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A small company intends to increase the capacity of its bottleneck operation by adding a new machine. Two alternatives, A and B, have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be $54,000 for A and $48,000 for B; variable costs per unit would be $10 for A and $13 for B; and revenue per unit would be $16 for A and $17 for B.a. Determine each alternative’s break-even point.

Question

A small company intends to increase the capacity of its bottleneck operation by adding a new machine. Two alternatives, A and B, have been identified, and the associated costs and revenues have been estimated. Annual fixed costs would be 54,000forAand54,000 for A and 48,000 for B; variable costs per unit would be 10forAand10 for A and 13 for B; and revenue per unit would be 16forAand16 for A and 17 for B.a. Determine each alternative’s break-even point.

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Solution

The break-even point is the point at which total revenue equals total cost, resulting in neither profit nor loss. It can be calculated using the formula:

Break-even point = Fixed Costs / (Selling Price per Unit - Variable Cost per Unit)

Let's calculate the break-even point for both alternatives:

Alternative A: Break-even point = 54,000/(54,000 / (16 - $10) = 9,000 units

Alternative B: Break-even point = 48,000/(48,000 / (17 - $13) = 12,000 units

So, the company would need to sell 9,000 units for alternative A and 12,000 units for alternative B to break even.

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