Blue Spruce Vita produces a wide range of herbal supplements sold nationwide through independent distributors. In response to an increasing demand for its products, the company is considering the purchase of a new packaging machine to replace the seven$-$yearold machine currently in use. The new machine will cost $$150,050,$ and installation will require an additional $$2,725.$ The machine has a useful life of $10$ years and is expected to have a salvage value of $$4,465$ at that time. The variable cost to operate the new machine is $$8\mathrm{.}65$ per carton compared to the current machine's variable cost of $$8\mathrm{.}75$ per carton, and Blue Spruce Vita expects to pack $236,000$ cartons each year. If the new machine is purchased, Blue Spruce Vita will avoid a required $$8,925$ overhaul of the current machine in four years. The current machine has a market value of $$11,575.$

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$($a$)$ Calculate the net present value of the new packaging machine. Assume that Blue Spruce Vita uses an $10\%$ discount rate. $($For calculation purposes, use $4$ decimal places as displayed in the factor table provided and round final answer to $2$ decimal places, e$.$g$.58,971\mathrm{.}75.$ Enter negative amount using a negative sign preceding the number, e$.$g$.-59,991$ or parentheses e$.$g$.(59,991).)$

Net present value

$

$($b$)$ Do you recommend that Blue Spruce Vita purchase the new machine?

$($c$)$ Assume that Blue Spruce Vita has adopted a new $14\%$ discount rate. Calculate the net present value of the new packaging machine. $($For calculation purposes, use $4$ decimal places as displayed in the factor table provided and round final answer to $2$ decimal places, eg$.58,971\mathrm{.}75.$ Enter negative amount using a negative sign preceding the number, e$.$g$.-59,991$ or parentheses e$.$g$.(59,991).)$

Net present value

$

Do you recommend that Blue Spruce Vita purchase the new machine?