HW 10: Replacement Problems
1.) (50 pts, total) A company is looking for the best option to replace an existing piece of equipment, and has identified four options (A – D) with the
required 10 year physical life. The cash flow data for the options are listed in the table (below). For each option, the table shows the 1st cost, annual
operating cost, and the estimated salvage value at the end of the first year. The amount that the annual operating cost will increase each following year
and the amount that the salvage value will decrease each successive year are also listed.
Option:
A
Life:
10
1st Cost:
$ 10,000
Ann. Cost:
$ 48,000
Increase:
$
1,000
Salvage:
$
6,000
Decrease:
10%
Ownership
Operating
Cost
5,200
Cost
$ 48,000
$
years
Option:
B
Life:
10
1st Cost:
$ 12,000
per year
Ann. Cost:
$ 48,000
per year
Increase:
$
950
Salvage:
$
9,000
per year
Decrease:
9%
Ownership
Operating
years
Option:
C
Life:
10
1st Cost:
$ 15,000
per year
Ann. Cost:
$ 47,000
per year
Increase:
$
Salvage:
per year
Decrease:
650
years
Life:
10
years
$ 18,000
per year
Ann. Cost:
$ 47,000
per year
per year
Increase:
$
per year
Salvage:
per year
Ownership
Operating
$
Cost
6,300
Cost
$ 47,000
EAC
$ 53,300
EAC
D
1st Cost:
$ 10,500
8%
Option:
Decrease:
650
$ 12,000
5%
per year
Ownership
Operating
$
Cost
8,160
Cost
$ 47,000
EAC
$ 55,160
EAC
$ 53,200
$
Cost
4,440
Cost
$ 48,000
$ 51,842
$
3,237
$ 48,448
$
4,319
$ 47,307
$ 51,625
$
5,273
$ 47,307
$ 52,580
$ 51,648
$
2,788
$ 48,878
$
3,612
$ 47,601
$ 51,213
$
4,285
$ 47,601
$ 51,886
$
2,377
$ 49,359
$ 51,736
$
2,532
$ 49,291
$
3,228
$ 47,883
$ 51,111
$
3,774
$ 47,883
$ 51,657
$
2,154
$ 49,775
$ 51,929
$
2,357
$ 49,686
$
2,977
$ 48,153
$ 51,131
$
3,455
$ 48,153
$ 51,608
$
1,996
$ 50,172
$ 52,168
$
2,227
$ 50,063
$
2,796
$ 48,412
$ 51,207
$
3,234
$ 48,412
$ 51,646
$
1,875
$ 50,551
$ 52,427
$
2,123
$ 50,424
$
2,656
$ 48,658
$ 51,314
$
3,070
$ 48,658
$ 51,728
$
1,780
$ 50,913
$ 52,693
$
2,038
$ 50,767
$
2,543
$ 48,894
$ 51,437
$
2,942
$ 48,894
$ 51,836
$
1,702
$ 51,257
$ 52,959
$
1,966
$ 51,095
$
2,450
$ 49,117
$ 51,568
$
2,839
$ 49,117
$ 51,957
$
1,637
$ 51,585
$ 53,222
$
1,904
$ 51,405
$
2,372
$ 49,330
$ 51,702
$
2,755
$ 49,330
$ 52,085
ESL:
years
ESL:
years
ESL:
years
ESL:
years
If the company uses a 12% per year cost of funds (compounded yearly), show your work and fill in the table to answer the following questions for a
replacement analysis:
a) (20 pts) Compute the missing ownership and operating cost values for Option A
b) (10 pts) Compute the missing EAC values until you know the ESL for Option B
c) (12 pts) Find the economic service lives for Options A, B, C, and D
d) (5 pts) Determine which of these options is the best choice for a challenger today
e) (3 pts) When should we next plan to replace the best choice challenger?
2.) (50 pts, total) Two years ago, an automated testing machine was installed to monitor product quality. The equipment originally cost $25,000 and is
capable of testing 400 units per day at a total operation and maintenance cost of $0.26 per unit. The O&M costs for this type of machine are predicted
to increase by $1, 000 per year, starting today. Product sales have now increased to the point that it is necessary to increase production to 700 units
per day and the company must choose between replacing the current equipment, or buying an additional machine of the same type. A new 400 unit per
shift machine would cost $27,000 today, and have O&M costs identical to the existing machine. An independent, used equipment reseller has offered
$10,000 for the existing equipment.
A larger machine with a capacity of 800 units per shift would cost $66,500 and have operating and maintenance costs of $0.22 per unit. These costs are
assumed to increase by a total of $800 each succeeding year.
It is expected that all testing equipment will be required for five more years, the total salvage value of the two older machines would be about $30,000
at the end of the current year, and the salvage value of the high-capacity machine would be $40,000 at the end of the current year. All salvages values
will decrease by 10% each year after that. Assuming the company continues on a single shift, 250 days-per year operation, determine which alternative
should be selected using a MARR of 12% per year, compounded annually.
a.)
b.)
c.)
d.)
(10 pts, 5 pts each) Draw the cash flow diagrams for both the Defender and the Challenger using the Opportunity Cost Approach
(30 pts, 15 pts each) Identify the economic service life and equivalent annual cost for both options
(5 pts) Identify which option should be chosen today, and
(5 pts) Identify when the current best option should be replaced
Hints: The salvage value can be modeled as S1 ( 1– d%)N – 1 if the rate of annual decrease (d%) is a percentage/year and is expressed in decimal form
(geometric decline).
The salvage value can be modeled as S1 – d$ (N – 1) if the rate of annual decrease (d$) is expressed as dollars/year (linear decline). These
would be good formulas to put in an engineering notebook!