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Solution
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Solution provided by AtoZmath.com
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Replacement Model-1.2 calculator
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1. The data collected in running a machine, the cost of which is Rs 60,000 are given below:
Year | 1 | 2 | 3 | 4 | 5 |
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Resale Value | 42,000 | 30,000 | 20,400 | 14,400 | 9,650 |
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Cost of spares | 4,000 | 4,270 | 4,880 | 5,700 | 6,800 |
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Cost of labour | 14,000 | 16,000 | 18,000 | 21,000 | 25,000 |
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Determine the optimum period for replacement of the machine.
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Example1. The data collected in running a machine, the cost of which is Rs 60,000 are given below:
Year | 1 | 2 | 3 | 4 | 5 |
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Resale Value | 42,000 | 30,000 | 20,400 | 14,400 | 9,650 |
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Cost of spares | 4,000 | 4,270 | 4,880 | 5,700 | 6,800 |
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Cost of labour | 14,000 | 16,000 | 18,000 | 21,000 | 25,000 |
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Determine the optimum period for replacement of the machine.
Solution:The data collected in running a machine, Year | 1 | 2 | 3 | 4 | 5 |
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Resale Value | 42,000 | 30,000 | 20,400 | 14,400 | 9,650 |
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Cost of spares | 4,000 | 4,270 | 4,880 | 5,700 | 6,800 |
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Cost of labour | 14,000 | 16,000 | 18,000 | 21,000 | 25,000 |
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The costs of spares and labour, together, determine the running cost The running costs and resale price of the machine in successive years Year | 1 | 2 | 3 | 4 | 5 |
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Resale Value | 42,000 | 30,000 | 20,400 | 14,400 | 9,650 |
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Running Cost | 18,000 | 20,270 | 22,880 | 26,700 | 31,800 |
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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) | 1 | 18,000 | 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) | 2 | 20,270 | 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) | 3 | 22,880 | 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) | 4 | 26,700 | 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) | 5 | 31,800 | 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.
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