One year$$ ago, your company purchased a machine used in manufacturing for $ $90$ comma $000.$ You have learned that a new machine is available that offers many$$ advantages; you can purchase it for $ $170$ comma $000$ today. It will be depreciated on a$$ straight$-$line basis over ten years and has no salvage value. You expect that the new machine will produce a gross margin$($revenues minus operating expenses other than$$ depreciation$)$ of $ $45$ comma $000$ per year for the next ten years. The current machine is expected to produce a gross margin of $ $20$ comma $000$ per year. The current machine is being depreciated on a$$ straight$-$line basis over a useful life of $11$ years, and has no salvage$$ value, so depreciation expense for the current machine is $ $8$ comma $182$ per year. The market value today of the current machine is $ $50$ comma $000.$ Your$$ company's tax rate is $42\%,$ and the opportunity cost of capital for this type of equipment is $11\%.$ Should your company replace its$$ year$-$old machine?

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Part $1$

The NPV of replacing the$$ year$-$old machine is $$$