CMA Ontario
Accelerated Program
MANAGEMENT ACCOUNTING
MODULE 3
Volume 2 of 2
Module 3 – Management Accounting 2
Table of Contents
5.
Cost Behaviour
146
6.
Activity Based Costing
184
7.
Service Department Cost Allocations
217
8.
Joint and By-Product Costing
240
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5.
Cost Behaviour
Learning Objectives
After completing this chapter you will:
1. Understand why understanding cost behaviour is important for management accountants
2. Understand the issues and limitations in using historical cost data to estimate cost
behaviour
3. Understand and be able to apply the five tools that management accountants use to
estimate cost behaviour
4. Understand how to evaluate statistically based estimates of cost behaviour
The Importance of Good Cost Information
The role of good cost estimates is pervasive in management accounting. Managers use cost
estimates to develop budgets, evaluate performance relative to plan, price new products, and
evaluate the profitability of existing products. In short the importance of management
accountants developing a solid understanding of cost behaviour and developing good estimates
of costs is critical in supporting management control and strategic analysis.
Boston’s Central Artery/Tunnel Project
(The Big Dig)
Estimated to cost $2.9 Billion in 1985 at the
outset of planning for Boston’s central
artery/tunnel project and to be completed in
1995, the eventual cost of the project was
estimated to be $22 Billion when the project
was completed in 2007. Observers have
attributed the cost overruns to management and
contractor incompetence. Picture Source:
Boston Globe
Canada’s Gun Registry
Estimated to cost less than $2 million when it
was introduced in 1995, in 2004 CBC news
estimated the cost to date of Canada’s Gun
Registry was $2 billion. Cost overruns were
attributed mainly to unexpected computer
systems and legal costs. Picture Source: CBC.
Approaches to Cost Estimation
The cost estimation process begins by defining the cost whose behaviour the analyst wants to
estimate/understand/predict. Examples include manufacturing overhead cost, materials costs,
labour costs, or even total product cost. The next step is to identify the cost driver or cost drivers
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that the analyst believes drives or causes the cost behaviour that the analyst wants to estimate.
Then the analyst can use various approaches to develop the equation that will be used to predict
the cost behaviour.
There are five common approaches to estimating costs: two involve the basic application of
process knowledge and judgement and three involve the use of historical data.
Judgement Approaches
The two judgement approaches exploit a good understanding of the process that creates the cost
to develop a plausible model of explaining the cost behaviour.
Engineering Estimates
The engineering estimate approach involves the estimation of costs based on the analysis of
product (good or service) specifications. This approach follows in the tradition of Frederick
Taylor’s scientific management method and the industrial engineering ideas developed by Frank
and Lilian Gilbreth. In the engineering estimate approach all the required material, labour time,
and machine time components of the product are laid out and the cost of each is estimated. Then
the costs of all the components are summed to estimate the product costs.
Account Analysis
Account analysis involves the evaluation of each of the costs in a ledger account and classifying
each cost as fixed or variable with regard to some cost driver.
For example, a study of the items in the manufacturing overhead account might lead the cost
analyst to classify supplies as variable, machine depreciation as fixed, supervisory salaries as
fixed, taxes on factory land as fixed, power as variable, and so on. The cost analyst would then
accumulate the classified costs into two pools – variable and fixed costs to create an equation
estimating cost behaviour.
Data Approaches
In the data approaches the management accountant uses historical operations data to estimate
cost behaviour. By considering the historical pattern of costs, the data approaches have the
greatest potential to yield realistic estimates of cost behaviour. However, there are inevitable
characteristics of historical cost data that can impair their relevance and usefulness in cost
estimation.
Contaminants of Historical Cost Data
The maintained assumption when management accountants use historical cost data is that there
has been no underlying change in the manufacturing process that is not captured in the recorded
data. Statisticians call this the omitted variable problem. The longer the period over which the
recorded data stretches extends the greater the possibility that there has been some change (such
as changes in technology, product design, learning, and inflation) that can affect costs but which
has not been picked up in the measurement process.
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Another potential contaminant of historical cost data is inaccurate cost accrual. The shorter the
cost recording period, for example weekly or monthly, the greater the chance that accruals are
less reliable and therefore misleading in the cost estimation process. For example, costs driven
by an activity in one period might be inaccurately assigned to the next period.
Generally the management accountant is forced to rely on quarterly accruals to provide a
minimum assurance of data integrity. This means that only 4 observations can be made a year to
develop the cost estimation database. Since the rule of thumb is that a minimum of 20
observations is needed to provide a reliable cost estimate this means that five years of time series
data is needed to provide a reasonable database for a cost estimate. The five year time period
however introduces the possibility of important changes in the manufacturing environment, such
as technological innovation, that may have taken place and are not captured in the data thereby
creating errors in cost estimation.
The way the accounting system treats costs can create issues of data integrity. For example if
fixed costs are allocated to production based on some activity level, such as units made, labour
hours, or machine hours, what is actually a fixed cost may appear to be variable.
Continuous growth creates issues when using regression analysis. Using an estimated cost
equation to predict costs beyond the range of experience is inappropriate since this can result in
significant estimation errors.
Observation
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Units
812
586
845
863
852
698
610
614
642
836
759
693
553
512
707
802
635
629
773
872
Cost
145300
139650
151125
151575
146300
147450
135250
145350
136050
140900
143975
137325
133825
127800
147675
145050
135875
145725
139325
146800
Finally there is the troubling issue of outliers which are
data points that are significantly different from the rest.
These extreme points create issues in cost estimation
particularly if regression analysis is used. The usual
treatment for an unusual item is to try to identify the
cause of the observation. If it is determined that the
cause was a nonrecurring item such as a natural disaster
or a strike the usual approach is to eliminate the outline
from the data set. Most analysts will avoid eliminating
an outlier from a data set if its cause cannot be
determined on the grounds that if the outlier cannot be
explained then the circumstances that created the outlier
cannot be accommodated in cost estimation.
High Low Method
Suppose that the data in the accompanying table for
Danny Company was recorded during the last 20
periods. Note that this data assumes that the number of
units made is the appropriate cost driver.
In the high low method the management accountant
computes the formula for the line connecting the lowest
and highest values of the cost driver.
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Therefore the pair of observations that would form the basis for estimating the cost relationship
would be
Highest Level of cost driver/cost- observation 20
872/146,800
Lowest Level of cost driver/cost – observation 14
512/127800
The slope of the line connecting the lowest and highest values of cost driver is computed using
the following formula:
Slope = Cost Associated with the highest level of cost driver - Cost Associated with the lowest level of cost driver
Highest value of cost driver - lowest value of cost driver
= (146,800 - 127,800) / (872 - 512) = 19,000 / 360 = $52.778
Substitute the slope value in either of the pair of observations to find the fixed cost estimate
1. High driver value observation fixed cost estimate = 146,800 – 52.778*872 = 100,778
2. Low cost observation fixed cost estimate = 127,800 – 52.778*512 = 100,778
The estimate of the cost function using the high low method is
Total cost = 100778 + 52.778*number of units made
Here is a plot of the data showing the high low estimate of the cost function.
The primary advantage of the high low method is that it is easy and straight-forward to apply.
The major disadvantage is that it ignores all the data except the two points used to develop the
cost estimate. This creates the possibility that the end points are not representative of the data
that has been gathered. A second disadvantage is that this approach can only be used with a
single cost driver – in this case number of units made. More on cost estimation with multiple
cost drivers follows below.
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Visual Fit
The second approach using cost data is the visual fit method. In this approach the analyst draws
a line through the data that seems to reflect the relationship between cost and the cost driver.
This approach is a particularly useful as an alternative to the high low method if the end points in
the high low method do not appear to be representative of the other data. This approach is
subjective and reflects the personal judgement of the analyst in fitting the line representing the
cost equation to the data.
Suppose that the analyst chooses the line shown in the figure above on the grounds that it
appears to pass through the centre of data after ignoring the observations associated with the
lower levels of the cost driver on the grounds that there may be cost inefficiencies at lower
production levels. The driver value/cost coordinates of the end points of the line shown in the
diagram below are 872/146800 and 586/139650. The cost estimation equation would be
developed as follows:
Slope = Cost Associated with the highest units observed - Cost Associated with the lowest units observed
Highest units observed - lowest units observed
= (146,800 - 139,650) / (872 - 586) = 7,150 / 286 = $25.00
Substitute the slope value in either of the pair of observations to find the fixed cost estimate
1. High cost observation fixed cost estimate = 146800 – 25*872 = 125,000
2. Low cost observation fixed cost estimate = 139650 – 25*586 = 125,000
The estimate of the cost function using visual inspection is
Total cost = 125,000 + 25*number of units made
Notice the significant difference between the two cost estimates.
High Low Estimate: Total cost = 10,778 + 52.778*number of units made
Visual Inspection Estimate: Total cost = 125,000 + 25*number of units made
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This shows how sensitive these approaches are to the assumptions made when generating them.
Statistical/Regression Approach
We turn now to consider the formal statistical approach to estimating the statistical relationship
appearing in a set of data which is a way of considering all the data (unlike the high low method)
and not relying on subjective judgement (unlike the visual inspection method).
The regression approach fits an equation to the observed data using the criterion of minimizing
the sum of the squared differences between the values predicted by the regression equation and
the original data. This criterion is summarized by the statistic r-square (r2) which is called the
goodness of fit measure.
The first step in applying the regression model is to choose the cost to be estimated (called the
dependent variable because it is assumed to be dependent upon the value of the cost driver(s)).
The second step is to choose the cost driver(s), called the independent variable, which is (are)
assumed to cause the behaviour of the independent variable. (We will consider the approach of
using multiple independent variables later). Note that when use the term cost driver we are
implying that we believe there is a plausible causal relationship between the cost driver and the
dependent variable.
In this case we have chosen the total cost as the dependent variable and number of units made as
the independent variable. This is a plausible relationship. Plausibility is important because we
cannot infer causality from a high goodness of fit (r2). A high goodness of fit only implies a
statistical relationship between the dependent variable and the independent variable(s) and not
causality.
Statisticians use the term spurious correlation to refer to a situation where there is a strong
statistical relationship between two variables but no cause and effect relationship between those
variables. To illustrate how this can happen suppose that event x causes both event y and event z
to happen. As x moves so will y and z and therefore y and z will move together. Someone
might observe y and z moving together and infer that one is causing the other which is not the
case – it is x causing them to move.
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Here is an example that is useful used to illustrate spurious correlation:
Someone observes that the more firefighters there are at a fire the more
damage occurs and concludes that the firefighters cause the damage. Of
course it is the severity of the fire that causes both more firefighters to be
called to the scene and the amount of damage.
So when choosing cost drivers to develop a cost estimation equation we must always be sure to
pick one that makes sense – and that should always be guided by experience of the process.
The third step in using regression is to plot the dependent variable (by convention on the y or
vertical axis) versus the independent variable (by convention on the x or horizontal axis). We do
this to determine where the relationship appears to be linear since the linear regression model
assumes that the relationship between the two variables is approximately linear.
Here is a plot of data that was observed in a study of the labour cost required to produce a
complex piece of electronic equipment.
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This relationship, which reflects a phenomenon called a learning effect, is common in labour
paced assembly operations. This relationship is clearly not linear and using a linear equation to
estimate this relationship would lead to significant errors. Luckily there are fairly straightforward
means of dealing with situations like this. (In fact the equation estimating this relationship is
shown on the graph.) However, discussion of dealing with non linear relationships is beyond the
scope of these notes.
Returning to our Danny Company example, we can see by inspecting the plot of total cost to
units produced that we did when we used the high low method that the relationship is
approximately linear.
The fourth step is to undertake the regression analysis. While there is specialized software for
regression analysis there are reasonable regression tools in most spreadsheet packages such as
Microsoft’s Excel and Open Office’s Calc.
If we enter the data for this problem into an Excel spreadsheet and use Excel to undertake a
regression analysis Excel produces the following output:
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The Estimated Coefficients
The regression model has estimated the following cost equation
Total cost = 113,520 + 40.014*units produced
The fifth step is to interpret the regression results. There are two items in the above output that
we will interpret in these notes.
Goodness of Fit
You will notice that there are three goodness of fit measures that Excel reports for each
regression.
1.
Multiple R which is a measure of correlation between the independent variable
and the dependent variable,
2.
R-square which is the correlation measure squared, and
3.
Adjusted R-square which is the R-square value adjusted for the number of
independent variables. Statisticians believe that the adjusted R-square is the best
measure of association between the independent variable and the dependent
variable. Adjusted R-square is interpreted as the proportion of variability in the
dependent variable that is explained by the independent variable. Following this
convention we will use adjusted R-square measure as the measure of goodness of
fit in our discussions that follow.
So the goodness of fit measure for this regression is 49.52%.
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The t-statistic
The t-statistic is actually used in a formal statistical test of the hypothesis that the coefficient
associated with the independent variable is zero. If the absolute value of the t-statistic is greater
than a critical value we reject the null hypothesis that the true value of the coefficient associated
with the independent variable is zero.
We will not discuss the formal statistical tests in these notes. Instead, we will use the common
approximation (rule of thumb) that if the absolute value of the t statistic is 2 or greater we
conclude that there is a statistically significant relationship between the independent variable and
the dependent variable. In everyday terms what we are saying is that the true value of the
coefficient is not zero and there is a relationship between the dependent variable and the
independent variable (the assumed cost driver).
In this case the value of the t statistic associated with the estimated coefficient is greater than 2
so we conclude that there is a relationship between units produced and total cost.
Here is a summary diagram showing the estimated regression equation (solid line), the high low
equation (dotted line), and the visual fit equation (dashed line).
