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TOPIC 1: COST CLASSFICATION AND ESTIMATION
TOPIC OUTLINE:
1. Definition of Cost and Cost Objects
2. Cost Classification
3. Cost Estimation Techniques
a. Industrial Engineering Methods
b. Conference Methods
c. Accounting Analysis Method
d. Graphical or Scatter Graph
e. High-Low Cost Estimation Methods
f. Regression Analysis
g. Learning Curve Method
1. Introduction
1. Cost is defined as a resource sacrificed or forgone to achieve a specific objective.
A cost (such as direct materials or advertising) is usually measured as the
monetary amount that must be paid to acquire goods or services. An actual cost
is the cost incurred (a historical or past cost), as distinguished from a budgeted
cost, which is a predicted or forecasted cost (a future cost).
2. Cost object is anything for which a separate measurement of cost is desired.
3. Cost Driver is anything that causes cost to increase. For example number of
output, machine hours, number of orders, number of batch, set ups etc.
2. Cost Classification
1. Cost Classification according to Traceability.
a. Direct Cost
b. Indirect Cost
2. Cost Classification according to Behavior
a. Variable cost
b. Fixed Cost
c. Semi-variable cost/ Semi-fixed Cost (Mixed Cost)
3. Cost classification according to function
a. Manufacturing cost
b. Non-manufacturing cost
4. Cost Classification according to Relevance.
a. Relevant Cost
b. Irrelevant Cost
5. Other classification
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Examples:
1. Classify each of the following as being usually fixed (F), variable (V), semi-fixed (SF)
or semi-variable (SV):
i.
direct labour;
ii.
depreciation of machinery;
iii.
factory rental;
iv.
supplies and other indirect materials;
v.
advertising;
vi.
maintenance of machinery;
vii.
factory manager’s salary;
viii.
supervisory personnel;
ix.
royalty payments.
2. For the relevant cost data in items (1)–(7), indicate which of the following is the
best classification?
(a) sunk cost; (b) incremental cost; (c) variable cost; (d) fixed cost; (e) semi-variable
cost; (f) semi-fixed cost; (g) controllable cost; (h) non-controllable cost;(i) opportunity
cost.
1. A company is considering selling an old machine. The machine has a book value
of £20 000. In evaluating the decision to sell the machine, the £20 000 is
a……………
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2. As an alternative to the old machine, the company can rent a new one. It will cost
£3000 a year. In analyzing the cost–volume behaviour the rental is a……………….
3. To run the firm’s machines, there are two alternative courses of action. One is to
pay the operators a base salary plus a small amount per unit produced. This makes
the total cost of the operators a………………………..
4. As an alternative, the firm can pay the operators a flat salary. It would then use
one machine when volume is low, two when it expands, and three during peak
periods. This means that the total operator cost would now be a…………………
5. The machine mentioned in (1) could be sold for £8000. If the firm considers
retaining and using it, the £8000 is a…………………….
6. If the firm wishes to use the machine any longer, it must be repaired. For the
decision to retain the machine, the repair cost is a………………………..
7. The machine is charged to the foreman of each department at a rate of £3000 a
year. In evaluating the foreman, the charge is a…………………..
3. A company manufactures and retails clothing. You are required to group the costs
which are listed below and numbered (1)–(20) into the following classifications (each
cost is intended to belong to only one classification):
(i) direct materials; (ii) direct labour; (iii) direct expenses; (iv) indirect production
overhead; (v) research and development costs;(vi) selling and distribution costs; (vii)
administration costs; (viii) finance costs.
1. lubricant for sewing machines;
2. floppy disks for general office computer;
3. maintenance contract for general office photocopying machine;
4. telephone rental plus metered calls;
5. interest on bank overdraft;
6. Performing Rights Society charge for music broadcast throughout the factory;
7. market research undertaken prior to a new product launch;
8. wages of security guards for factory;
9. carriage on purchase of basic raw material;
10. royalty payable on number of units of product XY produced;
11. road fund licences for delivery vehicles;
12. parcels sent to customers;
13. cost of advertising products on television;
14. audit fees;
15. chief accountant’s salary;
16. wages of operatives in the cutting department;
17. cost of painting advertising slogans on delivery vans;
18. wages of storekeepers in materials store;
19. wages of fork lift truck drivers who handle raw materials;
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20. developing a new product in the laboratory;
3. Cost Estimation Techniques
Determining how cost will change with output or other measurable factors of activity is
of vital importance for decision-making, planning and control. The preparation of budgets,
the production of performance reports, the calculation of standard costs and the provision
of relevant costs for pricing and other decisions all depend on reliable estimates of costs
and distinguishing between fixed and variable costs, at different activity levels.
