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1. The data collected in running a machine, the cost of which is Rs 60,000 are given below:
Year12345
Resale Value42,00030,00020,40014,4009,650
Cost of spares4,0004,2704,8805,7006,800
Cost of labour14,00016,00018,00021,00025,000

Determine the optimum period for replacement of the machine.

Solution:
The data collected in running a machine,

Year12345
Resale Value42,00030,00020,40014,4009,650
Cost of spares4,0004,2704,8805,7006,800
Cost of labour14,00016,00018,00021,00025,000

The costs of spares and labour, together, determine the running cost

The running costs and resale price of the machine in successive years

Year12345
Resale Value42,00030,00020,40014,4009,650
Running Cost18,00020,27022,88026,70031,800

In order to determine the optimal time n when the machine should be replaced, we first calculate the average cost per year during the life of the machine,

Year
`n`
(1)
Running Cost
`R(n)`
(2)
Cummulative Running Cost
`Sigma R(n)`
(3)
Resale Value
`S`
(4)
Depritiation Cost
`C-S`
(5)=60,000-(4)
Total Cost
`TC`
(6)=(3)+(5)
Average Total Cost
`ATC_n`
(7)=(5)/(1)
118,000 18,000 `18000 = 0 + 18000`
(3) = Previous(3) + (2)
42,000 18,000 `18000 = 60000 - 42000`
`(5)=60000-(4)`
 36,000 `36000 = 18000 + 18000`
`(6)=(3)+(5)`
 36,000 `36000 = 36000 / 1`
(7)=(5)/(1)
220,270 38,270 `38270 = 18000 + 20270`
(3) = Previous(3) + (2)
30,000 30,000 `30000 = 60000 - 30000`
`(5)=60000-(4)`
 68,270 `68270 = 38270 + 30000`
`(6)=(3)+(5)`
 34,135 `34135 = 68270 / 2`
(7)=(5)/(1)
322,880 61,150 `61150 = 38270 + 22880`
(3) = Previous(3) + (2)
20,400 39,600 `39600 = 60000 - 20400`
`(5)=60000-(4)`
 100,750 `100750 = 61150 + 39600`
`(6)=(3)+(5)`
 33,583.33 `33583.33 = 100750 / 3`
(7)=(5)/(1)
426,700 87,850 `87850 = 61150 + 26700`
(3) = Previous(3) + (2)
14,400 45,600 `45600 = 60000 - 14400`
`(5)=60000-(4)`
 133,450 `133450 = 87850 + 45600`
`(6)=(3)+(5)`
 33,362.5 `33362.5 = 133450 / 4`
(7)=(5)/(1)
531,800 119,650 `119650 = 87850 + 31800`
(3) = Previous(3) + (2)
9,650 50,350 `50350 = 60000 - 9650`
`(5)=60000-(4)`
 170,000 `170000 = 119650 + 50350`
`(6)=(3)+(5)`
 34,000 `34000 = 170000 / 5`
(7)=(5)/(1)


The calculations in table show that the average cost is lowest during the `4^(th)` year (Rs 33,362.5).

Hence, the machine should be replaced after every `4^(th)` years, otherwise the average cost per year for running the machine would start increasing.





This material is intended as a summary. Use your textbook for detail explanation.
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