The Durant corporation is considering replacing an existing piece of machinery

with a new machine. The old machine was purchased $3$ years ago at a cost of $$50,000,$ and this amount was being depreciated under MACRS, using a $5-$year recovery period. The machine has $5$ years of usable life remaining. The new machine being considered costs $$76,000$ and requires $$4,000$ in installation costs. The new machine would be depreciated under MACRS, using a $5-$year recovery period. The firm can currently sell the old machine for $$55,000$ without incurring

any removal or cleanup costs. The firm is subject to a tax rate of $21\%.$ The cost of capital is $12\%.$

The project will result in an increase in revenues and expenses $($excluding depreciation and interest,$)$ provided in Table $1$ below. Applicable depreciation rates are given in Table $2.$Table $1.$ Revenues and Expenses

Table $2.$ Rounded Percentages by Recovery Year Using MACRS

a$.$ What is the initial investment associated with this project? $(8$ points$).$

b$.$ What are the annual after$-$tax cash flows associated with this project for years $1$

through $6?($Note: Be sure to consider depreciation in year $6.)(24$ points$).$

c$.$ Should the new machine be purchased? $(18$ points$).$