A manufacturing company is considering two alternatives for a critical piece of equipment. The alternative A would entail buying a machine that is cheaper, but lasts for only $10$ years. The alternative B would entail buying a machine that is more expensive, but lasts for $15$ years. Either machine would be purchased with cash payment in full in year $0.$ Operating and maintenance costs do not differ across two alternatives, and both machine contribute equally to the product output. Salvage value at the end of machine life is zero. As the manager of the company, describe the method of investment analysis that you would use to determine which machine is the better investment. Please explain your answer