CIMA - C1 Fundamentals of Management Accounting
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140
6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour
Step 3
Determine the
optimum production plan
. Sufficient Bes will be made to meet the full sales demand, and
the remaining labour hours available will then be used to make Ays.
(a)
Hours
Hours
Priority of
Product
Demand
required
available
manufacture
Bes
5,000
5,000
5,000
1st
Ays
3,000
6,000
3,000
(bal)
2nd
11,000
8,000
(b)
Hours
Contribution
Product
Units
needed
per unit
Total
$
$
Bes
5,000
5,000
4
20,000
Ays
1,500
3,000
3
9,000
8,000
29,000
Less fixed costs
20,000
Profit
9,000
Conclusion
(a) Unit contribution is
not
the correct way to decide priorities.
(b) Labour hours are the scarce resource, and therefore contribution
per labour hour
is the correct way to decide
priorities.
(c) The Be earns $4 contribution per labour hour, and the Ay earns $3 contribution per labour hour. Bes therefore
make more profitable use of the scarce resource, and should be manufactured first.
If an assessment question asks you to determine the optimum production plan, you might find it useful to follow the
five-step approach used in the example above and shown below.
Step 1 Identify the limiting factor
Step 2 Calculate contribution per unit for each product
Step 3 Calculate contribution per unit of limiting factor
Step 4 Rank products (make product with highest contribution per unit of limiting factor first)
Step 5 Make products in rank order until scarce resource is used up (optimal production plan)
Question
Limiting factors
LF Co makes a single product for which the standard cost details are as follows.
$
Direct material ($3 per kg)
12
Direct labour ($8 per hour)
72
Production overhead
18
Total production cost
102
Demand for next period will be 20,000 units. No inventories are held and only 75,000 kg of material and 190,000 hours
of labour will be available. What will be the limiting factor next period?
Assessment
focus point
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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis
141
A Material only
B Labour only
C Material and labour
D There will be no limiting factor next period
Answer
The correct answer is A.
Material required = 20,000 units
×
($12/$3) = 80,000 kg
Material is therefore a limiting factor, since only 75,000 kg are available. This eliminates options B and D.
Labour required = 20,000 units
×
($72/$8) = 180,000 hours.
Labour is not a limiting factor, since 190,000 labour hours are available. This eliminates option C.
Question
POV Co
POV Co manufactures three products - X, Y and Z - that use the same machines. The budgeted income statements for
the three products are as follows:
X Y Z
$'000 $'000 $'000
Sales 1,000 1,125 625
Prime costs (500) (562.5) (437.5)
Variable overheads (250) (187.5) (62.5)
Fixed overheads (200) (315) (130)
Profit/(loss) 50 60 (5)
Annual sales demand (units) 5,000 7,500 2,500
Machine hours per unit 20 21 26
However, after the budget had been formulated, an unforeseen condition has meant that during the next period the
available machine capacity has been limited to 296,500 hours.
(a) The shortfall in available machine hours for next period is
hours
(b) The contribution earned per machine hour used on product X is $
(c) The management accountant has ranked the products in order of preference for production as follows:
1st product X
2
nd
product Y
3
rd
product Z
The number of units of each product that should be manufactured next period is:
(i) Product X
units
(ii) Product Y
units
(iii) Product Z
units
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142
6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour
Answer
(a)
The shortfall in available machine hours for next period is
26,000
hours.
Workings
Machine hours required to satisfy annual sales demand:
Hours
Product X 5,000 units
×
20 hrs
100,000
Product Y 7,500 units
×
21 hrs
157,500
Product Z 2,500 units
×
26 hrs
65,000
Total machine hours required
322,500
Machine hours available
296,500
Shortfall in available machine hours
26,000
(b)
The contribution earned per machine hour used on product X is $
2.50
.
Workings
$'000
Sales revenue
1,000
Prime costs
(500)
Variable overheads
(250
)
Contribution
250
Contribution per unit (
÷
5,000)
$50
Contribution per machine hour
(
÷
20)
$2.50
(c) (i)
Product X
5,000
units
(ii)
Product Y
7,500
units
(iii)
Product Z
1,500
units
Workings
Hours
Hours
Ranking
Product
Demand
required
available
Production
units
units
1
st
X
5,000 (
×
20)
100,000
100,000
5,000
2
nd
Y
7,500 (
×
21)
157,500
157,500
7,500
3
rd
Z
2,500 (
×
26)
65,000
39,000
*
1,500
296,500
* Balance (296,500 – 100,000 – 157,500)
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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis
143
Chapter Roundup
•
Breakeven analysis
or
cost-volume-profit analysis (CVP)
analysis
is the study of the interrelationships between costs,
volume and profits at various levels of activity.
• The
breakeven point
occurs when there is neither a profit nor a loss and so fixed costs equal contribution.
• The
C/S ratio
(or
P/V ratio
) is a measure of how much contribution is earned from each $1 of sales.
• 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.
• At the
breakeven point
,
there is no profit or loss and so
sales revenue = total costs
or
total contribution = fixed costs.
• 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.
• The breakeven point can also be determined graphically using a
breakeven chart
.
• A
contribution breakeven chart
depicts variable costs, so that contribution can be read directly from the chart.
• The
profit/volume (P/V) graph
is a variation of the breakeven chart and illustrates the relationship of profit to sales
volume.
• Despite the
advantages
of breakeven analysis, the technique has some serious
limitations
.
• In a
limiting factor situation
, contribution will be maximised by earning the biggest possible contribution per unit of
limiting factor.
