Understanding THE HIGH-LOW Method PDF

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Understanding THE HIGH-LOW Method...

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UNDERSTANDING THE HIGH-LOW METHOD

With the high-low method, we have been choosing two levels of activity and work out the difference, which gives us the variable elements. However, why does this difference give us variable costs? To illustrate this concept, let me take an example: Suppose we have the following data:

Level of activity (Units) 100 400

Total Costs (£) £700 £1,300

Variable cost per unit is constant within this range of activity and there is no step up in fixed cost.

We want to work out the variable cost per unit and the fixed cost. What we have been practising is using the high-low method to provide us with the answers. Let us understand this method. What we know is that variable cost per unit and total fixed cost is constant and that Total Cost = Total Variable Cost + Total Fixed Cost Hence, let us state that variable cost per unit (v.c.p.u) = V Total fixed cost = F

AT 400 units: Total Variable cost will be 400V and total Fixed Cost will be F. Since total costs is £1,300, we can re-write it as per the following: 400V + F = 1,300 Similarly, for 100 units: 100V + F = £700 S0, if I subtract one equation from the other, I will only be left with the variable elements since the fixed element will be eliminated. This is what we have been doing with the High-Low method

400 V + F = 1,300 100 V + F = 700 ----------------------------------300 V = 600 Put another way, the difference between high and low gives us the variable costs. So now, I can solve for V (Variable cost per unit), which will be 600/300 = £2

Samuel Hinds [email protected]

pg. 1

Once I have V, I simply replace it either in the 1st (High) OR 2ND (Low) equation to solve for F (fixed cost). Hence, choosing High, i.e., the 1st equation: 400 (2) + F = £1,300 800 + F = £1,300 F = £500, i.e., fixed cost is £500. You can also substitute V in the 2nd equation and you would still have the same answer. Therefore, you can work out the total costs at any activity level with the variable cost per unit and fixed cost.

Dealing with Step fixed Cost: (1) If you have understood the logic behind high-low, then you should not have any problems to deal with step fixed costs. Let us take another example to illustrate. Suppose we have the following data:

Level of activity (Units) 100 400

Total Costs (£) £800 £1,900

Variable cost per unit is constant within this range but there is a step up of £200 in fixed cost when the activity level exceeds 300 units.

So, using the same logic as previously: At 100 units 100 V + F = £800 At 400 units 400 V + F + £200 = £1,900 (Note that at 400 units, that there is a step up of £200 in the fixed cost. Hence, one way of dealing with it is to deduct this step up cost and proceed as usual) So, 400 V + F =£1,900-£200 = £1700 Similarly, we could have done the difference between high and low and then deduct the step up cost. This way, we will only have the variable costs.

Samuel Hinds [email protected]

pg. 2

400 V + F = £1,700 100 V + F = £800 -----------------------------300 V = £900 V = £900 / 300 = £3 V.C.P.U = £3. Substitute in low: 100 (3) +F = £800 F = £500 Substitute in High: 400 (3) + F = £1,900 (Note that I have used the original equation, which included the step up fixed cost) F = £700 (Note that this cost includes fixed cost and step up of £200 in fixed cost) So now that we have all the required information, we can easily work out the total cost for any given level of activity. Just make sure that you include or exclude the step up fixed cost!

Dealing with Step fixed Cost: (2) Another way of getting a question is when you do not know what the amount of step up in fixed cost is, but simply a percentage increase. Suppose we have the following:

Level of activity (Units) 100 300 500

Total Costs (£) £1,500 £2,700 £3,700

Variable cost per unit is constant within this range but there is a step up of 20% in fixed cost when the activity level exceeds 250 units.

Variable cost per unit (v.c.p.u) = V Total fixed cost = F Since we know that step up in fixed cost is 20%, we can state that it is 20% * F = 0.2 F

What we should realise is that activity level of 100 units does not include step up in fixed cost while at 300 and 500 units, the total costs given will include the step up in fixed costs since they are greater than 250 units. Samuel Hinds [email protected]

pg. 3

Since the 2 highest activity levels will both include the step fixed cost, it is easiest to use these two to work out the variable, fixed and step fixed cost. At 500 units and At 300 units: (Note that we have F + 20% of F)

500 V + 1.2 F = 3,700 300 V + 1.2 F = 2,700 ---------------------------------200 V = 1,000 V = £5 Replacing V in equation (High) 500 units to find F: 500 (5) + 1.2 F = £3,700 1.2 F = £1,200 F = 1200/1.2 = £1,000 Hence Step fixed cost = 20%*1,000 = £200. So we have all the data required to work out total costs at any activity level!

We could also have used activity level 100 units and 500 units to derive the answers: At 500 units and At 100 units: (Note that we have F + 20% of F for 500 units only!) 500 V +1.2 F = 3,700 100 V + F = 1,500 In this case, if we do the difference we will still have 2 unknowns (F and V since F will not be eliminated!) So we make one of the unknown the subject of formula and solve: Taking low: 100 V + F = 1,500 F = 1,500 – 100 V Replace F by the above in High 500 V + 1.2 (1,500 – 100 V) = 3,700 500 V + 1,800 – 120 V = 3,700 380 V = 1,900 V = 1,900/380 = £5 Replace V by £5 in any equation and you will get F = £1,000 and Step up fixed cost to be £200! Samuel Hinds [email protected]

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