Revision:A Level Accounts Module 4 - Costing and break-even

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Costing and break-even

In this section we look at costing and break-even. The sections we cover are:

• Types of costs
• Marginal costing and contribution
• Break-even analysis
• Limitations of break-even for decision-making

Types of costs

When calculating profits, costs are deducted from revenue. Profits are reported historically, that is, the profit figures calculated are based on what has already happened - it is focused on what has happened in the past (even if it is only the recent past). These costs incurred in business activity will arise out of many different sources. Costs are incurred in nearly all stages of business activity - such as, production, marketing, staff costs and so on.

A manager will be interested in the costs generated in the business for various reasons. One reason will be that of control. A manager will want to monitor costs and how they are incurred so that they can be controlled. Why would a firm want to control its costs? Well, if costs can either be reduced, or can be held down to a certain level, then profits may be improved. Profits will only increase if either revenue increases, or costs fall, or both. Therefore controlling costs may be the only way to boost overall profitability.

In order to control costs, one would need to understand where the cost comes from, i.e. why they are incurred. If a manager did not know why a cost was incurred then it would be very hard for that cost to be controlled. One way of controlling costs is by classifying each cost according to type.

In management accounting, costs are usually classified according to the cost and its relationship with the level of output of the business. The following costs are therefore defined in how they change in value, as the level of output changes.

Fixed costs

These costs are those that remain unchanged as the output level of firm changes. It does not matter what level of output the firm produces (even zero output makes no difference), any costs which is a fixed costs will remain the same. Common examples of fixed costs are as follows:

Examples of fixed costs

• Rent
• Office salaries
• Advertising
• Insurance
• Depreciation

Fixed costs can be represented on a graph and this would appear as follows:

Figure 1 - Fixed Costs

A common mistake that is made is to state that fixed costs will always remain constant. This is not the case, all we are saying is that these cost are fixed with respect to short - term changes in the level of output only.

Variable costs

Any cost which varies directly with the level of output would be classified as a variable cost. Varying directly means that the total variable cost will be totally dependent on the level of output. If output doubles, then the variable cost would double. If halved, the variable costs would halve. If output were zero, then no variable costs would be incurred.

Common examples of variable costs are as follows:

Example of variable costs

• Direct labour
• Raw materials and components
• Packaging costs
• Royalties

Variable costs can be represented on a graph and this would appear as follows:

Figure 2 Variable costs

Semi-variable costs

In reality, nearly all costs would not easily be classified into either fixed or variable. Most costs will fall somewhere between the two classifications. In this case, we can classify these costs as semi-variable costs.

For example, although the wages of the production staff may appear to be variable costs. In reality, they will vary with the level of output but not in a direct manner. The direct relationship is unlikely to hold over a long period of time. Similarly, many costs will have a fixed element but also a variable element (for example, most bills for gas and electricity will consist of a standing charge which is fixed and a variable element which depend on the usage).

What would the graph of a semi-variable cost curve appear like?

Because there is a link between the cost and the level of output, we would expect the semi-variable; cost curve to be upward sloping. However, there is no real 'textbook' appearance for this curve. It will normally slope upwards in a non-linear (i.e. curved) manner.

Direct costs

A direct cost is similar to a variable cost in that it compares the cost with the level of output. However, a direct cost is any cost which is directly related to the output level of a particular product. Direct cost is more appropriate for a firm that makes more than type of product.

For example, if a firm is producing furniture and the chairs produced use a certain type of wood, but the tables use another type of wood, then both types of wood would be direct costs because they are directly related to the level of output of a particular product not to the level of output in general

Indirect costs

An indirect cost is any cost which cannot be linked with the output of any particular product. These costs are sometimes known as overheads. They are related to the level of output of the firm but not in a direct manner and not for any one product.

For example, the cost of powering machinery will be related to the level of output but not to a particular product.

Generally, the terms indirect and direct are more likely to be used when the firm produces a range of products. In break-even analysis, the firm will only producing a certain product type. This means that the terms fixed and variable are more likely to be used

Total costs

Total cost would be calculated as all the costs totalled together for any particular level of output. If the output level were zero, then total costs would just consist of fixed costs.

