11.15 NewTech Insulations Company is considering replacing a broken inspection m

Question

11.15 NewTech Insulations Company is considering replacing a broken inspection machine, which has been used to test the mechanical strength of electrical insula- tors, with a newer and more efficient one. If repaired, the old machine can be used for another five years, although the firm does not expect to realize any salvage value from scrapping it in five years. Alternatively, the firm can sell the machine to another firm in the industry now for $5,000. If the machine is kept, it will require an immediate $1,200 overhaul to restore it to operable condition. The overhaul will neither extend the service life originally estimated nor increase the value of the inspection machine. The operating costs are estimated at $2,000 during the first

Explanation / Answer

In this problem, company has an inspection machine in broken condition. It can be overhauled at $1,200. The machine can be immediately sold at $5,000. Thereafter its value will declie by $1,000 per year. It can be used for 5 years. In first year operating cost is $2,000. It will increase by $1,000 per year. Rate of return is 15%. Based on these data economic life of old machine has been calculated. Steps are as follows:

1. Consider depreciation in the value of machine in each year. It is $1,000 here.

2. Consider operating cost of $2,000 in first year. Then increase it by $1,000 per year.

3. Ascertain total cost of each year by adding initial overhaul cost plus depreciation plus operating cost.

4. Take discounted value of a dollar using discounted rate of 15%. Multiply it by the corresponding annual cost to get discounted annual cost.

5. Add them to get cumulative discounted cost.

6. Also ascertain cumulative discounted value of dollar annuity.

7. Divide 5 by 6 to get weighted average annual cost per year.

Economic life is the number of year where weighted average cost is minimum.

Calculations are shown in the table below:

Result: Table shows that weighted average cost is continuously going up. So first year is the economic life of the machine where the cost is minimum as shown in the last column.

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Same procedure has been used to ascertain economic life of new machine. It is purchased at $10,000. At the end of first year its value is $6,000. So you have to charge depreciation of $4,000 in the first year. Then value will decline 15% in each year. Operating cost of first year is $2000. It will increase by $800 in each year. Based on these data, following table has been prepared.

Here also weighted average cost is continuously rising. So first year is economical life of the machine.

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Conclusion:

Now compare the last column data of defender (old machine) with new machine. weighted average cost of defender is low in comparison with new machine in first four years. So in fourth year, it should be replaced by a new one.

Weighted average annual cost of old machine Year Value of Ovehaul Depreciation Operating Total Discounting Discouted Cumulative Cumulative weighted old cost cost cost factors Total cost discounted discounted average machine total cost factor cost 0 5000 1200 0 1200 1 1200 1200 1 1 4000 1000 2000 3000 0.8695652 2608.7 3808.6957 1.869565 2037.21 2 3000 1000 3000 4000 0.7561437 3024.57 6833.2703 2.625709 2602.45 3 2000 1000 4000 5000 0.6575162 3287.58 10120.851 3.283225 3082.59 4 1000 1000 5000 6000 0.5717532 3430.52 13551.371 3.854978 3515.29 5 0 1000 6000 7000 0.4971767 3480.24 17031.608 4.352155 3913.37

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