Question

A city water and wastewater department has a four year old sludge pump that was initially purchased for $100000. This pump can be kept in service for an additional four years, or it can be sold for $52000 and replaced by a new pump. The purchase price of the replacement pump is $123500. The projected market values and operating and maintenance costs over four year planning horizon are shown in the table that follows. Assuming the MARR is 6%

a) determine the economic life of the defender and the annual cost of defender in its economic life.
b) determine the economic life of the challenger and the annual cost of challenger in its economic life

	Defender		Challenger
Year	MV at end of the year	Operation & maintenance cost	MV at end of the year	Operation & maintenance cost
1	52070	15400	84500	12890
2	46520	18020	74800	13550
3	34340	19050	52000	18670
4	26400	20300	28900	14600

IN EXCEL

Answer 1

Using Excel for ESL analysis of Defender

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,6%,n)	EUAC
A	B	C	D=C*B	E	F=E+52000	G	H=G*B	I=F-H	J	K = I*J
1	0.9434	15400.00	14528.30	14528.30	66528.30	52070.00	49122.64	17405.66	1.060000	18450.0
2	0.8900	18020.00	16037.74	30566.04	82566.04	46520.00	41402.63	41163.40	0.545437	22452.0
3	0.8396	19050.00	15994.75	46560.79	98560.79	34340.00	28832.53	69728.26	0.374110	26086.0
4	0.7921	20300.00	16079.50	62640.29	114640.29	26400.00	20911.27	93729.01	0.288591	27049.4
Discount factor	1/(1+0.06)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

Minimum EUAC in year 1 at 18450, so ESL of defender = 1 yr

Annual cost in ESL = 18450

Using Excel for ESL analysis of Challenger

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,6%,n)	EUAC
A	B	C	D=C*B	E	F=E+123500	G	H=G*B	I=F-H	J	K = I*J
1	0.9434	12890.00	12160.38	12160.38	135660.38	84500.00	79716.98	55943.40	1.060000	59300.0
2	0.8900	13550.00	12059.45	24219.83	147719.83	74800.00	66571.73	81148.10	0.545437	44261.2
3	0.8396	18670.00	15675.69	39895.52	163395.52	52000.00	43660.20	119735.32	0.374110	44794.2
4	0.7921	14600.00	11564.57	51460.09	174960.09	28900.00	22891.51	152068.58	0.288591	43885.7
Discount factor	1/(1+0.06)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

Minimum EUAC in year 4 at 43885.7, so ESL of challenger = 4 yr

Annual cost in ESL = 43885.70

As minimum Annual cost of challenger is more than annual cost of keeping the defender for 4 yrs, defender should be kept for 4 yrs

Showing formula for defender, challenger is similar to it, only values of salvage value, first cost and O&M cost needs to be changed

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,6%,n)	EUAC
A	B	C	D=C*B	E	F=E+52000	G	H=G*B	I=F-H	J	K = I*J
1	=1/(1.06)^A4	15400	=C4*B4	=D4	=52000+E4	52070	=G4*B4	=F4-H4	=0.06*((1 + 0.06)^A4)/((1 + 0.06)^A4-1)	=I4*J4
2	=1/(1.06)^A5	18020	=C5*B5	=E4+D5	=52000+E5	46520	=G5*B5	=F5-H5	=0.06*((1 + 0.06)^A5)/((1 + 0.06)^A5-1)	=I5*J5
3	=1/(1.06)^A6	19050	=C6*B6	=E5+D6	=52000+E6	34340	=G6*B6	=F6-H6	=0.06*((1 + 0.06)^A6)/((1 + 0.06)^A6-1)	=I6*J6
4	=1/(1.06)^A7	20300	=C7*B7	=E6+D7	=52000+E7	26400	=G7*B7	=F7-H7	=0.06*((1 + 0.06)^A7)/((1 + 0.06)^A7-1)	=I7*J7
Discount factor	1/(1+0.06)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)