A large city in the mid-West needs to acquire a street-cleaning machine to keep

Question

A large city in the mid-West needs to acquire a street-cleaning machine to keep its roads looking nice year round. A used cleaning vehicle will cost $85,000 and have a $20,000 market (salvage) value at the end of its five-year life. A new system with advanced features will cost $150,000 and have a $40,000 market value at the end of its five-year life. The new system is expected to reduce labor hours compared with the used system. Current street-cleaning activity requires the used system to operate 8 hours per day for 20 days per month. Labor costs $50 per hour (including fringe benefits), and MARR is 12% per year. (11.2) a. Find the breakeven percent reduction in labor hours for the new system. b. If the new system is expected to be able to reduce labor hours by 17% compared with the used system, which machine should the city purchase?

Explanation / Answer

Current System Nature of Cashflows Year Discount Factor @ 12% Cashflow Discounted Cashflows a b a*b Machinery Cost 0 1.0000 $85,000.00 $85,000.00 Operating Cash outflows 1 - 5 3.6048 $96,000.00 $346,058.52 = 8 hrs/day * 20days/month * 12 month * $50/hour PV Cash outflows $431,058.52 Less: Salvage Value of Machine 5 0.5674 $20,000.00 $11,348.54 PV of Net Cash outflows (A) $419,709.98 Annuity Factor for Machine Life (B) 3.6048 Equated Annual Cost (A/B) $116,431.63 a. Equated Annual Cost of New system has to be equal to $116,431.63 for break even. The reduction in hours is not known. Machine Cost - $150,000 Salvage Value - $40,000 EAC = [(150000 + 12000 * Labor hours/day * 3.6048) - 40000 * 0.5674] / 3.6048 or, 116431.63 = (150000 + 43257.31 * Labor hours/day - 22697.07) / 3.6048 or, 116431.63 = (127302.93 + 43257.31 * Labor hours/day ) / 3.6048 or, 116431.63 * 3.6048 = 127302.93 + 43257.31 * Labor hours/day or, Labor hours/day = 292407.05 / 43257.31 or, Labor hours/day = 6.76 Percent reduction in hours = (8 - 6.76) / 8 = 16% b. If the new machine is expected to reduce 17% labor hours, then the new machine should be purchased This is because, post break even point as computed above new machine would be economically viable.

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