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 $38,000 for A and $31,000 for B; variable costs per unit would be $7 for A and $11 for B; and revenue per unit would be $19.

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 10,000 units, which alternative would yield the higher profit (or the lower loss)?

Higher profit              (Click to select)   A   B

Answer 1

a. For alternate A

Selling price per unit = $19

Variable cost per unit = $7

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

= 19-7

= $12

fixed costs = $38,000

Break even point ( in units) = Fixed costs / Contribution margin per unit

= 38,000/12

= 3,167 Units

For alternate B

Selling price per unit = $19

Variable cost per unit = $11

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

= 19-11

= $8

fixed costs = $31,000

Break even point ( in units) = Fixed costs / Contribution margin per unit

= 31,000/8

= 3,875 units

b. Let the output at which both the alternatives will yield the same profit = y units

Profit for alternative A = Profit of alternative B

194-77-38,000 = 19y-11y-31,000

4y = 7,000

y = 1,750 units

Hence, when 1,750 units are sold, both the alternatives will yield same point.

c. If the expected annual demand is 10,000 units, Alternate A would provide the higher profit, Infact, if annual demand is more than 1,750 units, then alternative A provide higher profit.

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