ANALYTICAL TECHNIQUES IN BUDGETING AND
FORECASTING
The Learning Curve
The learning curve applies in a labour-intensive working environment. When a product is
made using a labour-intensive production process, there will be a certain amount of
repetition in the making of the product thus allowing the learning curve principle to be
applied. As employees repeat the same operations time and again, their skill at performing
those operations increases. The results are improvements in efficiency (in terms of labour
hours), better-quality products, and overall reduction in cost.
This relationship between repeating operations and improvements is called the learning
effect and can be graphically represented in the form of a learning curve.
Application
Learning curves are used in the following ways:
1)
2)
3)
To estimate costs such as future production costs and even life-cycle costs.
Organisations whose products compete based on price, for example, may rely on
learning-curve effects to bring costs down and achieve economies of scale over the
life of the product.
To conduct competitive analysis, for example, in negotiations with a supplier.
Estimates of the supplier's learning rate might permit purchasing managers to
obtain better price.
In other cases, learning curves may transcend a single product. In such cases
improvements in a single product through learning can be applied to other products
and processes to achieve firm-wide improvements.
Learning effects
Learning curves capture the relationship between the average amount of time it takes to
accomplish a task and the cumulative number of units produced
Each time output doubles, the average time taken is reduced to a certain % (learning rate)
of the average time taken before output doubled. This results in a progressive reduction in
the average time per unit. Note that, as more units are produced, the reduction in the
average number of labour hours becomes smaller and smaller. This reduction will continue
until learning effects stop or become negligible.
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Factors affecting learning
Evidence from actual applications indicates that learning rates can be quite high. Each
organisation encounters a different learning rate based on different factors. Examples of
these factors include:
• Product characteristics
• Activities required in making the product
• Skill level
• Labour-saving equipment
• Innovations in technology
• Process improvements
• Corporate culture
• Incentives offered for improvements
Changes in any of the above factors can influence the learning rate.
The learning curve equation
Learning curves can be described through an exponential function which takes the
following form:
y = axb
y: cumulative average time required to produce x units
x: number of units of output under consideration
a: time taken for the first unit
b: log of learning rate divided by log 2.
Limitations
• Is not always present
• Instability in the work environment may make it difficult for learning to
take place
• Must be continuous over a reasonably long period of time and repetitive to allow
learning effects to occur
• The learning rate may not always be constant or equal
• Workers might deliberately not allow time taken to go down because of
disagreement or demotivation
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FORECASTING
High-Low Method
This method uses historical cost data to break total costs down into its variable and fixed
components. It uses the concept that total fixed costs do not change when total costs and
volume increase.
It is a relatively easy method but one has to remain careful of the occasional problem that
a step-fixed cost could create. The method only takes account of two observations: the
highest and the lowest volume. To take account of all observations a more advanced
calculation is used.
Linear Regression Analysis
Using the least squares method, a line of best fit (trend line) and its equation can be
found.
This method can be used to find the mathematical equation for total costs by again using
the concept that total fixed costs do not change while total variable costs vary with
volume. A linear equation of the form y = a + bx is used whereby a represents the total
fixed costs while b represents the variable cost per unit and x the number of units. Then
bx will be the total variable costs and y the total costs.
The following formula can be used to find a and b in the equation y = a + bx
Correlation coefficient and coefficient of determination
The correlation coefficient r, called the linear correlation coefficient, depicts the linear
relationship (strength and direction) between two variables. The linear correlation
coefficient is sometimes referred to as the Pearson product moment correlation
coefficient in honor of its developer Karl Pearson.
r can be: -1 ≤ r ≤ +1.
• If x and y have a strong positive linear correlation, r is close to +1. Positive
correlation indicates that when x increases, y will also increase. Perfect positive
correlation means that r = +1 and indicates a perfect positive fit.
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•
•
•
If x and y have a strong negative linear correlation, r is close to -1. Negative
correlation indicates that when x increases, y will decrease. Perfect negative
correlation means that r = -1 and indicates a perfect negative fit.
If r = 0 there is no linear correlation. If r is near to 0, the linear correlation between
x and y is weak. This means that there is a random, non-linear relationship between
x and y.
When r > 0.8, correlation is strong whereas when r < 0.5, correlation is weak.
Coefficient of determination = r2 or R2
This represents the % of data closest to the line of best fit. If r = 0.9111, then r 2 = 0.83.
This means that 83% of the total variation in y can be explained (not necessarily caused)
by the variations in x (as described by the relationship between x and y through the
regression equation). The other 17% of the total variation cannot be explained.
