CASE:

Lee Enterprises operates in the leisure and entertainment industry and one of its
activities is to promote concerts at locations throughout the world. The company is
examining the viability of a concert in Singapore. Estimated fixed costs are £60 000.
These include the fees paid to performers, the hire of the venue and advertising
costs. Variable costs consist of the cost of a pre-packed buffet that will be provided
by a firm of caterers at a price, which is currently being negotiated, but it is likely to
be in the region of £10 per ticket sold. The proposed price for the sale of a ticket is
£20.
The management of Lee has requested the following information:
1 The number of tickets that must be sold to break even (that is, the point at which
there is neither a profit nor a loss).
2 How many tickets must be sold to earn £30 000 target profit?
3 What profit would result if 8000 tickets were sold?
4 What selling price would have to be charged to give a profit of £30 000 on sales of
8000 tickets, fixed costs of £60 000 and variable costs of £10 per ticket?
5 How many additional tickets must be sold to cover the extra cost of television
advertising of £8000?

Solution:

1 Break-even point in units (i.e. number of tickets sold)

Each ticket sold generates a contribution of £10 (£20 selling price – £10 variable
cost), which is available to cover fixed costs and, after they are covered, to
contribute to profit.
When we have obtained sufficient total contribution to cover fixed costs, the break-
even point is achieved, and so:

2 Units to be sold to obtain a £30 000 profit

To achieve a profit of any size we must first obtain sufficient contribution to cover the
fixed costs (i.e. the break-even point). If the total contribution is not sufficient to cover
the fixed costs, then a loss will occur. Once a sufficient total contribution has been
achieved any excess contribution represents profit.
Thus to determine the total contribution to obtain a target profit we simply add the
target profit to the fixed costs and divide by the contribution per unit, so that:

3 Profit from the sale of 8000 tickets

The total contribution from the sale of 8000 tickets is £80,000 (8000 x £10).

To ascertain the profit, we deduct the fixed costs of £60 000,

giving a net profit of £20 000.

Let us now assume that we wish to ascertain the impact on profit if a further 1000
tickets are sold so that sales volume increases from 8000 to 9000 tickets.
Assuming that fixed costs remain unchanged, the impact on a firm’s profits resulting
from a change in the number of units sold can be determined by multiplying the unit
contribution margin by the change in units sold.
Therefore, the increase in profits will be £10,000
(1000 units times a unit contribution margin of £10).

4 Selling price to be charged to show a profit of £30 000 on

sales of 8000 tickets
First, we must determine the total required revenue to obtain a profit of £30,000.
This is £170,000
{Fixed cost + Variable Cost + desired profit}
{60,000 + (8000x10) + 30,000}

Dividing the required sales revenues of £170,000 by the sales volume (8000 tickets):
gives a selling price of £21.25.
{170,000 / 8000 = £21.25}
5 Additional sales volume to meet £8000
additional fixed advertisement charges

The contribution per unit is £10 and fixed costs will increase by £8000.

Contribution needed for new fixed cost = 8000 / 10 = 800

Therefore, an extra 800 tickets must be sold to cover the additional fixed costs
of £8000.
Profit–Volume Ratio
The profit–volume ratio (also known as the contribution margin ratio) is the
contribution divided by sales.
It represents the proportion of each £1 of sales available to cover fixed costs
and provide for profit.

In our Example,
the contribution is £10 per unit, and
the selling price is £20 per unit;
Thus, profit–volume ratio is 0.5.
{Contribution / Sales = 10 / 20 = 0.5}

This means that for each £1 sale a contribution of £0.50 is earned.

Because we assume that selling price and contribution per unit are constant,
the profit–volume ratio is also assumed to be constant.
This means that the profit–volume ratio can be computed using either unit
figures or total figures.

Given an estimate of total sales revenue, it is possible to use the profit–

volume ratio to estimate total contribution.
For example,
if total sales revenue is estimated to be £200,000,
the total contribution will be £100,000
{PV = Contribution / Sales}
{Contribution = PV x Sales}
{£200 000 x 0.5 = 100,00}

To calculate the profit, we deduct fixed costs of £60,000

{Profit = Contribution – Fixed Costs = 100,000 – 60,000 = 40,000}

Thus, a profit of £40,000 will be obtained from total sales revenue of

£200,000.
This computation can be expressed in equation form:
We can rearrange this equation:

Therefore, the break-even sales revenue (where profit = 0)

= Fixed costs / PV ratio.

If we apply this approach to our Example,

the break-even sales revenue = Fixed Cost / PV Ratio
= £60,000 / 0.5
= £120,000

RELEVANT RANGE
It is vital to remember that CVP analysis can only be used for decisions that
result in outcomes within the relevant range.
Outside this range, the unit selling price and the variable cost are no longer
deemed to be constant per unit and any results obtained from the formulae
that fall outside the relevant range will be incorrect.
The concept of the relevant range is more appropriate for production settings
but it can apply within non-production settings.

