question about high-low method for stepped fixed costs

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  • Avatar of ansi
    ansi
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    Hi everyone,
    Recently i faced a question concerning the use of high-low method to determine fixed and variable part in stepped fixed costs.
    Well , here is the task .

    An organisation has the following total costs at three activity levels:

    Activity level (units) 4,000 6,000 7,500

    Total cost $40,800 $50,000 $54,800

    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 5,500 units.

    What is the total cost at an activity level of 5,000 units?
    A $44,000
    B $44,800
    C $45,400
    D $46,800

    Solution:

    A
    Calculate the variable cost per unit by comparing two output levels where fixed costs will be the same:

    Variable cost per unit = [(54,800 - 50,000) ÷ (7,500 - 6,000)] = $3.20

    1) Total fixed cost above 5,500 units = [54,800 - (7,500 x 3.20)] = $30,800
    2) Total fixed cost below 5,500 units = (10 ÷ 11) x 30,800 = $28,000
    3) Total cost for 5,000 units = [(5,000 x 3.20) + 28,000] = $44,000
    ______________________________________________________________________
    Everything’s pretty clear in this example except one thing : why to calculate the cost of 5,500 units , 10 is devided by 11. . Where this number comes from?
    I do understand that the cost was increased by 10% when the output reached 5500 units, but why to deduct those 10 % they devide it by eleven ?

    The answer may be quite obvious but i just can’t get it.

    Thank you in advance!
    Ansi


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    lume
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    I am not good at explanations
    so i will just do it step by step

    first in the task it states that the total fixed cost increases by 10% when the activity increases 5,500
    as in the part 2 of the answer the total fixed cost of activity above 5500 is calculated i.e 30800
    now this amount is 10% more than the total fixed cost below 5500
    so
    10% x (total fixed cost below 5500) + (total fixed cost below 5500) = (total fixed cost above 5500)
    [(10 + 100) x (total fixed cost below 5500)] / 100 = 30800
    [110 x (total fixed cost below 5500)] /100 = 30800
    total fixed cost below 5500 = 30800 x (100/110)
    = 30800 x (10/11)

    sorry for the long explanation,,but as i said i amnot good with explanations


    Avatar of ansi
    ansi
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    Hey Lume,

    Thank you very much for your reply!
    Now I understood why they use 11. Actually I tried to check those 110% but forgot to do that simple equation.

    Anyways, it’s great that your explanation is not short, that makes it quite clear for me!

    Have a nice day,
    Ansi


    Avatar of ansi
    ansi
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    I was just trying to calculate it and couldn’t understand why you add and devide by 100 and while trying to calculate it myself I found a slightly different way :D

    1. 10% x (total fixed cost below 5500) + (total fixed cost below 5500) = (total fixed cost above 5500) ;

    Suppose that total fixed cost below 5 500 is X then

    2. 10% x X + X = 38 800 ;
    3. 0,1X + X = 38 800;
    4. X(0,1 + 1) = 38 800 ;
    4. 1,1X = 38 800;
    5. X = 38 800 / 1,1 = $28 000


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    lume
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    hi
    to use your ‘X’ for fixed cost below 5500
    1. 10% x X + X = 38800
    2. (10/100)x X + X = 38800
    3. [{10/100} + 1] x X = 38800
    4. [{10/100} +{1/1}] x X = 38800
    in additions of fractions, you need common denominator..the denominator is the bottom one of a fraction..so in 10/100 the denominator is 100 and for 1/1 it is 1…so if you multiply 100 to the numerator of 1/1(numerator is the top one) and denominator the number doesn’t change..so [100x1]/[100x1]…now both fractions have common denominater..100
    5. [{10/100} + {100/100}] x X = 38800
    6. [ {10 +100}/100] x X = 38800
    7. 110/100 x X =38800

    i explained it this way because you wanted to know how the 10 /11 came out


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    fahmy
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    Hai, this is my Calculation

    [54800-40800] / [7500-4000] = 4 (variable cost per unit)

    Total fixed cost = (7500 X 4) – 54800
    = 24800
    Total Cost= Fixed cost + variable cost

    Total cost of 5000 unit is

    5000 X 4 = 20000 Variable cost

    24800 Fixed cost

    Total cost =20000+24800
    = 44800


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    fahmy
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    i Actually not understand that y u taking the answer A can any one comment on my post, may be i am wrong


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    lume
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    hi fahmy
    you have just missed one point in the question, that the fixed cost changes after 5500 so you should use 6000 and 7500..as high low method is used with constant fixed cost….


    Avatar of ansi
    ansi
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    There is a mistake in my previous post which may be misleading for others : the total fixed cost above should be 30 800 and not 38 800.

