A small firm intends to increase the capacity of a bottleneck operation by addin
ID: 395619 • 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 $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.)
b. At what volume of output would the two alternatives yield the same profit? (Round your answer to thenearest whole amount.)
c. If expected annual demand is 14,000 units, which alternative would yield the higher profit?
QBEP,A QBEP,B units unitsExplanation / Answer
Solution:
(a) Let the number of units at the break-even point be represented by Q units. Therefore, 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:
$37,000 + ($10 Q) = $15 Q
Qbep, A = 7,400 units
Alternative B:
$33,000 + ($11 Q) = $15 Q
Qbep, B = 8,250 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 ($15 - $10) - $37000] = [Q ($15 - $11) - $33000]
5Q - $37000 = 4Q - $33000
Q = 4000 units
Same profit at 4000 units.
(c) Demand = 14000 units
Profit of A is calculated as,
Profit (A) = Q (R - Va) - Fa
Profit (A) = [14000 x ($15 - $10)] - $37000
Profit (A) = $33,000
Profit of B is calculated as,
Profit (B) = Q (R - Vb) - Fb
Profit (B) = [14000 x ($15 - $11)] - $33000
Profit (B) = $23,000
At 14,000 units,
Higher profit = Alternative A