# Management Accounting – Fixed and Variable Costs

February 9, 2010 1 Comment

# Fixed and Variable Costs

You’ll remember from the previous post that there’s more than one way to define cost. The methods were:

- Differential future cash flows (DFC)
- Cost behaviour in relation to output
- Assignment to cost object
- Financial statement perspective
- Business function

The previous post focused on DFC, and this post is about cost behaviour in relation to output. What’s that in english? We’re on about fixed and variable costs.

## Fixed costs

These are costs that do not change with the output levels. What does this mean? I once heard that when a newspaper turns on their printing press it costs the same no matter if they print one newspaper or ten thousand… I have no idea if that’s really true, but it’s a great example of a fixed cost.

So let’s say it costs me £1,000 to make 100 ponies in my pony factory. That equates to £10 per pony. But as it is a fixed cost, if I make 200 ponies, it still costs me £1,000. Now that makes the cost of a pony £5. If I make 500 ponies, it still costs me £1,000 but each pony costs £2 now.

So when a cost is fixed, the cost per unit decreases as output increases.

Some things that might be a fixed cost:

- Salaries (when they are a fixed monthly salary)
- Rent
- Straight line depreciation

## Stepped Fixed Cost

This is a special type of fixed cost. When a cost is fixed but still rises in jumps from time to time, for example, let’s say there’s a new band called ‘Insane Ninjas of the Newbury Bypass’ (not a real band. Yet.). They’re playing a gig and need a venue for it, but they only have like 10 fans, so they just hire out a place that can house 10 people, for £50. Next time they play a gig, they now have 1,000 fans (they’re quite good) and so they hire out a 2,o00 seater venue for £500. Suddenly it all takes off for them, and they have 50,000 fans, so for their next gig they hire out Madison Square Garden, which costs £10,000.

So… what does this mean for costs? As the volume of activity (fans) increases, the cost increases, but in steps, from £50, to £500, to £10,000. Here’s a graph from the lecture notes to illustrate the point (copyright university of manchester etc)

## Variable costs

This is where the the total costs change in proportion the changes in the output. Using the ponies example from before, if it costs me £10 to make a pony, that £10 cost will not change no matter how many I make. So if I make 100 ponies, it costs me £1,000. If I make 200 ponies, it costs £2,000, and so on.

Things that might be variable costs:

- Raw materials
- Wages of people who are paid hourly (more hours they work, the more it costs you to pay them)
- Commission paid to a sales rep

## Example – Running a bar

Here are some costs that a bar would incur:

- Wages for staff — Fixed if the staff are salaried, variable if they are paid hourly
- Rent — Fixed, it stays the same no matter what happens in the bar
- Utility bills — Depends on how they are paid. If they are metered then variable, if they are paid at a fixed rate then fixed
- Alcohol (stock) — Depends on how busy the bar is. A busy bar means they need to order more alcohol as it gets sold faster. Therefore it’s variable
- Cleaning costs — Assuming that the bar pays to get cleaned regularly no matter how busy it is, fixed (ie a weekly clean)

Which of the costs are fixed and which are variable?

**Press Ctrl+A (Command+A on a Mac) for the answer!**

## Semi-fixed costs (aka semi-variable costs)

As you may have guessed, these land right in the middle of fixed and variable costs. They refer to costs that have both a fixed and variable part to them.

BT work in this way. You pay £12/month line rental, and then you’re charged for any calls you make on top of that. So the line rental is fixed, but the calls are a variable cost. Therefore it’s a semi-fixed cost.

## Breaking even

We have something called the break-even point. This is the level of production when total sales = total costs, meaning that we are making zero profit and zero loss.