We can see that the estimated relationships converge on the right hand side at higher values for
the cost driver but diverge substantially at lower values of the cost driver.
Suppose that, as suggested in the discussion of the visual fit, the analyst believes that some other
phenomenon was affecting costs at the two lowest levels of the cost driver. This situation is
handled by regressions using multiple cost drivers.
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Using Multiple Cost Drivers (Independent Variables)
Linear regression will accommodate multiple cost drivers when the cost analyst believes there is
more than one cost driver affecting the value of the dependent variable. Simple regression is the
term used when a single cost driver (independent variable) is used. Multiple regression is the
term when more than one cost driver (independent variable) is used.
After viewing the results of the simple regression model reported for Danny Company above the
cost analyst interviewed production staff and determined that the two low production periods
occurred when the most recently hired production staff were attending a quality control course.
More experienced staff managed the production process during these two periods resulting in
higher levels of efficiency and lower labour costs. The cost analyst decided to add a second
independent variable to account for this situation and prepared a revised data table. As you can
see from the table below the second independent variable is coded with a 0 for a non training
period and a 1 for the training period. If the information is correct the coefficient associated with
the training variable should be negative to account for increased productivity and lower costs
during these training periods.
Here is the regression result using these two independent variables.
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Note that the regression has estimated the following relationship:
Total cost = 30.492*units made – 6,388.40*(1 if this is a training period, 0 otherwise) + 120,964
The adjusted r-square is 54.20% which is an improvement over the simple regression result of
49.52% which we saw earlier in the simple regression.
The t statistics associated with the estimated values of the coefficients associated with the
number of units produced and the training period variable are 2.96 and -1.68 respectively. This
means that the estimated value of the units produced coefficient is statistically significant but the
estimated coefficient for the training period is not. While we can use the regression to predict
total costs it is not reasonable to make inferences about the coefficient associated with the
training period (that is the effect of the training period on total costs). As a practical matter it
would be best to throw out this regression and use the regression using only the units variable.
Other Statistical Tests
There are important tests that statisticians perform, mostly on the error terms (the difference
between the values predicted by the regression equation and the actual values) to determine
whether the estimated regression equation is reliable. While these tests are important for
practicing management accountants, their discussion beyond the scope of this review.
An Example – Estimating Route Time
Step 1 – Determine the Item of Interest – Dependent Variable
Always on Time Courier (ATC) Company is interested in estimating the time required for its
couriers to complete their routes and then to identify the cost of delivering packages to different
customers.
Step 2 – Identify Plausible Time Drivers
After speaking with the drivers the management accountant believes that the time required to
complete the route is determined by (that is the time drivers are): number of packages to be
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delivered, number of stops on the route, and the length of the route. This establishes the
plausibility of these drivers in explaining the total route time – remember evaluative plausibility
is done to avoid identifying a spurious relationship. The following data has been gathered by
sampling what are considered to be the average routes.
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Step 3 – Plot the Candidate Drivers against the Dependent Variable
Here are the plots of the total time against each of the three candidate time drivers.
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The plots of route time versus number of stops and route length appear to show linear
relationships. The plot of route time versus number of packages appears indeterminate or almost
random.
Step 4 – Run the Regression
Here are the results produced by Excel for this regression.
The relationship estimated by the regression is
Route time in minutes = 11.39+1.423*number of packages
+14.761*number of stops+4.550*number of kilometres on route
In practice the analyst would speak with the couriers to determine whether these values seem
reasonable as test of the regression results that uses experience and process understanding.
Step 5 – Evaluate the Results
Goodness of fit
The adjusted r-square is 69.21% which is good.
t-statistics
The t statistics of all the estimated time driver coefficients exceed the rule of thumb value of 2
Conclusion
This is a model that would likely be helpful in planning for route times. Although approximately
30% of the time variability remains unexplained that is likely the random traffic or customer
effects on the total route time.
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An Example – Estimating Overhead Cost
Princeton Metal Works manufactures copper and steel plumbing products. Products are made on
machines in batches to the customers’ orders.
Steps 1 and 2
The plant accountant, wanting to develop a better estimate of overhead to support planning and
product costing, asked plant personnel to help her identify what they felt were the cost drivers for
plant overhead. The plant personnel believed that units made, labour hours, machine hours,
number of batches of products made, and number of products made during the period were all
plausible candidates as cost drivers for plant manufacturing overhead. Over the next several
months the following data was gathered.
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Step 3
There are the plots of the variables identified as possible cost drivers (independent variables) for
manufacturing overhead costs.
None these plots, except the plot of overhead versus the number of products, appear to show
violations of the linearity assumption.
Step 4 – Run the Regression
Here is the regression result provided by Excel.
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Step 5 – Evaluate the Results
There are obvious problems evident in these results. The first and most glaring problem is that
the coefficient estimated for number of units is negative. It is neither plausible nor sensible that
as the number of units made goes up the manufacturing overhead would go down. This is clear
evidence that there is a problem in this regression result. Moreover, the absolute value of the t
statistic estimated for number of units and labour hours are both less than 2.
Usually but not always, a counter intuitive result like an unexpected estimated coefficient sign
occurs when one or more of the independent variables are highly correlated, which is true in this
case. The following correlation matrix shows that the variable units is highly correlated with
both labour hours and number of products.
How to decide what variables to eliminate when there are correlated independent variables (the
rule of thumb is that the absolute value of the correlation should be less than 0.5) is beyond the
scope of these notes. Assume that through a process of elimination the analyst decides to use
machine hours and number of products as the independent variables. The result follows.
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We now have a statistically significant regression equation that explains about 43% of the
variation in the manufacturing overhead. Our estimated equation is
Manufacturing overhead = 123,702 + 153.31*machine hours + 5,594.56*number of products
This estimate would be shown to production personnel for their evaluation, based on their hands
on experience with the production process, of whether this estimate appears to be plausible.
Summary
Good understanding cost behaviour provides important input to many management activities
including budgeting, pricing new products, and performance evaluation. Management
accountants have different tools to estimate costs one of which is the analysis of historical cost
data. Using historical cost data can be problematic for a number of reasons including the
reliability of data and the confidence that users can place in estimated cost behaviour. An
important requirement is that the management accountant conveys to the users of estimates of
cost behaviour the amount of confidence and the potential limitations of these estimates.
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Problems with Solutions
Multiple Choice Questions (note that for questions 1-6, there may be more than one correct
answer)
1. Which of the following statements is/are true about the high low method of estimating cost
behaviour?
a.
b.
c.
d.
Uses all the historical data available
Can be affected by extreme points
Requires a good knowledge of the production process
Requires a good knowledge of product specifications.
2. Which of the following statements is/are true about the account analysis method of
estimating cost behaviour?
a.
b.
c.
d.
Uses all the historical data available
Can be affected by extreme points
Requires a good knowledge of the production process
Requires a good knowledge of product specifications.
3. Which of the following statements is/are true about the engineering method of estimating
cost behaviour?
a.
b.
c.
d.
Uses all the historical data available
Can be affected by extreme points
Requires detailed knowledge of the production process
Requires a good knowledge of product specifications.
4. Which of the following statements is/are true about the visual inspection method of
estimating cost behaviour?
a.
b.
c.
d.
Uses all the historical data available
Can be affected by extreme points
Requires detailed knowledge of the production process
Requires a good knowledge of product specifications.
5. Which of the following statements is/are true about the proper method of handling data
outliers when doing cost estimation?
a.
b.
c.
d.
Outliers should always be eliminated
Outliers should never be eliminated
Outliers should not be eliminated if their cause is known
None of the above.
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6. Assuming that over or under applied overhead are charged to cost of goods sold, which of the
following statements is/are true about the effect of allocating fixed manufacturing costs to
production using a predetermined overhead rate on data used for cost estimation?
a.
b.
c.
d.
There will be no effect
There will be an indeterminate effect
The estimate of fixed cost will be affected
The estimate of variable cost will be affected.
Questions 7-10 are based on the following information:
Beaver Fine Foods is developing a new product for its line of food entrees. The estimated
variable costs for the new product are $0.95 for materials and $0.35 for labour. Based on the
experience with comparable products, management estimates that the new product will consume
0.03 hours of machine time.
Management wants to determine the manufacturing overhead costs that should be estimated for
this new product. Manufacturing overhead data was accumulated and after some analysis
decided to use manufacturing overhead as the dependent variable and machine hours as the
independent variable. Excel produced the following regression equation result:
7. Given these results would you conclude
a. The regression results are significant and should be accepted
b. The regression results are not significant and should not be accepted
c. The regression results should not be considered reliable because the sample size is too
small
d. The regression results should not be used because only one independent variable is used
to estimate total manufacturing cost.
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8. What is the best measure of goodness of fit in the regression results?
a.
b.
c.
d.
10.02
15.50
88.44%
None of the above
9. Assume that management estimates that the total manufacturing overhead in the upcoming
period will be $650,000 and that the expected number of machine hours will be 5,000. Based
on these expectations management has decided to allocate fixed manufacturing overhead to
production at the rate of $130 ($650,000/5,000) per machine hour. If management follows
this approach, what total cost per unit will it estimate for this new product?
a.
b.
c.
d.
$1.39
$2.89
$6.79
None
10. What variable cost would you estimate for the above product?
a.
b.
c.
d.
$1.39
$2.89
$6.79
None
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Problem 1
Bev’s Trattoria serves a varied menu of Italian food. A particular favourite is the pasta meat
sauce. The following ingredients are used to make 10 litres of the meat sauce:
2 kilograms of ground beef @ $4.95 a kilogram
2 large onions (approximately 0.6 kilograms each) @ $1.96 per kilogram
2 Green peppers (approximately 0.1 kilograms each) @ $2.19 per kilogram
2 Celery stalks (celery is purchased in a bunch that contains 5 stalks) @ $2.19 a bunch
2 Garlic cloves (garlic is purchased in a bulb that usually contains 8 cloves) @ $3.00 a bulb
1 large can tomato juice @ $2.29
1 large can tomato sauce @ $1.49
1 can tomato paste @ $1.19
Approximately $0.35 for salt and pepper
It takes a part time employee who is paid $8.00 per hour about 35 minutes to prepare the
ingredients which are put into a large pot and simmered for 4 hours. The gas burner is estimated
to consume approximately $1.40 of natural gas per hour.
Bev follows the common restaurant guideline that the food cost ingredients should be between
25 and 30% of the price of each menu item and has chosen the midpoint of 27.5% for pricing this
sauce in any menu item where it is used.
Required a. Use the engineering method to compute the variable cost of producing a serving of the sauce
if each serving amount is 0.2 litres.
b. What is the target price of a serving of sauce given the pricing formula that Bev uses? Round
to the nearest 2 decimal places.
Problem 2
Jacques, an enterprising and long time resident of Northern Ontario, owns and operates a thriving
but illegal business, Jacques’ Discount Beverages, whose sole product is swish.
Jacques makes swish in used Kentucky whiskey barrels (preferably oak) which he acquires in
truckload lots from US distilleries. The production process consists of filling a barrel with 1 litre
of grain alcohol, a cup of sugar, and 20 litres of water. The brew is allowed to “age”, as Jacques
calls it, for 3-4 weeks with the barrel being turned (swished) daily. (The swishing allows the
mixture to extract some of the whiskey that was absorbed into the barrel.) The result is a potent
beverage reputed to cause occasional blindness but nevertheless is in high demand from Jacques’
clients. After two uses, Jacques saws the barrel in half and sells the halves to a local gardening
centre for their customers to use as planters. The planters are in high demand because of their
remarkable effect on producing healthy and robust plants.
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Although all swish is made the same way variations in the barrels produce variations in the taste
of the swish and the taste determines the product’s price. Jacques believes that it is the source of
the barrels and not simple variations in the barrels themselves that determines the taste.
Following up on his hunch Jacques has gathered data on 100 batches of swish. Jacques treated
the price received per litre of the swish as the dependent variable and the distillery where Jacques
got the barrel as the independent variable. There were two distilleries so Jacques coded a 0 if the
barrel was obtained from one distillery and 1 if the barrel was obtained from the other.
Here is the Excel result run by one of Jacques’ clients who was promised several litres of product
in exchange for his services.
Required Do these results support Jacques’ hypothesis that it is the source of the barrel that affects the
quality and therefore the price of the swish?
Problem 3
The factory accountant at Scotland Manufacturing has developed data to help her estimate the
behaviour of manufacturing overhead. The accountant has developed two sources of data – an
analysis of the manufacturing overhead account and activity and cost data over the last 10
periods. Since the production process at Scotland Manufacturing is labour driven the accountant
believes that labour hours is the most appropriate driver to estimate manufacturing overhead.
Here is the data for the last ten periods and the plot of the data.
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Here is the result of the account analysis for the most recent period:
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Required a.
b.
c.
d.
Develop an estimate of manufacturing overhead using the high low method.
Develop an estimate of manufacturing overhead using account analysis
Would regression analysis be appropriate in this case? Explain.
Which of the estimates you developed in a) and b) do you think is more reasonable?
Why?
Module 3 – Management Accounting 6
Problem 4
Dora Manufacturing operates a number of plants all of which produce the same mix of mother
boards for computers. The management accountant in head office wants to develop an equation
to predict manufacturing data and believes that labour hours is the primary cost driver since
production involves a lot of labour and is therefore labour paced.
The management accountant has developed a data base of xx observations of labour hours and
manufacturing overhead and has plotted the data with the following result.
Excel produced the following regression output.
The management accountant observed “This regression analysis produced a good result with and
estimated coefficient that has a t statistic that is greater than 2. However, it is clear from the plot
Module 3 – Management Accounting 6
that there are seven observations that are outliers. I am going to rerun the regression with these
seven observations omitted.” This was the result of the second regression analysis.
