ACCA F2 Management Accounting - 2010 - Study text - Emile Woolf Publishing
Подождите немного. Документ загружается.
Chapter 3: Cost behaviour and cost estimation
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 45
For example, it might be assumed that the total selling and distribution costs for a
company each month are mixed costs. If this assumption is used, the total mixed
costs can be divided into two separate parts, fixed costs and variable costs.
If costs can be analysed as a fixed amount of cost per period plus a variable cost per
unit, estimating what future costs should be, or what actual costs should have been,
becomes fairly simple.
Example
The management accountant of a manufacturing company has estimated that
production costs in a factory that manufactures Product Y are fixed costs of $250,000
per month plus variable costs of $3 per unit of Product Y output.
The expected output next month is 120,000 units of Product Y. Expected total costs
are therefore:
$
Variable costs (120,000 × $3) 360,000
Fixed costs 250,000
Total costs 610,000
Paper F2: Management Accounting
46 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP
Other cost behaviour patterns
Stepped fixed cost
More unusual cost behaviour patterns
2 Other cost behaviour patterns
Some cost items are variable costs, fixed costs or mixed costs. Costs in total might
have a cost behaviour pattern that is very close to being a mixed cost. However
there are many cost items that have a more unusual cost behaviour pattern. Unusual
cost behaviour patterns can be shown on a cost behaviour graph.
2.1 Stepped fixed cost
A stepped fixed cost is a cost which:
has a fixed cost behaviour pattern within a limited range of activity, and
goes up or down in steps when the volume of activity rises above or falls below
certain levels.
On a cost behaviour graph, step fixed costs look like steps rising from left to right.
Total
cost
$
Activity level
Example
A company might pay its supervisors a salary of $4,000 each month. When
production is less than 3,500 hours each month, only one supervisor is needed: when
production is between 3,501 and 7,000 hours each month, two supervisors are
needed. When output is over 7,000 hours each month, three supervisors are needed.
These supervision costs are therefore fixed costs within a certain range of output,
b
ut go up or down in steps as the output level rises above or falls below certain
levels.
Chapter 3: Cost behaviour and cost estimation
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 47
A cost behaviour graph for the supervision costs can be drawn as follows.
$
2.2 More unusual cost behaviour patterns
You may be examined on your understanding of more unusual cost behaviour
patterns. Several are shown below.
Changes in total variable costs
T
otal variable
costs
(a) (b)
Total variable
costs
Volume of activity
Volume of activity
In (a), the variable cost per unit is a particular amount up to a certain level of
activity or output, and is a lower amount for all units above that level of activity.
For example, the cost might be $2 per unit up to 10,000 units and $1.50 per unit for
each unit over 10,000 units.
In (b), the variable cost per unit is a particular amount up to a certain level of
activity or output, and above that level of activity the variable cost per unit is a
lower amount for all units (not just for the units above that level of activity). For
example, a supplier might offer a price of $5 per unit for all units of a raw material,
up to 10,000 units per order. If the size of an order is more than 10,000 units, the cost
per unit will be $4.75.
Minimum and maximum charges
The cost behaviour pattern in the graph below illustrates a cost during a period
when there is a charge per unit, subject to a minimum charge and a maximum
charge per period.
Paper F2: Management Accounting
48 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP
Total cost
Volume of activity
Other patterns
In your examination, you might be given another unusual cost behaviour pattern,
and asked to identify the type of cost to which the cost behaviour pattern relates.
You will need to study the pattern to identify its fixed and/or variable
characteristics, and try to identify what type of cost fits the pattern shown. Here is
just one example.
Example
Study the following cost behaviour graph and identify which of the following cost
items is shown in the graph.
Total electricity charges for a factory, where the electricity supplier charges:
A a fixed annual charge plus a constant amount for each unit of electricity
consumed, subject to a maximum annual charge
B a constant amount for each unit of electricity consumed up to a certain
amount, and a lower charge per unit for consumption above that amount
C a constant amount for each unit of electricity consumed but if consumption
exceeds a certain amount the charge is reduced to a lower amount for the
total amount consumed
D a fixed charge for the year, then a constant amount for each unit of electricity
consumed up to a certain amount, and a lower charge per unit for
consumption above that amount
£
Total
cost
0
Volume of activity
The cost behaviour graph shows that there is some charge even when consumption
is zero. This means that there must be a fixed cost element in the annual charge.
Total costs then rise in a straight-line fashion up to a certain level of consumption
(so variable costs are a constant amount per unit) and above that level total costs
continue to rise but the rate of increase is less steep (so variable costs are a new but
lower constant amount per unit).
