Home Security Systems is analyzing the purchase of manufacturing equipment that will cost $$50,000.$ The annual cash inflows for the next three years will be:

Year Cash Flow

$1$ $$25,000\mathrm{.}00$

$2$ $$23,000\mathrm{.}00$

$3$ $$18,000\mathrm{.}00$

NOTE: to receive full credit show your work for ALL steps $-$ including your PV factor.

a$.$ Determine the internal rate of return.

b$.$ With a cost of capital of $18$ percent, should the machine be purchased?