In nearly cases, total costs will be the addition of fixed costs and total variable costs (where total variable cost is the variable cost per unit multiplied by the level of output).

Total variable costs = Variable cost per unit x output level.

Total costs = fixed costs + variable costs

Total costs can be represented on a graph and this would appear as follows:

Figure 3 Total, fixed and variable costs

Marginal costing and contribution

The term 'marginal cost' refers to the cost of producing one extra unit of output. The cost of producing an additional unit of output will be the variable costs and any other costs that are directly related to the level of output.

Marginal costing is a costing method that can be used by managers when making business decisions. This method considers how a product is to be 'costed' and will only use data relating to the variable or direct cost of production. Any fixed or indirect costs are ignored. The cost of a product will be the cost of actually producing this extra unit and no more.

• Marginal cost is the cost of producing one extra unit of output
• Marginal costing is a costing methods that only includes the direct (or variable) costs unless the question specifies that there is to be an increase in the fixed costs - usually this is not the case

Marginal costing is very useful for managers when making the following decisions:

• Accepting special orders (at a lower than normal price).
• Deciding whether to make a product or to buy the product in from an outside firm.
• How to allocate raw materials and other resources when they are scarce in the most profitable pattern.
• Deciding whether or not to close a branch or to discontinue production of one of a range of products

However, marginal costs will not prove as useful when attempting to set a selling price of a product. Consider the following example.

Example - marginal costing

B Pitt has just opened up a small restaurant. The following has been estimated for the cost of producing the typical meal:

Food and other ingredients £3.00

Waiting staff £0.50

Kitchen costs £0.50

How much should he charge for a meal? Try to work this out and follow the link below once you have had a go to see how you got on.

Total revenue

Revenue is the money earned from selling output. It is based on both the level of output and the selling price of this output. It is calculated as follows:

Total revenue = selling price x output level

Notice that in the above formula we assume that a buyer can be found for all units produced. This is viewed as a limitation of some of the costing scenarios that you may face.

The total revenue is also based on the assumption that the selling price remains constant. If this is the case then we illustrate total revenue graphically. This would appear as follows:

Figure 4 Total revenue curve

Contribution

Linked closely with marginal costs and marginal costing is the concept of contribution. Contribution is defined as the difference between the selling price of one unit of output and the variable cost of producing this extra unit of output.

Contribution per unit = selling price - variable cost per unit

Total contribution would be the same as the contribution per unit, but with each component would be multiplied by the level of output. The formula for this is as follows:

Total contribution = total revenue - total variable cost

Contribution can also be thought of as the profit (ignoring fixed costs). Although it cannot 'officially' be termed profit until all costs have been deducted. Contribution really refers to the amount each extra unit sold will contribute towards paying the fixed costs of the firm

Break-even analysis

Most firms will want to maximise their profits. Being profitable is not always possible. New firms, small firms and firms facing an economic slowdown may find that they cannot generate profits at all. In this situation, it may be a more realistic objective for firms to aim to simply break-even.

Break-even implies that the firm does not make any profit, but it also does not make any losses either. All the costs incurred by the firm are exactly matched by their revenues earned over a period of time.

Break-even occurs where total costs is equal to total revenue

The break-even point is measured by the level of output where total costs equals total revenue but in can also be measured in terms of sales value.

Break-even is measured either by output level or by sales value

Assumptions of break-even

The break-even model is based on some simplifying assumptions, which does make the model less realistic, but can also make it easier for us to use and to manipulate for changing circumstances. These assumptions are as follows:

1. All output is sold. The words output and sales are used interchangeably - there are not stocks of goods remaining unsold.
2. The firm only makes one type of product.
3. All costs are classified as either fixed costs or variable costs.
4. The firm can sell all the output it wants at each selling price

Based on the simplifying assumptions outlined earlier - that there are only two types of costs: fixed and variable - then the break-even point will always be found where:

Total revenue = fixed costs + variable costs

As long as the firm generates a positive contribution on each extra unit of output that is sold, then profits will always be higher (or its losses will be lower) if it sells an extra unit of output.