    Lume , i fully understand why you explained it to me that way and i’m very grateful to you. I showed one more way (which is actually almost the same) for others.
    And thank you for explaining about 100 as well:)


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    eddie247
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    hi guys,i am using the bpp txt at the moment,when it comes to the high-low calculations with step up in fixed costs,the examples are so straight forward…but the thing is they do not have any examples where we are given a set of more than two levels of activity ie like in ansi’s problem three levels of activity…..unless i am looking at a different book!my question is,when u are given more than two levels of activity like in this instance,would it be correct to ignore the level that is in this case 4000 units at the cost of $40800 and proceed with the other two levels because they are in excess of 5000 units,in otherwords is this a trick that the examiner can put forward to us the students,because like i said i use the bpp manual and all the examples i have worked through are straight forward with only two levels of activity and that’s it and it’s maybe not surprising to see why fahmy got that answer,because i don’t think he missed seeing the step up in fixed cost at ten percent,more likely than ever i think he has never really dealt with more than two activity levels being put into a problem question…….any advice?


    Avatar of ansi
    ansi
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    hey eddie247 ,

    Your conclusion is correct.
    In order to apply high-low method, you need to compare highest and lowest figures that contain equal/the same fixed cost. Otherwise they won’t be comparable.
    It works exactly like in the example provided above.
    The same technique appears when you apply high-low for situations where changes in variable costs per unit take place.

    Take the following example :
    ______________________________________
    Output (Units) 200 300 400
    7,000 8,000 8,600

    For output volumes above 350 units the variable cost per unit falls by 10%. (Note: this fall applies to all units – not just the excess above 350).

    Required:

    Estimate the cost of producing 450 units of Product x in __year.

    Solution

    Variable cost per unit (<350) = ($8,000 – $7,000) / 300 – 200
    = $10
    etc.

    Both previous and current examples are from kaplan, so I believe we can fully trust this information :)


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    sasajib
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    Hello guys…
    I am new to ACCA… And stuck in a question of High Low method…
    The question is ….


    A business has experienced the following labour costs :

    Code:
    Output Cost
    (units) ($)
    7000 86000
    12000 141000
    9000 97500

    Fixed costs increase by $15000 for output in excess of 10000 units.
    Using the high low method what is the estimated cost of producing 14000 units?
    A. 142000
    B. 157000
    C. 163000
    D. 178000


    Can anyone solve the problem and explain (why)…
    Thanks in advance….
    Shakil


    Avatar of ansi
    ansi
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    Hello Sasajib,

    I believe you already found solution to this question, however I will still answer it here, maybe it will be useful for anyone.

    The correct answer to this test is B = $157,000.
    If you are required to calculate fixed and variable costs using high-low method you need to analyze the data given , e.g. output and it’s cost. And if the row consists of more then two values then you need to find the minimum and maximum value of output.
    Then two values and related costs are compared. Fixed element is the same every month, only variable part change. So by finding the difference between two we find the variable part.
    In this test fixed cost increase when the output excess 10,000 units. That means that the fixed cost of producing 12,000 units is greater then the fixed cost of producing 9,000 or 7,000 units by $15,000.

    As fixed costs don’t affect variable part, this amount of excess ($15,000) should be declined from the total cost of producing 12,000 units before using high-low method.

    Calculations are the following:
    1. Variable cost per unit = {(141,000 – 15,000) – 86,000} / (12,000 – 7,000) = 40,000 / 5,000 = $8
    2.Fixed costs = Total cost – Variable costs = 126,000 – 12,000*8 = $30,000
    OR = 86,000 – 7,000*8 = 86,000 – 56,000 = $30,000
    3. The cost of producing 14,000 units = Variable costs + Fixed costs + Excess in costs because production is greater then 10,000 units = 14,000*8 + 30,000 + 15,000 = $157,000

    Good luck,
    Ansi


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    sadaf395
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    ______________________________________
    Output (Units) 200 300 400
    7,000 8,000 8,600

    For output volumes above 350 units the variable cost per unit falls by 10%
    Please some body help I don’t understand the criteria of choosing the highest and lowest level of activity in this example they choose 200 and 300 instead of 200 and 400 output units – why please advice


    Avatar of ansi
    ansi
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    Dear Sadaf395,

    High-low method helps to determine variable and fixed part of the cost because it is based on the assumption that for all the quantities regarded fixed and variable part PER UNIT remains the same. If thre is any change in fixed or variable cost per unit then high-low won’t give correct results, unless that change is adjusted.

    In your example the variable cost per unit changes when the output reaches 350 units.
    So you can’t compare 200 and 400 units as they have different variable cost per unit.
    So instead you need to choose from available data the highest and the lowest output with the same variable cost per unit.

    In this example it is 200 and 300 .
    Please see examples above in this topic, they will help you understand high-low better.
    And don’t forget that after you find the variable part you will need to decrease it to 10%.

    good luck ;)


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    zanganeh
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    tanx its very helpfull

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