A small firm intends to increase the capacity of a bottleneck operation by addin
ID: 399938 • 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 .............. answer A,B
Explanation / Answer
Solution:
(a) Let the number of units at the break-even point = Q units. At the break-even point,
Total cost = Total revenue
Fixed cost + (Variable cost per unit x Number of units) = (Revenue per unit x Number of units)
Alternative A:
$54,000 + ($9 Q) = $16 Q
Qbep, A = 7,714 units
Alternative B:
$27,000 + ($11 Q) = $16 Q
Qbep, B = 5,400 units
(b) Profit is calculated as,
Profit = Total Revenue - Total Costs
Profit = [(Revenue per unit x Number of units)] - [Fixed cost + (Variable cost per unit x Number of units)]
Profit = [R x Q] - [F + (V x Q)]
Profit = RQ - F - VQ
Profit = Q (R - V) - F
The volume of output at which the two alternatives will yield the same profit is calculated as,
Profit A = Profit B
[Q (R - Va) - Fa] = [Q (R - Vb) - Fb]
[Q ($16 - $9) - $54000] = [Q ($16 - $11) - $27000]
7Q - $54000 = 5Q - $27000
Q = 13,500 units
Same profit at 13,500 units.
(c) Demand = 13000 units
Profit of A is calculated as,
Profit (A) = Q (R - Va) - Fa
Profit (A) = [13000 x ($16 - $9)] - $54000
Profit (A) = $37,000
Profit of B is calculated as,
Profit (B) = Q (R - Vb) - Fb
Profit (B) = [13000 x ($16 - $11)] - $27000
Profit (B) = $38,000
At 13,000 units,
Higher profit = Alternative B