Consider each part below independently. $($Ignore income taxes in your calculations.$)$

Use the built$-$in PV functions for these calculations. Enter $PV(n$;$i)$ in a value box to calculate the present value of $$1$ over $n$ compounding periods with a periodic rate of $i.$ Similarly, use PVA $(n$;$i)$ to calculate the present value of an annuity. E$.$g$.,$ the present value of $$1,000$ with a periodic rate of $3\%,$ and $2$ compounding periods can be entered as ${1000}^{**}PV(2$;$3).$

a$)$ XYZ Co$.\text{'}$s required rate of return is $12\%$ on all investments. The company can purchase a new machine at a cost of $$60,000.$ The new machine would generate cash inflows of $$29,000$ per year and have an $18-$year useful life and no salvage value. Compute the machine's net present value and decide if the machine is an acceptable investment. Round your present values to the nearest dollar.

$\backslash$table$[[$Item$,$Present Value of Cash Flows$],[$Net annual cash inflows,$],[$Net present value,$],[$Is the machine an acceptable investment?,$($Select one$)]]$

b$)$ JenStar is investigating the purchase of a new machine that has a project life of $7$ years. It is estimated that the new machine will save $$12,000$ per year in cash operating costs. If the new machine costs $$43,260,$ what is its internal rate of return to the nearest whole percent? Is the machine an acceptable investment if the company's required rate of return is $15\%?$

Internal rate of return $=\%$

Is the machine an acceptable investment? $$

c$)$ Refer to the data in b$)$ for JenStar. How much would the annual net cash flows $($cost savings$)$ have to be for the new machine to provide the required $15\%$ rate of return? Round your answer to the nearest dollar.

Annual net cash flows $=$$