Unfortunately, costs are not easy to predict, since they behave differently under different
circumstances. Many costs are fairly easy to classify as purely variable (e.g. direct
materials), fixed (e.g. rental of equipment), or step-fixed (e.g. labour costs) but others
fall into a mixed-cost category (also known as semi-variable costs) such as machine
maintenance costs, telephone charge costs, sales or marketing costs, etc. Thus, it is semivariable costs or mixed costs that we need to separate into variable and fixed categories.
There several methods that includes both linear and non-linear estimation methods,
qualitative and quantitative methods. Include the following:1. Industrial Engineering Method
2. Conference Method
3. Accounting Analysis Method
4. Graphical or Scatter Graph Method
5. High–Low Cost Estimation Method
6. Regression Method
7. Learning Curve Method
The major aim of this chapter is to ascertain the activity measure or cost driver that
exerts the major influence of the cost of a particular activity.
3.1 Industrial Engineering Method
The method derive cost functions by analyzing the relationship between inputs and
outputs in physical terms. It make use of engineering analyses of technological
relationship between inputs and outputs. Example of engineering methods is work
sampling and time and motion studies. It is an appropriate tool when there is physical
relationship between costs and cost driver.
It uses direct observations of the quantities required for an activity and convert the final
results into costs estimates. For example, engineers estimate material quantities and
labour hours needed for various operations, then prices and rates are applied to obtain
the cost estimates.
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Usefulness of Industrial Engineering methods
1. Used in a repetitive process
2. Useful in estimating direct material costs, labour and machine time costs
3. It is not restricted to manufacturing activities, it is applied to well-structured
administrative and selling activities such as typing, invoicing and purchasing.
Disadvantages of Engineering Method
1. Not useful in estimating overheads costs
2. Not useful in separating semi-variable costs into their fixed and variable elements.
3.2 Conference Method
The method estimates cost functions on the basis of analysis and opinions about costs
and their drivers gathered from various departments of a company, including purchasing,
process engineering, human resource, and production department.
The Method encourages interdepartmental cooperation i.e. the pooling of expert
knowledge from different business functions. It is quicker as it doesn’t use past data
analysis. This pose a challenge on the accuracy of the method as it base more on opinions
rather than factual data.
3.3 Accounting Analysis Method
The account analysis method estimates cost functions by classifying various cost accounts
as variable, fixed, or mixed with respect to the identified level of activity. Typically,
managers use qualitative rather than quantitative analysis when making these costclassification decisions.
The method involves the departmental manager and the accountant inspect each item of
expenditure within the accounts for a particular period, and then classify each item of
expense as a wholly fixed, wholly variable or a semi-variable cost.
A single average unit cost figure is selected for the items that are categorized as variable,
whereas a single total cost for the period is used for the items that are categorized as
fixed. For semi-variable items the departmental manager and the accountant agree
(based on qualitative factors) on a cost function that appears to best describe the cost
behaviour.
Example.
The following cost information has been obtained from the latest monthly accounts for
an output level of 10 000 units for a cost centre.
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(TZS)
Direct materials
Direct labour
Indirect labour
Depreciation
Repairs and maintenance
100 000
140 000
30 000
15 000
10 000
295 000
The departmental manager and the accountant examine each item of expense and
analyze the expenses into their variable and non-variable elements. The analysis might
be as follows:
Direct Material
Direct Labour
Indirect Labour
Depreciation
Repairs and maintenance
Unit Variable costs
TZS 10 per unit
TZS 14 per unit
TZS 0.5 per unit
TZS 24.5 per unit
Total Non-Variable costs
TZS 30 000
TZS 10 000
TZS 5 000
TZS 45 000
The method is widely used as it is reasonably accurate, cost effective and easy to use.
However, one problem with this method is that the analysis of costs into their variable
and non-variable elements can be very subjective. Also, costs are normally based on the
latest details that are available from the accounts, and these figures may not be typical
of either past or future cost behaviour.
3.4 Graphical or Scattergraph Method
The graphical method involves drawing on a graph, dependent variable (costs) to the
vertical axis (y) and independent variable (cost driver) to the horizontal axis (x). Then,
straight line is fitted to the scatter plotted points by visual approximation.
The line should minimize the distance between the points above the line and points below
the line. A line would be used to estimate the cost function. The point where the line
crosses vertical axis, will represent non-variable costs i.e. fixed costs and the slope of the
line will be the variable cost per unit.
Example.
