Replacement theory MBA PRODUCTION MANAGEMENT

Replacement Theory

4/10/2013 Babasabpatilfreepptmba.com

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


Types of failure

• There are two types of failure

• Gradual failure

• Sudden failure


Gradual failure cases

• Increased running costs ( maintenance + operating cost)

• Decrease in productivity

• Decrease in the resale or salvage value


Sudden failure cases

• This type of failure occurs in items after some period of giving desired service rather than deteriorating while in service


MODEL 1

Replacement of items whose running cost increases with time and value of money remains constant during a period


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


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

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 3275 4/10/2013 Babasabpatilfreepptmba.com

MODEL 2

Replacement policy for items whose running cost increases with time but

value of money changes with constant rate during the period


100

100+r d=

Where d is the discount rate or depreciation value

r is the rate of change

n


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

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 4/10/2013 Babasabpatilfreepptmba.com

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 4/10/2013 Babasabpatilfreepptmba.com

• 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*0.6830+400*0.6209=Rs 2648.64

• Which is less than the total present worth of machine B .

• Thus machine A should be purchased 4/10/2013 Babasabpatilfreepptmba.com


Replacement theory MBA PRODUCTION MANAGEMENT

Education

cost rs

cost increases

overhead cost

cost price

average total cost

total cost atc

rate rs cost present

total rs