A new asset is available for $239,000. O&M costs are $24,000 each year for the first...

A new asset is available for $239,000. O&M costs are $24,000 each year for the first five years, $37,680 in year six, $57,700 in year seven, and $88,300 in year eight. Salvage values are estimated to be $198,000 after one year and will decrease at the rate of 17% per year thereafter. At a MARR of 12%, determine the economic service life of the asset. Enter your answer as an integer from 1 to 8.

Expert Solution

Formula Sheet

A1	B	C	D	E	F	G	H	I	J
2		Economic service life is the life of the machine at which equivalent uniform annual cost is minimum.
3		Total EUAC consist of two components: Capital recovery cost and Equivalent uniform annual cost of O&M.
4		Capital recovery cost in year n is calculated as follows:
5		CR_n = P(A/P,i,n)-S(A/F,i,n)
6		CR_n = (P-S)(A/P,i,n)+S(i)
7		Where P is the present value (Cost) of the machine and S are maket value on nth year and i is interest rate.
8		Equivalent uniform annual cost of O&M, EUAC (O&M) is calculated as follows:
9		To Calculate EUAC (O&M) for a period, NPV of costs for till the period needs to be calculated first.
10		Then EUAC (O&M) can be calculated as follows:
11		EUAC (O&M)	=NPV of Costs till year n*(A/P,i,n)
12		Then total EUAC for each of the year is calculated.
13		Total EUAC at year n	=CR_n+EUAC (O&M)
14
15		Calculation of EUAC for Existing Machine
16		MARR (i)	0.12
17		Year	Market Value (MV)	Operating cost ($ per year)
18		0	239000
19		1	=D18*(1-17%)	24000
20		2	=D19*(1-17%)	24000
21		3	=D20*(1-17%)	24000
22		4	=D21*(1-17%)	24000
23		5	=D22*(1-17%)	24000
24		6	=D23*(1-17%)	37680
25		7	=D24*(1-17%)	57700
26		8	=D25*(1-17%)	88300
27
28		For Year 1:
29		Capital Recovery Cost(CR₁)	= (P-S)(A/P,i,n)+S(i)
30			=(D18-D19)(1/PV(D16,C19,-1,0))+D19D16	=(D18-D19)(1/PV(D16,C19,-1,0))+D19D16
31		NPV of costs till year1	=E18+NPV(D16,E19)	=E18+NPV(D16,E19)
32		EUAC (O&M) till year1	=NPV of Costs till year n*(A/P,i,n)
33			=D31*(1/PV(D16,C19,-1,0))	=D31*(1/PV(D16,C19,-1,0))
34
35		Total EUAC at year 1	=CR₁+EUAC (O&M) for year 1
36			=D30+D33	=D30+D33
37
38		Similarly for other years it can be calculated as follows:
39		Interest rate (i)	=D16
40		Year	Market Value (MV)	Operating cost ($ per year)	Capital Recovery Cost	NPV of Cost	EUAC (O&M)	Total EUAC
41		0	=D18	=E18
42		1	=D19	=E19	=($D$41-D42)(1/PV($D$39,C42,-1,0))+D42$D$39	=E41+NPV(D39,E42)	=G42*(1/PV($D$39,C42,-1,0))	=F42+H42
43		2	=D20	=E20	=($D$41-D43)(1/PV($D$39,C43,-1,0))+D43$D$39	=$E$41+NPV($D$39,$E$42:E43)	=G43*(1/PV($D$39,C43,-1,0))	=F43+H43
44		3	=D21	=E21	=($D$41-D44)(1/PV($D$39,C44,-1,0))+D44$D$39	=$E$41+NPV($D$39,$E$42:E44)	=G44*(1/PV($D$39,C44,-1,0))	=F44+H44
45		4	=D22	=E22	=($D$41-D45)(1/PV($D$39,C45,-1,0))+D45$D$39	=$E$41+NPV($D$39,$E$42:E45)	=G45*(1/PV($D$39,C45,-1,0))	=F45+H45
46		5	=D23	=E23	=($D$41-D46)(1/PV($D$39,C46,-1,0))+D46$D$39	=$E$41+NPV($D$39,$E$42:E46)	=G46*(1/PV($D$39,C46,-1,0))	=F46+H46
47		6	=D24	=E24	=($D$41-D47)(1/PV($D$39,C47,-1,0))+D47$D$39	=$E$41+NPV($D$39,$E$42:E47)	=G47*(1/PV($D$39,C47,-1,0))	=F47+H47
48		7	=D25	=E25	=($D$41-D48)(1/PV($D$39,C48,-1,0))+D48$D$39	=$E$41+NPV($D$39,$E$42:E48)	=G48*(1/PV($D$39,C48,-1,0))	=F48+H48
49		8	=D26	=E26	=($D$41-D49)(1/PV($D$39,C49,-1,0))+D49$D$39	=$E$41+NPV($D$39,$E$42:E49)	=G49*(1/PV($D$39,C49,-1,0))	=F49+H49
50
51
52		Since total EUAC of machine is minimum in year 6 therefore economic life of the machine is 6 year.
53

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