The total maintenance costs and the machine hours for the past ten four-weekly
accounting periods were as follows:
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Period Machine
Hours (X)
1
2
3
4
5
6
7
8
9
10
400
240
80
400
320
240
160
480
320
160
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Maintenance
Cost (Y`000)
TZS
960.00
TZS
880.00
TZS
480.00
TZS
1,200.00
TZS
800.00
TZS
640.00
TZS
560.00
TZS
1,200.00
TZS
880.00
TZS
440.00
You are required to estimate the regression equation using the graphical method.
Solution:
Scattergraph Method
Maintenance Cost in TZS `000
TZS 1,440.00
TZS 1,200.00
TZS 960.00
TZS 720.00
TZS 480.00
TZS 240.00
TZS 0
100
200
300
400
500
Machine Hours
Y = 240 + 2X
The slope of the line was obtained based on any two points on the straight line, as for
example A (320; TZS 880) and B (160; TZS 560).
The cost equation above can be used to predict Maintenance cost for any level of activity.
The graphical method is simple to use, and it provides a useful visual indication of any
lack of correlation or erratic behaviour of costs. However, the method suffers from the
disadvantage that the determination of exactly where the straight line should fall is
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subjective, and different people will draw different lines with different slopes, giving
different cost estimates. To overcome this difficulty, it is preferable to determine the line
of best fit mathematically using the least-squares method.
3.5 High – Low Cost Estimation Method
This is among the simplest Cost estimation method that make use of liner cost equation.
The method consists of selecting the periods of highest and lowest activity levels and
comparing the changes in costs that result from the two levels.
Steps in Using High-Low Cost Estimation method
1. Select High level of activity with its respective cost.
2. Select Low Level of activity with its respective cost.
3. Calculate Variable cost per unit
B = High Cost – Low Cost
High Activity – Low Activity
4. Calculate Fixed Cost element
A = Mixed Cost – B (Activity Level)
Note Activity level must be either High or Low Activity level used in step 3 above.
5. Establish Cost Function that will be used in Cost estimation.
Y= A + B X
The challenges of the method are as follows:
1. Highest or Lowest levels are abnormal situations that do not represent the normal
situations of the costs.
2. It is inaccurate as it ignores other costs observations.
3. The Cost function is only valid for highest and lowest points.
3.6 Regression Method
Regression analysis is a statistical method that measures the average amount of change
in the dependent variable associated with a unit change in one or more independent
variables. The method also is called Least-Square Method. This is among the best method
that provides accurate answers.
Important Definitions
1. A regression equation identifies an estimated relationship between a dependent
variable (cost) and one or more independent variables (i.e. an activity measure or
cost driver) based on past observations.
2. A simple regression is a regression equation that has only one independent
variable. Simple regression line can be plotted in a graph.
3. A multiple regression is a regression equation that has two or more independent
variables.
4. Dependent Variable is thing that is affected by the independent variable. For
cost estimation topic, dependent variable or Y is always Mixed Costs.
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5. Independent variables are variables that explain the change in Mixed Costs.
These are cost drivers i.e. direct labour hours, machine hours, outputs etc.
Regression Equation
Y =a + bX
Where by:
𝒃=
𝒏∑𝒙𝒚−∑𝒙∑𝒚
𝒏∑𝒙𝟐 −(∑𝒙)𝟐
𝒂=
∑𝒚
𝒏
−𝒃
∑𝒙
𝒏
Test of Reliability
Regression method provide a more sophisticated way of measuring how well dependent
variable is explained by the independent variable. This measure is also called the
Goodness of Fit i.e. how well the regression line is fitted in the plotted points in the graph.
The reliability is tested by using Coefficient of Variation or R2. In particular, the
coefficient of variation measures the percentage variation in the dependent variable that
is explained by the independent variable. Coefficient of Variation is the square root of
correlation coefficient or R.
Correlation coefficient is calculated as follows:-
𝒓=
𝒏∑𝒙𝒚−∑𝒙∑𝒚
√(𝒏∑𝒙𝟐 −(∑𝒙)𝟐 ) (𝒏∑𝒚𝟐 −(∑𝒚)𝟐 )
The correlation coefficient (r) represents the degree of association between two variables,
such as cost and activity. If the degree of association between two variables is very close
it will be almost possible to plot the observations on a straight line, and r and r2 will
approximately be close to 1.
A SUMMARY OF THE STEPS INVOLVED IN ESTIMATING COST FUNCTIONS
There are six steps in estimating a cost function using quantitative analysis of a past cost
relationship:1. Select the dependent variable y (the cost variable) to be predicted;
2. Select the potential cost drivers;
3. Collect data on the dependent variable and cost drivers;
a. Time series data.
b. Cross Sectional data.
