Riesel Hay Haulers is considering the purchase of a new hay$$hauling machine that would automatically pick up square bales of hay instead of having to pay workers to manually pick up the bales.

The equipment has an initial cost of $$94,500,$ a useful life of $12$ years, and a salvage value of $$4,500.$ Currently, Riesel Hay Haulers pays $6$ employees a total of $$40,000$ to manually pick up the bales and stack them on a trailer. The automated equipment would have the following operating costs $($all cash$)$:

Operator & assistant $$14,000$

Insurance $$200$

Fuel $$1,800$

Maintenance $$3,000$

a$.$ Assume sales are $$75,000$ and are all for cash. Calculate the internal rate of return.

b$.$Calculate the simple rate of return.

c$.$ Calculate the payback period.