CIMA - C1 Fundamentals of Management Accounting
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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour
1 Breakeven analysis and contribution
Breakeven analysis or cost-volume-profit (CVP) analysis is the study of the interrelationships between costs, volume
and profit at various levels of activity.
Cost-volume-profit analysis (CVP) is the 'study of the effects on future profit of changes in fixed cost, variable cost,
sales price, quantity and mix'. CIMA Official Terminology
1.1 Contribution
Contribution, a concept we encountered in Chapter 4, is fundamental to CVP analysis. As you know, contribution per unit
is the difference between selling price per unit and variable costs per unit. The total contribution from the sales volume
for a period can be compared with the fixed costs for the period. Any excess of contribution is profit, any deficit of
contribution is a loss.
2 Breakeven point
The breakeven point occurs when there is neither a profit nor a loss and so fixed costs equal contribution.
The breakeven point is the 'level of activity at which there is neither profit nor loss'. CIMA Official Terminology
The management of an organisation usually wishes to know the profit likely to be made if the aimed-for production and
sales for the year are achieved. Management may also be interested to know the activity level at which there is neither
profit nor loss. This is known as the breakeven point.
The breakeven point (BEP) can be calculated arithmetically.
Breakeven point = Number of units of sale required to break even
=
Total fixed costs
Contribution per unit
=
Contribution required to break even
Contribution per unit
2.1 Example: breakeven point
Expected sales 10,000 units at $8 = $80,000
Variable cost $5 per unit
Fixed costs $21,000
Required
Compute the breakeven point.
Formula to
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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis
121
Solution
The contribution per unit is $(8
−
5) = $3
Contribution required to break even = fixed costs = $21,000
Breakeven point (BEP) = 21,000 ÷ 3
= 7,000 units
In revenue, BEP = (7,000
×
$8) = $56,000
Sales above $56,000 will result in profit of $3 per unit of additional sales and sales below $56,000 will mean a loss of $3
per unit for each unit by which sales fall short of 7,000 units. In other words, profit will improve or worsen by the
amount of contribution per unit.
7,000 units
7,001 units
$
$
Revenue
56,000
56,008
Less variable costs
35,000
35,005
Contribution
21,000
21,003
Less fixed costs
21,000
21,000
Profit
0
(= breakeven)
3
3 The contribution/sales (C/S) ratio
The
C/S ratio
(or
P/V ratio
) is a measure of how much contribution is earned from each $1 of sales.
3.1 C/S ratio and breakeven point
An alternative way of calculating the breakeven point to give an answer in terms of sales revenue and using the C/S ratio
is as follows.
Breakeven point
=
Sales revenue
required to break even.
=
Contribution required to break even
C/S ratio
=
Fixed costs
C/S ratio
3.2 Example: C/S ratio
In the example in Section 2.1 the C/S ratio is
$8
$3
= 37.5%
Breakeven is where sales revenue equals
37.5%
$21,000
= $56,000. At a price of $8 per unit, this represents 7,000 units of sales.
The C/S ratio is a measure of how much contribution is earned from each $1 of sales
. The C/S ratio of 37.5% in the
above example means that for every $1 of sales, a contribution of 37.5c is earned. Thus, in order to earn a total
contribution of $21,000 and if contribution increases by 37.5c per $1 of sales, sales must be:
37.5c
$1
×
$21,000 = $56,000
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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour
The C/S (contribution/sales) ratio is sometimes called the
profit/volume or P/V ratio
.
Question
C/S ratio
The C/S ratio of product W is 20%. IB, the manufacturer of product W, wishes to make a contribution of $50,000
towards fixed costs.
If the selling price is $10 per unit, the number of units of W that must be sold is
Answer
The number of units that must be sold is
25,000
.
Workings
ratio C/S
oncontributi Required
=
20%
$50,000
= $250,000
∴
Number of units = $250,000
÷
$10 = 25,000.
