Le Filet is a famous restaurant in the French Quarter of New Orleans. $$Bouillabaisse Nadia$$ is the house specialty. Management is currently considering the purchase of a machine that would prepare all the ingredients, automatically mix them and cook the dish to the restaurant$$s specifications. The machine will function for an estimated $12$ years and the purchase price, including installation, is $$250,000.$ Estimated residual value is $$25,000.$ This labor$-$saving device is expected to increase cash flows by an average of $$42,000$ per year during its estimated useful life. For capital investment decisions, the restaurant uses a $12$ percent minimum rate of return.

Use Tables $1$ and $2$ for future value and present value calculations.

$1.$ Using the net present value method, determine if the company should purchase the machine. Support your answer.

$2.$ If management had decided on a minimum rate of return of $14$ percent, should the machine be purchased? Show all computations to support your answer.