#Operations Research - OR
I) Replacement of an item the efficiency of which deteriorates with time
Model - II: Replacement Policy for the items the running costs of which increases with time considering the time value of money constant during the life of the asset
Criteria for replacement:
An assets should be replaced in the beginning of the year in which the annual running cost exceeds the "Weighted Average Total Cost per year" of the preceding year
(i) "Weighted Average Total Cost per year" means the "The Weighted Total Cost till the year divided by the cumulative PV Factor"
(ii) "The Weighted Total Cost till the year" means the summation of the "Cumulative PV of Running Cost" and "Depreciation Cost of the year"
(iii) "Cumulative PV Running Cost" means the cumulative total of the present values of the annual running costs till the year
(iv) "Depreciation Cost" means the cost of the asset minus the resale/scrap value of the asset for the year
How to calculate Present Value?
FV = P (1 + r)^n is the formula to find the future value of a sum
So, PV = FV / (1 + r)^n
and if we take PV of Re 1, then we can have the PV Factor as
PV = 1/(1 + r)^n
If we multiply the future values of the running costs, we can have the present values of all the future running costs and then, ultimately, the Cumulative PV of running costs.
Replacement Decision - 5
A company is considering to install a machine costing overall Rs. 60,000. The Running costs are estimated to be Rs. 10,000 for the first 5 years, increasing every year by Rs. 3,000 in the sixth and subsequent years. The rate of return on all the investments of the company is 10% What is the optimal replacement period?
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