Question

"A new delivery truck is available for $200,000. O&M costs are $21,000 each year for the first five years, $33,600 in year six, $52,100 in year seven, and $81,300 in year eight. Salvage values are estimated to be $150,000 after one year and will decrease at the rate of 17% per year thereafter. At a MARR of 17%, determine the economic service life of the truck. Enter your answer as an integer from 1 to 8."

Answer 1

Year	Salvage Value	AO&M	Capital Recovery Cost (CR)	EAC of AO&M	Total EAC (CR + EAC of AO&M)
1	$150,000	$21,000	$84,000	$20,999.98	$105,000
2	$124,500	$21,000	$68,790	$20,998.83	$89,789
3	$103,335	$21,000	$61,318	$21,001.36	$82,319
4	$85,768	$21,000	$56,218	$20,998.59	$77,217
5	$71,187	$21,000	$52,369	$21,002.78	$73,371
6	$59,086	$33,600	$49,303	$22367.31	$71,671
7	$49,041	$52,100	$46,816	$21551.06	$68,367
8	$40,704	$81,300	$44,784	$25600.61	$70,385

The minimum total EAC is in year 7. So the economic service life is 7 year.

Explanation for CR and EAC:

Capital Recovery (CR) = Purchase price x (A/P, i, n) – Salvage value x (A/F i, n)

Year 1:

CR = $ 200,000 x (A/P, 17 %, 1) – $ 150,000 x (A/F 17 %, 1)

      = $ 200,000 x 1.17 – $ 150,000 x 1

      = $ 234,000 - $ 150,000 = $ 84,000

EAC O&M = $ 21,000 x (P/F, 17 %, 1) x (A/P, 17 %, 1)

                    = $ 21,000 x 0.8547 x .1.17 = $ 20,999.98

Year 2:

CR = $ 200,000 x (A/P, 17 %, 2) – $ 124,500 x (A/F 17 %, 2)

      = $ 200,000 x 0.6308 – $ 124,500 x 0.4608

      = $ 126,160 - $ 57,370 = $ 68,790

EAC O&M = $ 21,000 x (P/F, 17 %, 1) + $ 21,000 x (P/F, 17 %, 2) x (A/P, 17 %, 2)

       = ($ 21,000 x 0.8547+ $ 21,000 x 0.7305) x 0.6308

       = ($ 17,948.70 + $ 15340.50) x 0.6308

      = $ 33,289.20 x 0.6308

       = $ 20,998.82736

Year 3:

CR = $ 200,000 x (A/P, 17 %, 3) – $ 103,335 x (A/F 17 %, 3)

      = $ 200,000 x 0.4526 – $ 103,335 x 0.2826

      = $ 90,520 - $ 29,202 = $ 61,318

EAC O&M = $ 21,000 x (P/F, 17 %, 1) + $ 21,000 x (P/F, 17 %, 2) +$ 21,000 x (P/F, 17 %, 3) x (A/P, 17 %, 3)

       = ($ 21,000 x 0.8547+ $ 21,000 x 0.7305 + $ 21,000 x 0.6244) x 0.4526

       = ($ 17,948.70 + $ 15340.50 + $ 13,112.40) x 0.4526

       = $ 46,401.60 x 0.4526

       = $ 21,001.36

Year 4:

CR = $ 200,000 x (A/P, 17 %, 4) – $ 85,768 x (A/F 17 %, 4)

      = $ 200,000 x 0.3645 – $ 85,768 x 0.1945

      = $ 72,900 - $ 16,682 = $ 56,218

EAC O&M = [$ 21,000 x (P/F, 17 %, 1) + $ 21,000 x (P/F, 17 %, 2) +$ 21,000 x (P/F, 17 %, 3) +$ 21,000 x (P/F, 17 %, 4)] x (A/P, 17 %, 4)

       = ($ 21,000 x 0.8547+ $ 21,000 x 0.7305 + $ 21,000 x 0.6244 + $ 21,000 x 0.5337) x 0.3645

       = ($ 17,948.70 + $ 15340.50 + $ 13,112.40 + $ 11,207.70) x 0.3645

       = $ 57,609.30 x 0.3645

       = $ 20,998.59

And so on….