1. Costs activity

An organisation for which you do voluntary work asks if it could use your car to visit a hostel 100 miles away. When you suggest this is rather a long way, the accountant says it is an emergency and in any case your car is not used enough ' a car needs good mileage to give economic performance and running it an extra 200 miles will improve its running costs per mile. He demonstrates this with the following schedule which shows that costs per mile decrease as mileage increases:

1. Are you convinced by this argument? If not, why not?
2. Which costs are fixed and which are variable? And which are semi-fixed (or semi-variable)?
3. Budget for the costs at 30,000 miles pa.

If the total costs above are plotted on a graph against the mileage, then the line joining the costs will be straight line and where the line crosses the zero mileage perpendicular it will show the total fixed costs, that is the fixed costs and the fixed element of the semi-fixed costs. In this case (£750 + £2,000 =) £2,750.

If you decided to charge for the use of your car, you could draw in the revenue line on your graph. Your income line would start at zero for zero miles. This is now a break-even chart because where the income line crosses the total cost line there will be neither surplus nor deficit. It shows the mileage at which income would exactly equal total costs and allows you to read off the expected surplus or deficit at mileages above or below the break-even point.

An understanding of the relationships between cost and volume is clearly important in budgeting and knowledge of break-even points is important, for example in circumstances where you need to fix prices so as to avoid loss.

It is useful in this area to appreciate the concept of contribution, the difference between the price charged for a product or service and the variable cost. For example if we had variable costs of 40p per mile and decided to charge 56p per mile this would give a contribution towards the fixed costs and surplus of 16p per mile.

To calculate the break-even point, divide the fixed costs by the contribution (in the example, fixed costs £2,750 divided by 0.16 gives a break-even of 17,187.5 miles - at that mileage there will be neither a surplus nor a deficit, which you can check arithmetically and against your break-even chart).

Check your answers with the sample answers to this activity.

2. Break-even activity

There is a policy that the canteen must break-even in any year. During last year the costs were as follows:

It is estimated next year that the cost of food per meal will rise to 50p, fuel etc. to 16p, annual wages to £38,000 and overheads to £25,000. The catering manager needs to know how many meals must be sold to break-even. How can you calculate this and what solution might you recommend to deal with the problem disclosed?

In a situation where it is possible to place a value on the outputs, then it is also possible to calculate the contribution made by those outputs. Thus the contribution made by each meal in the box above was 12p.

If there is a choice between different service outputs then priority should be given to the service which yields the greatest contribution in order to maximise the value added by the organisation. This rule does not apply when the resources are limited in such a way that demand for the services cannot be met and the limitation affects the different services unequally, in which case preference should be given to the service yielding the greatest contribution per unit of scarce resource.

Check your answers with the sample answers to this activity.