s Points mic service life at MARR10 pe the econo and estimat

(s Points) mic service life at MARR-10% pe the econo and estimated r year for a machine that has a first cost of ine ooo Operating Cost (SY Market Value () 1500 2200 3000 4000 5000 10000 7000 5000 3500 2 3 2500 5

Solution

Economic service life (ESL) is that year for which Annual worth (AW) of costs is minimized. AW of costs for each year is computed as follows.

AW, Year 1 ($) = 15,000 x A/P(10%, 1) + 1,500 - 10,000 x P/F(10%, 1) x A/P(10%, 1)

= 15,000 x 1.1 + 1,500 - 10,000 x 0.9091 x 1.1 = 16,499.84 + 1,500 - 10,000 = 7,999.84

AW, Year 2 ($) = 15,000 x A/P(10%, 2) + 2,200 - 7,000 x P/F(10%, 2) x A/P(10%, 2)

= 15,000 x 0.5762 + 2,200 - 7,000 x 0.8264 x 0.5762 = 8,643 + 2,200 - 3,333.20 = 7,509.80

AW, Year 3 ($) = 15,000 x A/P(10%, 3) + 3,000 - 5,000 x P/F(10%, 3) x A/P(10%, 3)

= 15,000 x 0.4021 + 3,000 - 5,000 x 0.7513 x 0.4021 = 6,031.61 + 3,000 - 1,510.49 = 7,521.12

AW, Year 4 ($) = 15,000 x A/P(10%, 4) + 4,000 - 3,500 x P/F(10%, 4) x A/P(10%, 4)

= 15,000 x 0.3155 + 4,000 - 3,500 x 0.683 x 0.3155 = 4,732.50 + 4,000 - 754.20 = 7,978.30

AW, Year 5 ($) = 15,000 x A/P(10%, 5) + 5,000 - 2,500 x P/F(10%, 5) x A/P(10%, 5)

= 15,000 x 0.2638 + 5,000 - 2,500 x 0.6209 x 0.2638 = 3,956.95 + 5,000 - 409.48 = 8,547.47

Since AW of costs is minimum in year 2 (= $7,509.80), Economic service life is 2 years.