# Costs

## Costs

#### Fixed, Variable and Total Costs

Generally speaking, a business will incur two types of cost when it produces goods and provides services to consumers:

1. Fixed costs.
2. Variable costs.

A fixed cost is one which is totally independent of the level of output, and it would be incurred even when output was zero. Examples include rent, mortgage payments, managers' salaries, and loan repayments. They are often referred to as overheads.

Total fixed costs (TFC) are represented in diagram 1:

Variable costs are those which vary directly with output (i.e. as the level of output increases, then variable costs increase). Examples include raw materials, production wages, other direct production costs, and utility bills.

Total variable costs (TVC) are represented in diagram 2:

When fixed costs are added to variable costs, then the total costs (TC) of the business can be calculated.

In other words, TFC + TVC = TC.

This helps the business to calculate its total costs at any given level of output. Total costs are represented in diagram 3:

Note that TC starts at the same point as TFC.

#### Average costs

Average fixed costs (AFC) are calculated by dividing total fixed costs by the level of output.

In other words:

Average fixed costs are represented in diagram 4:

It is clear to see that average fixed costs decline continuously - this is because the total fixed costs remain constant and they are, therefore, spread over a larger and larger amount of output. Thus, the average fixed cost (the fixed cost per unit) will decline.

Average variable costs (AVC) are calculated by dividing total variable costs by the level of output.

In other words:

Average variable costs are represented in diagram 5:

It is clear to see that average variable costs will start to decline over time. This is because the business becomes more efficient at producing its output, and it can produce each unit for less - hence AVC will decline. However, the business is likely to reach a level of output where it becomes less efficient at producing its output and its average variable costs (the variable cost per unit) will start to rise again.

Average costs (AC) are calculated by dividing total costs by the level of output.

In other words:

Average costs are represented in diagram 6:

It is clear to see that average costs will also start to decline over time. When this occurs in the long-run, then the business is said to have achieved economies of scale.

However, the business is likely to reach a level of output where average costs (the cost per unit) will start to rise again. In these circumstances, the business is said to be experiencing diseconomies of scale.

When average fixed costs are added to average variable costs, then the average total costs (AC) of the business can be calculated.

In other words:

AFC + AVC = AC

This helps the business to calculate its average cost at any given level of output.

#### Contribution Analysis

Contribution is one of the most important concepts in A-level Business Studies. Contribution is the term given to the amount of money that remains after all direct and variable costs have been deducted from the sales revenue of the business.

It is called 'contribution' because it represents the amount of money which is available to contribute towards covering the fixed costs of the business and, once these are covered, it represents the amount of money which will contribute towards the profit of the business. In other words, contribution - fixed costs = profit.

##### Contribution can be analysed in two ways:
1. Contribution per unit sold

Contribution per unit sold = Sales price per unit - Variable costs per unit.

For example, if a product has a selling price of £ 10, and its variable costs (labour, raw materials, etc) is £ 3 per unit, then it has a contribution of £ 7 per unit.

If a product is loss-making, but it nevertheless makes a contribution towards covering the fixed costs of a business, then it would be unwise to delete the product from the product portfolio. This is because the total profit of the business will actually decrease if the contribution from the loss-making product is no longer received. Therefore it is vital that a loss-making product is not deleted simply because it fails to produce a profit - if it produces a contribution towards fixed costs, then it is still worthwhile to produce it.

2. Total contribution

Total contribution = Total sales revenue - Total direct and variable costs.

For example, if a business has total sales revenue of £ 4 million, and its total variable and direct costs are £ 2.5 million, then the total contribution for the business is £ 1.5 million. This contribution will hopefully cover the fixed costs and then contribute towards profit.

#### Break-Even Charts

This is a graph showing the total revenue and the total costs of a business at various levels of output. It is a form of Management Accounting and it enables a manager to see the expected profit or loss that a product will face at different levels of output.

The break-even point is the point on a break-even chart where the total revenue (T.R) of a business (or product) is equal to its total cost (T.C).