If a firm had no fixed costs to worry about at all, then any units sold would lead to the firm making a profit. However, nearly all firms will have fixed costs that will be paid regardless of the level of output. In this case, for the firm to earn a profit, the contribution earned on the units of output actually sold must be higher than the overall level of fixed costs.

The break-even point must therefore be at the level of output where the contribution generated from these sales is exactly equal to the total level of fixed costs. This gives rise to the following formula:

(Break even point is measured in units of output)

Remember that contribution per unit is selling price - variable cost per unit

Example 1

A sole trader runs a sandwich shop. The average cost of each sandwich, in terms of ingredients, is £1. The average selling price is £1.50. The weekly running costs of the shop are £500 - this covers rent, heating and lighting and his own wages - these do not depend on the level of output.

How many sandwiches need to be sold on an average week to break-even? Have a go at working this out and then follow the link below to see how you've got on.

We can also measure the break-even point in sales revenue. We still use the formula to calculate the output level for break-even, but then we multiply the break-even output level by the selling price.

Break-even level in sales revenue = Break-even output x selling price

In our previous example, the sales revenue at the break-even point would be:

1,000 sandwiches x £1.50 = £1,500.

Break-even charts

The break-even model can also be expressed in a graphical format on a break-even chart. This will bring together the graphical representation of both costs and revenue curves that have been developed earlier.

The standard break-even chart will appear as follows:

Figure 1 Break-even chart

Note the following:

1. It is normal to plot the following three curves on to the break-even chart:
   • Total revenue
   • Total costs
   • Fixed costs
2. The horizontal axis measures the range of output from zero, to the maximum possible output (this will depend on the question as to which the scale of the output).
3. The vertical axis measures both costs and revenues - it measures financial values.
4. Both the fixed cost curve and the total costs curve will originate at the same point on the vertical axis as each other (this is because if no output is produced then fixed costs and total costs will be the same - there will be no variable costs at zero output).
5. The point of intersection of the total cost and the total revenue curve represent the break-even level of output. This can be found by drawing a line vertically down from the intersection to the horizontal axis to measure the actual break-even output level.
6. The sale revenue at the break-even level of output can be found by taking horizontal line from the total cost/total revenue intersection to the vertical axis.
7. Any output levels to the right of the break-even level of output will mean that the firm has generated a profit. However, any output levels to the left of the break-even will mean that the firm has generated a loss.

Plotting the break-even chart

The chart is based on the simple relationships between costs, revenues and output. As output increases, there will be an increase in costs and also in revenues. This can be summarised as follows:

Fixed costs will be represented by a horizontal line. This will be drawn from the vertical axis at the level of fixed costs and will be plotted across the chart.

Total costs consist of both fixed and variable costs. Therefore, as output increases, the total cost will also increase.

Total costs (TC) = Variable costs (VC) + fixed costs (FC)

TC = (VC per unit x output level) + FC

Total costs (TC) = VC per unit x output level + fixed costs

Example 2

A firm produces pine chairs, the variable element of which costs £15 to produce. The fixed costs incurred per week amount to £8,000.

What are the total costs for the firm at the output levels of zero, 100, 500 and 200 bookcases? Have a go at working them out and then follow the link below to see how you got on.

A quick way of plotting the total costs curve is as follows:

We know that at zero output the total costs and the fixed costs will be the same. This will be the first point on the total cost curve.

As output increases, we know that total costs will increase in linear (i.e. straight line) manner. If we simply find that end point of the total cost curve, then we can join up the end and the starting point to give us the full total costs curve. The total costs at the end point will simply be as follows:

Maximum output multiplied by the variable unit cost plus the fixed costs. Of course, if we make a mistake then the whole curve will be inaccurate. It may be wise to plot a third point on the curve just as a back up. Choose any output level and calculate the total costs at this point and simply plot this on the chart.

