Natural Lotion is considering the purchase of a new packaging machine. The machine costs $$150,000,$ and has a $10-$year life. The company uses the straight$-$line depreciation method, and the machine has no residual value. The machine will produce net cash inflows of $$37,000$ per year at the end of each year. For purposes of responding to each requirement below, you may assume no income taxes.

a$)$ Calculate the net present value of the machine investment, assuming a $12\%$ rate of return.

b$)$ Calculate the accounting rate of return for the machine investment.

c$)$ Calculate the internal rate of return for the machine investment.

d$)$ Calculate the payback period for the machine investment.