CIMA - C1 Fundamentals of Management Accounting

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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour

A breakeven chart has the following axes.

• A

horizontal

axis showing the

sales/output

(in value or units)

• A

vertical axis

showing $ for

sales revenues

and

costs

Although you will not be required to draw a breakeven chart in the assessment, a question may require you to identify

certain points on a chart provided. Furthermore, you may need to draw a chart for a task at work, or in examinations for

other subjects in the future. If you follow the description below carefully, it will provide a firm basis for your current and

future understanding and interpretation of breakeven charts.

6.1.1 Lines on a breakeven chart

The following lines are drawn on the breakeven chart.

(a) The

sales line

(i) Starts at the origin

(ii) Ends at the point signifying expected sales

(b) The fixed costs line

(i) Runs parallel to the horizontal axis

(ii)

Meets the vertical axis at a point which represents total fixed costs

total costs line

(i) Starts where the fixed costs line meets the vertical axis

(ii)

Ends at the point which represents anticipated sales on the horizontal axis and total costs of

anticipated sales on the vertical axis

The

breakeven point

is the

intersection

of the

sales line

and the

total costs line

The distance between the

breakeven point

and the

expected (or budgeted) sales

, in units, indicates the

margin of safety

6.1.2 Example: a breakeven chart

The budgeted annual output of a factory is 120,000 units. The fixed overheads amount to $40,000 and the variable costs

are 50p per unit. The sales price is $1 per unit.

Required

Construct a breakeven chart showing the current breakeven point and profit earned up to the present maximum capacity.

Solution

We begin by calculating the profit at the budgeted annual output.

Sales (120,000 units)

120,000

Variable costs

60,000

Contribution

60,000

Fixed costs

40,000

Profit

20,000

The breakeven chart is shown on the following page.

Assessment

focus point

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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis

131

The chart is drawn as follows.

(a) The

vertical axis

represents

money

(costs and revenue) and the

horizontal axis

represents the

level of activity

(production and sales).

(b) The fixed costs are represented by a

straight line parallel to the horizontal axis

(in our example, at $40,000).

variable costs

are added 'on top of' fixed costs, to give

total costs

. It is assumed that fixed costs are the

same in total and variable costs are the same per unit at all levels of output.

The line of costs is therefore a straight line and only two points need to be plotted and joined up. Perhaps the two

most convenient points to plot are total costs at zero output, and total costs at the budgeted output and sales.

(i)

At zero output, costs are equal to the amount of fixed costs only, $40,000, since there are no variable

costs.

(ii)

At the budgeted output of 120,000 units, costs are $100,000.

Fixed costs

40,000

Variable costs 120,000 × 50c

60,000

Total costs

100,000

(d) The sales line is also drawn by plotting two points and joining them up.

(i) At zero sales, revenue is nil.

(ii) At the budgeted output and sales of 120,000 units, revenue is $120,000.

100

120

Margin

of safety

Breakeven point

Budgeted profit

Budgeted variable costs

Budgeted fixed costs

Units

$’000

rea

even c

art

100604020

Fixed costs

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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour

6.1.3 Interpreting the breakeven chart

The breakeven point is where total costs are matched exactly by total revenue

. From the chart, this can be seen to

occur at output and sales of 80,000 units, when revenue and costs are both $80,000. This breakeven point can be

proved mathematically as:

unit per onContributi

costs)fixed ( oncontributi Required

unit per 50c

000,40$

= 80,000 units

The margin of safety can be seen on the chart as the difference between the budgeted level of activity and the breakeven

level.

6.1.4 The value of breakeven charts

Breakeven charts are used as follows.

• To

plan

the production of a company's products

• To

market

a company's products

• To give a

visual display

of breakeven arithmetic

6.2 The contribution breakeven chart

contribution breakeven chart

depicts variable costs, so that contribution can be read directly from the chart.

The main problem with the traditional breakeven chart is that it is not possible to read contribution directly from the

chart.

The contribution breakeven chart remedies this by

drawing the variable cost line instead of the fixed cost line

. A

contribution breakeven chart for the example in Section 6.1.2 would include the variable cost line passing through the

origin and the total variable cost of $60,000 for 120,000 units. The contribution breakeven chart is shown below.

Contribution breakeven chart

100

120

Breakeven point

Budgeted

profit

Budgeted

contribution

Unit

$’000

FAST FORWARD

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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis

133

If you look back at the breakeven chart in Section 6.1.2(d) you will see that the breakeven point is the same, but that the

budgeted contribution can now be read more easily from the chart.