Total revenue curves will always begin at the origin (0, 0). This is because if no output is sold, then no revenue will be received. The revenue curve will also rise in a liner, straight-line, manner.

Plotting the total revenue curve will involve calculating revenue at various levels of output. Total revenue will be calculated as follows:

Total revenue (TR) = selling price of output x output level

The quick method here would be to calculate total revenue at the maximum output level by multiplying this output level by the selling price and then joining this point up with the origin.

Example 3

As in the above example, the chairs produced are then sold for £30. What is the total revenue received by the firm at the output levels of zero, 100, 500 and 100 chairs? Have a go at working this out and drawing the total revenue curve and then follow the link below to see how you got on.

Break-even point

If we combine the data relating to the cost and the revenue situations of chairs as outline in the previous examples, we would arrive at the following:

Selling price = £30

Variable cost = £15

Fixed costs = £8000

If we assume that the maximum level of output that can be produced per week is 1000 chairs, then the data relating to costs and revenue at different output levels can be represented as follows:

It may help to think of the output levels as the horizontal co-ordinates on the chart and the money values as the vertical co-ordinates. For example, the total revenue curve will always start at (0, 0). Fixed cost and total cost curve both begin at (0, 8000).

Break-even chart in full

Figure 4 Break-even chart

Using a table as shown above may help you to eliminate any chance of errors being made. However, in an examination situation, the construction of such a table may take up valuable time, which you cannot afford to give up.

Hint - until you are confident in drawing break-even charts, use a full table as shown above.

When drawing a chart, it is sensible to first of all calculate the break-even point using the formula. This way, we can have a rough idea of what the chart should look like before we draw the chart.

Break-even level of output = £8000/(£30 - £15) = £8000 / £15 = 533.33 chairs

It always makes sense to round up the answer to the nearest whole. Number (unless output can be broken up into fractions).

In this case, the break-even level of output will be 534 chairs.

Using the break-even chart

The break-even chart can be used to measure profits and losses. This is achieved as follows:

Figure 5 Measuring profit from break-even chart

At any output level, the profit or loss can be calculated by simply drawing up a vertical line from the output level of the horizontal axis (in this case from 30 units). Sooner or later, this line will pass through both the total cost and the total revenue curve. As it intersects both of these curves, you should draw a horizontal line (i.e. at right angles to the original vertical line) towards the vertical axis (where we measure the money). The two lines (one from the total cost intersection and one from the total revenue intersection) will eventually hit the vertical axis. Now, all you have to do is measure the vertical gap between these lines in money terms (be careful of the scale you are using to measure money). This gap will be the profit or loss. On the diagram above, the profit will be the distance ab.

Example 2

With the same example of selling chairs, we can estimate the profit levels at different levels of output.

If the number of chairs sold was 700 then the profits could be calculated as follows:

Figure 6 Measuring profit from break-even chart

On the other hand, if only 300 chairs were sold then the losses would be shown as follows:

Figure 7 Measuring loss from break-even chart

Margin of safety

If a firm is generating a profit, then its output level will be higher than the break-even output level. A firm may wish to know how far output can fall safely, before the firm begins to experience losses. This idea is summarised in the concept of the margin of safety.

The margin of safety measure how far output can fall before the firm begins to make a loss. It is measured by the number of units of output between the current level of production and the break-even level of production. It can also be expressed as a percentage of the current output level.

Margin of safety (in units) = actual output - break-even output

Example 3

Continuing with the maker of chairs. If the actual output level were 650 chairs, then the margin of safety would be:

Margin of safety (in units) = 650 chairs - 534 chairs

Margin of safety (in units) = 116 chairs

In other words, output and sales can safely fall by 116 chairs before the firm stops making profits. If it falls by 117 chairs, then the firm would begin to make losses

Expressed as a percentage this would be: (116 / by 650) x 100 = 17.8% i.e. output and sales can fall by 17.8% before the firm stops making profits.

This is shown below:

Figure 8 Measuring margin of safety

Changes in costs and selling prices

It is possible to show the effects of price changes, changes in both the fixed costs of the firm and also the unit costs of the firm on the break-even chart.

