Replacement theory MBA PRODUCTION MANAGEMENT

1. Replacement Theory
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2. replacement
• The problem of replacement is felt when the job
performing units such as
• men
• Machine
• Equipments
• Parts etc.. Become less effective or useless due to either sudden
or gradual deterioration in their efficiency, failure or breakdown
• By replacing them with new ones at frequent intervals
maintenance and other overhead cost can be reduced
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3. Types of failure
• There are two types of failure
• Gradual failure
• Sudden failure
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4. Gradual failure cases
• Increased running costs ( maintenance +
operating cost)
• Decrease in productivity
• Decrease in the resale or salvage value
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5. Sudden failure cases
• This type of failure occurs in items after some
period of giving desired service rather than
deteriorating while in service
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6. MODEL 1
Replacement of items whose running cost
increases with time and value of money
remains constant during a period
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7. ATCn = TC/n
Where TC = C-S+ Σ R(n)
Where n = Replacement age of equipment
C = Capital or purchase cost of equipment
S = Scrap (salvage ) value of the equipment at the end of t years
R(n) = Running cost of the equipment
TC = Total Cost
ATC = Average Total Cost
After determining the ATCn find out which year the value of ATCn is
minimum which means it is the appropriate time for replacement
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8. E.g.:
1. A firm is considering replacement of a machine, whose cost
price is Rs 12,200, and the scrap value Rs 200.The running(
maintenance and operating) costs are found from the
experience to be as follows:
Year 1 2 3 4 5 6 7 8
Running cost
(Rs)
200 500 800 1200 1800 2500 3200 4000
When the machine should be replaced?4/10/2013 Babasabpatilfreepptmba.com

9. Soln.
Year of
service
n
Running
cost R(n)
(Rs)
Cumulative
running cost
ΣR(n)
(Rs)
Depreciation cost
C-S
(Rs)
Total Cost
TC
(Rs)
Average Cost
ATCn
(Rs)
1 200 200 12000 12200 12000
2 500 700 12000 12700 6350
3 800 1500 12000 13500 4500
4 1200 2700 12000 14700 3675
5 1800 4500 12000 16500 3300
6 2500 7000 12000 19000 3167
7 3200 10200 12000 22200 3171
8 4000 14200 12000 26200 32754/10/2013 Babasabpatilfreepptmba.com

10. MODEL 2
Replacement policy for items whose
running cost increases with time but
value of money changes with
constant rate during the period
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11. 100
100+r
d=
Where d is the discount rate or depreciation value
r is the rate of change
n
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12. E.g.:
• Let the value of the money be assumed to be 10 per cent
per year and suppose that machine A is replaced after
every 3 years where as machine B is replaced after every
6 years. the yearly cost (In Rs) of both the machines are
given as under:
Year 1 2 3 4 5 6
Machine
A
1000 200 400 1000 200 400
Machine
B
1700 100 200 300 400 500
Determine which machine should be purchased?4/10/2013 Babasabpatilfreepptmba.com

13. The discounted cost (present worth) at 10 percent rate for
machine A and machine B is given below
Discounted cost of Machine A
Year Discounted cost at 10% rate (Rs)
Cost present worth
1 1000 1*1000 1000.00
2 200 200* ( 100/(100+10) 181.82
3 400 400*(100/100+10)2 330.56
=0.9091
Total Rs 1512.38
Hence the average yearly cost of machine A is 1512.38/3=Rs 504.13
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14. Discounted cost of machine B
Year Discounted cost at 10% rate(Rs)
cost Present Worth
1 1700 1700*1 1700.00
2 100 100*0.9091 90.91
3 200 200*0.8264 165.28
4 300 300*0.7513 225.39
5 400 400*0.6830 273.20
6 500 500*0.6209 310.45
Total Rs 2765.23
The average yearly cost of machine B is 2765.23/6=Rs 460.87
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15. • With the data on average yearly cost of both machines ,
the apparent advantage is in purchasing machine B .but
the periods for which the costs are considered are
different .
• There fore , let us first calculate total present worth of
machine A for 6 years
• Total present worth
=1000+200*0.9091+400*0.8264+1000*0.7513+200*0.68
30+400*0.6209=Rs 2648.64
• Which is less than the total present worth of machine B .
• Thus machine A should be purchased
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