 # Study tips: Fixed variable and semi-variable costs

I have just spent a couple of frustrating hours trying to decipher the best deal for my broadband, phone and TV package.

I’m all for getting a good deal and am more than happy to switch providers plus I’m an accounting lecturer so I’m pretty good with numbers but the whole exercise has proved tricky.  Add into that mix Daniel, my 14-year-old son, is trying to persuade me that we need a fibre connection so he can stream more easily to his games console without glitches occurring.  It was during our conversation that he started asking about costs and I found myself giving him a ‘lesson’ in basic cost behaviour.

So, here it is, starting with some important definitions.

Fixed Costs – costs that do not change with output.

Variable Costs – costs that vary in direct proportion to output.

Semi-variable costs – costs that are a combination of the above, with both a fixed and variable element.

Using these accounting definitions is vital to understanding how costs behave, as they are not the same as a dictionary definition or how a non-financial person might explain them.  In terms of my package; it is made up of a number of parts and if we look at them individually they can be categorised based on their behaviour:

## Fixed Costs:

• Is unlimited and therefore the monthly fee is payable regardless of how many Megabits (Mb’s) are used.
• Line rental
• There is one line so one fixed fee per month. If there were two lines, then the cost would double but that would be due to the quantity rather than the output.
• TV package
• This excludes some channels as it is just a basic package but within the agreement we can watch as much or as little as we want and the cost will remain the same.

## Variable Costs:

• Films
• Can be watched on a ‘pay as you’ go basis. Put in the pin number and the costs will appear on the next bill.  The more films watched the more it costs, as the cost varies directly with output.

## Semi-Variable Costs:

• Call Charges
• There is a small monthly charge which enables calls, for up to an hour on the weekends or after 6pm on weekdays, to be made without them being charged at a per minute rate. So that is fixed as the charge is paid regardless of the number of calls made.  Outside of that, any other calls are charged at the levied rate per minute and the more calls made, the higher the cost, as it varies in direct proportion to output.

Hopefully, that is an example that resonates.  Now we have looked at the definitions and applied them to some examples, we need to use that theoretical understanding to help unpick what the figures actually mean in relation to cost classifications, especially when they are presented in a way that’s designed to test us (either because it’s an assessment or the media company is trying to present their latest offer in the best light.)

## This is how it works…

If costs at 15Mb are £16 per unit and at 40Mb costs are £6 per unit, how do we know what kind of cost this is?

The answer is to calculate the total costs so that the two can be compared.  If the totals are the same then it is a fixed cost as it hasn’t changed with output but if the totals are different, it’s likely to be variable.

15 units x £16     = £240

40 units x £6       = £240

The cost of the broadband is therefore fixed at £240 regardless of whether 15Mb or 40Mb are used but because of the way the figures are initially presented, it looks like the cost varies.  Economies of scale mean the more output there is, the more units (in this case Mb’s) there are to spread the fixed costs over and the result is the cost per unit decreases.

Once you have understood fixed costs, you can apply that knowledge to variable costs because they behave the opposite way round.  As they vary in direct proportion to output the cost per unit will stay the same but the total will increase as the number of units goes up.

If the costs are £40 for 10 films and £100 for 25 films, we can use the opposite calculation to the one above to work out what kind of cost this is ie. division instead of multiplication:

£40 / 10 units     = £4 per unit

£100 / 25 units   = £4 per unit

The cost of films is therefore a variable cost of £4 per film and the more films watched the higher the costs incurred.

Care needs to be taken to be sure what information is being presented.  Are the costs shown totals or costs per unit?  This fundamentally changes the calculation required to produce figures that can then be meaningfully compared and interpreted to see how they behave.

If the cost for 100 minutes is £34 and for 180 minutes it increases to £58, we need to calculate a cost per unit as we have been presented with the total costs and the number of units that pays for.  Therefore:

£34 / 100 units   = £0.34 per unit

£58 / 180 units   = £0.32 per unit

The cost of the calls can’t be variable as the cost per minute is not the same at the different levels of output.  However, it can’t be a fixed cost either as the total costs aren’t the same, which they would be regardless of the different output levels.  Therefore, the cost of the calls must be a combination of a fixed element and a variable element which makes it semi-variable.

I hope you have appreciated this ‘lesson’ more than Daniel did, although he has benefited from humouring me and is now happily enjoying a new faster broadband connection. 