The break-even level of output will always change if any of the following three items change:

• Fixed costs
• Variable cost per unit
• Selling price

Any changes in one or more of these will also change the curves as shown on the break-even chart. If any of the initial conditions changes, then it is possible to re-plot a new curve on top of the old chart, to all comparisons over different scenarios. For example, a firm may have an option of investing in new machinery, which would increase the fixed costs, but would also lower the variable cost per unit. The overall effect on profits can be seen by drawing a break-even chart.

The changes can be seen as follows:

Change in selling price

Figure 9 Increase in selling price - change in break-even

Here, any change in the selling price of each unit will simply 'swing' the total revenue curve either upwards or downwards. If the selling price is increased, then the curve will pivot around the origin in an upwards manner - this will lead to the firm breaking even at a lower output level than before. The opposite is also true.

Change in fixed costs

Figure 10 Increase in fixed costs - change in break-even

Here, a change in fixed costs will either shift the fixed cost curve up (if it increases) or down (if it decreases). This also has the direct affect on the total costs of the firm. If fixed costs increase, then the total costs curve will move upwards in a parallel manner. Similarly a fall in fixed costs will shift the total costs curve downwards in a parallel manner.

Change in variable cost

Figure 11 Increase in variable costs - change in break-even

Here, a change in the variable cost per unit will swing the total costs curve up (if the unit cost increases) or down (if the unit cost falls). The total cost line will still pivot around the total cost/fixed cost intersection (as long as fixed costs remain constant).

Limitations of break even for decision-making

The simple break-even model helps managers analyse the effects of changes in different variables. A manager can easily identify the impact on the break even level of output and the change in profit or loss at the existing output. However, simple break-even analysis also makes simplifying assumptions:

• In reality the variable cost per unit is likely to change with changes in output. As a firm expands, for example, it may be able to buy materials in bulk and benefit from purchasing economies of scale. Conversely, as output rises a firm may have to pay higher overtime wage rates to persuade workers to work longer hours. In either case, the variable costs per unit are unlikely to stay constant.

• Once a certain level of output is reached, a firm will have to spend more money on expansion. More machinery will have to be purchased and larger premises may be required (either for purchase or for rent). This means that the fixed costs are unlikely to be constant with respect to output - though this may only apply to large changes in output. This can be built into the break-even model but it makes it more compacted, and the simple formula cannot be used.

• Firms will incur other types of costs, which are partly but not directly related to the level of output. These are known as semi-variable expenses. For example, if a firm purchases more machinery, then maintenance costs will rise but possibly not in the same proportion as the increase in the capacity.

• Break-even analysis assumes that if output is produced it will automatically sell. In reality, sales may be higher than output (if the firm is using up stock) or less than output (if the firm is building up stocks).

• If a firm wishes to boost its profits then according to the break-even analysis, either the firm must increase its selling price or aim to sell more output. However, this assumes that price can be changed independently of competition. If price is increased, it is likely that sales will fall - thus leading to lower, rather than higher, revenue.

Exam tips - costing and break-even

• You must be able to distinguish between the different categories of cost and how they change with respect to changes in the level of output. A good definition of a type of cost would give both an example and would explore the relationship between the size of the cost and the level of output.

• To calculate the break-even point the three items of information that are needed are the selling price, the variable cost per unit and the level of fixed costs. The break-even level in revenue and in output can always be calculated if we have these three pieces of information.

• Although you will need to be able to draw a break-even chart from start to finish, it is highly unlikely that you would have to construct a full chart in the examination because there is not enough time. Remember, each modular Accounting AS exam only lasts for one hour and there is not enough time to have one long question on only one topic.

• The uses and limitations of break-even will need to be considered as well. In this situation, remember to use the information that you are given - break-even will be more useful to certain types of firms, in certain times, than in others - you must use this when writing on this topic.

Comments

These notes are aimed at people studying for AQA A Level Accounting Unit 4, but will also be suitable for other courses and exam boards.

Originally submitted by duke_stix on TSR Forums.