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Cost benefit analysis of new machinery

Suppose the plant manager of a manufacturing firm hires you to help him analyze a proposal to purchase a new and faster stamping machine. He provides you with the following information:

a. The new machine is four times as fast
b. The old machine is able to process material at a rate of 60 units per hour
c. Demand is approximately 100,000 stampings per year
d. The cost of direct labor is $15.00 per hour
e. The overhead factor for this process is 3 times direct labor
f. The net cost of the new machine is $40,000. (This includes the salvage value of the old machine)

Using the standard cost procedure, determine the total annual cost savings realized from the purchase of the new machine. Then, present a discussion of the reasons these figures could present a false picture of reality.

ATTEMPT AT PROBLEM SOLUTION
60UNITS X 4 (TIMES FASTER) = 240 UNITS WITH THE NEW MACHINE

240 UNITS X 2080 HOURS IN A YEAR = 499,200 UNITS PER YEAR (WITH THE NEW MACHINE)

15PER HOUR OF LABOR X 2080 = 31200

OVER HEAD FACTOR = 3 X 15 = 45

40,000 COST OF NEW MACHINE
-31200 DIRECT LABOR
-45 OVERHEAD
= 8800 - ANNUAL COST SAVINGS

I DON'T KNOW WHY THIS WOULD PRESENT A FALSE PICTURE OF REALITY.

I AM JUST VERY LOST AND HAVE ABOUT 10 SIMILAR PROBLEMS TO FIGURE OUT. IF I CAN GET A GRASP ON THIS ONE THEN I'M HOPING I WILL BE ABLE TO WORK SOME OF THE OTHER PROBLEMS.
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I am having trouble on how to approach this problem and don't understand how to calculate it. I am looking for a break down of the steps so I can understand the solution. I have spend three hours on this and have hit a wall. Thank you very much for your assistance. It requires a non complex solution and then an explanation of why.

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For each year this machinery will save $ 75000 for 4 years if ...

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This explains the way to do the cost benefit analysis of purchase of new machinery.

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