A manufacturer of refining various materials (earth, soil, ore, etc.) is considering installing a system that would recover a large part of the fine gold particles present in the various materials treated, particularly in the processing and purification of rare earths. Without a treatment system all the fine particles of gold would be lost. At the current gold price ($ 15 / gr) *, the annual loss of gold dust, for the first year, is estimated at $ 60,000 and should continue to increase by $ 6,000 per year per year. continuation (linear gradient). The proposed system, involving a network of exhaust ducts, suction and separators, will recover 70% of the gold dust that would otherwise be lost. The complete installation would cost $ 180,000 (investment). The estimated annual operating costs of the system, based on the operation of similar systems, are $ 10,000 per year for operating expenses, $ 2,200 per year for maintenance costs and 2% per year of initial acquisition and installation cost, for annual taxes and insurance. The lifetime fixed for this analysis is 10 years. The system will have no residual value at the end of the project. The minimum acceptable rate of return the company has set for itself is 15%. * gr = one gram of gold. a) Using the IRR (internal rate of return) method, does the company have to do this installation? (Calculate the IRR). b) Determine the payback period in years (without discounting) for this project. c) Determine the minimum value of the gold price ($ / gr.) that would guarantee the profitability of this investment. Reminder: Break-even analysis or NPV (i = the minimum acceptable rate of return) = 0. The price of gold ($ / gr) is the unknown we are looking for.