Three products will be manufactured in a new facility at the Apex Manufacturing Company. They each require an identical manufacturing$$ operation, but different production$$ times, on a broaching machine. Two alternative types of broaching machines $($M$1$ and M$2)$ are being considered for purchase. One machine type must be selected. For the same level of annual demand for the three$$ products, annual production requirements$($machine hours$)$ and annual operating expenses$($per machine$)$ are listed on the right.

Assumptions:

The facility will operate $2,100$ hours per year. Machine availability is $95\%$ for Machine M$1$ and $85\%$ for Machine M$2.$ The yield of Machine M$1$ is $90\%,$ and the yield of Machine M$2$ is $85\%.$ Annual operating expenses are based on an assumed operation of $2,100$ hours per year, and workers are paid during any idle time of Machine M$1$ or Machine M$2.$ Market values of both machines are negligible.

Work this problem on an after$-$tax basis when the MARR is $14\%$ per year. The effective income tax rate is $24\%,$ and MACRS depreciation is appropriate with a property class of five years. Recall that the market values of M$1$ and M$2$ are zero at the end of years five and eight, respectively.

a$.$ Calculate the AW value for Machine M$1$

b$.$ Calculate the AW value for Machine M$2.$