Question

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What is the economic life of an asset that was purchased for $12,000. O&M costs are $3000 for the first year and increase $1500/yr each year after that. Assume a 7% interest rate.

Answer 1

As salvage value is not given in question, it is assumed to be 0

EUAC for 1 yr of operation = 12000*(A/P,7%,1) + 3000

= 12000*1.07 + 3000

= 15840

EUAC for 2 yr of operation = 12000*(A/P,7%,2) + 3000 + 1200*(A/G,7%,2)

= 12000*0.553092 + 3000 + 1200*0.483092

= 10361.74

EUAC for 3 yr of operation = 12000*(A/P,7%,3) + 3000 + 1200*(A/G,7%,3)

= 12000*0.381052 + 3000 + 1200*0.954929

= 9005.01

EUAC for 4 yr of operation = 12000*(A/P,7%,4) + 3000 + 1200*(A/G,7%,4)

= 12000*0.295228 + 3000 + 1200*1.415536

= 8666.04

EUAC for 5 yr of operation = 12000*(A/P,7%,5) + 3000 + 1200*(A/G,7%,5)

= 12000*0.243891 + 3000 + 1200*1.864950

= 8724.11

EUAC for 6 yr of operation = 12000*(A/P,7%,6) + 3000 + 1200*(A/G,7%,6)

= 12000*0.209796 + 3000 + 1200*2.303217

= 8972.38

As EUAC has started rising, it will keep increasing if we increase yr of operation

Minimum EUAC = 8666.04 at 4 yr of operation

Economic service life = 4 yrs