So:

Break-even point: Total revenue = Total costs

But how do we know when revenue equals costs? The lecture notes have the proof of this, but it isn’t needed so here is the final formula:

Quantity that must be sold to break even = Fixed Costs ÷ (Sales Revenue per unit – Variable Costs per Unit)

Note: ‘Sales Revenue per unit – Variable Costs per Unit’ is sometimes known as the ‘Contribution Margin’

You might notice that the 2 parts of the contribution margin are both ‘per unit’. Therefore you can cancel out the ‘per unit’ part and just have the totals, ie:

Contribution Margin = (Sales Revenue per unit – Variable Costs per Unit)

OR

Contribution Margin = (Total Sales Revenue – Total Variable Costs)

## Target Profit

We can adapt the break-even formula slightly to show how many units must be sold to reach a certain profit. It’s very easy to do, you just add on the target profit to the fixed costs, so:

Quantity that must be sold to reach the target profit = (Fixed Costs + **Target Profit**) ÷ (Sales Revenue per unit – Variable Costs per Unit)

## Example

Let’s have a sample question.

There’s a company, we’ll call them ‘Lisas Llamas’. The fixed cost of running the llama factory is £500/month. Each llama costs £2 in materials to make, and takes an hour to make. The llama making workers are paid £10/hour. If the workers don’t work for any reason they aren’t paid. Each llama is sold for £14. What is the break even point?

**Press Ctrl+A (or Cmd+A on a Mac) for the answer!**

This is much easier than it sounds from the question. We need to know 3 thing: Fixed costs, variable costs per unit, and sales revenue per unit.

Fixed costs: £500

Variable costs per unit: £2 in materials + £10 in wages (remember it takes exactly one hour to make a llama) = £12

Sales revenue per unit: £14

So now we put them into the formula from earlier: **500 ÷ (14 – 12) = 250**

So, to break even, Lisa’s Llamas must sell 250 llamas a month.

Now let’s extend the example:

The company expects to sell 500 llamas a month. But they have seen a llama making machine and have the opportunity to rent one. If they rent it, the total fixed costs will rise to £3000/month. Also, the machine will reduce the time to make a llama down to half an hour. Workers still get £10/hour.

How much profit will they make if they rent the machine?

**Press Ctrl+A (or Cmd+A on a Mac) for the answer!**

So we need to work out how much it costs to make 500 llamas, and then subtract that from the how much revenue selling 500 llamas brings in.

The cost of making one llama is now **£7, **as it costs** £2 in materials **and** £5 for half an hour of the worker’s wages.**

So to make 500 llamas, it costs: £3000 (the fixed costs) + 500×£7 = **£6500**

The revenue is 500×£14 = **£7000**.

So, £7000 – £6500 = £500. The profit if they rent the machine is **£500/month.**

What about the profit if they don’t rent the machine?

**Press Ctrl+A (or Cmd+A on a Mac) for the answer!**

Cost to make 500: £500 + (500×12) = **£6500**

Revenue is still **£7000** like before.

Profit = **£500.**

So the profit is the same with or without you the machine.

If they rent the machine, what’s the new break even point?

**Press Ctrl+A (or Cmd+A on a Mac) for the answer!**

Like before we need to know the 3 parts of the formula:

Fixed costs: £3000

Variable costs per unit: **£7** (worked this out in the previous question)

Sales revenue per unit: **£14**

3000 ÷ (14 – 7) = 428.57 (round up to **429**)

So to break even, they have to sell 429 llamas.

## Margin of safety

This is a measure of how much the planned output level is above the break even point.

To demonstrate it let’s use the example with llamas from before.

Without the machine, the break even point is 250, and the expected sales is 500. Expected sales – break even point = 250. 250 ÷ 500 = 0.5, or 50%. The margin of safety is 50%.

With the machine, the break even point is 429, expected sales is 500. Expected sales – B.E.P. = 71. 71 ÷ 500 = 0.14, or 14%. The margin of safety is 14%.

A higher margin of safety means less risk, because if the actual sales are lower than expected, they have a greater chance of breaking even.

So, the company should not rent the machine as it won’t increase profit but will increase the risk.

…aaaaand that’s all for this section

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