106 ACCOUNTING FOR MANAGERS
costshave both fixed and variable components. A simple example is a telephone
bill, which will have a fixed component (rental) and a variable component (calls).
Maintenance of motor vehicles can be both time based (the fixed component) and
mileage based (the variable component).
This example introduces the notion of marginal cost. Themarginal costis the
cost of producing one extra unit. In the above example, to increase volume from
10,000 to 15,000 units incurs a marginal cost of £50,000 (which in this case is 5,000
additional units at a variable cost of £10 each). However, marginal costs may
include a fixed-cost element (in the case of semi-fixed costs).
The notion of cost is therefore quite difficult. Is the cost in the above example the
average cost or the marginal cost? If it is the average cost, what level of activity is
chosen to determine that average, given fluctuating volumes of sales from period
to period?
Cost – volume – profit analysis
A method for understanding therelationship between revenue, cost and sales
volume is cost – volume – profit analysis, or CVP. CVP is concerned with under-
standing the relationship between changes in activity (the number of units sold)
and changes in selling prices and costs (both fixed and variable). Typical questions
that CVP may help with are:
žWhat is the likely effect on profits of changes in selling price or the volume
of activity?
žIf we incur additional costs, what changes should we make to our selling price
or to the volume that we need to sell?
CVP is used by accountants in a relatively simplistic manner. While most busi-
nesses will sell a wide range of product/services at many different prices (e.g.
quantity discounts), accountants assume a constant product/service mix and aver-
age selling prices per unit. The assumption is that these relationships are linear,
rather than the curvilinear models preferred by economists that reflect economies
and diseconomies of scale. The accountant limits this problem by recognizing the
relevant range. Therelevant rangeis the volume of activity within which the busi-
ness expects to be operating over the short-term planning horizon, typically the
current or next accounting period, and the business will usually have experience
of operating at this level of output. Within the relevant range, the accountant’s
model and the economist’s model are similar.
Profit can be shown as the difference between revenue and costs (both fixed
and variable). This relationship can be shown in the following formula:
net profit=revenue−(fixed costs+variable costs)
net profit=(units sold×selling price)−[fixed costs+(units sold
×unit variable cost)]