A small firm intends to increase the capacity of a bottleneck operation by addin

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? (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? Higher profit

Explanation / Answer

Alternative A :

Contribution margin per unit = Revenue per unit - Variable cost per unit = $ 15 - $ 10 = $ 5

Break-even point in units = Fixed costs / Contribution margin per unit = $ 37,000 / $ 5 = 7,400 units

Alternative B:

Contribution margin per unit = Revenue per unit - Variable cost per unit = $ 15 - $ 11 = $ 4

Break-even point in units = Fixed costs / Contribution margin per unit = $ 33,000 / $ 4 = 8,250 units

b. Volume at which both alternatives would yield the same profit:

Let the volume be Q

5Q - 37,000 = 4Q - 33,000 Or

Q = 4,000 units

At 4,000 units, both alternatives yield a profit of $ (17,000), or a loss of $ 17,000

c. If expected annual demand is 14,000 units,

Profit of Alternative A = Total contribution margin - Fixed costs = $ 5 x 14,000 - $ 37,000 = $ 33,000

Profit of Alternative B = $ 4 x 14,000 - $ 33,000 = $ 23,000

Therefore Alternative A would yield higher profit.

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