A small firm intends to increase the capacity of a bottleneck operation by addin
ID: 434155 • Letter: A
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 $44,000 for A and $20,000 for B; variable costs per unit would be $10 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? (Round your answer to the nearest whole amount.) Profit units c. If expected annual demand is 18,000 units, which alternative would yield the higher profit? Higher profit
Explanation / Answer
Machine: A
Machine: B
Annual Fixed Cost (FC) = $44,000
Annual Fixed Cost (FC)=$20,000
Variable Costs Per Unit (VC)=$10
Variable Costs Per Unit (VC)=$11
Revenue Per Unit (R)=$19
Revenue Per Unit (R)=$19
a.
QBEP = FC
R – VC
Machine: A Machine: B
QBEP = FC QBEP = FC
R – VC R – VC
QBEP = 44,000 QBEP = 20,000
19-10 19 – 11
QBEP = 44,000 QBEP = 20,000
9 8
QBEP = 4889 units QBEP = 2,500 units
b.
Profit = Q (R -VC) - FC
Profit A = Profit B
Q (R - VC) - FC = Q (R - VC) - FC
Q (19-10) - 44,000 = Q (19-11) - 20,000
Q (9) - 44,000 = Q (8) - 20,000
Q =24,000 units.
C.
Given:
Expected annual demand is 18,000 units
Profit A
Profit A = Q (R - VC) - FC
Profit A = 18, 000 (19 -10) - 44,000
Profit A = 18,000 (9) - 44,000
Profit A = $1, 18,000
Profit B
Profit B = Q (R - VC) - FC
Profit B = 18,000 (19 - 11) - 20,000
Profit B = 18,000 (8) - 20,000
Profit B = $1, 24,000
“B” will yield the higher profit.
Machine: A
Machine: B
Annual Fixed Cost (FC) = $44,000
Annual Fixed Cost (FC)=$20,000
Variable Costs Per Unit (VC)=$10
Variable Costs Per Unit (VC)=$11
Revenue Per Unit (R)=$19
Revenue Per Unit (R)=$19
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