Question

A piece of equipment has a first cost of $160,000, a maximum useful life of 7 years, and a market (salvage) value described by the relation S = 120,000 – 17,000k, where k is the number of years since it was purchased. The salvage value cannot go below zero. The AOC series is estimated using AOC = 60,000 + 11,000k. The interest rate is 11% per year. Determine the economic service life and the respective AW.

The economic service life is year(s) and the AW value is $

Answer 1

Year	Salvage value	AOC	Capital Recovery Cost (CR)	EAC of AOC	Total EAC
1	$        103,000	$     71,000	$       280,600.00	$ 71,000.00	$        351,600.00
2	$          86,000	$      82,000	$         52,668.60	$ 76,214.00	$        128,882.60
3	$          69,000	$      93,000	$        44,827.20	$ 81,241.00	$        126,068.20
4	$          52,000	$    104,000	$         40,528.40	$ 86,070.00	$        126,598.40
5	$          35,000	$    115,000	$         37,675.00	$ 90,712.00	$        128,387.00
6	$          18,000	$    126,000	$        35,548.80	$ 95,178.00	$        130,726.80
7	$            1,000	$    137,000	$         33,849.80	$ 99,446.00	$        133,295.80

The minimum total Equivalent annual cost (EAC) is in year 3. Thus equipment’s Economic service life is 3 years.

AW for year 3 = CR – AOC = $ 44,827.20 - $ 93,000 = - $ 48,172.80

Explanation for CR and EAC:

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

CR for year 1:

CR = $ 160,000 x (A/P, 11%, 1) – $ 103,000 x (A/F 11%, 1)

      = $ 160,000 x 1.11 – $ 103,000 x 1

      = $ 177,600 - $ 103,000 = $ 280,600

EAC of AOC = $ 71,000

CR for year 2:

CR = $ 160,000 x (A/P, 11%, 2) – $ 86,000 x (A/F 11%, 2)

      = $ 160,000 x .5839 – $ 86,000 x .4739

      = $ 93,424 - $ 40,755.40 = $ 52,668.60

EAC of AOC = $ 71,000 + $ 11,000 x $ 11,000 (A/G 11%, 2)

                      = $ 71,000 + $ 11,000 x .474

                      = $ 71,000 + $ 5,214 = $ 76,214

CR for year3:

CR = $ 160,000 x (A/P, 11%, 3) – $ 69,000 x (A/F 11%, 3)

      = $ 160,000 x .4092 – $ 69,000 x .2992

      = $ 65,472 - $ 20,644.8= $ 44,827.2

EAC of AOC = $ 71,000 + $ 11,000 x $ 11,000 (A/G 11%, 3)

                      = $ 71,000 + $ 11,000 x .931

                      = $ 71,000 + $ 10,241= $ 81,241

CR for year 4:

CR = $ 160,000 x (A/P, 11%, 4) – $ 52,000x (A/F 11%, 4)

      = $ 160,000 x .3223 – $ 52,000 x .2123

      = $ 51,568- $ 11,039.6 = $ 40,528.4

EAC of AOC = $ 71,000 + $ 11,000 x $ 11,000 (A/G 11%, 4)

                      = $ 71,000 + $ 11,000 x 1.370

                      = $ 71,000 + $ 15,070 = $ 86,070

CR for year 5:

CR = $ 160,000 x (A/P, 11%, 5) – $ 35,000 x (A/F 11%, 5)

      = $ 160,000 x .2706 – $ 35,000 x .1606

      = $ 43,296 - $ 5,621 = $ 37,675

EAC of AOC = $ 71,000 + $ 11,000 x $ 11,000 (A/G 11%, 5)

                      = $ 71,000 + $ 11,000 x 1.792

                      = $ 71,000 + $ 19,712 = $ 90,712

CR for year 6:

CR = $ 160,000 x (A/P, 11%, 6) – $ 18,000 x (A/F 11%, 6)

      = $ 160,000 x .2364 – $ 18,000 x .1264

      = $ 37,824 - $ 2,275 = $ 35,549

EAC of AOC = $ 71,000 + $ 11,000 x $ 11,000 (A/G 11%, 6)

                      = $ 71,000 + $ 11,000 x 2.198

                      = $ 71,000 + $ 24,178 = $ 95,178

CR for year 7:

CR = $ 160,000 x (A/P, 11%, 7) – $ 1,000 x (A/F 11%, 7)

      = $ 160,000 x .2122 – $1,000 x .1022

      = $ 33,952 - $ 102.2 = $ 33,849.8

EAC of AOC = $ 71,000 + $ 11,000 x $ 11,000 (A/G 11%, 7)

                      = $ 71,000 + $ 11,000 x 2.586

                      = $ 71,000 + $ 28,446 = $ 99,446