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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:
 Year Running Cost 1 2 3 4 5 6 7 8 200 500 800 1,200 1,800 2,500 3,200 4,000

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)

 Year Running Cost 1 2 3 4 5 6 7 8 200 500 800 1,200 1,800 2,500 3,200 4,000

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,

 Yearn(1) Running CostR(n)(2) Cummulative Running CostSigma R(n)(3) Depritiation CostC-S(4) Total CostTC(5)=(3)+(4) Average Total CostATC_n(6)=(5)/(1) 1 200 200 200 = 0 + 200(3) = Previous(3) + (2) 12,000 12,200 12200 = 200 + 12000(5)=(3)+(4) 12,200 12200 = 12200 / 1(6)=(5)/(1) 2 500 700 700 = 200 + 500(3) = Previous(3) + (2) 12,000 12,700 12700 = 700 + 12000(5)=(3)+(4) 6,350 6350 = 12700 / 2(6)=(5)/(1) 3 800 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) 4 1,200 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) 5 1,800 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) 6 2,500 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) 7 3,200 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) 8 4,000 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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