ACCA F5 Performance Management - 2010 - Study text - Emile Woolf Publishing
Подождите немного. Документ загружается.
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 185
Paper F5
Performancemanagement
CHAPTER
8
Quantitative analysis
in budgeting
Contents
1 Cost estimation: high/low method
2 Cost estimation: linear regression analysis
3 Correlation and the correlation coefficient
4 Time series analysis
5 The learning curve
6 Other aspects of quantitative analysis in
budgeting
Paper F5: Performance management
186 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP
Cost estimation: high/low method
Cost estimation: analysing fixed and variable 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
1 Cost estimation: high/low method
1.1 Cost estimation: analysing fixed and variable costs
For the purposes of budgeting 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. One way of doing this is to estimate fixed costs
per period and variable costs per unit of activity from historical cost data.
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
b = the variable cost per unit of output or unit of activity.
The linear cost function equation y = a + bx can be drawn on a cost behaviour graph
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
Chapter 8: Quantitative analysis in budgeting
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 187
Two methods of estimating fixed and variable costs from historical data for total
costs are:
high/low analysis
linear regression analysis.
1.2 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.
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.
Paper F5: Performance management
188 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP
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.
Example
A company has recorded the following costs in the past six 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
40,600
May 6,500
44,500
June 7,500
47,100
Required
Using high/low analysis, prepare an estimate of total costs in July if output is
expected to be 7,000 direct labour hours.
Chapter 8: Quantitative analysis in budgeting
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 189
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 of total costs for 7,000 hours
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.
1.3 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.
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
Paper F5: Performance management
190 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP
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.
(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
Chapter 8: Quantitative analysis in budgeting
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 191
(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.
Example
A company has the following costs at three activity levels.
Activity Total cost
units $
5,000 180,000
8,000 240,000
11,000 276,000
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 20% when the activity level exceeds 7,500
units.
Required
Estimate the expected total cost when the activity level is 7,000 units.
Answer
There is an increase in fixed costs above 7,500 units of activity, which means that
total fixed costs and the variable cost per unit are the same for 8,000 units and 11,000
units of activity. These activity levels should be used to estimate the variable cost per
unit and total fixed costs.
Paper F5: Performance management
192 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 11,000 units
= 276,000
‘In-between’ 8,000 units
= 240,000
Difference: Variable cost of 3,000 units
= 36,000
Therefore variable cost per unit = $36,000/3,000 units = $12 per unit.
(2) Steps 3 and 4: Calculate fixed costs (above 7,500 units)
Substitute in the ‘high’ equation Cost
$
Total cost of 11,000 units 276,000
Variable cost of 11,000 units (× $12 per unit)
132,000
Therefore fixed costs (above 7,500 units) 144,000
(3) Calculate fixed costs at activity levels below 7,500 units
Fixed costs increase by 20% above 7,500 units.
Fixed costs above 7,500 units are therefore 120% of fixed costs below 7,500 units.
Fixed costs below 7,500 units are therefore: $144,000 × (11/120) = $120,000.
(Note: Make sure that you understand the adjustment here. We do not subtract 20%
from fixed costs above 7,500 units!)
(4) Using the cost analysis: Prepare a cost estimate
Cost estimate Cost
$
Fixed costs (below 7,500 units) 120,000
Variable cost (7,000 units × $12) 84,000
Estimated total costs 204,000
1.4 High/low analysis when there is a change in the variable cost per unit
High/low analysis can also be used when there is a change in the variable cost per
unit between the ‘high’ and the ‘low’ levels of activity. The same approach is needed
as for a step change in fixed costs, as described above.
When the change in the variable cost per unit is given as a percentage amount, a
third ‘in between’ estimate of costs should be used, and the variable cost per unit
will be the same for:
the ‘in between’ activity level and
either the ‘high’ or the ‘low’ activity level.
Chapter 8: Quantitative analysis in budgeting
© EWP Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides 193
High/low analysis may be applied to the two costs and activity levels for which
unit variable costs are the same, to obtain an estimate for the variable cost per unit
and the total fixed costs at these activity levels. The variable cost per unit at the third
activity level can then be calculated making a suitable adjustment for the percentage
change.
Example
A company has the following costs at three activity levels.
Activity Total cost
units $
20,000 300,000
25,000 320,000
30,000 356,000
The fixed costs are constant over this range of activity, but there is a 10% reduction
in the variable cost per unit above 24,000 units of activity. This reduction applies to
all units of activity, not just the additional units above 24,000.
Required
Estimate the expected total cost when the activity level is 22,000 units.
Answer
The variable cost per unit is the same for both 25,000 units and 30,000 units.
High/low analysis should therefore be applied to these activity levels.
(1) Calculate the variable cost per unit above 24,000 units
Units
$
High: Total cost 30,000 units
= 356,000
‘In-between’ 25,000 units = 320,000
Difference: Variable cost of 5,000 units
= 36,000
Therefore variable cost per unit = $36,000/5,000 units = $7.20 per unit.
(2) Calculate the variable cost per unit below 24,000 units
The variable cost per unit above 24,000 units is 90% of the cost below 24,000 units.
The variable cost per unit below 24,000 units is therefore (× 100/90) of the cost
above 24,000 units.
Variable cost per unit below 24,000 units = $7.20 × 100/90 = $8
Paper F5: Performance management
194 Go to www.emilewoolfpublishing.com for Q/As, Notes & Study Guides © EWP
(3) Calculate fixed costs
Substitute in the ‘low’ equation Cost
$
Total cost of 20,000 units 300,000
Variable cost of 20,000 units (× $8 per unit) 160,000
Therefore fixed costs (above 7,500 units) 140,000
(4) Using the cost analysis: Prepare a cost estimate
Cost estimate for 22,000 units Cost
$
Fixed costs 140,000
Variable cost (22,000 units × $8) 176,000
Estimated total costs 316,000