Example
You are comparing the charges of two car hire firms before you decide which one to use. Firm A offers a car at a fixed rate of £20 per day plus 20p for every mile. Firm B charges only £12 per day but 30p for every mile. The two alternatives can be drawn on one diagram as shown in Figure 13.2.
Figure 13.2 Comparison of car hire costs
The total cost of using either car comprises the daily fixed charge plus the mileage cost, which varies according to miles run.
We can conclude from the graph that firm B is the one to patronize if the daily mileage is expected to be less than 80 miles, while firm A should be chosen for a daily mileage in excess of 80. The total cost is equal where the two lines cross at £36 read off the vertical scale and is called the break-even point.
Example
A firm makes only one product, which sells for £10. The variable cost per unit is £5 and fixed costs total £75,000 pa. Maximum capacity is 25,000 units per annum, but the firm is presently operating at only 80 per cent capacity. Figure 13.3 shows the break-even chart drawn from this information.
Figure 13.3 Break-even chart
Break-even is reached at 15,000 units when sales just equals total costs of
£150,000. Output of less than this amount results in a loss, while greater output makes a profit. The size of profit or loss at any output can be read off the graph at a glance, being the vertical distance between the total cost line and sales line.
Margin of safety
Also represented on the graph is the margin of safetywhich represents the proportionate fall in output which can take place before a loss is incurred. In this example, the present level of output of 20,000 units can fall by 25 per cent to 15,000 units before a loss commences. Therefore the margin of safety is 25 per cent.
Marginal costing
Separation of fixed and variable costs
Although the theoretical distinction between fixed and variable costs is easily understood, it is not so easy in practice to separate them. Some costs fall into an in-between category called semi-fixedor semi-variable, where there is a fixed amount of cost plus an element that varies with output.
One way to separate total costs into fixed and variable types is to graph total costs against the relevant levels of output. If the data covers a number of years, the total costs should be updated to today’s prices using relevant cost indices. The scattergraph is obtained from plotting total costs against level of output and drawing a line of best fit through the plots. Where the line intersects the vertical line at the origin approx- imates to the level of fixed costs. Figure 13.4 shows this approach which identifies fixed costs at approximately £200,000.
Figure 13.4 Scattergraph used to separate fixed and variable costs
Another reason for the practical difficulty in separating costs into fixed and variable categories is that such analysis varies with time. In the very long run all costs are variable because offices or plants can be closed down and then no further costs will be incurred. In the very short run of a few days, most costs are fixed, apart from direct materials, power and possibly some wages, depending on the contracted method of payment.
Although we represent fixed costs as a horizontal line on a break- even chart, it is not true to say that fixed costs will remain constant over a wide range of output levels. It could be that more supervisors or managers are required the higher the level of output, or more space or machinery is needed which result in increased rates or depreciation.
Therefore fixed costs may increase in steps as output increases, corre- sponding more to the picture in Figure 13.5 than the horizontal line shown in previous diagrams.
Figure 13.5 Stepped fixed costs
Break-even charts are a useful way of depicting profit or loss at varying levels of output. They can be drawn for a firm as a whole or for one product only. In the latter case the fixed costs are those specifically appli- cable to the product, together with a share of the total to be apportioned over all products.
Limitations of break-even charts
It is probably true that break-even charts are seen more often in text- books than in real life. This is because the charts have some severe limi- tations. Clearly, costs do not move in a linear fashion across a wide range of activity levels. Nor does the product mix ratio stay constant in a multi- product firm. Any change in the mix will invalidate a chart as total sales value and total variable costs will vary with the mix. Finally, a chart cannot predict how many sales will be achieved at a certain price – that can only be attempted by market research. A break-even chart can only predict what profit will be made for a given selling price over a range of possible sales volumes.