A company is considering a new machine with an initial investment of $$75,000.$ The expected annual cash flows for the next five years are: Year $1$: $$20,000$ Year $2$: $$25,000$ Year $3$: $$30,000$ Year $4$: $$22,000$ Year $5$: $$18,000$The company's cost of capital is $12\%.$Required:$1.$ Calculate the project's payback period$\mathrm{.}2.$ Calculate the project's NPV using the provided cost of capital. $($Round to the nearest whole dollar$)3.$ Will you recommend the project?