2. A manufacturing company has the following utility cost distribution? Month Ja
ID: 1152411 • Letter: 2
Question
2. A manufacturing company has the following utility cost distribution? Month January February March April May Utility cost(S) Unit produced 4,000 5000 9,000 0,000 15,000 400 800 1200 1600 2,000 a. Use the two point method to separate the mixed cost into ts fixed and variable portions. What is the total cost for next September if it's expected that 1000 units will be produced? b. Use the leas t square method to separate the mixed cost into its fixed and variable portions if the utility cost and unit produced increased by 100% of its valuesExplanation / Answer
a.
This is the high-low method.
In this method the utility cost of highest units produced and the utility cost of lowest unit produced are considered for calculation.
Variable cost per unit = (Total utility cost of highest unit on May – Total utility cost of lowest unit on January) / (May’s unit – January’s unit)
= (15,000 – 4,000) / (2,000 – 400)
= $11,000 / 1600
= $6.875
Fixed cost = Total cost of January– Total variable cost of January
= $4,000 - (January’s unit × Variable cost per unit)
= $4,000 – (400 × $6.875)
= $4,000 - $2,750
= $1,250
Answer: Variable cost per unit is $6.875; Total fixed cost is $1,250
Total cost (September) = Total fixed cost + Total variable cost
= $1,250 + (September’s unit × Variable cost per unit)
= $1,250 + (1,000 × $6.875)
= $1,250 + $6,875
= $8,125 (Answer)
b.
Least square method: Y = a + bX
Total cost = Y
Total fixed cost = a
Variable cost per unit = b
Number of units = X
The increasing 100% unitily cost within the list: $5,000 to $10,000
Corresponding number of units are also increasing at 100% rate: 800 to 1600
By using formula,
Y = a + bX
5000 = a + b × 800
5000 = a + 800b ……….. (1)
Again,
Y = a + bX
10000 = a + b × 1600
10000 = a + 1600b ……….. (2)
By solving equation (1) and (2),
10000 = a + 1600b ……….. (2)
5000 = a + 800b ……….. (1)
(-) = (-) (-)
--------------------------------------------
5000 = 0 + 800b
800b = 5000
b = 5000 / 800
= 6.25
Now by putting this value in either (1) or (2)
5000 = a + 800b ……….. (1)
5000 = a + 800 × 6.25
5000 = a + 5000
a = 5000 – 5000
= 0
Answer: Fixed cost is 0, Variable cost per unit is $6.25
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