The coefficient of determination is a measure of how well the regression line represents
the data. If the regression line passes exactly through every point of data plotted on the
scatter graph, it would be able to explain all of the variation. The further the line is away
from the points, the less it is able to explain.
Time series
When forecasting sales (or output or production costs), a series of historical values for
sales volume (or output or production costs) would be plotted on a graph (historigram)
and a time series may then reveal a trend. This trend or relationship is however affected
by variations, such as seasonal (e.g., summer/winter) or short-term changes (e.g.,
Christmas sales), cyclical (e.g., economic downturn) or long-term trend (e.g., population
change) and random variations (e.g., earthquake). We can use moving averages to
remove seasonal variations from a time series through averaging to obtain the figures
that represent only the trend.
However, we still need to know these variations as they impact the final forecasts.
These variations are obtained by calculating the differences between actual and the trend.
Once the trend line has been adjusted for such variations a forecast of future sales (or
output or production costs) can be made. It should be noted that linear regression analysis
and time series assume that the past is an indication of the future.
Two models of time series (for short to medium term forecasting) can apply:
1. Additive Model:
Series (or forecast) = Trend + Seasonal + Random
2. Multiplicative Model:
Series (or forecast) = Trend x Seasonal x Random
Advantages of linear regression
1) Can be used with small sets of data to produce good forecasts,
2) For simple business forecasting, most relationships are linear and therefore linear
regression is very applicable,
3) It results in a simple equation that can be easily applied.
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Disadvantages of linear regression
1) Can be misleading if relationship between variables is non-linear,
2) The dependent variable Y may well be affected by several variables other than X,
3) The reliability of historical information as source data for forecasting is
questionable in many cases as cost and revenue relationships can alter radically
over time with technological and market changes,
4) It can be unreasonable (in a number of cases) to assume that observed
relationships within a range can also apply outside the observed range (problem of
extrapolation),
5) Forecasting accuracy is undermined where the observed data range is limited,
6) Inaccurate and false data will render the regression analysis equation unreliable.
Advantages of time series forecasting
1) Using time as a basis for forecasting is easy to apply and understand,
2) Forecasts can be easily updated by incorporating latest historical data into the
analysis to continuously update and improve the reliability of the forecasts.
Disadvantages of time series forecasting
1) Ignores other factors except time,
2) Considers that the trend line is a straight line,
3) There is no guarantee that the pattern of trend and seasonal variations will
continue over the future,
4) Reliability of the forecast depends on the amount of data available/used.
Note that in a situation where inflation is present, you must adjust the forecast costs to
the present inflation level (or index) from the original inflation level when the regression
was conducted or trend line was obtained.
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STANDARD COSTING, VARIANCES & PERFORMANCE
ANALYSIS
Standards
All amounts in £ or $ are made up of two components. The first component is the
physical quantity component, such as kilograms, units, litres, hours and such others. The
second one is the monetary value components, such as cost/unit, price/kg or rate/hour and
such others.
Therefore, any
Financial Amount = Physical measure x unitary monetary value
Thus $20 could stand for 2 cinema tickets @ $10 each or four train tickets @ $5 each.
Similarly, every financial amount can be broken down into two different measures. Each
component has its own standard.
From the above, we can see that standard costs are benchmarks based on standards
established in advance for
1) the quantity of activity resources that should be consumed by each unit of output and
2) the price of those resources.
Types of standards and behavioural/motivation impacts
Basic standard
A basic standard is one that remains unchanged for several years. Because it remains
unchanged, it allows efficiency trends over time to be identified. Basic standards may
become increasingly easy to achieve as time passes and hence, being undemanding, may
have a negative impact on motivation. Standards that are easy to achieve will give
employees little to aim at. Because basic standards do not reflect current conditions, they
are of limited use if current conditions differ significantly from those existing when the
standard was set. They are therefore seldom used.
Ideal standard
This is a standard that reflects perfect performance and is the minimum cost that is
possible under ideal operating conditions. Because ideal standards are unattainable, they
are unlikely to be used in practice, since inability to achieve them is likely to have a
demotivating effect on managers and employees. They are also unlikely to be accepted as
targets by the staff involved as they are unlikely to be achieved.
Attainable standard
This standard allows for normal levels of wastage and operation, and represents a cost
level achievable under reasonably efficient working. Attainable standards may be
difficult to achieve, but they do not represent impossible targets for employees. An
attainable standard is considered to represent the best target against which to compare
current activity and is the preferred standard to use in planning, budgeting and cost
control.
