Question

Find the optimum annual equivalent cost for the defender using the following information:

Current trade-in (re-sale) value=$7,000, decreasing by $2000 from the previous year's value

O&M = $2,000 in year 1, increasing by 30% per year

immediate overhaul required (if kept)=$500

Maximum possible lifespan is 5 additional years of service (from now)

Assume MARR = 10%

Answer 1

Using Excel for ESL 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,10%,n)	EUAC
A	B	C	D=C*B	E	F=E+7500	G	H=G*B	I=F-H	J	K = I*J
1	0.9091	2000.00	1818.18	1818.18	9318.18	5000.00	4545.45	4772.73	1.1000	5250
2	0.8264	2600.00	2148.76	3966.94	11466.94	3000.00	2479.34	8987.60	0.5762	5179
3	0.7513	3380.00	2539.44	6506.39	14006.39	1000.00	751.31	13255.07	0.4021	5330
4	0.6830	4394.00	3001.16	9507.55	17007.55	-1000.00	-683.01	17690.56	0.3155	5581
5	0.6209	5712.20	3546.83	13054.37	20554.37	-3000.00	-1862.76	22417.14	0.2638	5914
Discount factor	1/(1+0.10)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

Minimum EUAC = 5179 at 2 yr, ESL = 2yrs

AEC at ESL = 5179

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+7500	G	H=G*B	I=F-H	J	K = I*J
1	=1/(1.1)^A14	=2000	=C14*B14	=D14	=7500+E14	=7000-2000	=G14*B14	=F14-H14	=0.1*((1 + 0.1)^A14)/((1 + 0.1)^A14-1)	=I14*J14
2	=1/(1.1)^A15	=C14*1.3	=C15*B15	=E14+D15	=7500+E15	=G14-2000	=G15*B15	=F15-H15	=0.1*((1 + 0.1)^A15)/((1 + 0.1)^A15-1)	=I15*J15
3	=1/(1.1)^A16	=C15*1.3	=C16*B16	=E15+D16	=7500+E16	=G15-2000	=G16*B16	=F16-H16	=0.1*((1 + 0.1)^A16)/((1 + 0.1)^A16-1)	=I16*J16
4	=1/(1.1)^A17	=C16*1.3	=C17*B17	=E16+D17	=7500+E17	=G16-2000	=G17*B17	=F17-H17	=0.1*((1 + 0.1)^A17)/((1 + 0.1)^A17-1)	=I17*J17
5	=1/(1.1)^A18	=C17*1.3	=C18*B18	=E17+D18	=7500+E18	=G17-2000	=G18*B18	=F18-H18	=0.1*((1 + 0.1)^A18)/((1 + 0.1)^A18-1)	=I18*J18
Discount factor	1/(1+0.10)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)