Question

1. Suppose a company has a forklift but is considering purchasing a new electric lift truck that would cost $230000 and has operating cost of $25000 in the first year. For the remaining years, operating costs increase each year by 15% over the previous year’s operating costs. It loses 12% of its value every year from the previous year’s salvage value. The lift truck has a maximum life of 5 years. The firm’s required rate of return is 5%. Find the economic service life of this new machine.

Answer 1

Using Excel for Economic service life analysis

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,5%,n)	EUAC
A	B	C	D=C*B	E	F=E+230000	G	H=G*B	I=F-H	J	K = I*J
1	0.9524	25000.00	23809.52	23809.52	253809.52	202400.00	192761.90	61047.62	1.0500	64100
2	0.9070	28750.00	26077.10	49886.62	279886.62	178112.00	161552.83	118333.79	0.5378	63640
3	0.8638	33062.50	28560.63	78447.25	308447.25	156738.56	135396.66	173050.59	0.3672	63546
4	0.8227	38021.88	31280.69	109727.94	339727.94	137929.93	113475.30	226252.65	0.2820	63806
5	0.7835	43725.16	34259.80	143987.75	373987.75	121378.34	95103.11	278884.64	0.2310	64415
Discount factor	1/(1+0.05)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

Minimum EUAC = 63546 at yr 3

Economic service life = 3 yrs

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,5%,n)	EUAC
A	B	C	D=C*B	E	F=E+230000	G	H=G*B	I=F-H	J	K = I*J
1	=1/(1.05)^A18	25000	=C18*B18	=D18	=230000+E18	=230000*0.88	=G18*B18	=F18-H18	=0.05*((1 + 0.05)^A18)/((1 + 0.05)^A18-1)	=I18*J18
2	=1/(1.05)^A19	=C18*1.15	=C19*B19	=E18+D19	=230000+E19	=G18*0.88	=G19*B19	=F19-H19	=0.05*((1 + 0.05)^A19)/((1 + 0.05)^A19-1)	=I19*J19
3	=1/(1.05)^A20	=C19*1.15	=C20*B20	=E19+D20	=230000+E20	=G19*0.88	=G20*B20	=F20-H20	=0.05*((1 + 0.05)^A20)/((1 + 0.05)^A20-1)	=I20*J20
4	=1/(1.05)^A21	=C20*1.15	=C21*B21	=E20+D21	=230000+E21	=G20*0.88	=G21*B21	=F21-H21	=0.05*((1 + 0.05)^A21)/((1 + 0.05)^A21-1)	=I21*J21
5	=1/(1.05)^A22	=C21*1.15	=C22*B22	=E21+D22	=230000+E22	=G21*0.88	=G22*B22	=F22-H22	=0.05*((1 + 0.05)^A22)/((1 + 0.05)^A22-1)	=I22*J22
Discount factor	1/(1+0.05)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)