Question

An asset has a current market value of $50,000 and will last another 5 years before failure. Each year, the market value decreases by $4,000. The operating cost of the asset in year 1 is expected to be $25,000, and it will increase by $5,000 each year through year 5.  

What is the economic service life (ESL) of the asset if the MARR = 12%.

a) 1 year

b) 2 years

c) 3 years

d) 4 years

Answer 1

EUAC for 1 yr of operation = 50000*(A/P,12%,1) + 25000 - (50000-4000)*(A/F,12%,1)

= 50000*1.12 + 25000 - (50000-4000)

= 35000

EUAC for 2 yr of operation = 50000*(A/P,12%,2) + 25000 + 5000*(A/G,12%,2) - (50000-2*4000)*(A/F,12%,2)

= 50000*0.591698 + 25000 + 5000*0.471698 - (50000-2*4000)*0.471698

= 37132.08

EUAC for 3 yr of operation = 50000*(A/P,12%,3) + 25000 + 5000*(A/G,12%,3) - (50000-3*4000)*(A/F,12%,3)

= 50000*0.416349 + 25000 + 5000*0.924609 - (50000-3*4000)*0.296349

= 39179.23

EUAC for 4 yr of operation = 50000*(A/P,12%,4) + 25000 + 5000*(A/G,12%,4) - (50000-4*4000)*(A/F,12%,4)

= 50000*0.329234 + 25000 + 5000*1.358852 - (50000-4*4000)*0.209234

= 41142.01

EUAC for 5 yr of operation = 50000*(A/P,12%,5) + 25000 + 5000*(A/G,12%,5) - (50000-5*4000)*(A/F,12%,5)

= 50000*0.277410 + 25000 + 5000*1.774595 - (50000-5*4000)*0.157410

= 43021.17

As Annual cost of operation is minimum in 1 yr, ESL = 1 yr

First option is correct answer