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Current standard
This standard is one established for use over a short period of time and relates to current
conditions. Current standards are based on current operating conditions and incorporate
current levels of wastage, inefficiency and machine breakdown. If used as targets, current
standards will not improve performance beyond its current level and their impact on
motivation will be a neutral one. It is best to use this standard with attainable standard to
obtain currently attainable standard for positive motivational impact.
Ex ante and ex post standards
Ex ante standards are based on anticipated conditions and performance and are prepared
prior to the operating period to which they relate. If operating conditions have changed
significantly compared to the assumptions underlying ex ante standards, calculated
variances may be less relevant and useful than desired. To combat this weakness,
standards may be revised (ex post standards) to take account of changed operating
conditions. The differences between ex ante and ex post standards are taken into account
by calculating planning variances, while operational variances are prepared using ex post
standards, comparing actual results against revised standards.
Motivation
The theory of motivation suggests:
➢ that having a clearly defined target results in better performance than having no
target at all,
➢ that targets need to be accepted by the staff involved, and
➢ that more demanding targets increase motivation provided they remain accepted.
Participation in standard setting
In establishing targets, the importance of individuals taking ownership of the standards
has long been established: this is often facilitated by the adoption of a budgetary system
based on employee participation. This is also considered to be beneficial to the
organisation since it alleviates, or at the very least reduces, many of the dysfunctional
consequences associated with management control. In particular, managers who
participate in the standard-setting process are more likely to accept the standards set, feel
less job-related tension and have better relationships with their superiors and colleagues.
Participation does, however, provide opportunities for the introduction of budgetary slack
in order that any subsequent monitoring of activities presents a favourable outcome.
The challenge to management lies in finding the balance between what the company
views as achievable and what the employee views as achievable as this often proves to be
a source of organisational conflict.
Standard Costing System
A standard costing system requires preparation of standard costs, comparison of standard
costs with actual costs, investigation of variances and instigation of corrective action if
needed, and review of standard costs on a regular basis. Standard costs are predetermined
unit costs arising under efficient operating conditions. Standard costing can be applied to
repetitive or common operations where the input to produce a required output can be
clearly specified.
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Preparation of standard costs
Standards are required for amount of materials, labour and services required to perform a
particular operation, and cost standards are compiled from the standard costs of the
individual operations needed to produce a given product. The quantities and costs needed
for each standard can be derived using the engineering approach or through the analysis
of historical records.
The engineering approach requires a detailed study of each operation so that the
materials, labour and equipment used in the operation can be verified by observation, for
example by using time and motion studies.
Analysis of historical records can be carried out using quantitative analysis, including the
high-low method, scatter graphs and regression analysis. Standards are set by these
methods by averaging historical data and so there is a danger that past inefficiencies may
be perpetuated. This approach to standard setting is widely used in practice.
The uses of standard costs
Standard costs have many uses as listed below:
• They can be used to predict and forecast future costs for use in decision-making
and budgeting.
• They can be used as a basis for controlling costs arising in actual operations
through detailed variance analysis, that is, the comparison of actual results with
standard costs.
• They enable exception reporting through variance analysis. Variances enable
management to pinpoint which operational areas have performed poorly and to
direct investigations to areas with large variances.
• They can be used as a basis for measuring and assessing the performance of
managers and employees.
• They can provide targets for motivating managers and employees to improve
performance and meet organisational objectives.
• They can be used as a basis for profit measurement and stock valuation.
Variance analysis
Variances obtained by comparing standard costs with actual costs form the basis of cost
control and support the use of responsibility accounting. A wide range of variances can
be calculated, depending in part on the costing system employed. The causes of
individual variances can be investigated if a variance is deemed to be significant, in order
to instigate appropriate corrective action where necessary. Both favourable and adverse
variances should be investigated, since useful information can be derived from both.
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Sales Performance Analysis
One common method for analysing sales performance is sales variance analysis. This
approach examines the difference (variance) between actual sales performance and
budgeted sales performance by computing a set of variances, with each variance focusing
on some underlying aspects of sales performance. Sales variance analysis may be carried
out in three alternative ways:
1.
Focus on sales revenue. The first approach to sales variance analysis analyses the
difference (variance) between actual and budgeted sales revenue. (Turnover basis)
2.
Focus on contribution. The second approach to sales variance analysis analyses the
difference (variance) between actual and budgeted contribution margin. Under this
approach we are implicitly assuming that the organisation’s cost structure can be
represented by the traditional (and relatively simple) cost behaviour pattern that
includes only variable costs and fixed costs.
3.