4 The margin of safety
The
margin of safety
is the difference in units between the budgeted sales volume and the breakeven sales volume. It is
sometimes expressed as a percentage of the budgeted sales volume. Alternatively the margin of safety can be expressed
as the difference between the budgeted sales revenue and breakeven sales revenue, expressed as a percentage of the
budgeted sales revenue.
As well as being interested in the breakeven point, management may also be interested in the amount by which actual
sales can fall below anticipated sales without a loss being incurred. This is the
margin of safety
.
The
margin of safety
'indicates the percentage by which forecast revenue exceeds or falls short of that required to break
even'. CIMA
Official Terminology
Margin of safety =
sales Projected
point breakeven - sales Projected
× 100
4.1 Example: margin of safety
Mal de Mer Co makes and sells a product which has a variable cost of $30 and which sells for $40. Budgeted fixed costs
are $70,000 and budgeted sales are 8,000 units.
Required
Calculate the breakeven point and the margin of safety.
Important!
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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis
123
Solution
(a) Breakeven point =
unit per onContributi
costsfixedTotal
=
)3040$(
000,70$
−
= 7,000 units
(b) Margin of safety = 8,000
−
7,000 units = 1,000 units
which may be expressed as
100%
units8,000
units1,000
×
= 12½% of budget
(c) The margin of safety indicates to management that actual sales can fall short of budget by 1,000 units or 12½%
before the breakeven point is reached and no profit at all is made.
5 Breakeven arithmetic and profit targets
5.1 Breakeven arithmetic
At the
breakeven point
, there is no profit or loss and so
sales revenue = total costs
or
total contribution = fixed costs.
At the
breakeven point
, sales revenue equals total costs and there is no profit.
S = V + F
where S = Sales revenue
V = Total variable costs
F = Total fixed costs
Subtracting V from each side of the equation, we get:
S
−
V = F, that is,
total contribution = fixed costs
5.2 Example: breakeven arithmetic
Butterfingers Company makes a product which has a variable cost of $7 per unit.
Required
If fixed costs are $63,000 per annum, calculate the selling price per unit if the company wishes to break even with a
sales volume of 12,000 units.
Solution
Contribution required to break even (= Fixed costs)
=
$63,000
Volume of sales
=
12,000 units
$
Required contribution per unit (S
−
V)
=
$63,000
÷
12,000
5.25
Variable cost per unit (V)
=
7.00
Required sales price per unit (S)
=
12.25
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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour
5.3 Target profits
The
target profit
is achieved when sales revenue equals variable costs plus fixed costs plus profit. Therefore the
total
contribution required
for a target profit =
fixed costs + required profit.
A similar formula may be applied where a company wishes to achieve a certain profit during a period. To achieve this
profit, sales must cover all costs and leave the required profit.
The
target profit
is achieved when: S = V + F + P,
Where S = Sales revenue
V = Variable costs
F = Fixed costs
P = required profit
Subtracting V from each side of the equation, we get:
S
−
V = F + P, so
Total contribution required = F + P
5.4 Example: target profits
RB Co makes and sells a single product, for which variable costs are as follows.
$
Direct materials
10
Direct labour
8
Variable production overhead
6
24
The sales price is $30 per unit, and fixed costs per annum are $68,000. The company wishes to make a profit of $16,000
per annum.
Required
Determine the sales required to achieve this profit.
Solution
Required contribution = fixed costs + profit = $68,000 + $16,000 = $84,000
Required sales can be calculated in one of two ways.
(a)
unit per onContributi
oncontributi Required
=
24)$(30
$84,000
−
= 14,000 units, or $420,000 in revenue
(b)
ratio C/S
oncontributi Required
=
*20%
$84,000
= $420,000 of revenue, or 14,000 units.
* C/S ratio =
30$
24$30$
−
=
30$
6$
= 0.2 = 20%.
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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis
125
Question
Target profits
SLB Co wishes to sell 14,000 units of its product, which has a variable cost of $15 to make and sell. Fixed costs are
$47,000 and the required profit is $23,000.
