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. Quantitative break even point of A units per year Quantitative break even point of B units per year b. At what quantity would the two alternatives yield the same profit?Quantity units per yearc. If expected annual demand is 13,000 units, which alternative would yield higher profit?multiple choiceAB
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 48,000 for B; variable costs per unit would be 13 for B; and revenue per unit would be 17 for B.a. Determine each alternative’s break-even point. Quantitative break even point of A units per year Quantitative break even point of B units per year b. At what quantity would the two alternatives yield the same profit?Quantity units per yearc. If expected annual demand is 13,000 units, which alternative would yield higher profit?multiple choiceAB
Solution
a. The break-even point is calculated by dividing the fixed costs by the contribution margin per unit (revenue per unit - variable cost per unit).
For A: Break-even point = Fixed costs / Contribution margin per unit = 16 - $10) = 9,000 units per year
For B: Break-even point = Fixed costs / Contribution margin per unit = 17 - $13) = 12,000 units per year
b. To find the quantity at which the two alternatives yield the same profit, we set the profit equations for A and B equal to each other and solve for the quantity.
Profit A = Revenue A - Cost A = (54,000 + $10 * Quantity)
Profit B = Revenue B - Cost B = (48,000 + $13 * Quantity)
Setting Profit A = Profit B and solving for Quantity gives:
Quantity = (Fixed cost B - Fixed cost A) / (Unit variable cost A - Unit variable cost B + Unit price B - Unit price A) = (54,000) / (13 + 16) = 6,000 units per year
c. If expected annual demand is 13,000 units, we substitute this quantity into the profit equations for A and B and compare the results.
Profit A = (54,000 + 78,000
Profit B = (48,000 + 52,000
Therefore, alternative A would yield a higher profit at an annual demand of 13,000 units.
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