ACCA F2 Management Accounting - 2010 - Study text - Emile Woolf Publishing
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Paper F2
Management Accounting
CHAPTER
13
Cost-volume-profit (CVP)
analysis
Contents
1 ThenatureofCVPanalysis
2 ContributionandtheC/Sratio
3 Break‐evenanalysis
4 Break‐evenchartsandprofit‐volumecharts
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The nature of CVP analysis
Costing methods for planning and decision-making systems
Assumptions in CVP analysis
Calculating fixed and variable costs
1 The nature of CVP analysis
1.1 Costing methods for planning and decision-making
Previous chapters have described the use of costing systems to:
record costs
measure the cost of products, services and activities
measure profitability using either absorption costing or marginal costing
prepare functional budgets and a master budget
produce budgetary control reports and calculate variances for control purposes
in a system of standard costing.
Many of the costing methods described so far are concerned with measuring and
analysing historical costs and they are not used for forward planning and decision-
making. (Budgeting is an exception, but functional budgets are of only limited value
as management information.)
However there are some costing or management accounting techniques that can be
used to prepare forward-looking information and to help management to make
planning decisions and ‘one-off’ decisions. These include:
CVP analysis
relevant costs.
CVP analysis stands for ‘cost-volume-profit analysis’. It is used to analyse how
costs and profits will change with changes in the volume of activity, such as the
volume of production and the volume of sales. It is an application of marginal
costing concepts.
This chapter explains CVP analysis and some of its applications. Relevant costs are
described in a later chapter.
1.2 Assumptions in CVP analysis
The normal assumptions in CVP analysis are the assumptions used in marginal
costing, but they are applied to future costs.
Costs are either fixed or variable. The variable cost per unit is the same at all
levels of activity (output and sales). Total fixed costs are a constant amount in
each period.
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Profit is measured as contribution (sales revenue minus variable costs) minus
fixed costs.
$
Sales S
Variable costs V
Contribution (S – V) = C
Fixed costs F
Profit (C – F)
Some additional assumptions are normally used in CVP analysis.
Since fixed costs are normally assumed to remain unchanged at all levels of
output and sales, profit is maximised by maximising total contribution.
The contribution per unit is constant for each unit sold (of the same product).
The sales price per unit is also constant for every unit of product sold; therefore
the contribution to sales ratio is also a constant value at all levels of sales.
When marginal costing is used to report profits, changes in the level of finished
goods inventory is important. With CVP analysis, inventory levels are irrelevant.
Example
A company makes and sells a single product. The product has a variable production
cost of $8 per unit and a variable selling cost of $1per unit. Total fixed costs
(production, administration and sales and distribution fixed costs) are expected to be
$500,000. The selling price of the product is $16.
The contribution per unit is $16 – $8 – $1 = $7.
CVP analysis can be used to estimate what the profit will be at different volumes of
sales. The table below shows how the profit or loss would be calculated for 70,000
units, 80,000 units and 90,000 units of sale.
70,000 units 80,000 units 90,000 units
$ $ $
Contribution ($7 per unit) 490,000
560,000
630,000
Fixed costs (500,000)
(500,000)
(500,000)
Profit/(loss) (10,000)
60,000
130,000
A loss is incurred at 70,000 units of sales because total contribution is not large
enough to cover fixed costs. Profit increases as sales volume increases, and the
increase in profit is due to the increase in total contribution as sales volume
increases.
1.3 Calculating fixed and variable costs
A key to using CVP analysis is to identify fixed and variable costs, so that a
contribution per unit sold or a contribution/sales ratio can be calculated and
applied.
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If necessary mixed costs should divided into a variable cost per unit and fixed costs,
using techniques such as high/low analysis or linear regression analysis.
Example
A company has estimated that if it operates at 80% capacity, it will achieve the
following results:
$
Sales 800,000
Total production cost of sales 300,000
500,000
Other costs (in total) 400,000
Profit 100,000
It has been estimated that at this activity level, 60% of production costs and 70% of
other costs are fixed, and the rest are variable.
What is the expected profit at a 90% capacity level?
