A portable concrete test instrument used in construction for evaluating and profiling concrete surfaces $($MACRS$-$GDS $5-$year property class$)$ is under consideration by a construction firm for $$25,000.$ The instrument will be used for $6$ years and be worth $$2,250$ at that time. The annual cost of use and maintenance will be $$5,500.$ Alternatively, a more automated instrument $($same property class$)$ available from the manufacturer costs $$28,000,$ with use and maintenance costs of only $$7,500$ and salvage value after $6$ years of $$4,500.$ The marginal tax rate is $25\%,$ and MARR is an after$-$tax $12\%.$

Determine which alternative is less costly$,$ based upon comparison of after$-$tax annual worth.

Show the AW values used to make your decision:

Alternative $1$:$

Alternative $2$:$

Carry all interim calculations to $5$ decimal places and then round your final answer to the nearest dollar. The tolerance is $+-10.$