Focus on net profits. This third approach focuses on the difference between actual
and budgeted profits. In this approach, profit is used although it does not always
vary directly with volume.
Total Sales Variance
Sales Price Variance
Sales Volume Variance
Sales Mix Variance
Sales Quantity Variance
Market-Size Variance
(Sales Volume Planning
variance)
Market Share Variance
(Sales Volume Operational
variance)
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Criticisms of Standard Costing and Traditional Variance Analysis
1.
Use of past standards. Past standards can easily become outdated and variances
calculated there from could be unrealistic or even misleading. These standards
can also demotivate employees.
2.
Just meeting the standards can become an end in itself. Focusing on achieving
current or past standards may discourage improvement in performance.
3.
Interdependencies of variances sometime distort the understanding of the causes
and effects of variances being evaluated.
4.
The assignment of variance elements to manager raises questions about
performance, but variance calculations do not explain performance. Without
knowing the causes of variances, performance may be unfairly evaluated.
5.
There is also a tendency for managers to pay far closer attention to adverse
variances than to favourable ones.
6.
Traditional variance analysis does not distinguish between controllable and
uncontrollable variances.
7.
Standards focus on costs (minimization) and not on product quality, customer
service, and other non-financial performance issues (see JIT and TQM below).
Many firms are now making changes in their use of standard costing by using a variety of
cost drivers (using ABC), and having more frequent revisions of standards to reflect
efficiency improvements.
Review of standard costs
Standard costs must be reviewed and updated if they are to retain their relevance to an
organisation. The review should consider changes in the prices of inputs such as labour
and materials as well as changes in working practices and production methods.
Currently attainable standards only remain relevant if they continue to relate to current
circumstances, that is, if they are regularly reviewed to take account of any changes in
operating methods and any changes in the economic and business environment. If
changes are small and not significant, the standard may be left unchanged. If changes are
more significant, management may consider reporting planning and operational variances
to highlight differences that have arisen and to keep reported variances useful.
Standards have to be reviewed to enable the benefits of standard costing to continue. In
this respect, standards must change with the changing practices of an organisation. In
order to review standards, they must be continually assessed to ensure that the basis of
their calculation still applies. Moreover, the purposes of standards are undermined if they
are not continually reviewed. Thus, for example:
❑ The motivational impact of standards may no longer be effective if standards are
out of date.
❑ Assessment of managerial performance becomes inaccurate.
❑ The credibility of standards in their role in assisting with the budget setting
process is reduced.
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Planning & Operational Variances
A planning and operational approach to variance analysis assists in both planning and
control. The isolation of planning variances which are deemed to be non- controllable
leaves management free to focus on the operational variances.
Advantages include:
1. Short-term control can then be implemented by determining which variances are
controllable and which are not.
2. Efforts can then be concentrated on determining the cost/benefit of investigation
and elimination of the controllable elements.
3. The revision of standards also assists in forward planning. Future plans will be
improved by using updated standards for future budgets and variance analysis.
4. A further advantage is that highlighting the planning variances helps to identify
any errors in budgets so that the planning process can be continually refined.
The disadvantages of calculating these variances are:
• the possibility of operational variances being treated as planning variances,
• the possibility of subjectivity in determining the revised standard and
• the additional time and cost incurred.
Just In Time (JIT), Total Quality Management (TQM) and Variances
In manufacturing, the introduction of JIT is aimed at reducing inventory levels and
improving customer service by ensuring that customers receive their orders at the right
time and in the right quantity. Goods are produced to meet customer needs directly.
A JIT system is a ‘pull’ system that responds to demand and has a product line emphasis.
It requires a flexible labour force and excellent information /communication lines. It only
buys from suppliers who can guarantee zero defects deliveries and are ultra-reliable.
TQM is an approach where the underlying principle is that quality should be designed
into the process and the product from the outset. The aim is to do it right the first time
and achieve zero defects. It is based on the thinking that it is always cheaper to build all
the items correctly the first time rather than waste resources building substandard items
that have to be detected, then reworked or scrapped.
Consequently, traditional variances become inapplicable in a JIT/TQM environment:
1. The philosophy of a Just-in-Time (JIT) production system is that units should not be
produced to be held as inventory. The fixed overhead volume variance encourages overproduction and it clearly motivates managers to act against the principle of JIT.
2. TQM focuses attention on quality, whereas variance analysis draws attention to costs.
3. Due to long-term contractual arrangements, for example with suppliers, many companies
in the modern manufacturing environment operate under stable conditions and the
calculation of variances is unnecessary. For example, if strong purchasing links exist
with a supplier, there should not be a price variance.
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