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Good day,
I am seeking assistance with the following question and answer below.
I understand the question but I do not understand one thing with the answer.
To find total fixed cost below 11,000 units, why divide 10 by 11 then multiply by $154,000? is the 10 the percentage? and what does 11 represent?
QUESTION
An organization has the following total cost at three activity levels:
Activity Level (Units) 8,000 12,000 15,000
Total Costs $204,000 $250,000 $274,000
Variable cost per unit is constant within this activity range and there is a step up of 10% in the total fixed costs when the activity level exceeds 11,000 units.
What is the total cost at an activity level of 10,000 units?
Ans: Variable cost per unit= (274,000-$250,000) / (15000-12000)= $8
Total fixed cost above 11,00 units= 274,000- (15000 x $8)= $154,000
Total fixed cost below 11,000 units= (10/11) x $154,000=$140,000
Total cost for 10,000 units= (10000 x $8)+ $140,000= $220,000
The fixed costs are 10% higher when the activity is above 11,000 units.
So for every $100 fixed costs at the lower level, they increase to 100 + (10% x 100) = $110 at the higher level.
So…..for every $110 at the higher level then will only be $100 at the lower level.
Therefore the fixed costs at the lower level are 100/110 times the fixed costs at the higher level (same as 10/11).
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