a. At what level of operation (hours per year) would you be indifferent between

Question

a. At what level of operation (hours per year) would you be indifferent between the two pumping systerms? If the pumping system is expected to operate 2,000 hours per year, which system should be recommended?

Explanation / Answer

a) i) Let h be the operating hrs in a year. PUMP SYSTEM A : Annual operating cost, a = (15/0.60)*0.746*0.06 h = 1.119 h ($) Present cost, PC(A) = 2410 + 1.119 h (1.12^8-1)/(0.12*1.12^8) - 80/1.12^8 => = 2410 + 5.559 h - 32.31 => = 2377.69 + 5.559 h PUMP SYSTEM B: Annual operating cost, a = (10/0.75)*0.746*0.06 h = 0.597 h ($) Present cost, PC(B) = 4820 + 0.597 h (1.12^8-1)/(0.12*1.12^8) - 0 => = 4820 + 2.966 h PC(A) = PC(B) to be indifferent between A and B. 2377.69 + 5.559 h = 4820 + 2.966h h = 941.9 = say 942 hrs (ANSWER) ii) for 2000 hrs operation, PUMP SYSTEM A : Annual operating cost, a = (15/0.60)*0.746*0.06 *2000 = 2238 ($) Present cost, PC(A) = 2410 + 2238* (1.12^8-1)/(0.12*1.12^8) - 80/1.12^8 => = 13495.3 ($) PUMP SYSTEM B : Annual operating cost, a = (10/0.75)*0.746*0.06 *2000 = 1193.6 ($) Present cost, PC(B) = 4820+ 1193.6* (1.12^8-1)/(0.12*1.12^8) => = 10759.4 ($) As PC of B is less than that of A, System B is recommended. (ANSWER)

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