A$.$ One of your internship project is to evaluate if a $$5M$ investment in technology at the company will pay for itself in the first $10$ years. The technology is expected to reduce the number of workers by $10.$ Assume each worker costs $$75,000$ per year $(\frac{w}{?}$ no increases over time$).$ Use a $13\%$ discount rate. If you buy the system today, the implementation will take a year, so the savings in wages will start next year. $($Show general formula and work$).$ Based on your analysis, do you recommend investing in this technology?

Recommendation:

Hints: "Buy the system today" means you need the value TODAY, so PV$.$

"per year" and $"$in the first $10$ years" means "annuity". So this is a PV Annuity problem. Check notes sheet or notes for PV Annuity Formula. Finally, $a=75,00010$ worker $=$$$750,000$ each year for $10$ years starting next year. Exactly how the PV formula is set up$.$ Compare the savings from the formula to the cost today of $$5M.$ If you save more than $$5M,$ then buy.