Hello - I need help with the following problem: \"The company is considering the
ID: 1096946 • Letter: H
Question
Hello - I need help with the following problem:
"The company is considering the purchase of a new machine for the insertion of electronic components into a printed circuit board. The machine was purchased three years ago at a cost of $500,000 and is operating adequately, although maintenance costs and defect rates are rising. A new machine is available for $350,000. The new machine should have lower costs and better defect rates. The estimation of the costs are given in the following table:
The company
Explanation / Answer
Table showing calculation of cost per annum of Defender
Year
Salvage
Value
Dep.
operating
Cost
Cum.
operating
cost
total
cost
Disc.
Factor
Present value
Cum Disc factors
Average
cost
Steps:
1. Consider total depreciation of the machine. It is found out by deducting sale value of the current year from initial value of the machine at time 0. In year 2, the sale value of defender is $100,000. Deduct it from initial cost of $150,000. Thus total depreciation of first two years is $150,000-$100,000=$50,000. It is shown in third column above
2. Now consider operating cost of each year. It is shown in column 4. Calculate cumulative operating cost from the figures of column 4.This cumulative figure is shown in column 5. Note that for year 2 cumulative operating cost is $40,000+$45,000=$85,000.
3. Now add figures of column three and column 5 to get total cost. It is shown in column 6.
4. Next calculate discounted value of a year. It is found out by the formula 1/(1.1)^n where n is the number of year. This discounted figures are shown in column 7.
5. Multiply total cost of column 6 and disciounting factors of column 7 to get discounted present value of total cost. It is shown in column 8.
6. Now consider cumulative discounting factors. It has been ascertained from figures of column 7. These figures are shown in column 9.
7. Finally divide figures of column 8 by the figures of column 9. Result is average cost in terms of its present value. Figures are shown in column 10. Note that average discounted costs are decreasing but after year 2 it has started going up. Thus figure of year 1 in the last column is EAUC.
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Table showing calculation of cost per annum of Challenger
Salvage
value
operating
cost
Cum.
operating
cost
total
cost
Disc
factor
Present
value
Cum.
Disc.
factor
Average
annual
cost
Result: EAUC of defender is $33,175 and of challenger is $21,327. It is the minimum average annual present value cost. For both machine this minimum cost is observed in the first year.
Since EAUC of Challenger is less than defender, the machine defender should be replaced by challenge
Year
Salvage
Value
Dep.
operating
Cost
Cum.
operating
cost
total
cost
Disc.
Factor
Present value
Cum Disc factors
Average
cost
0 150,000 150,000 1 150,000 1 120,000 30,000 40,000 40,000 70,000 0.9009 63,063 1.9009 33,175 2 100,000 50,000 45,000 85,000 135,000 0.8116 109,569 2.7125 40,394 3 80,000 70,000 50,000 135,000 205,000 0.7312 149,894 3.4437 43,527 4 60,000 90,000 55,000 190,000 280,000 0.6588 184,444 4.1024 44,960Related Questions
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