The activated sludge unit of a wastewater treatment plant requires an aerator. Two options exist and have the characteristics shown in the table. The city owner of the treatment plant sets an interest

To determine which aerator to purchase, we need to compare the present worth and annual worth of each option. - Present worth analysis: Calculates the net present value (NPV) of each option. The option with the higher NPV is better. The formula to calculate NPV is: NPV = - Initial Cost + (Annual Operating Cost / (1 + i)^n) + Salvage Value / (1 + i)^n where i is the interest rate (8% p.a.), n is the analysis period (10 years) For Aerator A: NPV = - 400,000 + (60,000 / (1 + 0.08)^n) + 60,000 / (1 + 0.08)^n = - 400,000 + 33,111.77 + 33,111.77 = - 333,776.46 For Aerator B: NPV = - 200,000 + (75,000 / (1 + 0.08)^n) + 20,000 / (1 + 0.08)^n = - 200,000 + 45,723.42 + 7,820.51 = - 146,456.07 Therefore, Aerator B has a higher NPV and is the better option according to the present worth analysis. - Annual worth analysis: Calculates the equivalent annual cost (EAC) of each option. The option with the lower EAC is better. The formula to calculate EAC is: EAC = (NPV * i) / (1 - 1 / (1 + i)^n) For Aerator A: EAC = (-333,776.46 * 0.08) / (1 - 1 / (1 + 0.08)^10) = 61,284.88 For Aerator B: EAC = (-146,456.07 * 0.08) / (1 - 1 / (1 + 0.08)^5) = 49,218.16 Therefore, Aerator B has a lower EAC and is the better option according to the annual worth analysis. In conclusion, both the present worth and annual worth analyses show that Aerator B is the better option due to its lower cost.