The cost item shown in the graph must therefore be D.
Chapter 3: Cost behaviour and cost estimation
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 49
Cost estimation: high/low method
Cost estimation
A linear cost function for total costs
High/low analysis
High/low analysis when there is a step change in fixed costs
High/low analysis when there is a change in the variable cost per unit
3 Cost estimation: high/low method
3.1 Cost estimation
For the purposes of planning and decision-making, it is often necessary to prepare
an estimate of costs. For example, it is often necessary to estimate the total annual
costs of an activity or a responsibility centre, or the total annual costs of production
overheads or marketing overheads.
Unless there are reasons for a different approach, it is usual to make a cost estimate
on the assumption that total costs (for a large number of different cost items
together) are a mixture of fixed costs and variable costs. In order to estimate costs, it
is therefore necessary to make an estimate of:
fixed costs for the period, and
the variable cost per unit of output or sales, or the variable cost per unit of
activity (for example, the variable cost per hour worked).
In the same way, individual items of mixed cost can be divided into fixed and
variable cost elements. Two cost estimation techniques are:
high/low analysis
linear regression analysis.
This chapter explains the high/low method. The linear regression method will be
explained in a later chapter.
3.2 A linear function for total costs
If total costs can be divided into fixed costs or variable costs per unit of output or
unit of activity, a formula for total costs is:
y = a + bx
where
y = total costs in a period
x the number of units of output or the volume of activity in the period
a = the fixed costs in the period
Paper F2: Management Accounting
50 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP
b = the variable cost per unit of output or unit of activity.
Graph of linear cost function
On a cost behaviour graph, total costs would be shown as a straight line, rising with
the total volume of activity. (It is a cost behaviour graph for a mixed cost.) This
rather simple formula is therefore a ‘linear function’ for total costs.
The linear cost function equation y = a + bx can be drawn as follows.
Total
cost
y
gradient of cost function = b
(variable cost per unit)
cost function
y = a + bx
(total cost line)
a = fixed cost
Volume of activit
y
x
3.3 High/low analysis
High/low analysis can be used to estimate fixed costs and variable costs per unit
whenever:
there are figures available for total costs at two different levels of output or
activity
it can be assumed that fixed costs are the same in total at each level of activity,
and
the variable cost per unit is constant at both levels of activity.
High/low analysis therefore uses two historical figures for cost:
the highest recorded output level, and its associated total cost
the lowest recorded output level, and its associated total cost.
It is assumed that these ‘high’ and ‘low’ records of output and historical cost are
representative of costs at all levels of output or activity.
The difference between the total cost at the high level of output and the total cost at
the low level of output is entirely variable cost. This is because fixed costs are the
same in total at both levels of output.
Chapter 3: Cost behaviour and cost estimation
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 51
The method
There are just a few simple steps involved in high/low analysis.
Step 1
Take the activity level and cost for:
the highest activity level
the lowest activity level.
Step 2
The difference between the total cost of the highest activity level and the total cost of
the lowest activity level consists entirely of variable costs. This is because the fixed
costs are the same at all levels of activity.
Activity
level
$
High: Total cost of A
= TCa
Low: Total cost of B
= TCb
Difference: Variable cost of (A – B) units (A – B)
= TCa - TCb
From this difference, we can therefore calculate the variable cost per unit of activity.
Variable cost per unit = $(TCa – TCb)/ (A – B) units
Having calculated a variable cost per unit of activity, we can now calculate fixed
costs.
Step 3
Having calculated the variable cost per unit, apply this value to the cost of either the
highest or the lowest activity level. (It does not matter whether you use the high
level or the low level of activity. Your calculation of fixed costs will be the same.)
Calculate the total variable costs at this activity level.
Step 4
The difference between the total cost at this activity level and the total variable cost
at this activity level is the fixed cost.
Substitute in the ‘low’ equation Cost
$
Total cost of (low volume of activity) TCb
Variable cost of (low volume of activity) V
Therefore fixed costs per period of time TCb - V
You now have an estimate of the variable cost per unit and the total fixed costs.
The high/low method is a simple but important technique that you need to
understand. Study the following example carefully.
Paper F2: Management Accounting
52 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP
Example
A company has recorded the following costs in the past four months:
Month Activity
Total cost
Direct labour hours
$
January 5,800
40,300
February 7,700
47,100
March 8,200
48,700
April 6,100
40,650
Required
Using high/low analysis, prepare an estimate of total costs in May if output is
expected to be 7,000 direct labour hours.