Required a. Which regression equation would you use? Explain why.
b. Suppose that the Vice President Manufacturing sees this data and observes that the seven
observations that were deleted in the second regression were the seven observations taken at
one plant. Would this change your response in part a)? Explain why.
Module 3 – Management Accounting 6
Problem 5
A cost analyst at Downeast Engineering is using regression analysis to develop an equation for
manufacturing overhead. The cost analyst has identified two possible cost drivers – units
produced and machine hours. The analyst has run three regressions with the following Excel
output.
Using units as the independent variable
Module 3 – Management Accounting 6
Using machine hours as the independent variable
Required a. Choose the regression result that you think is best and explain why you think it is the best.
b. What is the manufacturing overhead equation predicted by the regression equation that you
chose?
Module 3 – Management Accounting 6
Problem 6
Panther Brewery produces a single product, a pilsner beer. Panther Brewery competes in the
discount beer market which is extremely competitive resulting in highly volatile sales.
The product is priced at $1 per bottle which is the price in this market niche. The marketing
manager believes that sales volatility is affected by two factors, Panther’s advertising and the
actions of competitors in this market niche.
The marketing manager believes that advertising has the greatest effect in the current period but
also has residual effects in the two following periods.
The marketing manager has constructed a competitive index that reflects the advertising
activities of competitors. The index value ranges from 1 reflecting low competitor advertising
activities to 9 reflecting very high competitor advertising activities.
Sales and advertising data were gathered for 30 periods and a regression was run. The following
is the Excel result.
Required:
a. Based on these results would you agree:
i. That advertising does have a residual (lagged) effect on sales.
ii. That the index of competitor advertising activities is a useful variable to predict sales
b. Based on these results what are the effects of advertising (both Panther’s and its competitors’
on sales?
Module 3 – Management Accounting 6
SOLUTIONS
Multiple Choice Questions
Question 1
a.
b.
c.
d.
Uses all the historical data available (false only uses two points)
Can be affected by extreme points (true if either end is extreme)
Requires a good knowledge of the production process (false only looks at the data)
Requires a good knowledge of product specifications.(false only looks at the data)
Question 2
a. Uses all the historical data available (false only looks at current account balances)
b. Can be affected by extreme points (possibly but since all current data is considered the effect
of extreme points will be mitigated)
c. Requires a good knowledge of the production process (true since this is the basis for
classifying the cost as fixed or variable)
d. Requires a good knowledge of product specifications (false the focus is only on costs)
Question 3
a.
b.
c.
d.
Uses all the historical data available (false since this approach usually prospective costs)
Can be affected by extreme points (false since this is based on single point values)
Requires detailed knowledge of the production process (true)
Requires a good knowledge of product specifications (true)
Question 4
a. Uses all the historical data available (true)
b. Can be affected by extreme points (possibly but the visual method usually allows the analysis
to discount these)
c. Requires detailed knowledge of the production process (false)
d. Requires a good knowledge of product specification (false)
Question 5
a.
b.
c.
d.
Outliers should always be eliminated (false only if a cause can be determined)
Outliers should never be eliminated (false can be if a cause can be determined)
Outliers should not be eliminated if their cause is known (false the opposite is true)
None of the above (true)
Module 3 – Management Accounting 6
Question 6
a.
b.
c.
d.
There will be no effect (false – see part d))
There will be an indeterminate effect (false – see part d))
The estimate of fixed cost will be affected (false – see part d))
The estimate of variable cost will be affected (true – using a predetermined overhead rate to
allocate fixed manufacturing overhead to production will cause the estimated variable cost to
increase by the amount of the rate. Moreover if over or underappled overhead are charged
directly to cost of goods sold the values of manufacturing overhead each period will be
misstated by the amount of the over or underapplied overhead with the consequential effect
on the estimated cost equation.)
Question 7
a. The regression results are significant and should be accepted (true – goodness of fit is
reasonable and the t-statistic associated with the estimated coefficient is greater than 2.
b. The regression results are not significant and should not be accepted (false – see a))
c. The regression results should not be considered reliable because the sample size is too small
(false – a sample size of 30 is reasonable)
d. The regression results should not be used because only one independent variable is used to
estimate total manufacturing cost. (false – the goodness of fit is reasonable and there is no
other evident cost driver)
Question 8
The best measure is the r-square adjusted value which is 77.44%
Question 9
The cost will be .95 + .35 + (52.97 * 0.03) + (130 * 0.03) = $6.79
Question 10
The cost will be .95 + .35 + (52.97 * 0.03) = $2.89
Module 3 – Management Accounting 6
Problem 1
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Problem 2
The price equation estimated by the regression analysis is
Price = $2.99 - $0.26 * distillery code
The expected price is $2.99 for the product made in the barrels obtained from the distillery that
was coded as 0 and $2.73 ($2.99 – 0.26) if the product is made in barrels obtained from the
distillery that was coded as 1. The estimated coefficient is significant implying a strong result
and that Jacques’ intuition is correct. However, the estimated equation has an adjusted r-square
of 38% implying that there are other factors, possibly the season or the activities of Jacques’
cousin, a competitor, that are affecting the price.
Module 3 – Management Accounting 6
Problem 3
a.
The observations with the highest and lowest values of the cost driver are, respectively,
observations 1 and 6 and the paired values are (1564, 268121) and (1268, 259405).
Therefore the estimate of the slope (variable cost) of the graph is:
Variable Cost = Cost at highest driver value - Cost at lowest driver value
Highest driver value - Lowest driver value
= ($268,121 - 259,405) / (1,564 - 1,268)
= $29.45
Substitute this value in either of the observations to get the fixed cost
Fixed cost = 268,121 – 29.45*1,564 = $222,068, or
Fixed cost = 259,405 – 29.45*1,268 = $222,068
The estimated cost equation is
Manufacturing overhead = 222068 + 29.45 * number of labour hours
b.
Total Variable Costs
Cost Driver Activity Level
Variable Cost per LH
Total Fixed Costs
$63,637
1415
$44.97
$199,869
Therefore the estimated manufacturing overhead equation using the account analysis
method is
Manufacturing overhead = 199,869 + 44.97*number of labour hours
c.
It would be unreasonable to use regression analysis in this case since there are too few
observations to develop a reliable estimate
d.
Visual inspection suggests that high low estimate may understate the slope of the cost
line because the line would fall under many of the data points (that is the line should be
rotated clockwise). In this case the account analysis estimate seems more reasonable.
Module 3 – Management Accounting 6
Problem 4
a.
Judiciously pruning outlier data will always improve goodness of fit but improving
goodness of fit is not a sufficient reason to eliminate data without an adequate
explanation of what caused the outlier. Eliminating data without explanation creates a
false confidence in the predictive ability of the equation since the situation that
produced the outliers could reoccur.
b.
Identifying the source of the variation is sufficient reason to eliminate the data since the
cause is understood. Another approach is to add a second independent variable with a
value of 1 if the observation is from this plant that produces the outliers and 0
otherwise. The excess cost will load on this new independent variable as shown in the
following result.
This regression suggests the following equation for manufacturing overhead
Manufacturing overhead = 117,889 + 46.44 * labour hours + 12,120 (if the plant is coded as 1)
Module 3 – Management Accounting 6
Problem 5
a.
Pick result 3 the regression using only machine hours as the independent variable.
Although the regression with both units and machine hours has the highest adjusted rsquare the estimated coefficient associated with units produced is not significant. This
means that although this regression equation has the strongest predictive power for total
manufacturing overhead the coefficient estimated for units produced would not produce
reliable results if it were used separately to make inferences about how units produced
affects total overhead.
The regression equation estimated using units produced has the lowest r-square and is
inferior to the regression equation estimated using machine hours although both
regression equations have estimated coefficients with t statistics greater than 2. What
might be happening here is that different units require different amounts of machine
hours and it is the number of machine hours that is driving manufacturing overhead.
b.
Manufacturing overheard = 264,299 + 116.80*machine hours
Problem 6
a.
i.
ii.
b.
The regression has estimated coefficients for all the advertising levels and all are
significantly (statistically) different from zero. Therefore the manager’s
hypothesis is supported.
The estimated coefficient associated with the index of competitors’ advertising
levels is statistically significant which supports the relevance of the manager’s
index in predicting sales.
Given these results the estimated effect on sales of the various variables are:
i.
Current sales will increase by $20.94 for every dollar of advertising in the current
period
ii.
Current sales will increase by $10.36 for every dollar of advertising in the last
period
iii.
Current sales will increase by $1.04 for every dollar on advertising in the second
previous period
iv.
Current sales will decrease by $11,191,975.44 for each unit increase in the
competitor index the marketing manager has created.
Module 3 – Management Accounting 6
6.
Activity Based Costing
Learning Objectives
After completing this chapter you will understand and be able to explain:
1. The critical design choices management accountants make when designing costing
systems.
2. The perspective of activity based costing (ABC) systems (a decision oriented approach)
and how that differs from conventional costing systems (a responsibility oriented
approach).
3. How and why activity based costing systems provide an improved potential for costing
system accuracy.
4. The organization conditions under which activity based costing systems have the
potential to improve costing accuracy.
Costing System Architecture
The following diagram provides a simple schematic of the critical design issues and choices in
all costing systems.
Module 3 – Management Accounting 6
Yes
No
Is the
cost
direct?
Indirect cost pool
Design indirect cost
pool structure and
assign indirect cost to
the appropriate cost
pool
Indirect cost pool
Indirect cost pool
Choose the cost driver and the allocation rate for each indirect cost pool
and allocate the costs from each indirect cost pool to the cost objects
Assign cost to the
appropriate cost
object
The various cost
objects
Step 1 – Identifying Costs as Direct or Indirect
The first step in costing system design is to develop a method that allows a cost to be identified
as direct or indirect. If you would like to refresh your understanding of direct and indirect you
can return to the material in Chapter 2. As we discussed in Chapter 2, if the cost is identified as
direct to a cost object it is assigned to that cost object. If the cost is indirect, it is assigned to an
indirect cost pool.
Step 2 – Designing Indirect Cost Pools
The second step in costing system design is to develop the system of indirect cost pools. Chapter
3 provided some initial insights into approaches to designing indirect cost pools and we will now
develop those ideas in more detail.
We need to remember that indirect cost pools will be required for both manufacturing and non
manufacturing costs. In the past many firms used indirect cost pools only for manufacturing
costs because their accounting systems were oriented to supporting financial accounting. In
financial accounting virtually all non manufacturing costs are charged to the income statement as
current period costs. This promoted the design and use of single plant wide indirect cost pools to
accumulate indirect manufacturing costs.
Module 3 – Management Accounting 6
In the early part of the 20th century as organizations became larger decision making authority and
responsibility were delegated down the organization hierarchy creating a need for accountability
arose. Within the factory, department managers were assigned the responsibility to control costs.
This focus on accountability, in turn, led to an interest in designing cost centres and therefore
indirect manufacturing cost pools around various departments within the plant such as receiving,
machining, assembly, finishing, and shipping. The focus was on accumulating cost by
department so that the accumulated costs could be compared to some budget or standard.
Driven by competitive issues, particularly beginning in the 1980s, managers began to demand
better cost information – not only about the behaviour of indirect manufacturing costs but about
other indirect costs such as product development and customer related costs – such as order
taking and order processing. This led not only to an interest in developing different indirect
manufacturing cost pool designs but also the design and use of indirect cost pools to accumulate
non manufacturing costs.
Objective in Indirect Cost System Design
The objective in indirect cost system design is to develop better cost information to support
organization decision making. Chapter 5 introduced some of the major decision making support
roles of cost information. The most widely touted roles being to improve accuracy in forecasting
budgets for budgeting and product pricing and supporting efforts to identify opportunities for
cost reduction.
Improved cost information allows decision maker to avoid opportunity costs caused by faulty
cost information. Examples of opportunity costs caused by bad cost information include the
losses caused by:
1. Continuing to make a product that appears to be profitable but is not.
2. Inappropriate pricing in cost plus environments such as contract pricing.
3. Failing to recognize opportunities for process improvement.
4. Inappropriate budget projections creating cash flow problems
5. Inappropriate product mix choices when allocating constrained capacity.
The objective of costing system
improvements is not to increase cost
accuracy at any cost. The consensus
amongst experts seems to be that the
incremental cost of designing and
operating a costing system increases
exponentially in the system’s
complexity and the marginal value
provided by improved costing
system accuracy declines
logarithmically. The accompanying
graph summarizes this conventional
Module 3 – Management Accounting 6
wisdom and the point at which the marginal benefit and marginal cost of increased complexity
are equal.
Recall that costing issues by designing inappropriate indirect cost pools since direct costs should
always be assigned to the appropriate cost object. Therefore we take as given in the following
discussion that the focus is on improving the design of the indirect cost pools.
How Do We Know When the Costing System Needs Improvement?
You Know you Need a New Costing System When
Vendor bids are lower than expected
Functional managers want to drop seemingly
profitable lines.
Profit margins are hard to explain.
Hard-to-make products show big profits.
Departments have their own cost systems.
You have a high-margin niche all to yourself.
Competitors’ prices are unrealistically low.
Customers don’t mind price increases.
The results of bids are hard to explain.
Based on an extensive study of costing
systems Robin Cooper prepared a list
of symptoms of a costing system that
is producing inaccurate information
causing inappropriate decision
making. This list is shown in the
accompanying text box.
As an exercise, see if you can explain
why each of these in the text box
suggests a costing system that has
gone awry.
Source: Harvard Business Review, Jan-Feb 1989
An Example
At this point it is useful to develop an example to illustrate how costing systems can produce
inaccurate and misleading cost information.
Drumbo Aerospace produces three products all aircraft components. The following is a
summary from a recent production period.