Answer
The first step is to identify the variable costs. We cannot calculate a variable cost per
unit, because there is no information about the number of units produced. However,
we can calculate the amount of variable costs as a percentage of sales revenue, using
the information provided about costs at the 80% capacity level.
$
$
Sales 800,000
Variable costs
Production variable costs (40% × $300,000)
120,000
Other variable costs (30% × $400,000)
120,000
Total variable costs 240,000
Variable costs are equal to 30% of sales revenue (= $240,000/$800,000).
Sales at 80% capacity level are $800,000. At a 90% capacity level, the sales will be
$800,000 × 90%/80% = $900,000. The expected profit will be:
$
$
Sales
900,000
Variable costs (30% of sales)
270,000
Contribution
630,000
Fixed production costs (60% × $300,000)
180,000
Other fixed costs (70% × $400,000)
280,000
Total fixed costs
460,000
Profit
170,000
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Contribution and the C/S ratio
The importance of contribution
Contribution/sales ratio (C/S ratio)
Calculating the sales price from the C/S ratio and variable cost
Calculating fixed costs with CVP analysis
2 Contribution and the C/S ratio
2.1 The importance of contribution
In marginal costing analysis, contribution is a key concept:
Total profit is total contribution (S – V) minus fixed costs (F).
If the selling price per unit of product is a fixed amount, it follows that:
The contribution per unit (= sales price minus variable cost) is a constant
amount.
Total contribution = Contribution per unit × Number of units sold.
2.2 Contribution/sales ratio (C/S ratio)
The contribution/sales ratio or C/S ratio is the ratio of the contribution per unit to
the sales price per unit. If the sales price is a fixed amount per unit, and the
contribution per unit is a constant amount, it follows that the contribution/sales
ratio is also a constant value at all levels of output and sales.
The C/S ratio is a measure of the contribution earned per $1 of sales, expressed as a
percentage.
The C/S ratio is an important concept in CVP analysis.
Example
An entity expects to achieve sales of $5,000,000 next year. Fixed costs will be
$3,000,000 and variable costs $1,500,000.
How would the profit be affected if actual sales are 10% higher than the expected
amount?
Answer
Contribution = Sales – Variable costs.
When sales are $5 million, contribution = $3.5 million (= $5 million – $1.5 million).
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C/S ratio = $3.5 million/$5 million = 0.70 or 70%.
If sales are $500,000 higher than expected, total contribution and total profit will be
higher by: 70% × $500,000 = $350,000.
2.3 Calculating the sales price from the C/S ratio and variable cost
If you are given the C/S ratio for a product and the variable cost per unit, you can
calculate the selling price per unit.
Example
A company makes and sells a product that has a variable cost of $18 per unit and a
contribution/sales ratio of 60%.
Since the contribution/sales ratio is 60%, it follows that the variable cost/sales ratio
is 40% (since variable cost + contribution must add up to 100%).
$
Variable cost (40% of sales price) 18
Therefore contribution (60% of sales price) = $18 × 60/40
27
Sales price per unit 45
An alternative calculation would be as follows:
Variable cost/sales ratio = 40%
Therefore selling price = $18/0.40 = $45
Therefore contribution per unit = $45 - $18 = $27.
2.4 Calculating fixed costs with CVP analysis
Examination questions on CVP analysis might require you to calculate a ‘missing
figure’ from available information, by applying CVP analysis techniques.
For example, it is possible to calculate the fixed costs for a period given information
about the profit at a particular level of sales, the variable cost per unit and the C/S
ratio.
Example
A company makes and sells a product that has a variable cost of $12 per unit and a
contribution/sales ratio of 25%. At a volume of 30,000 units of sales, total profit
would be $25,000.
What are the fixed costs for the period?
Answer
The contribution per unit can be calculated from the variable cost per unit and the
C/S ratio. The C/S ratio is 25%; therefore the variable cost is 75% of the sales price.
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$
Variable cost (75% of sales price) 12
Therefore contribution (25% of sales price) = $12 × 25/75
4
We know the total profit at 30,000 units of sale. We can also calculate the total
contribution at this sales level. Fixed costs are the difference between total
contribution and profit.