The required sales price per unit is $
.
Answer
The required sales price per unit is $
20
.
Workings
Required contribution = fixed costs plus profit
= $47,000 + $23,000
= $70,000
Required sales = 14,000 units
$
Required contribution per unit sold
5
Variable cost per unit
15
Required sales price per unit
20
Question
Sales revenue
G Co has a budgeted breakeven sales revenue of $600,000 and fixed costs of $210,000 for the month of September.
Calculate the sales revenue needed to achieve a profit of $75,250 in September.
Answer
Sales revenue to breakeven =
ratio C/S
costs Fixed
∴
$600,000 =
ratio C/S
$210,000
∴
C/S ratio = $210,000/$600,000
= 0.35
Total contribution for target profit = fixed costs + required profit
= $210,000 + $75,250
= $285,250
To convert this target contribution into target sales revenue, we use the C/S ratio
$285,250/0.35 = $815,000
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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour
5.5 Variations on breakeven and profit target calculations
You may come across variations on breakeven and profit target calculations in which you will be expected to consider
the effect of altering the selling price, variable cost per unit or fixed cost.
5.5.1 Example: change in selling price
Stomer Cakes Co bake and sell a single type of cake. The variable cost of production is 15c and the current sales price is
25c. Fixed costs are $2,600 per month, and the annual profit for the company at current sales volume is $36,000. The
volume of sales demand is constant throughout the year.
The sales manager, Ian Digestion, wishes to raise the sales price to 29c per cake, but considers that a price rise will
result in some loss of sales.
Required
Ascertain the minimum volume of sales required each month to raise the price to 29c.
Solution
The minimum volume of demand which would justify a price of 29c is one which would leave total profit at least the
same as before, ie $3,000 per month. Required profit should be converted into required contribution, as follows.
$
Monthly fixed costs
2,600
Monthly profit, minimum required
3,000
Current monthly contribution
5,600
Contribution per unit (25c
−
15c) = 10c
Current monthly sales = 56,000 cakes
The minimum volume of sales required after the price rise will be an amount which earns a contribution of $5,600 per
month, no worse than at the moment. The contribution per cake at a sales price of 29c would be 14c.
Required sales =
unitper oncontributi
oncontributi required
=
14c
$5,600
= 40,000 cakes per month.
5.5.2 Example: change in production costs
Close Brickett Co makes a product which has a variable production cost of $8 and a variable sales cost of $2 per unit.
Fixed costs are $40,000 per annum, the sales price per unit is $18, and the current volume of output and sales is 6,000
units.
The company is considering whether to have an improved machine for production. Annual hire costs would be $10,000
and it is expected that the variable cost of production would fall to $6 per unit.
Required
(a) Determine the number of units that must be produced and sold to achieve the same profit as is currently earned,
if the machine is hired.
(b) Calculate the annual profit with the machine if output and sales remain at 6,000 units per annum.
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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis
127
Solution
The current unit contribution is $(18
−
(8+2)) = $8
(a)
$
Current contribution (6,000 × $8)
48,000
Less current fixed costs
40,000
Current profit
8,000
With the new machine fixed costs will go up by $10,000 to $50,000 per annum. The variable cost per unit will fall
to $(6 + 2) = $8, and the contribution per unit will be $10.
$
Required profit (as currently earned)
8,000
Fixed costs
50,000
Required contribution
58,000
Contribution per unit = $10
Sales required to earn $8,000 profit = 5,800 units
(b)
If sales are 6,000 units
$ $
Sales (6,000 × $18)
108,000
Variable costs: production (6,000 × $6)
36,000
sales (6,000 × $2)
12,000
48,000
Contribution (6,000 × $10)
60,000
Less fixed costs
50,000
Profit
10,000
Alternative calculation
$
Profit at 5,800 units of sale (see (a))
8,000
Contribution from sale of extra 200 units (× $10)
2,000
Profit at 6,000 units of sale
10,000
5.6 More applications of breakeven arithmetic
It may be clear by now that, given no change in fixed costs,
total profit is maximised when the total contribution is at
its maximum
. Total contribution in turn depends on the unit contribution and on the sales volume.
