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Answer :
A) The break-even number of gears for Lathe B is 1,269. The revenue at break-even is found by multiplying the break-even number of gears by the selling price: 1,269 x $150 = $190,350.
B) The fixed cost for Lathe B is $175,000. Dividing it by the contribution margin per gear gives us: $175,000 / $138 = 1,268.12. The break-even number of gears for Lathe B is 1,269.
C) The initial investment for Lathe B is higher at $175,000 compared to $80,000 for Lathe A. Lathe B has a higher upfront cost.
(a) To find the break-even number of gears for Lathe A, we need to calculate the total cost and the cost per gear. Given that the gear sells for $150 each and the cost to make it on Lathe A is $75, the contribution margin per gear is $150 - $75 = $75.
The fixed cost for Lathe A is $80,000. To cover this fixed cost, we divide it by the contribution margin per gear: $80,000 / $75 = 1,066.67.
Therefore, the break-even number of gears for Lathe A is 1,067.
To calculate the revenue at break-even, we multiply the break-even number of gears by the selling price: 1,067 x $150 = $160,050.
(b) Similarly, to find the break-even number of gears for Lathe B, we calculate the total cost and the cost per gear. The cost to make the gear on Lathe B is $12, and the contribution margin per gear is $150 - $12 = $138.
The fixed cost for Lathe B is $175,000. Dividing it by the contribution margin per gear gives us: $175,000 / $138 = 1,268.12.
Therefore, the break-even number of gears for Lathe B is 1,269.
The revenue at break-even is found by multiplying the break-even number of gears by the selling price: 1,269 x $150 = $190,350.
(c) To determine which lathe should be purchased, we need to consider the cost and break-even analysis.
For Lathe A, the break-even point is lower at 1,067 gears compared to 1,269 gears for Lathe B. This means that Lathe A requires fewer gear sales to cover its fixed costs.
However, the initial investment for Lathe B is higher at $175,000 compared to $80,000 for Lathe A. Therefore, Lathe B has a higher upfront cost.
In this scenario, the decision will depend on factors such as the company's financial position, production capacity, and sales forecast. If the company anticipates selling more than 1,269 gears, Lathe B could generate higher profitability. On the other hand, if the sales forecast is less than 1,269 gears, Lathe A would be a more cost-effective choice. It is crucial to assess the long-term production requirements, operational efficiency, and financial implications to make an informed decision on which lathe to purchase.
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