Question

(Based on problem 8.9 of Hyman, Fundamentals of Engineering Design, Prentice-Hall, 2nd ed., 2003.) You are considering upgrading some manufacturing facilities by purchasing one of three different machines, each with the same production capacity. Machine A costs $40,000, has a useful life of 20 years, annual maintenance costs of $2500, and salvage value of $5000. Machine B costs $30,000, has a useful life of 10 years, annual maintenance of $3000, and salvage value of $3000. Machine C costs $15,000, has a useful life of 5 years, annual maintenance of $5000, and no salvage value. You are planning for a total period of operation of 20 years. Assume that (i) Machines B and C will be replaced one or more times by identical new units at the end of their useful lifetimes and (ii) machine purchase prices, annual maintenance, and discount rates are constant throughout the analysis period. A. Which is the most economical choice, based on total costs without considering time value? Which is the best choice, based on minimizing annualized value of total costs over the 20-year period, assuming i = 7% / year? Provide a spreadsheet similar to Tables 8.1 or 8.3 in the text. B. What is the Benefit/Cost ratio (as a percentage return on investment) during the first five years of operation for the reduced annual maintenance cost versus the increased initial machine cost for (i) Machine A compared to Machine C and (ii) Machine B compared to Machine C?

Answer 1

Part A

Please find the cost summary as below (refer detailed calculation* after answer):

	Cost of Project without time Value	Present Value of Cost of Project @ 7%
Machine A	85000	65192.94
Machine B	114000	74732.22
Machine C	160000	91726.79

Machine A is most economical as the Total Cost without time value and with time value both are least in this case. Therefore, Machine A should be selected.

*Calculation:

Calculate the Present Value of Cost @ 7%:
Calculation of PV Factor = 1/(1+r)^t
r = 7%
t= Year
Machine A
Year	Particular	Outflow	PV Factor @ 7%	Present value of Outflow
0	Machine Cost	40000	1	40000.00
1	Maint. Cost	2500	0.9346	2336.45
2	Maint. Cost	2500	0.8734	2183.60
3	Maint. Cost	2500	0.8163	2040.74
4	Maint. Cost	2500	0.7629	1907.24
5	Maint. Cost	2500	0.7130	1782.47
6	Maint. Cost	2500	0.6663	1665.86
7	Maint. Cost	2500	0.6227	1556.87
8	Maint. Cost	2500	0.5820	1455.02
9	Maint. Cost	2500	0.5439	1359.83
10	Maint. Cost	2500	0.5083	1270.87
11	Maint. Cost	2500	0.4751	1187.73
12	Maint. Cost	2500	0.4440	1110.03
13	Maint. Cost	2500	0.4150	1037.41
14	Maint. Cost	2500	0.3878	969.54
15	Maint. Cost	2500	0.3624	906.12
16	Maint. Cost	2500	0.3387	846.84
17	Maint. Cost	2500	0.3166	791.44
18	Maint. Cost	2500	0.2959	739.66
19	Maint. Cost	2500	0.2765	691.27
20	Maint. Cost	2500	0.2584	646.05
20	Salvage Value	-5000	0.2584	-1292.10
	Total	85000		65192.94
Machine B
Year	Particular	Outflow	PV Factor @ 7%	Present value of Outflow
0	Machine Cost	30000	1.0000	30000.00
1	Maint. Cost	3000	0.9346	2803.74
2	Maint. Cost	3000	0.8734	2620.32
3	Maint. Cost	3000	0.8163	2448.89
4	Maint. Cost	3000	0.7629	2288.69
5	Maint. Cost	3000	0.7130	2138.96
6	Maint. Cost	3000	0.6663	1999.03
7	Maint. Cost	3000	0.6227	1868.25
8	Maint. Cost	3000	0.5820	1746.03
9	Maint. Cost	3000	0.5439	1631.80
10	Maint. Cost	3000	0.5083	1525.05
10	Salvage Value of old machine	-3000	0.5083	-1525.05
10	New Machine Cost	30000	0.5083	15250.48
11	Maint. Cost	3000	0.4751	1425.28
12	Maint. Cost	3000	0.4440	1332.04
13	Maint. Cost	3000	0.4150	1244.89
14	Maint. Cost	3000	0.3878	1163.45
15	Maint. Cost	3000	0.3624	1087.34
16	Maint. Cost	3000	0.3387	1016.20
17	Maint. Cost	3000	0.3166	949.72
18	Maint. Cost	3000	0.2959	887.59
19	Maint. Cost	3000	0.2765	829.52
20	Maint. Cost	3000	0.2584	775.26
20	Salvage Value	-3000	0.2584	-775.26
	Total	114000		74732.22
Machine C
Year	Particular	Outflow	PV Factor @ 7%	Present value of Outflow
0	Machine Cost	15000	1.0000	15000.00
1	Maint. Cost	5000	0.9346	4672.90
2	Maint. Cost	5000	0.8734	4367.19
3	Maint. Cost	5000	0.8163	4081.49
4	Maint. Cost	5000	0.7629	3814.48
5	Maint. Cost	5000	0.7130	3564.93
5	New Machine Cost	15000	0.7130	10694.79
6	Maint. Cost	5000	0.6663	3331.71
7	Maint. Cost	5000	0.6227	3113.75
8	Maint. Cost	5000	0.5820	2910.05
9	Maint. Cost	5000	0.5439	2719.67
10	Maint. Cost	5000	0.5083	2541.75
10	New Machine Cost	15000	0.5083	7625.24
11	Maint. Cost	5000	0.4751	2375.46
12	Maint. Cost	5000	0.4440	2220.06
13	Maint. Cost	5000	0.4150	2074.82
14	Maint. Cost	5000	0.3878	1939.09
15	Maint. Cost	5000	0.3624	1812.23
15	New Machine Cost	15000	0.3624	5436.69
16	Maint. Cost	5000	0.3387	1693.67
17	Maint. Cost	5000	0.3166	1582.87
18	Maint. Cost	5000	0.2959	1479.32
19	Maint. Cost	5000	0.2765	1382.54
20	Maint. Cost	5000	0.2584	1292.10
	Total	160000		91726.79

Part B

Machine A to C Benefit/ Cost
	Increased intial cost (Cost)	Saving of Maint. Cost (Sum of PV of 5 Years Maint Cost) (Benefit)	Benefit/ Cost Percentage
Machine A	40000	10250.49
Machine C	15000.00	20500.99
	25000.00	10250.49	41%

Machine B to C Benefit/ Cost
	Increased intial cost (Cost)	Saving of Maint. Cost (Sum of PV of 5 Years Maint Cost) (Benefit)	Benefit/ Cost Percentage
Machine B	30000	12300.59
Machine C	15000.00	20500.99
	15000.00	8200.39	55%