Separation of a Semi-Variable Cost Worked Examples

This is a technique that you are taught that you will almost certainly never do in reality. never mind, it is easy, so easy marks in the exam.

The idea is that you compare the total cost of doing something in one period to the total cost of doing the same thing in another period. The change in Total Cost will be caused solely by the change in the number of units you made (the Variable Cost), because the Fixed Cost won’t have changed. You’ll see that done in the examples below.

When would you need to do it?

When you have a Total Cost that you know includes Fixed and Variable elements, but you don’t know how much of each, but you do know the number of units involved. Plus you have at least two, so you can compare them.

You can then use that knowledge to predict a cost for a given level of production.

‘Practical’ examples?

Bills where you are charged a standing charge for having the facility (e.g. rental of a photocopier, telephone, gas supply, electricity supply, water supply) and a charge for how much you use (sheets that go through the copier (not the paper itself, just the use of the machine), minutes on the phone, amount of gas, electricity, water used).

If I wanted to predict what the cost would be next month if I used the photocopier 2,200 times, or used x amount of gas, electricity, water I think I would look at the last bill or the contract.

Have you ever had a gas bill that doesn’t tell you separately how much you used and the standing charge? No, me neither. Even if it is estimated, it tells you the rate per therm.

More practical might be where you have a machine producing something. You know the Total Cost of operating the machine and how much you produced (at least two totals of course). You could compare the two periods and work out the Variable Cost and then the Fixed Cost element. But why not use the information you already have?

If you know the Total Cost, that can only be because you have already added up all the Variable and Fixed Costs. Surely? In which case, use that data.

So why are you taught it?

The value in doing the method is then you will have a better understanding of the relationship of Variable Costs to Total Cost and get easy marks if you are asked to do it in an exam.

Watch out for long series of data. Always use the two most recent records. If you use old data then it is likely that both the Variable Cost per unit and the Fixed Cost will be different. Costs change over time. Using anything but the most recent will give you mathematical answers that are calculated correctly but are useless in reality.

It’s easy, so easy marks in an exam, but don’t ever think you will really do it.

How to separate the Fixed and Variable elements in semi-variable cost.

Let’s use the information we used in the graphs we used on the basic concepts page above and pretend we don’t know what the variable cost per unit is nor do we know what the fixed costs are.

We would look for two sets of costs, ideally close together in time. Let’s pretend that the two of the total costs given are actually for two months.

January 60 tables with total cost of £1,700
February 70 tables with total cost of £1,900

Because fixed costs don’t change (with output within a range – remember?), any change in the total has to be caused by the increase in units made. So the increase in total cost of £200 is caused by an increase in units made of 10.

£1,900 – £1,700 = £200 change in costs (an increase here).

70 tables – 60 tables = 10 change in tables (an increase here)

It’s nice and easy to see that £200/10 = a variable cost of £20 per table.

Now we need to work out the fixed costs. Remembering that

total cost = total variable costs + fixed costs

we can see that the total cost of £1,700 for January’s 60 tables is made up of 60 tables @ £20 each + the fixed costs. So, £1,700 = £1,200 + fixed costs. Obvious what it is here, but the method to calculate is £1,700 – £1,200 = £500. That’s total cost – total variable = fixed.

We were expecting £500 as we already knew what the numbers were, but, to prove you know what you are doing, work out the fixed costs from the February costs and units, you know that the variable cost is £20 per unit.

In a test you should calculate the fixed costs from both sets of data to make sure you get the same answer. If you just do one, you might make a mistake and you wouldn’t know.

Where would we use this technique? When we have bills which include a fixed cost element, but we don’t know what it is and we want to make a prediction of costs in the future at different levels of production.

Photocopying bills are a common example. A company may pay a lease to have the copier (the fixed cost element) and a charge per page printed (the variable cost element).

How do we know it is a semi-variable cost in the first place and not just a variable cost?

If it were just a fixed cost, it would be unlikely to change for a small increase in units. It’s possible that we were at the edge of a step change, but unlikely.

If it were just a variable cost, then dividing the total cost by the number of units would give you the same cost per unit. try it with the numbers we used above. You’ll see they are not the same, therefore there has to be some fixed cost in there somewhere.

These clips are from live lectures of mine and are unedited.

I give the data for the question, so that you can have a go then I show me solving the calculation.

Worked Example.