Question

A manufacturing processing company currently owns a hydraulic pressing machine that was bought for $250,000 three years ago. This machine is worth $90,000 today. The operating and maintenance (O&M) cost of the machine is $15,000 in year 1, which increases by $1,000 ever year after that till the end of its remaining 3 years. If this machine is kept and sold after one year, it market value will be $50,000. If it is not sold in year 1, it has to be kept for two more years and its market value at the end of year 3 will be $10,000.

A replacement hydraulic machine can be purchased for $200,000. The useful life of this machine is 5 years. Its O&M cost is $6,000 in year 1 and it increases by 3% every year after that. This machine can only be sold in year 3 for $80,000 or in year 5 for $50,000.

If the MARR is 7%, determine when the best time to replace the current machine is.

(all by hand, no excel)

Answer 1

Defender can be kept for 1 year or 3 yrs

EUAC of defender for 1 yr of operation = 90000*(A/P,7%,1) + 15000 - 50000*(A/F,7%,1)

= 90000*1.07 + 15000 - 50000

= 61300

EUAC of defender for 3 yr of operation = 90000*(A/P,7%,3) + 15000 + 1000*(A/G,7%,3) - 10000*(A/F,7%,3)

= 90000*0.381052 + 15000 + 1000*0.9549229 - 10000*0.311052

= 47139.08

Challenger can be kept for 3 or 5 yrs

Present worth of geometric series = A*[1 - (1+g)^n / (1+i)^n] /(i-g)

Present worth of annual cost for 3 yrs = 6000*[1 - (1+0.03)^3 / (1+0.07)^3] /(0.07-0.03)

= 6000*[1 - (1.03)^3 / (1.07)^3] /(0.04)

= 6000 * 2.700231

= 16201.39

Present worth of annual cost for 5 yrs = 6000*[1 - (1+0.03)^5 / (1+0.07)^5] /(0.07-0.03)

= 6000*[1 - (1.03)^5 / (1.07)^5] /(0.04)

= 6000 * 4.336340

= 26018.04

EUAC for 3 yrs of operation = 200000 * (A/P,7%,3) + 16201.39*(A/P,7%,3) -80000*(A/F,7%,3)

= 200000 * 0.381052 + 16201.39*0.381052 -80000*0.311052

= 57499.81

EUAC for 5 yrs of operation = 200000 * (A/P,7%,5) + 26018.04*(A/P,7%,5) - 50000*(A/F,7%,5)

= 200000 *0.243891 + 26018.04*0.243891 - 50000*0.173891

= 46429.22

As EUAC of challenger is lowest for 5 yrs operation, and is also lower than EUAC of Defender, therefore

Defender should be replaced immediately and challenger should be kept for 5 yrs