A production operation in a company is performed with equipment on$-$hand and labor costs of $$75,000$ per year. The equipment is very low$-$maintenance and should last indefinitely. A newequipment item for the same operation, also very low$-$maintenance but requiring replacement every $6$ years, can be purchased for $$170,000.$ It will cut labor costs in half. The firm$$s minimum attractive rate$-$of$-$return $($MARR$)$ is $10$ percent.

$($a$)$ Should the company buy the new equipment. Explain why or why not?

$($b$)$ What is the internal rate of return of the alternative whereby the new equipment is purchased? Show your work in your response.