An engineer is trying to decide which process to use to reduce sludge volume prior to disposal. Belt filter presses (BFP) will cost $203,000 to buy and $85,000 per year to operate. Belts will be replaced one time per year at a cost of $5500. Centrifuges (Cent) will cost $396,000 to buy and $119,000 per year to operate, but because the centrifuge will produce a thicker “cake”, the sludge hauling cost to the monofill will be $37,000 per year less than for the belt presses. The useful lives are 5 and 10 years for alternatives BFP and Cent, respectively, and the salvage values are assumed to be 10% of the first cost of each process whenever they are closed down or replaced. Use PW evaluation to se­lect the more economical process at an interest rate of 6% per year over (a) the LCM of

Question

lives, and (b) a study period of 8 years. Are the decisions the same?

What will be an ideal response?

Answer 1

(a) PWBFP = -203,000 – 90,500(P/A,6%,10) – 182,700(P/F,6%,5) + 20,300(P/F,6%,10)
= -203,000 – 90,500(7.3601) – 182,700(0.7473) + 20,300(0.5584)
= $-994,285

PWCent = -396,000 – (119,000 - 37,000)(P/A,6%,10) + 39,600(P/F,6%,10)
= -396,000 – 82,000(7.3601) + 39,600(0.5584)
= $-977,416
Centrifuges have a slightly lower PW

(b) PWBFP = -203,000 – 90,500(P/A,6%,8) – 182,700(P/F,6%,5) + 20,300(P/F,6%,8)
= -203,000 – 90,500(6.2098) – 182,700(0.7473) + 20,300(0.6274)
= $-888,782
PWCent = -396,000 – (119,000 - 37,000)(P/A,6%,8) + 39,600(P/F,6%,8)
= -396,000 – 82,000(6.2098) + 39,600(0.6274)
= $-880,359

Centrifuges still have a slightly lower PW, but by a smaller amount