Quick Quiz
1 Use the following to make up four formulae which can be used to calculate the breakeven point.
Contribution per unit
Contribution per unit
Fixed costs
Fixed costs
Contribution required to break even
Contribution required to break even
C/S ratio
C/S ratio
(a) Breakeven point (sales units) =
or
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144
6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour
(b) Breakeven point (sales revenue) =
or
2 The P/V ratio is a measure of how much profit is earned from each $1 of sales.
True
False
3 Profits are maximised at the breakeven point.
True
False
4 At the breakeven point, total contribution = …………………………………. .
5 The total contribution required for a target profit = ……………………………………………….. .
6 Breakeven charts show approximate levels of profit or loss at different sales volume levels within a limited range. Which
of the following are true?
I The sales line starts at the origin
II The fixed costs line runs parallel to the vertical axis
III Breakeven charts have a horizontal axis showing the sales/output (in value or units)
IV Breakeven charts have a vertical axis showing $ for revenues and costs
V The breakeven point is the intersection of the sales line and the fixed cost line
A I and II
B I and III
C I, III and IV
D I, III, IV, and V
7 On a breakeven chart, the distance between the breakeven point and the expected (or budgeted) sales, in units, indicates
the ………………………………. .
8 Thornbury produces a single product X and has a contribution to sales ratio of 35%. The annual fixed costs are
$157,500. In order to breakeven, how many units of X will Thornbury need to make and sell?
A 196,000
B 450,000
C 60,000
D Cannot say without more information
9 The following information is available for product H.
Breakeven point 70,000 units
Contribution per unit $4.50
Margin of safety 30%
Calculate the budgeted profit
A $100,000 C $315,000
B $135,000 D $765,000
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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis
145
10 Give seven limitations of CVP analysis.
•
………………………………………………………………………………………………………
•
………………………………………………………………………………………………………
•
………………………………………………………………………………………………………
•
………………………………………………………………………………………………………
•
………………………………………………………………………………………………………
•
………………………………………………………………………………………………………
•
………………………………………………………………………………………………………
11 When determining the optimum production plan using limiting factor analysis, what five steps are involved?
Step 1……………………………………………………………………………………………
Step 2……………………………………………………………………………………………
Step 3……………………………………………………………………………………………
Step 4……………………………………………………………………………………………
Step 5……………………………………………………………………………………………
Answers to Quick Quiz
1 (a) Breakeven point (sales units) =
unit per onContributi
costs Fixed
or
unit per onContributi
even break to required onContributi
(b) Breakeven point (sales revenue) =
ratio C/S
costsFixed
or
ratio C/S
evenbreaktorequired onContributi
2 False. The P/V ratio is a measure of how much
contribution
is earned from each $1 of sales.
3 False. At the breakeven point there is no profit.
4 At the breakeven point, total contribution = fixed costs
5 The total contribution required for a target profit = fixed costs + required profit
6 C The fixed cost line runs parallel to the horizontal axis and the breakeven point is the intersection of the sales line
and the total costs line
7 Margin of safety
8 D The sales revenue can be calculated as $157,500/0.35 = $450,000. The number of units cannot be calculated with
the information supplied.
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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour
9 B $135,000
Breakeven point =
on/unitContributi
costs Fixed
∴
70,000 units =
$4.50
costs Fixed
∴
Fixed costs = 70,000 units x $4.50
= $315,000
Margin of safety =
units sales Budgeted
units sales Breakeven - units sales Budgeted
∴
0.3 =
units sales Budgeted
70,000 - units sales Budgeted
Let x = budgeted sales units
0.3 =
x
70,000 - x
∴
0.3x = x – 70,000
∴
70,000 = x – 0.3x
∴
70,000 = 0.7x
∴
x = 100,000 = budgeted sales units
Total profit = Contribution – fixed costs
= (100,000 units x $4.50) – $315,000
= $135,000
10
•
It
can only apply to a single product
or a single mix of a group of products.
•
A breakeven chart may be
time-consuming
to prepare.
•
It
assumes
fixed costs are constant at all levels of output.
•
It
assumes
that
variable costs
are the
same
per unit at all levels of output.
•
It
assumes
that
sales prices
are
constant
at all levels of output.
•
It assumes
production
and
sales
are the
same
(inventory levels are ignored).
•
It
ignores
the
uncertainty
in the estimates of fixed costs and variable cost per unit.
11
Step 1 Identify the limiting factor
Step 2 Calculate contribution per unit for each product
Step 3
Calculate contribution per unit of limiting factor
Step 4 Rank products (make product with highest contribution per unit of limiting factor first)
Step 5
Make products in rank order until scarce resource is used up
(optimal production plan)
Now try the questions below from the Question Bank
Question numbers Page
26–31 356
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Part B
Standard costing
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Topic list Learning outcomes Syllabus references Ability required
1 Standard costing C(i), C(ii) C(1) Comprehension
2 Preparation of standards C(iii) C(2) Application
3 Other aspects of standard costing C(i), (ii) C(1) Comprehension
4 The standard hour C(vii) C(5) Analysis
5 Standard labour costs and incentive schemes C(vii) C(5) Analysis
Standard costing
Introduction
Just as there are standards for most things in our daily lives (cleanliness in hamburger
restaurants, educational achievement of nine year olds, number of trains running on time),
there are standards for the costs of products and services. Moreover, just as the standards in
our daily lives are not always met, the standards for the costs of products and services are
not always met. We will not, however, be considering the standards of cleanliness of
hamburger restaurants in this chapter but we will be looking at standards for costs, what
they are used for and how they are set.
In the next chapter we will see how standard costing forms the basis of a process called
variance analysis, a vital management control tool.
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