Question

A city water and wastewater department has a four year old sludge pump that was initially purchased for $90400. This pump can be kept in service for an additional four years, or it can be sold for $51010 and replaced by a new pump. The purchase price of the replacement pump is $101840. 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 11%

a) (4 points) determine the economic life of the defender and the annual cost of defender in its economic life.

b) (4 points) determine the economic life of the challenger and the annual cost of challenger in its economic life.

c) (3 points) determine when the defender should be replaced
.

	defender	defender	challenger	challenger
year	MV at end of year	Operation & maintenance costs	MV at end of year	Operation & maintenance costs
1	46930	16820	81500	12620
2	41300	18170	73400	13760
3	36350	19990	54400	15140
4	32350	21390	28900	15900

Answer 1

a.

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+51010	G	H=G*B	I=F-H	J	K = I*J
1	0.9009	16820.00	15153.15	15153.15	66163.15	46930.00	42279.28	23883.87	1.1100	26511.1
2	0.8116	18170.00	14747.18	29900.33	80910.33	41300.00	33520.01	47390.33	0.5839	27672.8
3	0.7312	19990.00	14616.52	44516.85	95526.85	36350.00	26578.81	68948.04	0.4092	28214.4
4	0.6587	21390.00	14090.26	58607.10	109617.10	32350.00	21309.95	88307.16	0.3223	28463.7
Discount factor	1/(1+0.11)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

Minimum EUAC in year 1 at 26511.10, so ESL of defender = 1 yr

Annual cost in ESL = 26511.10

b.

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,11%,n)	EUAC
A	B	C	D=C*B	E	F=E+101840	G	H=G*B	I=F-H	J	K = I*J
1	0.9009	12620.00	11369.37	11369.37	113209.37	81500.00	73423.42	39785.95	1.1100	44162.4
2	0.8116	13760.00	11167.92	22537.29	124377.29	73400.00	59573.09	64804.21	0.5839	37841.4
3	0.7312	15140.00	11070.24	33607.53	135447.53	54400.00	39776.81	95670.72	0.4092	39149.7
4	0.6587	15900.00	10473.82	44081.35	145921.35	28900.00	19037.33	126884.03	0.3223	40898.1
Discount factor	1/(1+0.11)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

Minimum EUAC in year 2 at 37841.40, so ESL of challenger = 2 yr

Annual cost in ESL = 37841.40

c

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,11%,n)	EUAC
A	B	C	D=C*B	E	F=E+51010	G	H=G*B	I=F-H	J	K = I*J
1	=1/(1.11)^A4	16820	=C4*B4	=D4	=51010+E4	46930	=G4*B4	=F4-H4	=0.11*((1 + 0.11)^A4)/((1 + 0.11)^A4-1)	=I4*J4
2	=1/(1.11)^A5	18170	=C5*B5	=E4+D5	=51010+E5	41300	=G5*B5	=F5-H5	=0.11*((1 + 0.11)^A5)/((1 + 0.11)^A5-1)	=I5*J5
3	=1/(1.11)^A6	19990	=C6*B6	=E5+D6	=51010+E6	36350	=G6*B6	=F6-H6	=0.11*((1 + 0.11)^A6)/((1 + 0.11)^A6-1)	=I6*J6
4	=1/(1.11)^A7	21390	=C7*B7	=E6+D7	=51010+E7	32350	=G7*B7	=F7-H7	=0.11*((1 + 0.11)^A7)/((1 + 0.11)^A7-1)	=I7*J7
Discount factor	1/(1+0.11)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)