Module 3 – Management Accounting 6
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Initially the factory accountant allocated indirect manufacturing costs equally to all units of
product using a rate of $37.56 ($586,000/15,600) per unit. Product 1 sales manager complained
arguing that the indirect manufacturing costs should be allocated based on machine hours as that
was a more relevant cost driver for indirect manufacturing costs.
Following up on this idea, the factory accountant computed a rate per machine hour as follows
Total Indirect Manufacturing Costs / Total Machine Hours
= $586,000 / 1,800
= $325.56
The indirect manufacturing cost to be allocated to each unit of production was computed as
follows
machine hour rate * machine hours used by product group
number of units in the product group
For example, the calculation for product 3 was:
($325.56 * 400) / 2,300
= $56.62
Drumbo marked up a product’s total cost by 50% to compute its selling price. Recently several
customers have complained arguing that prices seem too high based on what competitors have
offered.
Module 3 – Management Accounting 6
After discussions with factory engineers the factory accountant believed that there were three
major activities in the factory:
1.
Batch related activities which included moving work in process about the plant and
setting up equipment for production runs.
2.
Inspection activities which involved subjecting parts to laser and x-ray inspection.
3.
Machining activities required to produce the products.
With this insight the factory accountant developed the following information:
Product
1
2
3
Cost Driver Units
Units
Produced
Batches
Inspection
Hours
Machine
Hours
8,600
4,700
2,300
20
30
50
100
500
200
800
600
400
15,600
100
800
1,800
$16,000
$120,000
$450,000
$160
$150
$250
Total cost
Cost / Cost Driver Unit
This exhibit shows the cost driver and the rate per unit of the cost driver identified using this
data.
Finally the indirect manufacturing cost to be allocated to each unit of production was computed
and is shown in the following table as the activity rate.
For comparison purposes the rate using units produced and machine hours as the cost drivers are
also shown.
Module 3 – Management Accounting 6
For example the indirect manufacturing cost assigned to product 2 is computed as follows:
Total Indirect manufacturing cost allocated to product 2 =
Number of batches * cost driver rate per batch +
Number of inspection hours * cost driver rate per inspection hour +
Number of machine hours * cost driver rate per machine hour =
30*160 + 500*150 + 600*250 = $229,800
Indirect manufacturing cost per unit of product 2 = 229,800/4,700 = $48.89
You should verify your understanding of this approach by verifying the indirect manufacturing
costs shown for products 1 and 3.
This approach to costing reflects the recognition that it is activities the organization undertakes to
produce goods and services that create costs and this focus on using activities as the cost driver
for indirect costs led to this approach being called activity based costing. The underlying idea is
that indirect cost allocations should be based on cause and effect relationships and that it is the
level of activities performed in an organization that determines, in the long run, the level of
indirect costs.
This idea is readily illustrated in a diagram that has come to be known as the ABC cross.
This diagram summarizes the idea that the production of a cost object creates the need to
undertake activities which, in turn, create a demand for resources. The cost driver reflects the
Module 3 – Management Accounting 6
rate at which a cost object consumes an activity and the resource driver reflects the rate at which
an activity consumes a resource. This is called the cost view of what is going on in the
organization and is shown as the vertical plane of the ABC cross. The horizontal plane reflects
the process view which reflects that cost drivers draw on activities and are summarized by
performance measures that assess how well the work is being done. Therefore the vertical view
is the control or performance measurement view of the process.
The Drumbo example illustrates how cost distortions arise. The setting in the Drumbo example
is that expensive indirect resources are used at different rates by the different cost objects. If the
costs of these indirect resources are grouped together into a single indirect cost pool and
allocated in proportion to some quantity measure – such as units produced, machine hours, or
labour hours, the high volume products will tend to pick up more than their fair share of costs if
resource use is not proportional to volume.
To illustrate this important idea consider an organization that produces 100,000 units of product
1 and 100,000 units of product 2. Product 1 is produced in batches of 1000 units and product 2 is
produced in batches of 500 units. Therefore 100 batches will be used to produce product 1
(100,000/1,000) and 200 (100,000/500) batches will be used to produce product 2. If the cost of
processing a batch (setup costs and costs of moving work in process about the factory) are $400
per batch, product 1 creates $40,000 ($400 * 100) of setup costs and product 2 creates $80,000
($400 * $200) of step costs. The total batch related costs will be $120,000 (40,000 + 80,000).
Now if these batch costs, which are indirect manufacturing costs, are allocated in proportion to
units produced (or any volume measure such as labour hours or machine hours) then each
product will be allocated $60,000 of batch costs resulting in product 1 being overcosted by
$20,000 ($80,000 - $60,000) and product 2 being undercosted ($60,000 - $80,000).
The ABC Cost Hierarchy
ABC proponents have developed what they call the ABC cost hierarchy which consists of the
following elements
•
Unit level (costs that vary directly with the level of production such as factory supplies –
commonly called variable manufacturing costs)
•
Batch level (examples include setting up machines for a production run and shipping a
truckload of products)
•
Product sustaining (examples include advertising to support a product and developing and
implementing a product design change)
•
Facility sustaining (examples include plant depreciation and the factory manager’s salary) –
these costs are not usually allocated since there is no apparent cause and effect relationship
with activity levels.
•
Customer sustaining (examples include the cost of the sales representative visiting the
customer and special customer shipping requirements)
•
Organization sustaining (examples include the fees paid to the Board of Directors members
and depreciation on the administrative office suite) – these costs are not usually allocated
since there is no apparent cause and effect relationship with activity levels.
Module 3 – Management Accounting 6
1031-2 05 Allocation of Indirect Costs
Indirect Costs must be accumulated in appropriate
indirect cost pools, reflecting a contractor's
organizational or operational lines and these pools
subsequently allocated to contracts in accordance
with the following two principles:
the costs included in a particular indirect cost
pool should have a similarity of relationship
with each contract to which that indirect cost
pool is subsequently distributed; further, the
costs included in an indirect cost pool should
be similar enough in their relationship to
each other that the allocation of the total
costs in the pool provides a result which
would be similar to that achieved if each cost
within that pool were separately distributed;
The insight provided by this cost
hierarchy is that most of the cost
drivers for these costs are not volume
related. Therefore accumulating these
costs in single cost pool and
allocating these costs to products
using a volume based driver will
cause costing distortions.
In summary indirect cost pools should
be designed so that all the costs in an
indirect cost pool have the same cost
driver and costs should be allocated
from that indirect cost pool to cost
objects using that cost driver. The
attached excerpt from the
Government of Canada’s Contract
Costing Principles 1031-2
summarizes this idea well.
the allocation basis for each indirect cost pool
should reflect, as far as possible, the causal
relationship of the pooled costs to the
contracts to which these costs are distributed.
Activity Based Costing Example
Danny Company produces two versions of a single product – standard and deluxe. Here is a
summary of the most recent period’s activities.
Investigation of these results establishes three facts:
1. Indirect manufacturing cost, which totals $2,500,000 for this organization, is currently
being allocated to units using direct labour costs based on the observation that production
Module 3 – Management Accounting 6
in the plant involves a lot of manual assembly and therefore is labour paced. Since the
regular product comprises 75% (150,000/(150,000+50,000) of the total direct labour cost
the regular product is allocated 75% of the total indirect manufacturing cost (75% *
2,500,000).
2. Prices as set by marking up manufacturing cost per unit by 70%, which is standard
practice in this industry.
3. While sales of the regular product continue to exceed expectations, sales staff is reporting
difficulty in maintaining sales volumes of the deluxe product and have been pushing for a
price decrease on the deluxe product.
The plant manager attended an ABC seminar, concluded that the current costing system may be
deficient, and ordered a study of plant costs. The study reported the following results.
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The plant manager has asked you to recast the manufacturing cost to reflect the ABC perspective
on costing.
The first step is to compute the indirect manufacturing cost per cost driver unit. To do this
divide the total cost in each indirect cost pool by the total number of cost driver activity units
associated with that pool.
Here is the result
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We now have the cost per unit for each cost driver. With this information we can now reallocate
the indirect manufacturing costs to the two products. Here is the allocation for the regular
product:
Materials handling: 800 moves * $500 per move = $400,000
Module 3 – Management Accounting 6
Production support: 100 production runs * $8,125 per production run = $812,500
Shipping: 500 shipments * $1,000 per shipment = $500,000
Here is the completed table for both products. You should take a few moments and verify the
calculations for the deluxe product.
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This example illustrates a common distortion where a high volume product that puts relatively
fewer demands on production activities than a lower volume product ends up, in a volume based
allocation system like direct labour hours, being overcosted. Here are the percentages of activity
units demanded by each product underlying this production schedule.
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Another Activity Based Costing Example
Gene’s Foods (GF) is a wholesale distributor of ethnic foods. GF has three groups of customers:
supermarket chains, convenience store chains, and individual high end food stores. Here is a
summary of operations for the most recent period. Indirect overhead is allocated to each
customer group based on cost of merchandise sold which is taken as a good measure of the
activities involved in handling customer orders.
Module 3 – Management Accounting 6
For several years the sales manager has been arguing that GF should focus on the convenience
store and high end store segments and phase out its unprofitable supermarket business.
Patricia Conroy, the company President, is leery about this suggestion based on comments,
primarily relating to good and bad customers, she has heard from various staff members.
Based on her intuition Patricia ordered a study of the overhead costs allocated to the customer
groups. The study produced the following results.
Given this information was Patricia’s concern about the sales manager’s recommendation
justified?
We can begin this analysis by developing an activity summary like the following.
Module 3 – Management Accounting 6
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This exhibit confirms what Patricia has been hearing from the staff. GF has been using cost of
merchandise sold as a proxy for activities when allocating indirect costs while the demand for
activities by the various groups differs substantially from this proxy. The pattern is that the
smaller customers make smaller and more frequent orders and place relatively more demands on
order picking, shipping, and invoicing and adjustments.
Now that it looks like ABC will give us a different picture, we can calculate the cost per unit of
the cost driver for each of the activities.
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Module 3 – Management Accounting 6
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(You should take the time to check your understanding of the ABC calculations by verifying the
overhead allocations. The calculations follow the same process that was used in the first
example.)
For example, the overhead allocations to Supermarkets were determined as follows (remember
the numbers in the above table reflect Excel level significance):
Order taking:
500 * 5,833.33 = $2,916,667
Order picking:
100 * 8,510.64 = $ 851,064
Shipping: 300 * 10,476.19 = $3,142,857
Invoicing: 650 * 6,578.95 = $4,276,316
Patricia’s intuition is confirmed! The two smaller customer groups are placing excessive
(relative to the supermarkets) and costly demands on the system. It is now up to Patricia to
decide what to do. (One approach is to charge customers for each of the activities to try to
promote less costly behaviour on their parts.
Conclusion
Activity based costing tries to model the cause and effect relationship between activities
undertaken to produce a good or service and the cost of those activities. The objective is to
provide improved cost information for decision making. However these ABC costing systems
are expensive to design and maintain so organizations must decide whether the costs of these
systems are justified by the benefits provided by improved decisions resulting from the ABC
costs.
Module 3 – Management Accounting 6
Problems with Solutions
Multiple Choice Questions
1.
Which of the following represents a major difference between activity-based costing
(ABC) and traditional product-based costing?
a. ABC accumulates indirect costs in many cost pools whereas traditional product-based
costing accumulates indirect costs in one or a few cost pools.
b. ABC assigns overhead costs based on cost drivers whereas traditional product-based
costing assigns overhead costs using cost application bases that are not cost drivers.
c. ABC assigns overhead costs based on both financial and non-financial cost drivers
whereas traditional product-based costing assigns overhead costs based on financial
cost drivers only
d. ABC uses indirect application bases as cost drivers whereas traditional product-based
costing uses direct cost application bases as cost drivers.
e. None of the above
2.
Activity-based costing in service organizations should be considered if
a. operating personnel have little faith in the accuracy of the existing cost information.
b. they have a widely diverse set of operating activities.
c. services offered change frequently over time.
d. all of the above are true
e. only a and c above are true.
Module 3 – Management Accounting 6
The following information is for questions 3 - 4:
Scissors Inc. is a manufacturer of scissors. The company has always used a plant-wide rate for
allocating manufacturing overhead to its products. The plant manager believes it is time to
change to a better method of cost allocation. The accounting department has been able to
establish some new relationships between production activities and the manufacturing overhead.
They are as follows:
Activity
Material handling
Assembly
Inspection
Cost Driver
Allocation Rate
Number of parts
$ 4 per part
Labour hours
Time Item is at inspection station
$40 per hour
$ 6 per minute
The previous allocation method is based upon direct manufacturing labour hours, and if that
method is used the rate is $400 per labour hour.
3. What are the indirect manufacturing costs per scissors assuming the traditional method is
used and a batch of 1,000 scissors were produced? The batch requires 2,000 parts, 20
direct manufacturing labour hours, and 30 minutes of inspection time.
a. $8.00
b. $9.80
c. $8,000.00
d. $8,980.00
e. none of the above
4. What are the indirect unit manufacturing costs of a batch of 100 scissors assuming the
activity base method is used? The batch requires 200 parts, 12 direct manufacturing
labour hours, and 5 minutes of inspection time.
a. $8.00
b. $13.10
c. $48.00
d. $1,310.00
e. none of the above
Module 3 – Management Accounting 6
5. Which costs not be allocated in an ABC costing system?
a. Product-sustaining costs
b. Facility-sustaining costs
c. Batch-level costs
d. Unit-level costs
6. Which one of the following is NOT one of the ABC cost hierarchy?
a. Customer sustaining
b. Facility sustaining
c. Fixed costs
d. Batch level costs
7. Which of the following would NOT be an example of an organization sustaining cost?
a. The Chief Executive Officer’s salary
b. Insurance on the manufacturing facility
c. Legal department costs
d. Annual fees paid to the external auditors
8. Which of the following would NOT be a cost that would be allocated using ABC?
a. The cost of wood used in a factory making furniture.
b. Costs associated with handling customer complaints
c. The costs of heating a batch of steel
d. Product advertising
9. Which of the following statements about ABC is TRUE?
a. ABC will always produce more accurate costs than a costing system using a
single indirect cost pool.
b. ABC can be used for non-manufacturing costs.
c. ABC costing systems are only useful in manufacturing organizations.
d. The benefits of an ABC system will always outweigh its costs.
