Question

A city water and waste-water department has a four year old sludge pump that was initially purchased for 65,000. This pump can be kept in service for an additional 4 years, or it can be sold for 36,000 and replaced by a new pump. The purchase price of the replacement pump is 51,500. The projected MVs and operating maintenance cost over the four year planning horizon are shown in the table that follows. Assuming the MARR is 8%, A. determine the economic life of the challenger and B. determine when the defender should be replaced?

4 of 7 (2 complete) HT ic) Defender Challenger Year MV at EOY 0&M Costs 0&M Costs MV at EOY 1 $26,500 $19,500 $38,500 $14000 2 23,000 22,000 31,500 16,500 19 500 24 500 24 500 19 nn0 year(s). (Round to the nearest whole number) er is OX and then click Check Answer Clear All

please show all steps.

Answer 1

Using Excel to perform Economic life analysis

Economic Life 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,8%,n)	EUAC
A	B	C	D=C*B	E	F=E+51500	G	H=G*B	I=F-H	J	K = I*J
1	0.92593	14000.00	12962.96	12962.96	64462.96	38500.00	35648.15	28814.81	1.08000	31120.00
2	0.85734	16500.00	14146.09	27109.05	78609.05	31500.00	27006.17	51602.88	0.56077	28937.31
3	0.79383	19000.00	15082.81	42191.87	93691.87	24500.00	19448.89	74242.98	0.38803	28808.76
4	0.73503	21500.00	15803.14	57995.01	109495.01	17500.00	12863.02	96631.99	0.30192	29175.21
Discount factor	1/(1+0.08)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

As EUAC is Lowest in yr 3 at 28808.76, therefore Economic life of challenger is 3 yrs

Economic Life 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,8%,n)	EUAC
A	B	C	D=C*B	E	F=E+36000	G	H=G*B	I=F-H	J	K = I*J
1	0.92593	19500.00	18055.56	18055.56	54055.56	26500.00	24537.04	29518.52	1.08000	31880.00
2	0.85734	22000.00	18861.45	36917.01	72917.01	23000.00	19718.79	53198.22	0.56077	29831.92
3	0.79383	24500.00	19448.89	56365.90	92365.90	19500.00	15479.73	76886.17	0.38803	29834.41
4	0.73503	27000.00	19845.81	76211.71	112211.71	16000.00	11760.48	100451.23	0.30192	30328.32
Discount factor	1/(1+0.08)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)

As minimum EUAC of Defender is 29831.92 at yr 2, which is more than the minimum EUAC of Challenger of 28808.76, therefore defender should be replaced immediately

Showing formula for economic 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,8%,n)	EUAC
A	B	C	D=C*B	E	F=E+36000	G	H=G*B	I=F-H	J	K = I*J
1	=1/(1.08)^A44	19500	=C44*B44	=D44	=36000+E44	26500	=G44*B44	=F44-H44	=0.08*((1 + 0.08)^A44)/((1 + 0.08)^A44-1)	=I44*J44
2	=1/(1.08)^A45	22000	=C45*B45	=E44+D45	=36000+E45	23000	=G45*B45	=F45-H45	=0.08*((1 + 0.08)^A45)/((1 + 0.08)^A45-1)	=I45*J45
3	=1/(1.08)^A46	24500	=C46*B46	=E45+D46	=36000+E46	19500	=G46*B46	=F46-H46	=0.08*((1 + 0.08)^A46)/((1 + 0.08)^A46-1)	=I46*J46
4	=1/(1.08)^A47	27000	=C47*B47	=E46+D47	=36000+E47	16000	=G47*B47	=F47-H47	=0.08*((1 + 0.08)^A47)/((1 + 0.08)^A47-1)	=I47*J47
Discount factor	1/(1+0.08)^n
(A/P,i,n)	i((1 + i)^n)/((1 + i)^n-1)