Topaz company is consdierng the pruchase of a new machine the machine costs $$500,000$ is expected to have a useful life of $5$ years$(15$ points$)$ Topaz

Company.is considering the purchase of a new machine. The machine costs

$$500,000$ is expected to have a useful life of five years. Topaz uses straight$-$line depreciation and

expects this machine to have zero terminal disposal value at the end of five years. Working capital

at the time of purchase is $$50,000.$ This working capital is expected to be fully recovered at the end

of the useful life. The new machine will reduce current operating expenses by $$120,000$ per year for

the machine's useful life. The machine is expected to have a salvage value of $$30,000$ at the end of

its useful life. Alvarez pays taxes at a rate if $20\%$ and requires an $8\%$ rate of return on investments.

Calculate the net present value $($NPV$)$ of the project $($round your solution to dollars$).$

b$.$ What is the payback period of the project $($round your solution to two decimal places$)?$

c$.$ Should the project be accepted or rejected? Why?