The Factory is considering a three$-$year project to improve its production efficiency. Buying a new machine for $$400,000$ is estimated to result in $$200,000$ in annual pretax cost savings. The press falls in the MACRS five$-$year class, and it will have a pre tax salvage value at the end of the project of $$70,000.$ The MACRS rates are $\mathrm{.}2,\mathrm{.}32,\mathrm{.}192,\mathrm{.}1152,\mathrm{.}1152,$ and $\mathrm{.}0576$ for Years $1$ to $6,$ respectively. Ignore bonus depreciation. The press also requires an initial investment in inventory of $$20,000,$ along with an additional $$5,000$ in inventory for each succeeding year of the project. The inventory will return to its original level when the project ends. The tax rate is $20$ percent and its discount rate is $15$ percent. Should the firm buy and install the machine? Why or why not?