Answer
(1) Steps 1 and 2: Calculate the variable cost per hour
Take the highest level of activity and the lowest level of activity, and the total costs
of each. Ignore the other data for levels of activity in between the highest and the
lowest.
Hours
$
High: Total cost of 8,200 hours
= 48,700
Low: Total cost of 5,800 hours
= 40,300
Difference: Variable cost of 2,400 hours
= 8,400
Therefore variable cost per direct labour hour = $8,400/2,400 hours = $3.50.
(2) Steps 3 and 4: Calculate fixed costs
Substitute in the ‘high’ equation Cost
$
Total cost of 8,200 hours 48,700
Variable cost of 8,200 hours (× $3.50 per hour) 28,700
Therefore fixed costs per month 20,000
(3) Using the cost analysis: Prepare a cost estimate
Cost estimate for May Cost
$
Fixed costs 20,000
Variable cost (7,000 hours × $3.50 per hour) 24,500
Estimated total costs 44,500
The technique can be used any time that you are given two figures for total costs, at
different levels of activity or volumes of output, and you need to estimate fixed
costs and a variable cost per unit.
Chapter 3: Cost behaviour and cost estimation
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 53
3.4 High/low analysis when there is a step change in fixed costs
High/low analysis can be used even when there is a step increase in fixed costs
between the ‘low’ and the ‘high’ activity levels, provided that the amount of the step
increase in fixed costs is known.
The method of analysis to use depends on whether the step increase in the fixed cost
is stated as a money amount of cost, or whether it is stated as a percentage increase.
The step increase in fixed costs is given as a money amount
If the step increase in fixed costs is given as a money amount, the total cost of the
‘high’ or the ‘low’ activity level should be adjusted by the amount of the increase, so
that total costs for the ‘high’ and ‘low’ amounts are the same.
The high/low method can then be used in the normal way to obtain a fixed cost and
a variable cost per unit. The fixed cost will be either the fixed cost at the ‘high’ level
or at the ‘low’ level, depending on how you made the adjustment to fixed costs
before making the high/low analysis. You can then calculate the fixed costs at the
other level of activity by adding or subtracting the step change in fixed costs, as
appropriate.
Example
A company has the following costs at two activity levels.
Activity Total cost
units $
17,000 165,000
22,000 195,000
The variable cost per unit is constant over this range of activity, but there is a step
fixed cost and total fixed costs increase by $15,000 when activity level equals or
exceeds 19,000 units.
Required
Using high/low analysis, calculate the total cost of 20,000 units.
Answer
There is an increase in fixed costs above 19,000 units of activity, and to use the
high/low method, we need to make an adjustment for the step fixed costs. Since we
are required to calculate the total cost for a volume of activity above 19,000 units, the
simplest approach is to add $15,000 to the total cost of 17,000 units, so that the fixed
costs of 17,000 units and 22,000 units are the same and are also the amount of fixed
costs for 20,000 units.
Paper F2: Management Accounting
54 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP
(1) Steps 1 and 2: Calculate the variable cost per unit
Units
$
High: Total cost 22,000 units
= 195,000
Low: Adjusted total cost: $(165,000 + 15,000) 17,000 units
= 180,000
Difference: Variable cost of 5,000 units
= 15,000
Therefore variable cost per unit = $15,000/5,000 units = $3 per unit.
(2) Steps 3 and 4: Calculate fixed costs (above 19,000 units)
Substitute in the ‘high’ equation Cost
$
Total cost of 22,000 units 195,000
Variable cost of 22,000 units (× $3 per unit) 66,000
Therefore fixed costs (above 19,000 units) 129,000
(3) Using the cost analysis: Prepare a cost estimate
Cost estimate Cost
$
Fixed costs (above 19,000 units) 129,000
Variable cost (20,000 units × $3) 60,000
Estimated total costs 189,000
The step increase in fixed costs is given as a percentage amount
When the step change in fixed costs between two activity levels is given as a
percentage amount, the problem is a bit more complex, and to use high/low
analysis we need a third figure for total cost, at another level of activity somewhere
in between the ‘high’ and the ‘low’ amounts.
Total fixed costs will be the same for:
the ‘in between’ activity level and
either the ‘high’ or the ‘low’ activity level.
High/low analysis should be applied to the two costs and activity levels for which
total fixed costs are the same, to obtain an estimate for the variable cost per unit and
the total fixed costs at these activity levels. Total fixed costs at the third activity level
(above or below the step change in fixed costs) can then be calculated making a
suitable adjustment for the percentage change.