Module 3 – Management Accounting 6
10 Which of the following would NOT be an appropriate cost driver for assigning batch
related costs to a product?
a. The number of hours spent moving a batch around the factory floor
b. Number of hours spent setting up for the product
c. Number of set ups done for the product
d. The number of direct labour hours needed to make the product
Module 3 – Management Accounting 6
Problem 1
There on Time (TOT) is provides regional courier service in Eastern Canada. Although sales
have been increasing profits have been following. The controller Dana Strict has ordered a cost
study.
An exhaustive cost study resulted in identifying the following major activities at TOT.
1.
2.
3.
4.
Pick up activities
Sorting activities
Transportation activities
Delivery activities
Further investigation reveals the following cost estimates.
1. Cost to pick up a single parcel at an urban location averaged $5.00 plus $0.20 per parcel
picked up. Cost behaviour in rural locations averaged $8.00 plus $0.20 per parcel.
2. At the hub, parcels were sorted either automatically by machines or manually depending
on the nature of the parcel and any special handling requirements. The cost per parcel
sorted automatically was $1.00 and the cost of a parcel that required manual sorting cost
$6.00.
3. Parcels were transported either by ground or air. The average cost of an air shipment was
estimated as $12 per unit and the average cost of a ground shipment was estimated as
$1.50
4. The cost of delivering shipments averaged $2.00 per parcel in urban locations and $3.00
per unit in rural locations.
5. The parcel weight affects the costs of all activities. For convenience parcels were
organized into three groups: 1 kilogram or less, between 1 and five kilograms, and more
than five kilograms. The additional costs created by these three weight groups were:
$0.50, $2.00, and $9.00 respectively.
Required:
With the above information estimate the total costs of each of these shipments:
a. A shipment of 1,000 parcels was picked up at a warehouse in a rural location. 40% of the
parcels required manual handling during sorting. 80% of the parcels went by ground.
90% of the parcels were delivered to urban locations. The distribution of 1, 1 to 5, and
over 5 kilogram parcels was 60%, 35%, and 5%.
b. Two shipments, each of 500 parcels, were picked at two warehouses – one in an urban
and the other in a rural location. 10% of the parcels required manual handling during
Module 3 – Management Accounting 6
sorting. 50% of the parcels went by ground. 60% of the parcels were delivered to urban
locations. The distribution of 1, 1 to 5, and over 5 kilogram parcels was 90%, 10%, and
0%.
c. A shipment of 1,000 parcels was picked up at a warehouse in an urban location. 0% of
the parcels required manual handling during sorting. 0% of the parcels went by ground.
90% of the parcels were delivered to urban locations. The distribution of 1, 1 to 5, and
over 5 kilogram parcels was 70%, 30%, and 0%.
Problem 2
Down East Consulting (DEC) provides consulting services to its clients. For planning purposes
DEC divides consulting jobs into three groups: simple, medium, and complex. DEC uses four
staff classifications for people who work on these jobs: support, analyst, manager, and nonparticipating partner. Here are the average time (in days) required by each type of consulting job
of each of the four staff classifications.
The following table summarizes the number of employees in each group, the total number of
days of work available in that group, and the salary paid to each employee in the group.
Required a. Suppose that DEC develops a charge rate per day by summing all the salaries that are
paid to all employees and dividing that total by the total days provided by all employees.
Then for each job the cost allocated equals the number of days worked in the job by all
employees multiplied by the rate. Compute the cost allocated to each job using this
approach.
Module 3 – Management Accounting 6
b. Suppose now that DEC develops a charge rate per day for each staff group by dividing
the total salaries paid to that group by the total number of days of work supplied by that
group. The cost allocated to each job from each staff group will be the number of days
worked on the job by the group multiplied by that group’s charge rate. Compute the cost
allocated to each job using this approach.
c. If DEC develops a price for each job by taking the cost allocated to the job and
multiplying the cost by 1.5, which is the convention in this industry, what would be the
likely consequence of the approach in part a) relative to pricing the jobs using the costs
developed in the approach in part b).
Problem 3
Elora Corporation manufactures several different types of printed circuit boards: however, two of
the boards account for the majority of the company’s sales. The first of these boards, a TV
circuit board, has been a standard in the industry for several years. The market for this type of
board is competitive and therefore price sensitive. Elora plans to sell 65,000 of the TV boards in
20X9 at a price of $150 per unit. The second high volume product, a PC circuit board, is a
recent addition to Elora’s product line. Because the PC board incorporates the latest technology,
it can be sold at a premium price; the 20X9 plans include the sale of 40,000 PC boards at $300
per unit.
Elora’s management group is meeting to discuss strategies for 20X9, and the current topic of
conversation is how to spend the sales and promotion dollars for next year. The sales manager
believes that the market share for the TV board could be expanded by concentrating Elora’s
promotional efforts in this area. In response to this suggestion, the production manager said,
“Why don’t you go after a bigger market for the PC board? The cost sheets that I get show that
the contribution margin from the PC board is more than double the contribution from the TV
board. I know we get a premium price for the PC board; selling it should help overall
profitability.”
Elora uses the following data in its current costing system.
Variable manufacturing costs are allocated based on direct labour hours. For 20X9, variable
manufacturing costs are budgeted at $1,120,000 and direct labour hours are estimated at 280,000.
The hourly rates for machine time and direct labour are $10 and $14 respectively. Elora applies
a materials handling charge of 10% of materials cost; this materials handling charge is not
included in variable manufacturing costs. Total 20X9 expenditures for material are budgeted at
$10,600,000.
Module 3 – Management Accounting 6
Pat Toste, Elora’s controller, believes that before the management group proceeds with the
discussion about allocating sales and promotional sales efforts to individual products, it may be
worthwhile to look at these products based on the activities involved in their production. Toste
has prepared the following schedule for the management group.
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“Using this information,” Toste explained, “we can calculate an activity-based cost for each TV
board and each PC board and then compare it to the cost computed using our current system.
The only cost that remains the same for both systems is the cost of direct materials. The cost
drivers will replace the direct labour, machine time, and support costs in the existing costing
system.
Required a. Compute the cost of each product using the current costing system.
Module 3 – Management Accounting 6
b. Compute the cost of each product using the activity based costing system.
c. Explain how the new costing system might change the promotional decisions made by
Elora’s management group.
Problem 4
Pepper Company, a growing mail-order clothing and accessory company, is concerned about its
growing marketing, distribution, selling, and administration expenses. It therefore examined its
customer ordering patterns for the past year and identified four different types of customers, as
illustrated in the following table. Pepper sends catalogues and flyers to all its customers several
times a year. Orders are taken by mail or over the phone. Pepper maintains a toll-free number for
customers to use when placing orders over the phone. Pepper prides itself on the personal
attention it provides shoppers who order over the phone. All purchases are paid for by check or
credit card. Pepper has a very generous return policy if customers are not satisfied with the
merchandise received. Customers must pay return shipping charges, but their purchase price is
then fully refunded.
Initial Sales
Number of items returned
Dollar value of items returned
Number of all orders per year
Number of phone orders per year
Time spent on phone placing orders
Number of overnight deliveries
Number of regular deliveries
Customer 1
$1000
0
0
1
1
0.25 hours
1
0
Customer 2
$1000
4
$200
6
0
0
0
6
Customer 3
$2,500
2
$500
4
0
0
0
4
Customer 4
$3,000
24
$1,500
12
12
1 hour
12
0
Prices are set so that cost of goods sold is on average about 75% of the sales price. Customers
pay actual shipping charges, but extra processing is required for overnight deliveries. Pepper has
developed the following activity cost driver rates for its support costs:
Activity
Process mail orders
Process phone orders
Process returns
Process overnight delivery requests
Maintain customer relations (send catalogues and
respond to customer comments or complaints)
Activity Cost Driver Rate
$5 per order
$80 per hour
$5 per item returned
$4 per request
$50 per year
Module 3 – Management Accounting 6
Required
a. Using activity-based costing, determine the yearly profit associated with each of the four
customers described.
b. Comment on which customers are most profitable and why.
c. What advice do you have for Pepper regarding managing customer relationships with the
different types of customers represented?
Problem 5
Adrian Rose, senior vice president for sales for Oakville Shoes, Inc., noticed that the company
had substantially increased its market share for the high-quality boomer boots (BB) and lost
market share for the lower-quality lazy loafers (LL). Adrian found that Oakville’s prices were
lower than the competitors’ for BB but higher for LL. He did not understand the reasons for
these price differences because all companies used the same production technology and were
equally efficient.
The manufacturing process is relatively simple. Oakville’s manufacturing facility has a cutting
department and an assembly department. The high-quality BB is produced in small batches
(1,000 pairs of shoes each), and the lower-quality LL is produced in large batches (3,000 pairs
each). Adrian has asked you, the company’s new controller, to analyze the product costing
method to see if the product prices should be changed.
The company currently uses a plantwide cost driver rate based on direct labour hours. The rate is
computed at the beginning of the year using the following budgeted data:
Total manufacturing support costs
Total direct labour hours
Total machine hours
Total setup hours
$1,200,000
49,000
49,400
520
Your assistant has provided you with the following additional information about the production
of batches of BB and LL:
Item
Direct labour hours
Machine hours
Setup hours
Direct costs
Each Batch of BB: 1,000 Pairs
Cutting
Assembly
80
120
160
120
3
1
$7,500
$6,000
Total
200
280
4
$13,500
Module 3 – Management Accounting 6
Each Batch of LL: 3,000 Pairs
Cutting
Assembly
150
180
150
120
1
1
$9,000
$7,200
Item
Direct labour hours
Machine hours
Setup hours
Direct costs
Total
330
270
2
$16,200
Upon further inquiry, your assistant has been able to trace the support costs to the two service
departments and the two production departments and to identify the following details for
potential cost drivers for the service departments:
Item
Support costs
Direct labour hours
Machine hours
Setup hours
Maintenance
$160,000
0
0
0
Setup
$400,000
0
0
0
Cutting
$440,000
21,400
27,800
340
Assembly
$200,000
27,600
21,600
180
Totals
$1,200,000
49,000
49,400
520
Your assistant has also collected the following information on activities and their cost drivers:
Support Activities
Maintenance
Setups
Cutting supervision
Cutting depreciation
Assembly supervision
Assembly depreciation
Cost
$160,000
400,000
280,000
160,000
160,000
40,000
Activity Category
Product sustaining
Batch related
Batch related
Business sustaining
Unit related
Business sustaining
Cost Driver
Machine hours
Setup hours
Setup hours
Machine hours
Direct labour hours
Machine hours
Required
a. Using a single, plantwide cost driver rate based on direct labour hours, determine the
costs per pair of BB and LL.
b. Determine the costs per pair of BB and LL using activity-based costing.
Module 3 – Management Accounting 6
SOLUTIONS
1.
a
Activity-based costing focuses on activities as the fundamental cost objects
and uses the costs of these activities as building blocks for compiling the costs
of other cost objects. The final product costs are built up from the costs of the
specific activities undergone in manufacturing the product. Because of the
many activity areas, indirect costs are accumulated in many indirect cost
pools.
Traditional product-based costing is much simpler and more general in that
costs are accumulated in only one or a few cost pools. Costs may be allocated
based on cost drivers, such as direct labor hours or machine hours, or a cost
application base could be financial, such as direct labor costs or direct
material costs.
Organizations that are most likely to benefit from activity-based costing have
operating personnel with little faith in the accuracy of existing cost
information, a widely diverse set of operating activities and many changes in
activities over time, among other characteristics.
2.
d
3.
a
20 hours x $400 / 1,000 scissors = $8.00
4.
b
(200 x $4) + (12 x $40) + (5 x $6) = $1,310 / 100 = $13.10
5.
b
Since these costs have not apparent cause and effect relationship with activity
levels in the organization
6.
c
7.
b
Insurance on a factory would be properly treated as a facility-sustaining
activity
8.
a
This is a direct materials cost – ABC only allocates indirect costs
9.
b
10.
d
Only properly designed ABC systems have the potential to produce more
accurate estimates of product cot. ABC costing systems can be used in any
type of organization including service, not for profit, and government. ABC
systems can be very expensive and, in some cases, not cost effective.
There is no apparent relationship between the number of direct labour hours
needed to make the product and the batch-related costs.
Module 3 – Management Accounting 6
Problem 1
Here is the solution with the calculation for the costs in part a) shown in the calc column
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Module 3 – Management Accounting 3
Problem 2
a)
Here is the formula for total salaries: 20 * 50000 + 35 * 75000 + 13 * 130000 + 8 * 275000
The cost for each job will be computed by multiplying the rate per day by the total number of all
staff members working on the job. For example, the cost for Simple jobs will be:
(8+15+5+2)*$466.34
b)
c)
If we take the costs computed in part b) as more accurate the costing approach in part a) is over
costing all the jobs. If cost is marked up by 50% and if DEC’s competitors have the same cost
structure, DEC will be quoting higher prices for all its jobs and will lose business if the market is
competitive (that is it is unable to differentiate its services so that it can charge a higher price.