It can also be calculated mathematically by using the following formula:

For example:

A business produces just one product, which it sells for £ 9 per unit. The variable cost of each unit is £ 4 and the business faces fixed costs per year of £ 1 million.

The business currently produces and sells 500,000 units.

What is the break-even level of output and what profit will the business make if it sells all of its output?

In order to assist the drawing of the break-even chart, we can calculate the break-even level of output and the amount of profit using simple formulae:

In other words, the business will need to produce 200,000 units before it breaks-even.

Any level of output below 200,000 will yield a loss.

Any level of output above 200,000 will yield a profit.

The profit is equal to total revenue minus total cost (or profit = TR - TC).

Total revenue (TR) is calculated by multiplying the selling price by the number of units sold.

In this example, the selling price is £ 9 and the number of units sold is 500,000.

Therefore the total revenue (TR) is £ 9 x 500,000 = £ 4.5 million.

The total cost (TC) is calculated by adding together the total fixed costs (TFC) to the total variable costs (TVC).

In this example, the fixed costs are £ 1 million and the total variable costs are £ 4 x 500,000 units = £ 2 million.

Therefore the total cost (TC) is £ 3 million.

The profit is, therefore, TR - TC,

which gives us: £ 4.5 million - £ 3million = £ 1.5million.

We can now draw a break-even chart and check the figures on the chart with the answers above.

In order to have an accurate break-even chart, three lines must be plotted:

Total Fixed Costs (TFC),

Total Costs (TC)

Total Revenue (TR).

The x-axis is labelled as 'Output' (in units). In this example, the axis will go up to 500,000 units.

The y-axis is labelled as 'Costs, Revenue and Profit' (in £ ). In this example, the axis will go up to £ 4.5 million.

As you can see, the answers on the chart correlate with the answers calculated using the two formulae above. The break-even point (shown as a red dot) is the point where the TC and the TR lines cross. This is then measured by dropping a vertical red line down to the x-axis, to give 200,000 units.

The profit at 500,000 units is then calculated by taking a red vertical line up from the 500,000 unit mark to where it hits the TC line. This is then measured across to the y-axis (again using a red line) to give us total costs of £ 3 million.

The vertical red- line from the 500,000 unit mark is then extended to where it hits the TR line. Again, this is then measured across to the y-axis to give us a total revenue of £ 4.5 million.

Therefore, the profit is the difference between TR and TC (i.e. £ 1.5 million).

Although break-even analysis is a very useful tool, it does have several drawbacks:

1. It assumes that the TFC, the TC and the TR functions are linear. In reality, this is very unlikely.
2. It assumes that the selling price is constant, in reality the selling price is likely to vary from customer to customer and region to region.
3. It assumes that the business only produces one product.
4. It assumes that the business can sell all of its output. In reality, very few businesses will be able to do this and some will remain as unsold stock.

The data used to construct the break-even chart may well be out-of-date and therefore inaccurate.

#### Cost Centres and Profit Centres

A cost centre is an area of a business where costs stem from and can easily be recorded (i.e. a department or a person where costs can be identified as being incurred). These costs include wages and salaries, raw materials and capital expenditure (e.g. machinery).

Cost centres are used for several reasons:

1. Allowing the business to see which departments and people are spending the most money.
2. To see if the departments and people are generating enough benefits for the business with the money that they spend.

Direct costs (i.e. those costs which are incurred directly as a result of production) are easy to allocate to cost centres, but indirect costs (e.g. rent, rates, loan repayments, etc) are far more difficult to allocate to a specific cost centre.

A profit centre is an area of a business where revenue can be identified as being earned, (and, hopefully, profit will be made).

Profit centres generally include different product lines and retail outlets, and they are frequently used by businesses which are large and diversified. They allow a business to see which parts of the business and which products generate the most revenue.

The main reasons for using cost-centres include:

1. Loss-making departments of the business and loss-making products can be easily identified.

2. Each profit centre can be viewed as operating independently and this can lead to higher levels of motivation amongst the staff in each profit centre.

Overall, the use of cost centres and profit centres allows a business to exercise a degree of financial control over its operations, and to monitor the efficiency and profitability of its various departments and product-lines.