An increase in the sales price will increase unit contribution, but sales volume is likely to fall because fewer customers
will be prepared to pay the higher price. A decrease in sales price will reduce the unit contribution, but sales volume may
increase because the goods on offer are now cheaper. The
optimum combination
of sales price and sales volume is
arguably the one which
maximises total contribution
.
5.6.1 Example: profit maximisation
C Co has developed a new product which is about to be launched on to the market. The variable cost of selling the
product is $12 per unit. The marketing department has estimated that at a sales price of $20, annual demand would be
10,000 units.
However, if the sales price is set above $20, sales demand would fall by 500 units for each 50c increase above $20.
Similarly, if the price is set below $20, demand would increase by 500 units for each 50c stepped reduction in price
below $20.
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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour
Required
Determine the price which would maximise C Co's profit in the next year.
Solution
At a price of $20 per unit, the unit contribution would be $(20
−
12) = $8. Each 50c increase (or decrease) in price would
raise (or lower) the unit contribution by 50p. The total contribution is calculated at each sales price by multiplying the
unit contribution by the expected sales volume.
Unit price Unit contribution Sales volume Total contribution
$ $ Units $
20.00 8.00 10,000 80,000
(a)
Reduce price
19.50 7.50 10,500 78,750
19.00 7.00 11,000 77,000
(b)
Increase price
20.50 8.50 9,500 80,750
21.00 9.00 9,000 81,000
21.50 9.50 8,500 80,750
22.00 10.00 8,000 80,000
22.50 10.50 7,500 78,750
The total contribution would be maximised, and therefore profit maximised, at a sales price of $21 per unit, and sales
demand of 9,000 units.
Question
Breakeven point
Betty Battle Co manufactures a product which has a selling price of $20 and a variable cost of $10 per unit. The company
incurs annual fixed costs of $29,000. Annual sales demand is 9,000 units.
New production methods are under consideration, which would cause a $1,000 increase in fixed costs and a reduction in
variable cost to $9 per unit. The new production methods would result in a superior product and would enable sales to
be increased to 9,750 units per annum at a price of $21 each.
If the change in production methods were to take place, the breakeven output level would be:
A 400 units higher C 100 units higher
B 400 units lower D 100 units lower
Answer
The correct answer is B.
Current
Revised
Difference
$
$
Selling price
20
21
Variable costs
10
9
Contribution per unit
10
12
Fixed costs
$29,000
$30,000
Breakeven point (units)
2,900
2,500
400 lower
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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis
129
Breakeven point (BEP) =
unit per onContributi
costsfixed Total
Current BEP =
$10
$29,000
= 2,900 units
Revised BEP =
$12
$30,000
= 2,500 units
Question
Breakeven point percentages
Chocco Co produces a single product and the following information is available.
$
Selling price per unit 28
Variable cost per unit 13
Fixed overheads 105,000
The breakeven point was calculated using these figures but management have decided that the variable cost and selling
price will rise by 1.9% and 5% respectively.
What will happen to the breakeven point when the new cost and price are taken into account?
A It will rise by 7.14% C It will fall by 7.14%
B It will rise by 1.14% D It will fall by 1.14%
Answer
C
Now
Revised
$
$
Selling price
28
29.40
Variable cost
13
13.25
Contribution
15
16.15
Breakeven volume 105,000/$15 = 7,000 $105,000/$16.15 = 6,500
Decrease in breakeven volume = (7,000 – 6,500)/7,000 = 7.14%
6 Breakeven charts and profit/volume graphs
6.1 Breakeven charts
The breakeven point can also be determined graphically using a
breakeven
chart
.
A
breakeven chart
is a chart that indicates approximate profit or loss at different levels of sales volume within a limited
range.
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