$
Total contribution at 30,000 units of sale: 30,000 × $4
120,000
Total profit at 30,000 units of sale: given 25,000
Therefore total fixed costs 95,000
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Break-even analysis
Break-even analysis
Calculating the break-even point
Margin of safety
Target profit
3 Break-even analysis
3.1 Break-even analysis
CVP analysis can be used to calculate a break-even point for sales.
Break-even point is the volume of sales required in a period (such as the financial year)
to ‘break even’ and make neither a profit nor a loss. At the break-even point, profit is 0.
Management might want to know what the break-even point is in order to:
assess the probability of avoiding a loss, or
identify the minimum volume of sales that must be achieved in order to avoid a
loss, or
assess the amount of risk in the budget, by comparing the budgeted volume of
sales with the break-even volume.
3.2 Calculating the break-even point
The break-even point can be calculated using simple CVP analysis.
At the break-even point, the profit is $0. If the profit is $0, total contribution is
exactly equal to total fixed costs.
We therefore need to establish the volume of sales at which fixed costs and total
contribution are the same amount.
Two methods of calculating the break-even point
There are two methods of calculating the break-even point, if the total fixed costs for
the period are known:
Method 1
The first method is to calculate the break-even point using the contribution per unit.
This method can be used where a company makes and sells just one product.
Break-even point in sales units = Total fixed costs
Contribution per unit
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Total fixed costs are the same as the total contribution required to break even, and
the break-even point can therefore be calculated by dividing the total contribution
required (= total fixed costs) by the contribution per unit. Remember to include any
variable selling and distribution costs in the calculation of the variable cost per unit
and contribution per unit.
Method 2
The second method calculates the break-even point in sales revenue.
ratio C/S
costs Fixed
= revenue $in volumesaleseven -Break
Having calculated the sales revenue required to break even , the break-even point
can be converted into units of sales required to break even if the sales price per unit
is known.
Example
A company makes a single product that has a variable cost of sales of $12 and a
selling price of $20 per unit. Budgeted fixed costs are $600,000. What volume of sales
is required to break even?
Answer
Method 1
unit peron Contributi
even) break toon contributi Total(= costs Fixed
= sales of unitsin pointeven -Break
Contribution per unit = $20 – $12 = $8.
Therefore break-even point = $600,000/$8 per unit = 75,000 units of sales.
In sales revenue, the break-even point is 75,000 units × $20 per unit = $1,500,000 of
sales.
Method 2
ratio C/S
costs Fixed
= revenue $in volumesaleseven -Break
C/S ratio = $8/$20 = 40%
Therefore break-even point in sales revenue = $600,000/0.40 = $1,500,000 in sales
revenue.
Break-even point in units = $1,500,000/sales price of $20 per unit = 75,000 units of
sale.
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Example
A company sells a range of products. If it sells its products in the budgeted
proportions, it expects to achieve an average contribution/sales ratio of 60%. Its
budgeted fixed costs for the year are $1,500,000.
What volume of sales (sales revenue in $) will be required to break even?
Answer
Break-even point = $1,500,000/60% = $2,500,000 of sales revenue.
Exercise 1
A company sells widgets. These cost $7.50 per unit and sell for $12 each. Budgeted
fixed costs are $1,350,000.
What is the break-even point?
3.3 Margin of safety
The margin of safety is the difference between:
the budgeted sales (in units or $) and
the break-even amount of sales (in units or $).
It is usually expressed as a
percentage of the budgeted sales. However, it may also
be measured as:
a quantity of units (= the difference between the budgeted sales volume in units
and the breakeven sales volume), or
an amount of sales revenue (= the difference between the budgeted sales
revenue and the total sales revenue required to break even).
It is called the margin of safety because it is the maximum amount by which actual
sales can be lower than budgeted sales without incurring a loss for the period. A
high margin of safety therefore indicates a low risk of making a loss.
Example
A company budgets to sell 25,000 units of its product. This has a selling price of $16
and a variable cost of $4. Fixed costs for the period are expected to be $240,000.
The break-even point = $240,000/($16 – 4) = 20,000 units.
The budgeted sales are 25,000 units.
Margin of safety = Budgeted sales – break-even sales
= 25,000 – 20,000 = 5,000