Rouse Production Company would like to further automate its production process by purchasing production equipment for $$660,000.$ The equipment is expected to have a useful life of $8$ years and will be sold at the end of $8$ years for $$40,000.$ The equipment requires significant maintenance work at an annual cost of $$75,000.$ Labor and material cost savings, shown in the table, are also expected to be significant. Year $1$ $$160,000$ Year $2$ $$190,000$ Year $3$ $$200,000$ Year $4$ $$240,000$ Year $5$ $$280,000$ Year $6$ $$220,000$ Year $7$ $$180,000$ Year $8$ $$155,000$ The companys required rate of return is $11$ percent. Assume the company requires all investments to be recovered within five years.

Required:

a$.$ Find the net present value of this investment. Round to the nearest dollar.

b$.$ Use trial and error to approximate the internal rate of return for this investment proposal.

c$.$ Determine the payback period for this investment.

d$.$ Based on your findings in requirements a$,$ b$,$ and c$,$ should the company purchase the production equipment? Explain.