Page 215 - DCOM303_DMGT504_OPERATION_RESEARCH

Operations Research

Notes Year Total outlay
Machine A Machine B
1 900 1,400
2 600 100
3 700 700
Total outlay 2,200 2,200

As the total outlay of both the machines are equal, both the machines are good.
2. When future value of money is considered at a constant rate of 10% p.a., then the total
outlay differs. The following calculations support of this view:
Year Total outlay Working
Machine A Machine B
1 900.00 1,400.00 100
600 × = 545.00
100
2 545.45 90.91 100
100 × = 90.91.00
100
3 578.51 578.51
2
100 
700 ×   = 578.51
110 
Total 2,023.96 2,069.42

Inference

It is evident from the above table that the outlay on machine A is better than machine B. Hence,
machine A is better than machine B.

Example: A manufacturer is offered 2 machines A and B. A is priced at ` 5,000 and the
running costs are estimated at ` 800 for each of the 1st year, increasing by ` 200 per year in the 6th
and subsequent years. Machine B, has the same capacity as A, costs ` 2,500. But, it will have
running costs of ` 1,200 per year for 6 years increasing by ` 200 per year thereafter.
If money is worth 10% per year, which machine should be purchased [assume that machines will
eventually be sold for scrap at a negligible price]?
Solution:

Calculation of weighted average cost for machine A

n-1
N Rn V RnV RnV C+RV V TC/V
n-1
n-1
n-1
n-1
n-1
1 800 1.000 800 800 5,800 1.0000 5,800
2 800 0.9091 727.28 1,527.28 6,527.28 1.9091 3,419.04
3 800 0.8264 661.12 2,188 7,188.4 2.7335 2,627.8
4 800 0.7513 601.04 2,789.4 7,789.4 3.4868 2,233.98
5 800 0.6830 546.4 3,335.8 8,335.8 4.1698 1,999.09
6 1,000 0.6209 620.9 3,956.7 8,956.7 4.7907 1,869
7 1,200 0.5645 677.4 4,634.1 9,634.14 5.3552 1,799
8 1,400 0.5132 718.48 5,352.6 10,352.6 5.8684 1,762
9 1,600 0.4665 746.4 6,099.02 11,099.02 6.3349 1,752
10 1,800 0.4241 763.38 6,862.41 1,862.4 6.7590 1,503

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