Module 3 – Management Accounting 3
Problem 3
a)
b)
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Module 3 – Management Accounting 3
c)
The current system is over costing the TV board and under costing the PC board. The major
culprit causing the distortions is the manual insertion cost. The consequence is that the TV
boards are more attractive than the current system would recognize and the PC boards are less
attractive. Another managerial implication is that the organization might consider developing a
system for machine insertions on the PC boards.
Module 3 – Management Accounting 3
Problem 4
a.
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b.
The profit divided by net sales measure identifies the effect of customer demands on
this organization’s costs. This measure identifies customer 4 as, by far, the worst
customer who inflicts significant customer related costs on the organization.
c.
While customer 4 has the highest level of initial sales the returns and other customerrelated costs are so excessive for this customer that it becomes the least profitable.
Clearly the returns policy is promoting unreasonable behaviour from this customer.
Pepper Company should consider levying a restocking fee when returns exceed a certain
level – for example 10% of sales.
Module 3 – Management Accounting 3
Problem 5
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Module 3 – Management Accounting 3
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Module 3 – Management Accounting 3
7.
Service Department Cost Allocation
Learning Objectives
After completing this chapter you will:
1. Understand and be able to explain the nature of support departments and why
organizations allocate support department costs to other departments.
2. Be able to undertake the calculations for the direct, step (sequential), and reciprocal
methods of support department cost allocation.
3. Understand why variable and fixed support department costs should be allocated
separately and how each should be allocated.
Support and Production Departments
All organizations have production departments that make goods or services and other
departments, called support departments, which provide the services the production departments
need to do their work.
There are a number of reasons why organizations allocate support department costs to production
departments:
1. Since these non production departments provide the support the production departments
need to complete their work, it is appropriate to allocate support costs to the production
departments so that the costs of products made in the production departments will reflect
these needed support services. By including production and non production costs in total
product costs organizations have a better understanding of the costs of all the resources
needed to produce a product (good or service) and therefore a better basis to evaluate
product profitability.
2. Allocating non production costs to the production departments and making the
production department managers accountable for those costs, motivates production
department managers to use support departments wisely.
3. In contractual situations, such as reimbursement costing, international transfer pricing,
and insurance claims, organizations may be either required or motivated by their own self
interest to include the costs of both manufacturing and non manufacturing resources in
the product cost.
The system structure
It is most common to organize non manufacturing cost pools by function. Common examples of
support departments include: accounting, legal, administrative, human resources, and
information technology.
The following diagram shows the structure of flow of costs.
Module 3 – Management Accounting 3
Costs are initially traced to the departments that incurred the costs – these are the direct costs of
each of these departments. The first stage of the cost allocation process is for the support
departments to allocate their direct costs to the production departments. Note that this first stage
can involve the support departments allocating costs to themselves. The second stage of the cost
allocation process is for the production departments to allocate their costs to the final cost
objects.
An Example
The process of allocating support departments costs is best illustrated using an example. Brant
Metal Industries (BMI) has the following four departments:
1. Production departments
a. Cutting
b. Assembly
2. Support Departments
a. Maintenance
b. Engineering
Module 3 – Management Accounting 3
Here is a summary of the most recent activities and costs in BMI. Costs incurred directly by the
Cutting and Assembly Departments totalled $7,800,000 and $6,700,000 respectively.
Direct Method of Support Cost Allocation
In the direct method of support cost allocation the costs of the support departments are allocated
directly to the production departments. All support services provided to support departments are
ignored.
Operating Department's Overhead
Allocation from maintenance:
$2,400,000 x 1,800 / 2,800 | 1,000 / 2,800
Allocation from engineering:
$750,000 x 800 / 1,200 | 400 / 1,200
Cutting
Assembly
$7,800,000
$6,700,000
1,542,857
857,143
500,000
250,000
$9,842,857
7,807,143
The rate per unit of service under the direct method can be calculated as follows:
Maintenance: $2,400,000 / 2,800 = $857.14
Engineering: $750,000 / 1,200 = $625.00
Module 3 – Management Accounting 3
Step Method (also known as the step-down method and the sequential method)
In the step method the approach is to allocate the support department costs sequentially. One
support department is chosen to allocate its direct costs first. That support department computes
its cost driver rate by dividing its direct costs by the total of all support units provided to other
departments – both support and production. Then that support department allocates its costs to
the other departments. Each department is allocated an amount equal to the number of support
units it receives multiplied by the cost driver rate. Then the support department whose costs
have been allocated is dropped from the process and the next support department repeats the
same process by allocating its direct cost plus the cost it has been allocated by the previous
support department(s).
Order makes a difference. The order in which the support departments allocate their costs will
affect the final support department cost allocations to the production departments. For this
reason folklore has developed surrounding the appropriate order. Perhaps the most popular
approach is to start with the support department that provides the highest proportion of its costs
to the remaining support departments. Let’s illustrate this approach using the data for BMI
Here is the distribution of services showing the proportions each support department provides to
other support departments.
Maintenance provides 19.44% of its services to Engineering while Engineering provides 13.33%
of its services to Maintenance. So using the above rule for choosing order we will allocate the
Maintenance Department costs first. Here is the result.
Module 3 – Management Accounting 3
Let’s study the calculations in this exhibit. We chose the Maintenance Department to go first.
Note how the support units that Maintenance supplies to itself are ignored. The cost driver rate
of $685.71 for Maintenance is computed by dividing its direct cost of $2,400,000 by 3,500, the
total number of cost driver units it provides to other departments. This rate is then used to
allocate the Maintenance Department’s direct costs to all the other departments. For example,
the $480,000 cost allocated to Engineering equals the service units of 700 provided to
Engineering multiplied by the $685.71 rate. (Remember the earlier warning that in these
calculations the amounts are rounded to two decimal places but the spreadsheet accuracy is
maintained.)
Now that the Maintenance Department costs have been allocated we pretend that the
Maintenance Department does not exist and turn to consider the Engineering Department. Now
we turn to allocate the Engineering Department’s costs. The Engineering Department’s cost to
be allocated is $1,230,000 which includes its direct costs of $750,000 and the $480,000 of costs
allocated to it from the Maintenance Department. We divide the total of these costs by the total
units of support provided to the remaining 2 departments (1200) to compute the driver rate of
$1025.00 per unit of support. This rate is now used to allocate the Engineering Department costs
to the two production departments where the cost allocated to each department equals the driver
rate multiplied by the support units provided to that department.
The allocation of support department costs is now complete. The production departments will
add the costs allocated to them by the support departments to their direct costs to determine the
costs that they will each allocate to the final cost objects.
The calculation of the support department cost allocations if the Engineering Department goes
first is left as an exercise at the end of this chapter.
Module 3 – Management Accounting 3
Reciprocal Method
The reciprocal method of support department cost allocation recognizes all support department
activities and therefore provides the most accurate modelling of the support patterns.
The first step in the reciprocal method is to compute what is called the reciprocal cost for each of
the support departments. The reciprocal cost for each support department is its direct cost plus its
share, based on proportion of support units consumed, of the direct costs of the other support
departments. We ignore any support department’s self-service units. (It turns out whether or not
we ignore self service units results in the same service department cost allocations.)
Here is what the three reciprocal cost equations would be for BMI where M is the reciprocal cost
of the maintenance department and E is the reciprocal cost of the engineering department–
remember we ignore self service units.
M = 2,400,000 + (200/1400) E
E = 750,000 + (700 / 3500) M
We have two equations in two unknowns that we now have to solve to find M and E. These
equations can be quickly solved using Excel but they can also be solved using what is called the
method of substitution. Here is how that works for this example.
We substitute the second equation into the first equation to get the following:
M = 2,400,000 + (200/1400)(750,000 + 700/3500*M)
M = 2,400,000 + 107,143 + (14/490)M
M = 2,507,143 + (1/35)M
(34/35)M = 2,507,143
M = 2,507,143 (35/34) = $2,580,882
We can now substitute this value for RCM in either of the initial reciprocal cost equations to find
E.
Using the second equation we have:
E = 750,000 + (700 / 3500) M
E = 750,000 + (700 / 3500) 2,580,882
E = 1,266,176
We now use these reciprocal costs to determine the allocations to the production departments.
Each production department is assigned its share of the reciprocal cost of each support
department based on its proportion consumed of the department’s support units:
Module 3 – Management Accounting 3
Operating Department's Overhead
Allocation from maintenance:
$2,580,882 x 1,800 / 3,500 | 1,000 / 3,500
Allocation from engineering:
$1,266,176 x 800 / 1,400 | 400 / 1,400
Cutting
Assembly
$7,800,000
$6,700,000
1,327,311
737,395
723,529
361,765
$9,850,840
7,799,160
The rate per unit of service under the reciprocal method can be calculated as follows:
Maintenance: $2,580,882 / 3,500 = $737.39
Engineering: $1,266,176 / 1,400 = $904.41
Here is the summary of the support cost allocations to the production departments for each of the
three methods (recall that other allocation sequences in the step method will result in different
cost allocations).
Direct Method
Step Method
Reciprocal method
Cutting
Assembly
Total
$9,842,857
9,854,286
9,850,840
$7,807,143
7,795,714
7,799,160
$17,650,000
$17,650,000
$17,650,000
At first glance, there does not appear to be much difference between the three methods.
However, if we compare the rate per unit of service, the distortions become much clearer:
Direct Method
Step Method
Reciprocal method
Maintenance
Engineering
$857.14
685.71
737.39
$625.00
1,025.00
904.41
Support Department Allocations – Variable and Fixed Costs
To this point we have discussed support department cost allocations without considering the
nature of the support department costs. Many management accountants believe that each support
department should maintain two support cost pools – one for variable costs and one for fixed
costs. Variable costs should be allocated following the procedure that we have already described
– that is variable costs should be allocated based on the number of cost driver units. This results
in a so-called dual rate system of support department cost allocations.
Module 3 – Management Accounting 3
Management accountants supporting the dual rate system of allocating support department costs
argue that the cost driver for variable support costs is actual use while the cost driver for fixed
support cost is the amount of capacity acquired or the average long run use of capacity by the
various departments. Therefore, proponents of the dual rate system believe that fixed support
costs should be allocated based on the planned use of support department capacity or long run
average use of the capacity. Note that if the relative use of support department capacity is stable
then short run use will approximate long run average use and once again allocating both fixed
and variable support costs together is deemed to be appropriate.
The only other consideration is whether all fixed support costs should be allocated. Some
management accountants argue that if average long run use of capacity is less than practical
capacity then not all fixed support costs should be allocated. For example, if the total fixed
support costs of a support unit equal $1,000,000 and that, on average, only 90% of the practical
capacity of the support department is used, then management accountants advocating this
approach would argue that only $900,000 ($1,000,000 * 90%) of the fixed support costs should
be allocated with the balance of the fixed support costs charged to the income statement each
year as an idle capacity cost.
The issue of whether fixed and variable support costs should be allocated separately require the
judgement of each management accountant. The overriding consideration is whether the
resulting cost allocations reflect the decision-making and motivational objectives of undertaking
the cost allocations.
Module 3 – Management Accounting 3
Problems with Solutions
Multiple Choice Questions
1.
2.
B.F. Spurs Co. has two service departments, A and B, and two production
departments. The two service departments render services to each other as well as
to the production departments. The costs of service department A are allocated to
the other three departments based on their direct usage of department A's services.
The costs of service department B are then allocated to the production departments.
Which of the following cost allocation methods is being used to allocate the service
departments' costs?
a) Dual-rate
b) Direct
c) Step-down (sequential)
d) Activity-based
e) Reciprocal (simultaneous-equations)
A business uses the step-down method to allocate service department costs to the
manufacturing departments. Assume there are two service departments and two
manufacturing departments, as shown below:
Costs
Labour hours
Space occupied (m2)
Service
Departments
Plant
Custodial
Admin.
Services
$90,000
$360,000
25,000
6,000
10,000
1,000
Manufacturing
Departments
Cutting
$261,000
18,000
5,000
Polishing
$689,000
30,000
45,000
Plant administration costs are allocated based on labour hours, and custodial
services costs are allocated based on space occupied. The total costs of the cutting
and polishing departments (rounded to the closest .000), after allocating all the
service department costs, starting with plant administration
a)
b)
c)
d)
e)
cutting - $396,000, and polishing - $914,000.
cutting - $405,000, and polishing - $995,000.
cutting - $381,000, and polishing - $889,000.
cutting - $394,000, and polishing - $1,006,000.
cutting - $380,000, and polishing - $892,000.
Module 3 – Management Accounting 3
The Following Data Apply to Items 3-4:
The managers of Rochester Manufacturing are discussing ways to allocate the cost of service
departments such as Quality Control and Maintenance to the production departments. To aid
them in this discussion, the controller has provided the following information.
Quality
Total
Control Maintenance Machining Assembly
Budgeted overhead costs
$350,000
$200,000 $400,000 $300,000 $1,250,000
before allocation
Budgeted machine hours
-
-
50,000
-
50,000
Budgeted direct labor
-
-
-
25,000
25,000
hours
Budgeted hours of service:
Quality Control
-
7,000
21,000
7,000 35,000
Maintenance
10,000
-
18,000
12,000
40,000
3.
4.
Using the direct method, the total amount of overhead allocated to each machine
hour in the Machining Department would be
a) $2.40
b) $5.25
c) $8.00
d) $9.35
e) $15.65
If Rochester Manufacturing uses the step-down method of allocating service costs
beginning with Quality Control, the Maintenance costs allocated to the Assembly
Department would be a) $70,000
b) $108,000
c) $162,000
d) $200,000
e) $210,000
Module 3 – Management Accounting 3
Problem 1
Repeat the step allocation exercise for BMI but allocate the support department costs in the
following order: Engineering and then Maintenance to show that order in the step method does
make a difference in terms of the final cost allocations.
