You are the manager of a manufacturing firm, and you are considering purchasing a new machine for your assembly-line process. The machine costs $105,000. The economists that work for the company estimate that the additional income from the machine will be a constant $7800 for the first year, then will increase by $700 each year after that. In order to buy the machine, the company needs to be convinced that it will pay for itself by the end of 8 years with this additional income. Money can earn 2.7% per year, compounded continuously. Should the company buy the machine? Please provide your analysis to the chief operating officer (COO) of the company.