4. Plot the observations on a graph;
5. Estimate the cost function;
6. Test the reliability of the cost function.
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SAMPLE EXAM QUESTIONS:
QUESTION 1: CPA IRELAND SMA APRIL 2007
Mama Chuwa has been in restaurant business for 10 years now. Her famous dish “Kisinia
cha Tanga” has become famous as such one embassy with office in Dar es Salaam has
approached her for a customized meal pack to be delivered every Friday of the week.
Mama Chuwa has met with Administration officer of that embassy and the following
information were collected from the meeting, with regard to the order.
1. The embassy works 5 days of the week, and 4 weeks of the month and there are
20 staff in that office.
2. Goat Meat will be required and 5 kilos are enough for 20 people. The price of Goat
meat is TZS 10,000 per kg.
3. The pack will include biriyani, and 1 kilo of biriyani is enough for four persons. The
price of a kilo is TZS 7500.
4. Usually, every meal pack have some additions that includes
a. Eggs – the cost of an egg is TZS 500.
b. Banana fruit – the average cost of a banana is TZS 200
5. Other ingredients necessary for cooking “Kisinia cha Tanga” usually costs around
TZS 30,000 per meal of 20 people.
6. Mama Chuwa usually delivers the meal pack in a branded package that cost TZS
1,000 per package.
There are other monthly costs that are incurred in the business, which includes: •
•
•
•
Cooking gas – TZS 200,000
Cooking oil – TZS 50,000
Transport cost – TZS 100,000
Internet and social media adverts – TZS 115,000 a month.
Required:
1. Identify direct costs and indirect costs assuming cost object is the meal pack of
one person.
2. Repeat the above exercise, but assume the cost object is Embassy Order.
3. Compute the monthly total cost of the order, assuming Mama Chuwa usually sells
1000 plates in her business every month.
4. What is the suitable selling price per meal pack, assuming she desires a profit of
TZS 1,000 per meal pack.
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QUESTION 2: CPA IRELAND SMA APRIL 2007
Newport Ltd. manufactures oven-ready meals which it sells in bulk to catering firms.
There is a considerable amount of seasonal variation in the level of production. The
following production cost data for last year is available:
Production period
January -February
March – April
May- June
July- August
September – October
November – December
Batches of output
3,589
8,211
2,430
9,320
12,223
7,441
Total production cost
TZS 1,257,300
TZS 2,694,100
TZS 1,173,300
TZS 3,097,500
TZS 4,832,200
TZS 2,632,000
A regression analysis was carried out on this data in an attempt to determine whether
the level of production cost in any period is dependent on the number of batches of
output. The regression results were as follows:
Coefficient of determination (“R-squared”):
Intercept:
Slope:
Standard error of the coefficient:
Standard error of the estimate:
0.955
TZS 16,315
TZS 360.73
TZS 39.29
TZS 320,627
Management now wishes to forecast total production cost for the first production period
of next year. Production will be 4,120 batches in that period.
REQUIRED:
Note: The t-statistic for 4 degrees of freedom and 5% significance is 2.776.
(a) Make the forecast required by management, using the ‘high-low’ and ‘regression’
methods. (6 marks)
(b) Calculate a 95% confidence interval for each of the following: variable costs per batch,
and total costs for the first production period of next year. Then, explain clearly the
significance of the confidence intervals and the regression results. (10 marks)
(c) In your opinion, what are the two most significant advantages of using the regression
method rather than the high-low method to forecast costs? Explain your answer. (4
marks)
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QUESTION 3: CIMA ADAPTED
Anna Martinez, the financial manager atthe Casa Real restaurant, is checking to see if
there is any relationship between newspaper advertising and sales revenues at the
restaurant. She obtains the following data for the past 10 months:
March
April
May
June
July
August
September
October
November
December
Month Revenues
Advertising Costs
$50,000
70,000
55,000
65,000
55,000
65,000
45,000
80,000
55,000
60,000
$2,000
3,000
1,500
3,500
1,000
2,000
1,500
4,000
2,500
2,500
Required:
(a) Use the high-low method to compute the function, relating advertising costs and
revenues.
(b) Use regression analysis method estimate revenue function.
(c) Using (a) the regression equation and (b) the high-low equation, what is the increase
in revenues for each $1,000 spent on advertising within the relevant range? Which
method should Martinez use to predict the effect of advertising costs on revenues?
Explain briefly.
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