Study tips: Management accounting: decision and control. High low with stepped fixed costs

MDCL: High low technique series for AAT Professional Diploma students

• Part 1 – High low technique with discounts
• Part 2 – High low technique with stepped fixed costs

I watched a TED talk recently about mastery based learning. The basic premise was that you wouldn’t want to live in a house that has incomplete foundations, because one day it’ll collapse.

Similarly, if we try to use advanced level techniques in our studies, without first understanding the basics, then at some point we’re likely to hit a brick wall.

The talk made me think of using the high-low technique at professional level. The basic technique, of separating a total semi-variable cost into its variable and fixed elements, is first taught at foundation level and is consolidated at advanced level.

This foundation is then built on at professional level when the reality of stepped fixed costs and bulk discounts complicate the theory of cost behaviour, on which the technique is built.

So if you feel your foundation about how costs are categorised and how they behave, isn’t totally solid, then have a quick re-cap about fixed, variable and semi-variable costs. Equally, a refresher of the basic high-low technique is advisable if you want to shore up your knowledge and understanding before you continue.

Looking at the high-low technique with stepped fixed costs

In this article we’re going to focus on using the high-low technique when the fixed element of the total cost includes stepped fixed costs. A stepped cost increases by a fixed amount at a certain level of output and then remains fixed, at the increased level, until the next step is reached, unlike a normal fixed cost which remaining the same at all levels of output.

Let’s assume we’re the cost accountant for a manufacturing organisation and that we have the following information about the company’s factory overheads:

We also know the overhead cost is semi-variable and that the fixed element contains a step of £1,250 every 2,500 units once production levels exceed 15,000 units.

The company is planning an increase in production levels and you have been asked to calculate the total overhead cost of manufacturing 30,250 units.

Calculating total overhead costs

Our fundamental understanding of cost behaviour and of the basic high-low technique enables us to adapt the normal calculations to accommodate the stepped fixed cost. This is because we know that the total semi-variable cost is made up of the variable and fixed elements but that the fixed element is also made up of two sub-elements, the normal fixed costs and the stepped fixed costs.

The key to using the high-low method in these circumstances is to recognise that, because each element behaves differently, it must be accounted for individually.

When there is no stepped fixed cost, the high-low technique calculates the variable element first. This is done by dividing the difference in the total costs by the difference in the volumes to give the variable cost per unit. However, when a stepped cost is involved, the calculation of the variable cost per unit needs to be adjusted to exclude the stepped element from the total cost because it needs to be accounted for separately. Therefore, in these situations, the first step in the high-low process must be to calculate the stepped fixed element:

Step 1 – stepped fixed element

In order to calculate the value of the stepped fixed element we first need to ascertain the number of steps included at each level. In this case, it is one for 15,500 units ((15,500 – 15,000) ÷ 2,500 = 0.2) and five for 26,250 units ((26,250 – 15,000) ÷ 2,500 = 4.5).* This means that £1,250 of the total fixed cost is incurred due to the single step in costs when 15,500 units are produced and £6,250 of stepped fixed cost is incurred for five steps when 26,250 units are produced:

Step 2 – variable element

Now the stepped cost element has been separated, the variable element can be calculated. The variable cost per unit is the difference in the total costs (£279,375 – £183,000 = £96,375) less the difference in the stepped elements (£96,375 – (£6,250 – £1,250) = £91,375). This is then divided by the difference in the volumes (£91,375 ÷ (26,250 – 15,500) = £8.50) to calculate the variable cost per unit. 

The value of the variable element for 15,500 units is therefore £131,750 and £223,125 for 26,250 units:

Step 3 – fixed element

The table is completed by deducting both the stepped element and variable element from the total cost which for 15,500 units is £183,000 – £1,250 – £131,750 = £50,000. Due to the way fixed costs behave, we already know that the fixed cost at both production levels should be the same.

Therefore, reconciling the figures at the other level of production, in this case 26,250 units, confirms that our calculations are accurate (£279, 375 – £6,250 – £223,125 = £50,000):

Forecast

Now that we’ve established the costs of the three individual elements of the total cost, we can use them alongside our knowledge of how they behave, to predict the total overhead cost of manufacturing 30,250 units.

1. Number of steps = 7 ((30,250 – 15,000) ÷ 2,500 = 6.1)*, therefore the stepped fixed element is £8,750
2. Variable element is £257,125 (30,250 units x £8.50 per unit)
3. The fixed element is £50,000

Therefore the total overhead cost of manufacturing 30,250 units is £315,875.

If you’ve found this article useful, then further reading about adjusting the high-low technique when bulk discounts have been applied, might be of interest.  You might also like to watch the TED talk I referred to at the start.

* It’s important to realise that if the number of steps requires rounding, they will always need to be rounded up in order to be accurate.

Gill Myers is a self-employed accounts consultant. She has taught AAT qualifications since 2005 and written numerous articles and e-learning resources.