6.3 The profit/volume (P/V) graph

The

profit/volume

(

P/V) graph

is a variation of the breakeven chart and illustrates the relationship of profit to sales

volume.

6.3.1 Construction of a profit/volume graph

A P/V graph is constructed as follows (look at the chart in the example that follows as you read the explanation).

(a) 'P' is on the y axis and actually comprises not only 'profit' but contribution to profit (in monetary value),

extending above and below the x axis with a zero point at the intersection of the two axes, and the negative

section below the x axis representing fixed costs. This means that at zero production, the firm is incurring

a loss equal to the fixed costs.

(b) 'V' is on the x axis and comprises either volume of sales or value of sales (revenue).

the y axis representing the level of fixed costs, and with a gradient of contribution/unit (or the C/S ratio if

sales value is used rather than units). The P/V line will cut the x axis at the breakeven point of sales

volume. Any point on the P/V line above the x axis represents the profit to the firm (as measured on the

vertical axis) for that particular level of sales.

6.3.2 Example: P/V graph

Let us draw a P/V graph for our example in Section 6.1.2. At sales of 120,000 units, total contribution will be 120,000

$(1 – 0.5) = $60,000 and total profit will be $20,000.

T F

RWAR

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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour

6.3.3 The advantage of the P/V graph

(a) If the budgeted selling price of the product in our example is increased to $1.20, with the result that

demand drops to 105,000 units despite additional fixed costs of $10,000 being spent on advertising, we

could add a line representing this situation to our P/V chart.

(b) At sales of 105,000 units, contribution will be 105,000

$(1.20 – 0.50) = $73,500 and total profit will be

$23,500 (fixed costs being $50,000).

sales revenue (71,429 units instead of 80,000 units), although this is not a particularly large decrease

when viewed in the context of the projected sales volume. It is also possible to see that for sales above

50,000 units, the profit achieved will be higher (and the loss achieved lower) if the price is $1.20. For sales

volumes below 50,000 units the first option will yield lower losses.

(d) The P/V graph is the clearest way of presenting such information; two conventional breakeven charts on

one set of axes would be very confusing.

(e) Changes in the variable cost per unit or in fixed costs at certain activity levels can also be incorporated

easily into a P/V graph. The profit or loss at each point where the cost structure changes should be

calculated and plotted on the graph so that the profit/volume line becomes a series of straight lines.

(f) For example, suppose that in our example, at sales levels in excess of 120,000 units the variable cost per

unit increases to $0.60 (perhaps because of overtime premiums that are incurred when production

exceeds a certain level). At sales of 130,000 units, contribution would therefore be 130,000

$(1 - 0.60) =

$52,000 and total profit would be $12,000.

Make sure that you can visualise what will happen to the graph if the breakeven point changes. The breakeven point will

change if either fixed costs or contribution changes.

P/V graph (2)

Assessment

focus point

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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis

135

Breakeven point

Fixed

costs

BREAKEVEN

LOSS

PROFIT

Profit/loss

$’000

P/V graph (3

)

Sales volume

(units)

120,000 130,000

Question

Breakeven chart

Match the following labels to (a), (b), (c) and (d) marked on the breakeven chart below.

Fixed costs Margin of safety

Budgeted profit Budgeted variable costs

Answer

Fixed costs (d) Budgeted profit (b)

Margin of safety (a) Budgeted variable costs (c)

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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour

Question

G Co

G Co manufactures and sells a single product. The profit statement for May is as follows.

Sales value

80,000

Variable cost of sales

48,000

Contribution

32,000

Fixed costs

15,000

Profit

17,000

The management accountant has used the data for May to draw the following profit/volume graph.

$’000

Sales revenue

(a) The monetary values indicated on the graph as A, B and C are:

A $

B $

C $

(b) The term used to describe the distance D on the graph is the

variable costs and selling price achieved will be the same as that achieved during May, and that fixed costs for the

year will be $180,000, the profit for the whole year will be

(d) The annual margin of safety for G Co's product is

% of budgeted sales.

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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis

137

Answer

(a)

A $17,000

B (–$15,000)

C $37,500

Workings

A: profit achieved from $80,000 sales revenue = $17,000

B: loss at zero sales revenue = fixed costs = (–$15,000)

C: breakeven point = $37,500 sales revenue (see below)

C/S ratio = 32/80 = 40%

Breakeven point =

ratio C/S

costs fixed

0.4

$15,000

= $37,500 sales revenue

(b)

The term used to describe the distance D on the graph is the

margin of safety

This is the difference between the sales revenue budgeted or achieved, and the revenue required to break even.

