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$)$ SouthCo's required rate of return is $15\%$ on all investments. The company can purchase a new machine at a cost of $$80,000.$ The new machine would generate cash inflows of $$30,000$ per year and have an $11-$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$)$ EastCo is investigating the purchase of a new machine that has a project life of $11$ years. It is estimated that the new machine will save $$24,000$ per year in cash operating costs. If the new machine costs $$103,848,$ 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 $16\%?$

Internal rate of return $=$ Is the machine an acceptable investment? $($Select one$)$

c$)$ Refer to the data in b$)$ for EastCo. How much would the annual net cash flows $($cost savings$)$ have to be for the new machine to provide the required $16\%$ rate of return? Round your answer to the nearest dollar.

Annual net cash flows $=$$