Question

13-24

A 2,000-pound, counterbalanced, propane forklift can be purchased for $30,000. Due to the intended service use, the forklift’s market value drops 20% of its prior year’s value in Years 1 and 2 and then declines 15% until Year 10 when it will have a scrap/market value of $1,000. Maintenance of the forklift is $400 per year during Years 1 and 2 while the warranty is in place. In Year 3 it jumps to $750 and increases by $200 per year thereafter. What is the optimal life of the forklift using i = 10%?

Answer 1

We need to calculate economic life of the forlift

I = 10%

Initial cost = 30000

Salvage value = 20% drop in first year from initial cost, 20% in next year. 15% drop per year afterwards

Maintenance cost = 400 in year 1 and 2, 750 in yr 3 and increase by 200 per year after wards

using excel

Year	Discount factor	O&M cost	PV (O&M)	Cumulative (O&M)	Cumulative (O&M) + Initial Cost	Salvage value	PV (Salvage value)	NPV	(A/P,10%,n)	EUAC
A	B	C	D=C*B	E	F=E+30000	G	H=G*B	I=F-H	J	K = I*J
1	0.90909	400.00	363.64	363.64	30363.64	24000.00	21818.18	8545.45	1.10000	9400.00
2	0.82645	400.00	330.58	694.21	30694.21	19200.00	15867.77	14826.45	0.57619	8542.86
3	0.75131	750.00	563.49	1257.70	31257.70	16320.00	12261.46	18996.24	0.40211	7638.67
4	0.68301	950.00	648.86	1906.56	31906.56	13872.00	9474.76	22431.80	0.31547	7076.58
5	0.62092	1150.00	714.06	2620.62	32620.62	11791.20	7321.41	25299.22	0.26380	6673.87
6	0.56447	1350.00	762.04	3382.66	33382.66	10022.52	5657.45	27725.21	0.22961	6365.91
7	0.51316	1550.00	795.40	4178.06	34178.06	8519.14	4371.67	29806.39	0.20541	6122.40
8	0.46651	1750.00	816.39	4994.45	34994.45	7241.27	3378.11	31616.34	0.18744	5926.29
9	0.42410	1950.00	826.99	5821.44	35821.44	6155.08	2610.35	33211.08	0.17364	5766.79
10	0.38554	2150.00	828.92	6650.35	36650.35	1000.00	385.54	36264.81	0.16275	5901.93
Discount factor	1/(1+0.10)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

As EUAC is lowest in yr 9, so optimum life is 9 years

Showing formula in excel

Year	Discount factor	O&M cost	PV (O&M)	Cumulative (O&M)	Cumulative (O&M) + Initial Cost	Salvage value	PV (Salvage value)	NPV	(A/P,10%,n)	EUAC
A	B	C	D=C*B	E	F=E+30000	G	H=G*B	I=F-H	J	K = I*J
1	=1/(1.1)^A66	400	=C66*B66	=D66	=30000+E66	=30000*0.8	=G66*B66	=F66-H66	=0.1*((1 + 0.1)^A66)/((1 + 0.1)^A66-1)	=I66*J66
2	=1/(1.1)^A67	400	=C67*B67	=E66+D67	=30000+E67	=G66*0.8	=G67*B67	=F67-H67	=0.1*((1 + 0.1)^A67)/((1 + 0.1)^A67-1)	=I67*J67
3	=1/(1.1)^A68	750	=C68*B68	=E67+D68	=30000+E68	=G67*0.85	=G68*B68	=F68-H68	=0.1*((1 + 0.1)^A68)/((1 + 0.1)^A68-1)	=I68*J68
4	=1/(1.1)^A69	=C68+200	=C69*B69	=E68+D69	=30000+E69	=G68*0.85	=G69*B69	=F69-H69	=0.1*((1 + 0.1)^A69)/((1 + 0.1)^A69-1)	=I69*J69
5	=1/(1.1)^A70	=C69+200	=C70*B70	=E69+D70	=30000+E70	=G69*0.85	=G70*B70	=F70-H70	=0.1*((1 + 0.1)^A70)/((1 + 0.1)^A70-1)	=I70*J70
6	=1/(1.1)^A71	=C70+200	=C71*B71	=E70+D71	=30000+E71	=G70*0.85	=G71*B71	=F71-H71	=0.1*((1 + 0.1)^A71)/((1 + 0.1)^A71-1)	=I71*J71
7	=1/(1.1)^A72	=C71+200	=C72*B72	=E71+D72	=30000+E72	=G71*0.85	=G72*B72	=F72-H72	=0.1*((1 + 0.1)^A72)/((1 + 0.1)^A72-1)	=I72*J72
8	=1/(1.1)^A73	=C72+200	=C73*B73	=E72+D73	=30000+E73	=G72*0.85	=G73*B73	=F73-H73	=0.1*((1 + 0.1)^A73)/((1 + 0.1)^A73-1)	=I73*J73
9	=1/(1.1)^A74	=C73+200	=C74*B74	=E73+D74	=30000+E74	=G73*0.85	=G74*B74	=F74-H74	=0.1*((1 + 0.1)^A74)/((1 + 0.1)^A74-1)	=I74*J74
10	=1/(1.1)^A75	=C74+200	=C75*B75	=E74+D75	=30000+E75	1000	=G75*B75	=F75-H75	=0.1*((1 + 0.1)^A75)/((1 + 0.1)^A75-1)	=I75*J75
Discount factor	1/(1+0.10)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)