# question about high-low method for stepped fixed costs

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This topic contains 17 replies, has 9 voices, and was last updated by  Andrew 2 months, 2 weeks ago.

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• ansi
Moderator

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.

Ansi

lume
Participant

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

ansi
Moderator

Hey Lume,

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

ansi
Moderator

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

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

lume
Participant

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 [100×1]/[100×1]…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

fahmy
Member

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

fahmy
Member

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

lume
Participant

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….

ansi
Moderator

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:)

eddie247
Participant

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?

ansi
Moderator

hey eddie247 ,

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

sasajib
Member

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)…
Shakil

ansi
Moderator

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

Member

______________________________________
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

ansi
Moderator

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 .
And don’t forget that after you find the variable part you will need to decrease it to 10%.

good luck

zanganeh
Participant

Fran
Participant

Great thread. This helps tremendously as I have chosen to self-study. I’m thankful to have chanced upon this site.

All the best studying everyone!

Andrew
Participant

Hi guys, if you go to the top most. just the first question, i dont understand how 50,000 was deducted instead of 40,800. the formula says “cost at high level of activity-cost at low level”. so how was 50,000 low level??? thanks

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