The following data is used in Problem 2 -5:
This data reflects the actual service units provided by the support departments to the two
production departments.
e
This data reflects the long run average planned service units provided by the support departments
to the two production departments and the costs shown are the fixed costs for the two support
departments.
Problem 2
Using the actual support units provided and the total costs, allocate the support department costs
to the production departments using:
a. The direct method
b. The step method with Power first and then Maintenance
c. The step method with Maintenance first and then Power
d. The reciprocal method.
Module 3 – Management Accounting 3
Problem 3
Using the actual support units provided and the variable costs, allocate the support department
costs to the production departments using:
a. The direct method
b. The step method with Power first and then Maintenance
c. The step method with Maintenance and then Power
d. The reciprocal method
Problem 4
Using the long run average support units provided and the fixed costs, allocate the support
department costs to the production departments using:
a. The direct method
b. The step method with Power first and then Maintenance
c. The step method with Maintenance and then Power
d. The reciprocal method.
Problem 5
Summarize your results in Questions 2 through 4 and discuss the implications of those results.
Module 3 – Management Accounting 3
SOLUTIONS
Multiple Choice Questions Solutions
1.
c
The step-down allocation method allows partial recognition of services
rendered by service departments to other service departments. This method
involves a sequence of allocations such as that described for B.F. Spurs Co.
2.
d
Plant administration allocation
= $360,000 ÷ (6,000 + 18,000 + 30,000) = $6.667/hr.
Custodial services allocation
= [$90,000 + (6,000 x $6.667)] ÷ (5,000 + 45,000) = $2.60/m2
Cutting department costs
= $261,000 + (18,000 x $6.667) + (5,000 x $2.60) = $394,000
Polishing department costs
= $689,000 + (30,000 x $6.667) + (45,000 x $2.60) = $1,006,000
3.
e
Quality control: $350,000 x 21,000 / 28,000
Maintenance: $200,000 x 18,000 / 30,000
Add Machining department's overhead costs
4.
b
Allocate Quality:
$350,000 x 7/35
Quality
Maintenance
$350,000
$200,000
Assembly
70,000
$270,000
Allocate Maintenance:
$270,000 x 12/30
$262,500
120,000
400,000
$782,500
/50,000 MH
$15.65
$108,000
Module 3 – Management Accounting 3
Problem 1
Problem 2
a.
Module 3 – Management Accounting 3
b.
c.
Module 3 – Management Accounting 3
d.
P = 2,700,000 + 1,400/4,400 M
M = 900,000 + 1,100/8,300 P
Simplifying the fractions, we get:
P = 2,700,000 + 7/22 M
M = 900,000 + 11/83 P
Substituting the second equation into the first, we get:
P = 2,700,000 + 7/22 (900,000 + 11/83 P)
P = 2,700,000 + 286,364 + 77/1,826*P
1,749 / 1,826 *P = 2,986,364
P = 2,986,364 * 1,826 / 1,749
P = 3,117,839
M = 900,000 + 11/83(3,117,839)
= 1,313,208
Fabrication
Finishing
Allocation from power:
$3,117,839 x 4,500 / 8,300 | 2,700 / 8,300
$1,690,395
$1,014,237
Allocation from maintenance:
$1,313,208 x 1,800 / 4,400 | 1,200 / 4,400
537,221
358,148
$2,227,616
$1,372,385
The rate per unit of service under the reciprocal method can be calculated as follows:
Power: $3,117,839 / 8,300 = $375.64
Maintenance: $1,313,208 / 4,400= $298.46
Module 3 – Management Accounting 3
Problem 3
a.
b.
Module 3 – Management Accounting 3
c.
Module 3 – Management Accounting 3
d.
P = 1,200,000 + 1,400/4,400 M
M = 600,000 + 1,100/8,300 P
Simplifying the fractions, we get:
P = 1,200,000 + 7/22 M
M = 600,000 + 11/83 P
Substituting the second equation into the first, we get:
P = 1,200,000 + 7/22 (600,000 + 11/83 P)
P = 1,200,000 + 190,909 + 77/1,826*P
1,749 / 1,826 *P = 1,390,909
P = 1,390,909 * 1,826 / 1,749
P = 1,452,144
M = 600,000 + 11/83(1,452,144)
= 792,453
Allocation from power:
$1,452,144 x 4,500 / 8,300 | 2,700 / 8,300
Allocation from maintenance:
$792,453 x 1,800 / 4,400 | 1,200 / 4,400
Fabrication
Finishing
$787,307
$472,384
324,185
216,124
$1,111,492
$688,508
The rate per unit of service under the reciprocal method can be calculated as follows:
Maintenance: $1,452,144 / 8,300 = $174.96
Engineering: $792,453 / 4,400= $180.10
Module 3 – Management Accounting 3
Problem 4
a.
b.
Module 3 – Management Accounting 3
c.
Module 3 – Management Accounting 3
d.
P = 1,500,000 + 1,700/4,800 M
M = 300,000 + 1,200/8,900 P
Simplifying the fractions, we get:
P = 1,500,000 + 17/48 M
M = 300,000 + 12/89 P
Substituting the second equation into the first, we get:
P = 1,500,000 + 17/48 (300,000 + 12/89 P)
P = 1,500,000 + 106,250 + 204/4,272*P
4,068 / 4,272 *P = 1,606,250
P = 1,606,250* 4,272 / 4,068
P = 1,686,799
M = 300,000 + 1,200/8,900 (1,686,799)
= 527,434
Allocation from power:
$1,686,799 x 4,800 / 8,900 | 2,900 / 8,900
Allocation from maintenance:
$527,434 x 1,600 / 4,800 | 1,500 / 4,800
Fabrication
Finishing
$909,734
$549,631
175,811
164,823
$1,085,545
$714,454
The rate per unit of service under the reciprocal method can be calculated as follows:
Maintenance: $1,686,799 / 8,900 = $189.53
Engineering: $527,434 / 4,800= $109.88
Module 3 – Management Accounting 3
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"'%$ !( "(%( !( %&!" #& One of the important principles in management accounting is that an appropriate cost driver
should be used to allocate any indirect cost. If we accept that planned or average use is the cost
driver for fixed costs and that actual use is the driver for variable costs then we would conclude
that doing separate allocations for fixed and variable costs will result in the most appropriate cost
allocations. So we can take the cost allocations in questions 3 and 4 as the most reasonable and
compare the costs allocations in question 2 to those. Within questions 3 and 4, the reciprocal
allocation method provides the cost allocations that track the actual support use patterns. Note
that the direct cost allocations come very close to the values produced by the reciprocal method
when fixed costs and variable costs are allocated separately.
Module 3 – Management Accounting 3
8.
Joint and By-Product Costing
Learning Objectives
After completing this chapter you will understand:
1. The nature of joint products, joint costs, and byproducts
2. Why management accountants allocate joint costs
3. Be able to apply, the five major approaches to joint cost
4. The insights provided by joint costs in decision making.
Joint Costs, Joint Products and Byproducts
In some production environments a single
raw material produces multiple products.
For example refining a barrel of crude oil
will produce (amongst other products)
gasoline, diesel fuel, gas, naphtha, and
kerosene. Products that are jointly
produced from a single raw material, in
this case crude oil, are called joint
products. A byproduct is a joint product
that has a relatively low (or negative
value). The point at which the single raw
material is rendered into the joint and
byproducts is called the split off point and
the cost incurred up to the split off point
is called the joint cost.
•
•
•
Why Allocate Joint Costs
As we will discuss below there is no decision making need to allocate joint costs. Any economic
decisions can be made without allocating joint costs. In fact, basing economic decisions on joint
cost allocations will almost always lead to incorrect decisions. Moreover, it is important to
remember that all joint cost allocations are arbitrary and are therefore subject to debate and
criticism.
There are many practical reasons to allocate joint costs – almost all of which relate to contractual
reasons.
1. Joint cost allocations are required to prorate joint costs between inventory and cost of
goods sold for external reporting or taxation purposes.
Module 3 – Management Accounting 3
2. Joint cost allocations may be used for transfer pricing purposes within organizations. We
will discuss transfer pricing in chapter 20.
3. Joint cost allocations may be required for cost-based contracts wherein the price paid is a
mark up on reported costs.
4. Joint cost allocations may be required for insurance purposes when a joint product is lost,
damaged, or stolen.
5. Joint cost allocations may be required by regulators when one of the joint products is sold
in a regulated industry and the allowed product price is cost-based.
6. Joint cost allocations may be required in litigation – for example in a predatory pricing
environment to determine whether a product is being sold below its costs.
Again, remember that joint cost allocations are not required for any economic based decision
making.
Joint Cost Allocation Methods
While there are variations of the basic methods, there are four basic methods for allocating joint
costs to joint products. These are
1. Physical output
2. Value at split-off
3. Net realizable value
4. Constant gross margin percent
The following example will be used to illustrate these four methods. Jack Chemical Company
manufactures chemicals used for industrial applications requiring bleaching and cleaning.
Chemicals are made in batches of 1,000 litres. The process begins by blending 400 litres of
alpha costing $30 per litre with 600 litres of beta costing $50 per litre. The mixture is then
subjected to pressure and heating to produce 300 litres of product A, 600 litres of product B, and
100 litres of product C. This manufacturing process costs (exclusive of the raw materials cost)
$15,000 per batch.
Products A, B, and C can be sold for $90, $60, and $2 per litre respectively. Product A can be
sold as is or refined in batches of 300 litres at a cost of $8,000 per batch to produce product D
that can be sold for $120 per litre. In what follows we will assume that Jack Chemical Company
treats all the products as joint products.
The Decision
To underline the point that economic decision making does not require any cost allocations,
consider the decision relating to whether or not to process a batch of chemicals. The following
diagram and table summarize the process and the financial facets of this decision.
Module 3 – Management Accounting 3
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Begin by noting that selling product A at the split off point provides a contribution of $27,000
while refining product A to produce product D provides an incremental profit contribution of
$28,000. Therefore processing product A further increases the batch contribution.
The following table summarizes the contribution provided by each batch. Notice that neither the
decision of whether to process a batch of chemicals nor the decision of whether to sell product A
or process it further to produce product D required an allocation of joint costs.
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Module 3 – Management Accounting 3
Physical Output Method
The physical output method allocates joint costs based on some physical measure such as litres
or kilograms. In this setting the physical output method would allocate the joint costs of $57,000
based on the volume of joint products produced. Here is a table summarizing the joint cost
allocation that would result following the physical output method.
Value at Split off Method
The value at split off method allocates joint costs based on the value of the joint products at the
split off point. The following table summarizes the joint cost allocations that would result from
applying this method.
Net Realizable Value Method
The net realizable value method allocates the joint costs based on the net realizable value of each
joint product. The net realizable value for each product is computed by subtracting any
additional cost required to complete that product beyond the split off point from the product’s
revenue. From the above analysis we know that product A will be refined to produce product D.
The following table summarizes the joint cost allocations that would result from using the net
realizable value method.
Module 3 – Management Accounting 3
Constant Gross Margin Percent Method
In the constant gross margin method the joint costs are allocated so that each product reports the
same gross margin percent where gross margin equals revenue minus total cost and gross margin
percent equals (revenue – costs)/revenue. Again recall that the best disposition of chemical A is
to refine it to produce chemical D.
When applying this method we begin by computing the overall or combined gross margin
percentage for all the products
Overall gross margin percentage = Batch Contribution / Total Revenue
= 7,200 / 72,200 = 9.97%
This percentage is then multiplied by each product’s revenue to compute the gross margin for
that product. The difference between each product’s revenue and gross margin is the total
product cost. Finally the separable cost is deducted from each product’s total cost to determine
the joint cost that will be allocated to that product.
Here are the cost allocations that would result using the constant gross margin percent method
Byproducts
As mentioned above joint products that have small values are called byproducts. In the above
example joint product C would clearly qualify as a byproduct.
Management accountants have developed different approaches to account for byproducts. Here
are the two most widely used.
1. Recognize the byproduct’s net realizable value at the point of split-off and net that value
against the joint cost. Therefore if the net realizable value of the product is positive joint
cost will be reduced. The journal entries to accomplish this would be to debit a
byproduct inventory account at the split off point for the byproduct’s net realizable value
and credit work in process by the net realizable value. At the time of sale the byproduct
inventory account would be credited and cash or accounts receivable debited for the sale
price. If the net realizable value is negative the journal entries described above would be
adjusted in the opposite direction. Most management accountants agree that this is the
preferred treatment of byproducts. Moreover International Accounting Standard # 2
requires the use of this method.
2. Recognize the byproduct’s net realizable value at the time of sale. Between the split-off
point and the point of sale the byproduct is not recognized on the income statement. At
Module 3 – Management Accounting 3
the time of sale the byproduct’s net realizable value is recorded either as other income
(debit cash or accounts receivable and credit other income for the sales revenue) or as a
reduction of cost of goods sold (debit cash or accounts receivable and credit cost of goods
sold for the sales revenue). The objection to this approach is that since the byproduct
inventory does not appear on the balance sheet it can be used by management to
manipulate income by timing the sale of the byproduct to a period when an income
increase is wanted. For this reason recognizing the byproduct’s net realizable value at the
time of sale is not illustrated in what follows.
Return now to the Jack Chemical Company example above. It would certainly be appropriate to
recognize Chemical C as a byproduct. Here are the joint cost allocations that would result under
each of the methods described earlier if Chemical C were treated as a byproduct and its expected
net realizable value recognized at the split-off point. Recall in what follows that Chemical C’s
estimated net realizable value is $200 so the joint cost to be allocated now is $56,800 ($57,000 $200).