(c)

The profit for the whole year will be $

180,000

Workings

Contribution achieved =

sales revenue

C/S ratio

$900,000

0.4

$360,000

Fixed costs

$180,000

∴

Profit for whole year

$180,000

(d)

The annual margin of safety for G Co's product is

% of budgeted sales.

Workings

Annual breakeven point =

ratio C/S

costsfixed

0.4

$18,000

= $450,000 sales revenue

Margin of safety = $900,000 – $450,000 = $450,000 sales revenue

= 50% of budgeted sales

6.4 The economist's breakeven chart

’000

Breakeven

point 1

Breakeven

point 2

Tot a l c o st

Revenue

Profit

Activit

leve

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6: Breakeven analysis and limiting factor analysis ⏐ Part A Cost determination and behaviour

In economics, the lines on the breakeven chart are curved rather than straight. This is because economists assume that

costs per unit and revenues per unit are not constant at every level of activity. Note that the total cost line falls initially

and then rises again. This is because production is assumed to be more efficient as the number of goods being produced

is increased. This is known as

economies of scale

7 Limitations of breakeven analysis

Despite the

advantages

of breakeven analysis, the technique has some serious

limitations

CVP analysis is a useful technique for managers. It can provide

simple

and

quick

estimates, and

breakeven charts

provide a

graphical representation

of breakeven arithmetic. It does, however, have a number of limitations.

• 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.

8 Limiting factor analysis

In a

limiting factor situation

, contribution will be maximised by earning the biggest possible contribution per unit of

limiting factor.

8.1 Limiting factors

One of the more common problems faced by management is a situation where there are not enough resources to meet

the potential sales demand, and so a decision has to be made about what mix of products to produce, using what

resources there are as effectively as possible. The resource that limits the organisation's ability to meet sales demand is

called a

limiting factor

key factor

limiting factor

key factor

is 'anything which limits the activity of an entity. An entity seeks to optimise the benefit it

obtains from the limiting factor. Examples are a shortage of supply of a resource or a restriction on sales demand at a

particular price'. CIMA

Official Terminology

limiting factor

could be sales if there is a limit to sales demand but any one of the organisation's resources (labour,

materials and so on) may be insufficient to meet the level of production demanded.

It is assumed in limiting factor analysis that management wishes to maximise profit and that

profit will be maximised

when contribution is maximised

(given no change in fixed cost expenditure incurred). In other words,

marginal costing

ideas are applied

T F

RWAR

FAST FORWARD

Key term

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Part A Cost determination and behaviour ⏐ 6: Breakeven analysis and limiting factor analysis

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8.2 Limiting factor situations

For example if grade A labour is the limiting factor, contribution will be maximised by earning the biggest contribution from

each hour of grade A labour worked.

The limiting factor decision therefore involves the determination of

the contribution earned by each different product

from each unit of the limiting factor

8.2.1 Example: limiting factor

AB Co makes two products, the Ay and the Be. Unit variable costs are as follows.

Direct materials

Direct labour ($3 per hour)

Variable overhead

The sales price per unit is $14 per Ay and $11 per Be. During July 20X2 the available direct labour is limited to 8,000

hours. Sales demand in July is expected to be 3,000 units for Ays and 5,000 units for Bes.

Required

Determine the profit-maximising production mix, assuming that monthly fixed costs are $20,000, and that opening

inventories of finished goods and work in progress are nil.

Solution

Step 1

Confirm that the limiting factor is something other than sales demand.

Ays

Bes

Total

Labour hours per unit

2 hrs

1 hr

Sales demand

3,000 units

5,000 units

Labour hours needed

6,000 hrs

5,000 hrs

11,000 hrs

Labour hours available

8,000 hrs

Shortfall

3,000 hrs

Labour is the limiting factor on production

Step 2 Identify the contribution earned by each product per unit of limiting factor, that is per labour hour worked.

Ays

Bes

Sales price

Variable cost

Unit contribution

Labour hours per unit

2 hrs

1 hr

Contribution per labour hour (= unit of limiting factor)

Although Ays have a higher unit contribution than Bes, two Bes can be made in the time it takes to make

one Ay. Because labour is in short supply it is more profitable to make Bes than Ays.

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