In Lee Enterprises Example,

we shall now assume that the caterers’ charges will be higher per ticket if
ticket sales are below 4000; but lower if sales exceed 12,000 tickets.
 Thus, the £10 variable cost relates only to a sales volume within a range of
4000 to 12 000 tickets.
 Outside this range, other costs apply.

Thus, we will assume that the relevant range is a sales volume of 4000 to
12,000 tickets and outside this range the results of our CVP analysis do not
apply.
Margin of Safety
The margin of safety indicates by how much sales may decrease before a loss
occurs.
Using our Example,
unit selling price = £20
variable cost = £10
fixed costs = £60,000,

we noted that the break-even point was 6000 tickets or £120 000 sales value.

If sales are expected to be 8000 tickets or £160,000,

the margin of safety will be 2000 tickets or £40,000.

Alternatively, we can express the margin of safety in a percentage form based

on the following ratio:
THE BREAK-EVEN CHART

Using the data in our Example, we can construct the break-even chart for Lee
Enterprises
Note that activity/output is plotted on the horizontal axis and monetary
amounts for total costs, total revenues and total profits (or loss) are recorded
on the vertical axis.

In constructing the graph, the fixed costs are plotted as a single horizontal line
at the £60 000 level.
Variable costs at the rate of £10 per unit of volume are added to the fixed
costs to enable the total cost line to be plotted.
Two points are required to insert the total cost line.
 At zero sales, volume total cost will be equal to the fixed costs of
£60,000.
 At 12,000 units, sales volume total costs will be £180,000 consisting
of £120,000 variable costs plus £60 000 fixed costs.
The total revenue line is plotted at the rate of £20 per unit of volume.
 At zero output, total sales are zero and at 12,000 units, total sales
revenue is £240,000.
 The total revenues for these two points are plotted on the graph and
a straight line is drawn that joins these points.

The constraints of the relevant range consisting of two vertical lines are then
added to the graph; beyond these lines, we have little assurance that the CVP
relationships are valid.

The point at which the total sales revenue line cuts the total cost line is the
point where the concert makes neither a profit nor a loss.
 This is the break-even point and is 6000 tickets or £120 000 total sales
revenue.
 The distance between the total sales revenue line and the total cost line
at a volume below the break-even point represents losses that will occur
for sales levels below 6000 tickets.
 Similarly, if the company operates at a sales volume above the break-
even point, the difference between the total revenue and the total cost
lines represents the profit that results from sales levels above 6000
tickets.
Operating Leverage
Companies can sometimes influence the proportion of fixed and variable expenses
in their cost structures. For example, they may choose to rely heavily either on
automated facilities (involving high fixed and low variable costs) or on manual
systems (involving high variable costs and low fixed costs).
The chosen cost structure can have a significant impact on profits.
Consider the situation presented in example, where the managers of an airline
company are considering an investment in automated ticketing equipment.
Sensitivity of profits arising from changes in sales for an automated and
manual system

The above cost structure suggests that the automated system yields the higher
profits.

However, if sales decline by 10 per cent the following calculations show that the
manual system will result in the higher profits:
What will happen if sales are 10 per cent higher than the predicted sales for the
period?

The sales revenue where both systems result in the same profits is £960 000.
The automated system yields higher profits when periodic sales revenue exceeds
£960,000 whereas the manual system gives higher profits when sales revenue is
below £960,000.
{The profit–volume ratio is 0.7 for the automated system and 0.2 for the manual
system. Let x = periodic sales revenue:
the indifference point is where 0.7x – £600 000 = 0.2x – £120 000,
so, x = £960 000. }
It is unclear which system should be chosen.
If periodic sales exceed £960 000, the automated system will result in higher profits.
Automation enables the company to lower its variable costs by increasing fixed
Costs.
This cost structure results in greater increases in profits as sales increase compared
with the manual system.
Unfortunately, it is also true that a high fixed cost and lower variable cost structure
will result in a greater reduction in profits as sales decrease.

The term operating leverage is used as a measure of the sensitivity of profits to

changes in sales. The greater the degree of operating leverage, the more that
changes in sales activity will affect profits.
The degree of operating leverage can be measured for a given level of sales by
the following formula:

The degree of operating leverage in our example,

for sales of £1 million is 7 (£700 000/£100 000) for the automated system, and
2.5 (£200 000/£80 000) for the manual system.
This means that profits change by seven times more than the change in sales for the
automated system and 2.5 times for the manual system.

Thus, for a 10 per cent increase in sales from £1 million to £1.1 million, profits
increase by 70 per cent for the automated system (from £100 000 to £170 000) and
by 25 per cent for the manual system (from £80 000 to £100 000).
In contrast, if sales decline by 10 per cent from £1 million to £0.9 million, profits
decrease by 70 per cent (from £100 000 to £30 000) for the automated system and
by 25 per cent from (£80 000 to £60 000) for the manual system.