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 $36,000 for A and $35,000 for B; variable costs per
unit would be $7 for A and $11 for B; and revenue per unit would be
$20.
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 (or loss)? (Round your
answer to the nearest whole
amount.)
Profit
units
c. If expected annual demand is 16,000 units,
which alternative would yield the higher profit (or the lower
loss)?
Higher profit
(Click to
select) A B
Solution:
(a) Break-even point:
At the breakeven point,
Total costs = Total revenue
Where,
Total costs = Fixed cost + (Variable cost per unit x Number of units)
Total revenue = Revenue per unit x Number of units
Alternative A:
Let the number of units be represented by Q. Therefore, at the breakeven point,
Total costs = Total revenue
Fixed cost + (Variable cost per unit x Number of units) = (Revenue per unit x Number of units)
$36,000 + $7Q = $20Q
Q = 2,769.23 or 2,769 (Rounding off to the nearest whole amount)
QBEP, A = 2,769 units
Alternative B:
$35,000 + $11Q = $20Q
Q = 3,888.89 or 3,889 (Rounding off to the nearest whole amount)
QBEP, B = 3,889 units
(b) Profit:
Profit is calculated as,
Profit = Total revenue - Total cost
Profit for Alternative A = $20Q - ($36,000 + $7Q)
Profit for Alternative B = $20Q - ($35,000 + $11Q)
For Alternative A and Alternative B to have the same profit,
$20Q - ($36,000 + $7Q) = $20Q - ($35,000 + $11Q)
Q = 250 units
Profit (or loss) will be same at 250 units.
(c) Annual demand = 16,000 units
Profit for Alternative A = ($20 x 16,000) - $36,000 - ($7 x 16,000) = $172,000 (Higher)
Profit for Alternative B = ($20 x 16,000) - $35,000 - ($11 x 16,000) = $109,000
Higher profit = Alternative A
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