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2. Example-2
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1. Example-1



1. A firm is considering the replacement of a machine, whose cost price is Rs 12,200 and its scrap value is Rs 200. From experience the running (maintenance and operating) costs are found to be as follows:
Year12345678
Running Cost2005008001,2001,8002,5003,2004,000

When should the machine be replaced?

Solution:
We are given the running cost, `R(n)`, the scrap value `S` = Rs 200 and the cost of machine, `C` = Rs 12,200

Depreciation Cost = cost price - scrap value = 12,200 - 200

The given running cost, `R(n)`


Year12345678
Running Cost2005008001,2001,8002,5003,2004,000


Depreciation Cost = 12,000

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)
Depritiation Cost
`C-S`
(4)
Total Cost
`TC`
(5)=(3)+(4)
Average Total Cost
`ATC_n`
(6)=(5)/(1)
1200 200 `200 = 0 + 200`
(3) = Previous(3) + (2)
12,000 12,200 `12200 = 200 + 12000`
`(5)=(3)+(4)`
 12,200 `12200 = 12200 / 1`
(6)=(5)/(1)
2500 700 `700 = 200 + 500`
(3) = Previous(3) + (2)
12,000 12,700 `12700 = 700 + 12000`
`(5)=(3)+(4)`
 6,350 `6350 = 12700 / 2`
(6)=(5)/(1)
3800 1,500 `1500 = 700 + 800`
(3) = Previous(3) + (2)
12,000 13,500 `13500 = 1500 + 12000`
`(5)=(3)+(4)`
 4,500 `4500 = 13500 / 3`
(6)=(5)/(1)
41,200 2,700 `2700 = 1500 + 1200`
(3) = Previous(3) + (2)
12,000 14,700 `14700 = 2700 + 12000`
`(5)=(3)+(4)`
 3,675 `3675 = 14700 / 4`
(6)=(5)/(1)
51,800 4,500 `4500 = 2700 + 1800`
(3) = Previous(3) + (2)
12,000 16,500 `16500 = 4500 + 12000`
`(5)=(3)+(4)`
 3,300 `3300 = 16500 / 5`
(6)=(5)/(1)
62,500 7,000 `7000 = 4500 + 2500`
(3) = Previous(3) + (2)
12,000 19,000 `19000 = 7000 + 12000`
`(5)=(3)+(4)`
 3,166.67 `3166.67 = 19000 / 6`
(6)=(5)/(1)
73,200 10,200 `10200 = 7000 + 3200`
(3) = Previous(3) + (2)
12,000 22,200 `22200 = 10200 + 12000`
`(5)=(3)+(4)`
 3,171.43 `3171.43 = 22200 / 7`
(6)=(5)/(1)
84,000 14,200 `14200 = 10200 + 4000`
(3) = Previous(3) + (2)
12,000 26,200 `26200 = 14200 + 12000`
`(5)=(3)+(4)`
 3,275 `3275 = 26200 / 8`
(6)=(5)/(1)


The calculations in table show that the average cost is lowest during the `6^(th)` year (Rs 3,166.67).

Hence, the machine should be replaced after every `6^(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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2. Example-2
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