful life of $6$ years with an estimated salvage value of $$1,000.$ This lathe falls into the MACRS $5-$year class, so the applicable depreciation rates are $20\mathrm{.}00\%,32\mathrm{.}00\%,19\mathrm{.}20\%,11\mathrm{.}52\%,11\mathrm{.}52\%,$ and $5\mathrm{.}76\%.$ The new lathe is more efficient and allows for increased production, resulting in an annual sales increase of $$1,500.$ Additionally, the new machine's improved technology reduces operating expenses by $$1,200$ per year. To accommodate the higher production volume, the new machine would necessitate an increase in inventories by $$2,000,$ while accounts payable would simultaneously increase by $$500.xYZ\text{'}$s marginal federal$-$plus$-$state tax rate is $35\%,$ and the project cost of capital is $12\%.$ Should it replace the old lathe?