A small firm intends to increase the capacity of a bottleneck operation by addin
ID: 390957 • 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 $54,000 for A and $27,000 for B; variable costs per unit would be $9 for A and $11 for B; and revenue per unit would be $16.
a. Determine each alternative’s break-even point in units. (Round your answer to the nearest whole amount.)
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 13,000 units, which alternative would yield the higher profit?
Higher profit (Click to select) B A
Explanation / Answer
For alternative A
Fixed cost (FC) = $54000
Variable cost (VC) = $9
For alternative B
Fixed cost (FC) = $27000
Variable cost (VC) = $11
Revenue (R) = $16
a) Break even point for alternative A = FC / (R-VC) = 54000/(16-9) = 54000/7 = 7714 units
Break even point for alternative B = FC/(R-VC) = 27000/(16-11) = 27000/5 = 5400 units
b) Let the volume of output = Q
Profit for alternative A = profit for alternative B
=> Q(R-VC) - FC = Q(R-VC) - FC
=> Q(16-9)- 54000 = Q(16-11) - 27000
=> 7Q - 54000 = 5Q - 27000
=> 7Q - 5Q = - 27000+54000
=> 2Q = 27000
=> Q = 27000/2
=> Q = 13500
So at a volume of output of 13500 units the two alternatives yield the same profit
C) If volume of output (Q) = 13000 units
Profit for alternative A = Q(R-VC) - FC
= 13000(16-9) - 54000
= (13000 x 7) - 54000
= 91000 - 54000
= $37000
Profit for alternative B = Q(R-VC) - FC
= 13000(16-11) - 27000
= (13000 x 5) - 27000
= 65000 - 27000
= $38000
So alternative B would yield the higher profit.