Question

A small firm intends to increase the capacity of a 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 $37,000 for A and $33,000 for B; variable costs per unit would be $10 for A and $11 for B; and revenue per unit would be $15.

a. Determine each alternative’s break-even point in units. (Round your answer to the nearest whole amount.)

QBEP,A	units
QBEP,B	units

b. At what volume of output would the two alternatives yield the same profit (or loss)? (Round your answer to the nearest whole amount.)

Profit              units

c. If expected annual demand is 14,000 units, which alternative would yield the higher profit (or the lower loss)?

Higher profit               (Click to select)   A   B

Answer 1

Product A

Fixed cost = $37,000

Variable cost per unit = $10

Selling price per unit = $15

Contribution margin per unit = Selling price per unit - variable cost per unit

= 15-10

= $5

Product B

Fixed cost = $33,000

Variable cost per unit = $11

Selling price per unit = $15

Contribution margin per unit = Selling price per unit - variable cost per unit

= 15-11

= $4

a. Break even point for Product A = fixed cost / Contribution margin per unit

= 37,000/5

= 7,400 units

Break even point for Product B = fixed cost / Contribution margin per unit

= 33,000/4

= 8,250 units

b.

Let at K units, profit is same for both the production profit of Product A = Profit of Product B

Sales - Variable cost - Fixed costs = Sales - Variable cost - Fixed costs

15K-10K-37,000=15K-11K-33,000

c.

Profit at 14,000 units of Product A = Sales - Variable cost - Fixed costs

= 14,000 x 15 - 14,000 x 10 - 37,000

= 210,000-140,000-37,000

= $33,000

Profit at 14,000 units of Product B = Sales - Variable cost - Fixed costs

= 14,000 x 15 - 14,000 x 11 - 33,000

= 210,000-154,000-33,000

= $23,000

Higher profit Product A is $33,000

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