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.
Sales – Variable costs = Contribution
We refer to different products making a contribution towards fixed costs and profit, by which we mean that they contribute to the common pool from which fixed costs are paid and profit remains.
Contribution – Fixed costs = Profit
Combining these two formulae, we get:
Sales – Variable costs = Contribution – Fixed costs = Profit
Contribution break-even chart
It is possible to draw a break-even chart in a slightly different manner. If the variable cost is drawn first and then the fixed cost on top, the result- ant total cost is the same as if we had represented costs in the original reverse order. The reason for changing the order is to be able to show the value of contribution.
Example
Using the same basic data as for Figure 13.3, the break-even chart which identifies contribution as the shaded area is shown in Figure 13.6.
Figure 13.6 Contribution break-even chart
The profit and loss areas are still identifiable as such and the break-even point remains the same at 15,000 units.
Contribution analysis
A most important use of the concept of contribution occurs when deci- sions have to be made concerning product profitability. It might be thought that the size of the profit or loss would be the determining factor here, but this is not necessarily the case.
Example
Imet Ltd manufactures three products, A, B and C, of which the first two have been making acceptable profits, but C has been losing money for some time and the directors are considering whether to drop it. The most recent results for last month are as follows:
Product A B C Total
£000 £000 £000 £000
Sales 60 120 90 270
LessTotal costs 42 99 93 234
Profit or (Loss) 18 21 (3) 36
The directors have considered a number of possible courses of future action, but meanwhile have no new products available. Nor can they sell more of products A or B without dropping the selling price. The immediate decision is whether to drop product C and apparently save £3,000 per month.
On investigation by the accountant, it is found that the total costs of the products includes £54,000 of fixed costs apportioned £12,000, £24,000, and £18,000 respectively. The fixed costs of £18,000 presently borne by product C will continue irrespective of whether that product is made or discontinued.
A more helpful analysis of the situation is to set out the contribution made by each product to the total fixed costs incurred by the firm and the overall profit achieved. This is shown in Figure 13.7.
Product A B C Total
£000 £000 £000 £000
Sales 60 120 90 270
Less Variable costs 30 75 75 180
Contribution 30 45 15 90
LessFixed costs 54
Profit 36
Figure 13.7 Contribution analysis by products
Marginal costing
The directors of Imet Ltd can now conclude that it is better to continue selling product C for the moment because it is making a contribution of
£15,000 towards fixed costs. If product C is discontinued, the contribu- tions from the remaining two products will not change, neither will the fixed costs incurred by the firm. Profit will therefore fall by £15,000 to only £21,000. So discontinuing product C immediately is not advisable.
Contribution ratio
Another use of the concept of contribution is when measuring the prof- itability of products. If the profitability is measured by expressing the net profit as a percentage of sales, product managers may argue about the unfairness of the apportionment of fixed costs to their own product.
Because of the general nature of most fixed costs, there is no direct link between them and individual products. One way around this endless debate is to express the contribution as a percentage of sales by calculat- ing what is known as the profit/volume ratioor contribution ratio:
Contribution × 100
Contribution ratio = %
Sales Example
Using the information in Figure 13.7, the contribution ratios for the three products are calculated and are now shown in Figure 13.8, where Product C is shown to be the least profitable product with the lowest contribution ratio.
Product A B C Total
£000 £000 £000 £000
Sales 60 120 90 270
Contribution 30 45 15 90
Contribution ratio 50% 37.5% 16.7% 33.3%
Figure 13.8 Assessing product profitability by contribution ratios