The Australian Baking Corporation (ABC) considers annual fixed costs of producin
ID: 387902 • Letter: T
Question
The Australian Baking Corporation (ABC) considers annual fixed costs of producing bread in Darwin, Perth and Sydney, and transport costs from those centres to intended markets. It is anticipated that annual sales of bakery products would not exceed 1 500 000 tonnes. Because of tax packages offered, and generally low rental and labour costs in Darwin, annual fixed costs in that city are found to be $1.0 million. Corresponding costs are $3.5 million in Perth and $8.0 million in Sydney Average transport costs per tonne from Darwin are $20, $12 from Perth and $8 from Sydney. Calculate break-even (BE) quantities for . Darwin, Perth Darwin, Sydney .Perth, Sydney State which locations are to be preferred if annual production consists of: a) b) c) 500 000 tonnes 750 000 tonnes 1 000 000 tonnesExplanation / Answer
Solution
Annual sales = 1,500,000 tonnes
Darwin:
Fixed cost = $1 million = $1,000,000
Variable cost = $20 per tonne
Perth:
Fixed cost = $3.5 million = $3,500,000
Variable cost = $12 per tonne
Sydney:
Fixed cost = $8 million = $8,000,000
Variable cost = $8 per tonne
(A) (I) Breakeven quantity for Darwin-Perth:
Let the breakeven quantity be represented by Q. At the breakeven point the total cost at Darwin will be equal to total cost at Perth.
Total cost = Fixed cost + (Variable cost x Number of units)
At breakeven point,
$1,000,000 + $20 Q = $3,500,000 + $12 Q
8 Q = 2,500,000
Q = 312,500
Breakeven quantity for Darwin-Perth = 312,500 tonnes
(II) Breakeven quantity for Darwin-Sydney:
Let the breakeven quantity be represented by Q. At the breakeven point the total cost at Darwin will be equal to total cost at Sydney.
At breakeven point,
$1,000,000 + $20 Q = $8,000,000 + $8 Q
12 Q = 7,000,000
Q = 583,333
Breakeven quantity for Darwin-Sydney = 583,333 tonnes
(III) Breakeven quantity for Perth-Sydney:
Let the breakeven quantity be represented by Q. At the breakeven point the total cost at Perth will be equal to total cost at Sydney.
At breakeven point,
$3,500,000 + $12 Q = $8,000,000 + $8 Q
4 Q = 4,500,000
Q = 1,125,000
Breakeven quantity for Perth-Sydney = 1,125,000 tonnes
(B) Annual production quantity:
(I) 500,000 tonnes:
Darwin = $1,000,000 + $20 Q = $1,000,000 + ($20 x 500000) = $11,000,000
Perth = $3,500,000 + $12 Q = $3,500,000 + ($12 x 500000) = $9,500,000 (lowest)
Sydney = $8,000,000 + $8 Q = $8,000,000 + ($8 x 500000) = $12,000,000
Preferred location = Perth
(II) 750,000 tonnes:
Darwin = $1,000,000 + $20 Q = $1,000,000 + ($20 x 750000) = $16,000,000
Perth = $3,500,000 + $12 Q = $3,500,000 + ($12 x 750000) = $12,500,000 (lowest)
Sydney = $8,000,000 + $8 Q = $8,000,000 + ($8 x 750000) = $14,000,000
Preferred location = Perth
(III) 1,000,000 tonnes:
Darwin = $1,000,000 + $20 Q = $1,000,000 + ($20 x 1000000) = $21,000,000
Perth = $3,500,000 + $12 Q = $3,500,000 + ($12 x 1000000) = $15,500,000 (lowest)
Sydney = $8,000,000 + $8 Q = $8,000,000 + ($8 x 1000000) = $16,000,000
Preferred location = Perth
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