 Today we will give you an additional tool for your arsenal, known as the ‘high low method’ of cost accounting. I know that saying ‘cost is a fascinating subject’ sounds nerdy (it is); but it is also invaluable for giving you business insight in many different ways.

Sometimes fixed costs are only fixed within certain levels of activity, you might have a situation where the more you make the cheaper it gets, or the inverse. An understanding of fixed and variable costs is therefore often insightful.

High Low method uses the following equation: y = a + b(x) where

y = total cost
a = fixed cost
b = unit or variable cost
x = amount or volume

apply it to the following:

Output (units)            Total Cost (€)

100                6000
200                7000
300                8000

what is the variable cost per unit?

Simple: it is the high total cost minus the low total cost divided by the high output minus the low output

8000 – 6000/ 300 – 100 = 2,000/200 or €10 variable cost.

What does that tell you? It tells you your fixed costs at any stage!

100×10 = 1000 in the first output of 100 units, therefore fixed costs are equal to what is left over (€5,000) and the same calculation holds true for the rest of them, at 300 units the fixed cost are still 8000 – (300 units x €10) = 5,000

So if output was 440 units total cost would be €9,400 (5,000 fixed costs + (440 units x 10 variable cost).

That is easy right? You can also use this with more complex situations where you might have ‘stepped costs’ – a ‘stepped cost’ is where a cost goes up in order to meet a new level of output. Imagine a situation whereby to make 100 widgets you need to rent one factory at €5,000 per year, to make 200 you then have to rent another factory, in this example you’d have a ‘stepped cost’ of €5,000 to make anything more than 100 widgets (assuming you can’t find efficiency or ability to do it in the first factory – we’ll pretend it alreayd runs at capacity 24/7 so you need a new place to do it).

If that was the case you might find out that you see this:

Fixed costs remain the same up to 4,800 widgets, but after that variable costs go up 23% and you are operating factory 1 at capacity.

output:     4,000        6,000          8,000

Total costs:     36,000        69,520        79,360

What is the cost of making 5,000 widgets?

solution:

You can’t use the ‘high low’ between 4 & 6,000 units because there are cost changes within it, therefore you jump to the next sampling section that has consistency, the 6-8,000 units area and you get the following:

79,360 – 69,520 / 8,000 – 6,000 = 9,840 / 2,000 = 4.92 Variable cost (or cost per unit)

We now know that 4.92 x 8,000 = variable cost (€39,360) so the fixed cost portion of this must be €40,000! Wow? Yes, wow, because we also know that it represents two factories of fixed cost! So one factory is €20,000.

We also know that 4.92 = 23% cost increase (123%) so let’s net that down and get 4.92/1.23 = 4 and that gives us the proof of our earlier answer (for the smarties: if we figured a factory cost €20,000 then 16,000 is the cost of 4,000 units and therefore €4 a pop)

so 4 x 4000 = 16,000 and that means a fixed cost of 20,000, so far so good.

so 5000 widgets would be:

4,800 x 4 + 20,000
200 (to make the total 5,000) x 4.92 + 20,000 (for the 2nd factory)

= 19,200 + 20,000 = 39,200
and
= 984 + 20,000 = 20,984

add them both and you get 60,184 being the cost to make 5,000 widgets.
Now tell me there isn’t some fun in that?!