Physical Output Method
Product
A
B
Units
% Total
300
600
33%
67%
900
Joint Cost
Allocation
$18,933
37,867
$56,800
Value at Split off Method
Product
Revenue
% Total
Joint Cost
Allocation
A - 300 x $90
B - 600 x $60
$27,000
36,000
42.86%
57.14%
$24,343
32,457
$63,000
$56,800
Net Realizable Value Method
Product
B - 600 x $60
D - (300 x $120) - 8,000
Net Realizable
Value
% Total
Joint Cost
Allocation
$36,000
28,000
56.25%
43.75%
$31,950
24,850
$64,000
$56,800
Module 3 – Management Accounting 3
Constant Gross Margin Percent Method
As above we begin by computing the overall or combined gross margin percentage for all the
products.
Overall gross margin percentage = Batch Contribution / Total Revenue
= 7,200 / 72,000 = 10%
Here are the cost allocations that would result using the constant gross margin percent method
Conclusion
We have reviewed four approaches that management accountants use to allocate joint costs to
joint products. A remaining question is what are the advantages and disadvantages of each of
these methods. Note that three of the four methods are revenue based and therefore require
estimates of future revenues when they are used. Two of the revenue methods (net realizable
value method and constant gross margin percent method) also require estimates of future
processing costs. A desire to avoid the subjectivity of estimating future costs and revenues may
be a strong motivation for using the physical output method. However, as a counterpoint, the
physical output method takes no account of the value of the individual joint products and using
this approach might lead to a situation where the joint cost allocated to a joint product could
exceed any reasonable estimate of the product’s eventual selling price – an inventory valuation
consideration that would sway the choice toward using a value base approach to cost allocation.
Within the revenue methods management accountants might object to the value at split off
method because it ignores potentially significant value adding activities beyond the split off
point, as we saw with chemicals A and D in the Jack Chemical Company. A mitigating factor
supporting the value at split off method is that it does not require estimates of future processing
costs.
With regard to the choice between the net realizable value method and the constant gross margin
percent method the choice appears to be one based on a form of equity consideration. The
argument is that given that all joint cost allocations are inherently arbitrary one might impose a
fairness or equity consideration by requiring that the cost allocations result in the same gross
margin percent for all joint products.
Management accountants will exercise judgement to determine which approach suits the
decision making and the external reporting objectives of their respective organizations.
Module 3 – Management Accounting 3
Problems with Solutions
Multiple Choice Questions
The following information pertains to questions 1-2:
Omega Company manufactures three chemicals in a joint process. The
manufacturing costs of the joint process include $25,000 of direct materials and
$35,000 of conversion costs. All three chemicals are then processed further before
they are sold. Other pertinent data are as follows:
Chemicals
Sales Value at Split-off
Separable Costs
Final Sales Value
A
$50,000
$28,000
$100,000
B
40,000
10,000
60,000
C
30,000
12,000
40,000
Using the estimated net realizable value method, the joint costs allocated to
Chemical A would be
a) $16,800
b) $25,000
c) $28,800
d) $30,000
e) $33,600
The decision to process all three chemicals beyond the split-off point is suboptimal.
If the optimal decision had been made, the income of Omega Company would have
improved by
a) $2,000
b) $10,000
c) $30,000
d) $60,000
e) an amount different from the above amounts
3.
The main purpose of allocating joint costs to products is to
a) determine prices for the products
b) make decisions about dropping the products
c) rationalize economic decisions concerning the products
d) determine the cost of the products
e) determine budgets for the production of the products
1.
2.
Module 3 – Management Accounting 3
The following information pertains to questions 4-5:
SMT Ltd. manufactures three products. Production begins with a joint process and the three
outputs of the joint process are processed further to produce products L, M and N. The outputs at
split-off have no market value. Last year, the joint costs amounted to $600,000. Other data for
last year are as follows:
Selling price per unit
Costs per unit after split-off to complete and sell
Total output at split-off used in production
Production in units
Sales in units
Product L Product M Product N
$160
$300
$400
$100
$200
$350
16,400 kg 10,000 kg 8,400 kg
20,000
10,000
7,000
18,000
8,000
7,000
4.
Using the physical quantities method (also called the physical measure method or
the average method) of joint costing, the total joint costs allocated to the production
of product L last year was
a)
b)
c)
d)
e)
5.
Using the estimated (approximate) net realizable value method of joint costing, the
inventory cost per unit of product M is
a)
b)
c)
d)
e)
$200,000.
$327,273.
$282,759.
$324,324.
$282,353.
$226.91.
$223.53.
$221.52.
$220.00.
$217.24.
Module 3 – Management Accounting 3
6.
Raynor Manufacturing purchases rough-cut trees and processes them up to the
splitoff point, where two products (paper and pencil casings) are obtained. The
products are then sold to an independent company that markets and distributes them
to retail outlets. In October, Raynor processed 50 trees (yield is 30,000 sheets of
paper and 30,000 pencil casings and no scrap), and had the following production
and sales:
Production:
30,000 sheets of paper and 30,000 pencil casings
Sales:
29,000 sheets of paper at $0.04 per page
30,000 pencil casings at $0.10 per casing
Cost of purchasing 50 trees and processing them up to the splitoff point to yield
30,000 sheets of paper and 30,000 pencil casings is $1,500. Opening inventories are
nil.
What are the approximate joint costs assigned to the paper ending inventory if joint
costs are allocated using the sales value at splitoff method?
a) $14.29
b) $50.00
c) $435.00
d) $750.00
e) $915.00
Module 3 – Management Accounting 3
7.
Beverage Drink Company processes direct materials up to the splitoff point, where
two products, A and B, are obtained. The following information was collected for
the month of July:
Direct materials processed: 2,500 litres (with 20 percent shrinkage)
Production: A
1,500 litres
B
500 litres
Sales:
A
$15.00 per litre
B
$10.00 per litre
Cost of purchasing 2,500 litres of direct materials and processing it up to the
splitoff point to yield a total of 2,000 litres of good products was $4,500. There
were no inventory balances of A and B.
Product A may be processed further to yield 1,375 litres of Product Z5 for an
additional processing cost of $150. Product Z5 is sold for $25.00 per litre. There
was no beginning inventory and ending inventory was 125 litres.
Product B may be processed further to yield 375 litres of Product W3 for an
additional processing cost of $275. Product W3 is sold for $30.00 per litre. There
was no beginning inventory and ending inventory was 25 litres.
What is Product Z5's estimated net realizable value at the splitoff
a) $11,100
b) $22,350
c) $24,225
d) $29,375
e) $34,225
Module 3 – Management Accounting 3
Problem 1
Downeast Fisheries operates a fish processing plant. Fish is processed in batches of 10,000
kilograms. Processing fish yields three products:
1. Fillets which are sold fresh or quick frozen
2. Fish pieces which are sold to another fish products plant to be used in breaded fish cakes.
3. Offal (unused parts of the fish) which is transported to a fertilizer plant.
The following table summarizes the yield and financial characteristics of processing a batch of
fish.
Yield (kilograms)
Revenue (disposal cost) per kilogram
Separable processing and selling cost per kilogram
Fresh Fish
2,000
$6.00
$1.50
Pieces
1,000
$3.00
$1.00
Offal
7000
-$0.20
0
Fresh fish can be quick frozen with an associated separable processing and selling cost of $0.50
per kilogram and sold for $5.50 per kilogram. Quick freezing also incurs a fixed cost of $500
per batch. If the fresh fish is frozen the $1.50 separable cost of processing the fresh fish would
be avoided.
a. Should the fillets be sold as fresh fish or quick frozen.
b. Assume that the joint cost, which includes the cost of purchasing and processing the fish,
is $7,000 per batch and that the offal is treated as a byproduct that is recognized at the
splitoff point. Allocate the joint cost to each of the products using
i. Physical output method
ii. Net realizable value method
iii. Constant gross margin
Module 3 – Management Accounting 3
Problem 2
Jacques (see Chapter 5 Question 2) who has been selling his used barrels to customers for $25
when they have outlived their usefulness making swish has decided that he has a better use for
his barrels. Jacques is now cutting up the barrels to produce wood he is selling to barbecue pit
enthusiasts to impart, what Jacques calls, “a unique flavouring to all you’re barbecuing.”
Jacques will use a transfer price of $25 to transfer each barrel from his drinks business to his
barrels business. Jacques pays his cousin Clementine $5 to disassemble each barrel.
The barrels render three joint products:
1. staves that Jacques packages into bundles and sells to barbecue enthusiasts,
2. solid white oak barrel tops and bottoms that Jacques sands sells to craft enthusiasts, and
3. steel barrel hoops that Jacques sells to the local scrap yard.
The following table summarizes the yield from the average barrel.
Product
Volume (weight)
Sales value at splitoff
Top/Bottom
5
$15
Hoops
1
$0.10
Staves
40
$20
a. Assuming that the tops and bottoms and the staves are treated as joint products and the
hoops as byproducts use each of the following methods to allocate the joint cost of each
barrel – assume that Jacques recognizes the byproducts at the time production is
completed.
i. Physical output method
ii. Sales value at splitoff
iii. Constant gross margin
b. Clementine advises Jacques that her brother Philip has been buying staves, rendering
them into charcoal, and selling them as “Philip’s Fantastic BBQ Charcoal”. Upon
investigation Jacques discovers that the batch of staves from each barrel could be
rendered into charcoal for $6 a batch, packaged for $1 per batch, and sold for $35.
Should Jacques get into the charcoal business and, if so, recalculate the joint cost
allocations assuming that the allocation alternatives are:
i. Physical output method
ii. Net realizable value
iii. Constant gross margin
Module 3 – Management Accounting 3
Problem 3
a. Return to the data in question 2 part b). Suppose that Fred, cut off from his supply of
staves, has retaliated by burning Jacques’ inventory of staves. Miraculously Jacques has
insured his inventory. The insurance policy covers the cost of the lost inventory. The
lost quantity is the staves lost from 20 barrels. Assuming that Jacques reports honestly,
what value will he report as his loss?
b. Comment on the accounting implications of your result in part a).
Problem 4
Multi Product Company processes a raw material with a joint cost of $25,000 to produce joint
Product A and joint Product B with a new realizable value of $15,000 and $25,000 respectively.
The processing also produces a byproduct, Product C, with a net realizable value of $4,000. All
Product A and Product B have been sold this period. However, none of the Product C has been
sold. Consider each of the following questions separately.
a. The President of Multi Product Company is going to retire at the end of this year and
would like to make his bonus, which is computed as a percentage of current profits, as
high as possible. What treatment of Product C will the President prefer?
b. Suppose that Multi Product Company has had a bad year overall. Profits are expected to
be so low that the President will not earn a bonus. What treatment of Product C will the
President prefer?
Problem 5
Return to question 1 and suppose that Downeast Fisheries can sell a maximum of 1,500
kilograms of fresh fish or quick frozen fish. How would this change your allocations in question
1?
Module 3 – Management Accounting 3
SOLUTIONS
Multiple Choice Questions
1.
2.
c
a
3.
d
4.
5.
c
b
Net Realizable Value
A
$ 72,000
B
50,000
C
28,000
$150,000
$60,000 x (72 ÷ 150) = $28,800
Only C should not be processed further - improvement in income by not
processing C further = $30,000 - 28,000 = $2,000
Allocating joint product costs is useful for pricing and production decisions;
however, the main purpose of allocating joint costs is to determine inventory
cost and cost of goods sold for internal and external reporting
$600,000 x [16,400 ÷ (16,400 + 10,000 + 8,400)] = $282,759 Joint costs are allocated on the basis of the relative estimated net realizable
value (i.e. expected final sales value minus expected separable costs to
complete and sell the total production).
Total net realizable value of all products
= ($160 - $100) x 20,000 units of L produced + ($300 - $200) x 10,000 units
of M produced + ($400 - $350) x 7,000 units of N produced
= $1,200,000 + $1,000,000 + $350,000 = $2,550,000
6.
7.
a
e
Inventory cost per unit of Product M
= $200 + [$600,000 x ($1,000,000/$2,550,000) ÷ 10,000]
= $200 separable costs + $23.53 joint costs = $223.53 Sales value at split-off:
Paper: 30,000 x $0.04 = $1,200
Pencil casings: 30,000 x $0.10 = 3,000
Joint costs allocated to paper = $1,500 x (1,200/4,200) = $428.57
Allocated to remaining inventory: $428.57 x 1,000/30,000 = $14.29
Net realizable value of Product A: (1,375 x $25) - 150 = $34,225
Module 3 – Management Accounting 3
Problem 1
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b.
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Module 3 – Management Accounting 3
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Module 3 – Management Accounting 3
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revenue will be $43 comprised of $28 for the staves ($35-6-1) and $15 for the top and bottom.
Module 3 – Management Accounting 3
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Module 3 – Management Accounting 3
Problem 3
a. The cost assigned to the staves inventory is highest under the physical output method and
equals $26.58 for the staves from each barrel. Therefore Jacques would choose the
physical output method to allocate the joint costs and would report a loss of $531.60
($26.58 * 20).
b. The variation in cost allocations under the three different approaches raises the possibility
of accounting manipulation. Note that Jacques is not committing any fraud in choosing
the accounting method that best supports his goal of maximizing reimbursement from the
insurance company – this is pure accounting system manipulation.
Problem 4
a. The President would prefer that the byproduct value be recognized at the time of
production since this will reduce costs by $4,000 for this year.
b. The President would prefer that the byproduct value be recognized at the time of sale.
All the joint costs of the batch will be recognized in the current year when the President
is not going to earn a bonus anyway. The $4,000 of byproduct will be available to
increase sales in the next year.
Problem 5
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Module 3 – Management Accounting 3
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