As a result of improvements in product engineering, United Automation is able to sell one of its two milling machines. Both machines perform the same function but differ in age. The newer machine could be sold today for $\backslash (\backslash$$ $72,500\backslash ).$ Its operating costs are $\backslash (\backslash$$ $23,000\backslash )$ a year, but at the end of five years, the machine will require a $\backslash (\backslash$$ $18,500\backslash )$ overhaul $($which is tax deductible$).$ Thereafter, operating costs will be $\backslash (\backslash$$ $31,500\backslash )$ until the machine is finally sold in year $10$ for $\backslash (\backslash$$ $7,250\backslash ).$

The older machine could be sold today for $\backslash (\backslash$$ $26,500\backslash ).$ If it is kept, it will need an immediate $\backslash (\backslash$$ $27,500\backslash )($tax$-$deductible$)$ overhaul. Thereafter, operating costs will be $\backslash (\backslash$$ $36,900\backslash )$ a year until the machine is finally sold in year $5$ for $\backslash (\backslash$$ $7,250\backslash ).$

Both machines are fully depreciated for tax purposes. The company pays tax at $\backslash (21\backslash \%\backslash ).$ Cash flows have been forecasted in real terms. The real cost of capital is $\backslash (11\backslash \%\backslash ).$

a$.$ Calculate the equivalent annual costs for selling the new machine and for selling the old machine. Note: Do not round intermediate calculations. Enter your answers as a positive value rounded to $\backslash (\backslash$mathbf$\{2\}\backslash )$ decimal places.

b$.$ Which machine should United Automation sell?