GIMPA Business School

Management Accounting

Determining How Cost Behavior

Lecture 6

1
 Learning Objectives

At the end of this lecture , students should be able

to:
• Understand how fixed and variable costs behave
and how to use them to predict costs
• Analyse the total cost function
• Segregate total cost into its fixed and variable
components using any of the methods: high/low,
scatter graph and regression analysis, and
• Establish a linear function using regression
analysis and interpret the results.

2
 Cost Classification
• Costs behave in different ways as the level of
activity changes.
• Costs can be classified by how they behave.
There are three cost behaviour patterns:
– Variable cost
– Fixed Cost
– Mixed or semi-variable cost
• The relative proportion of each type of cost in
an organization is known as its cost structure
3
 Variable Costs
• Variable cost is a cost whose total cedi amount varies in direct
proportion to changes in the activity level. If the activity level
doubles, the total variable cost also doubles. If the activity level
increase by 10% the total variable cost increases by 10% as well.
Examples include:
– Material used to manufacture a unit of output or to provide a type of
service
– Labour costs
– Commission paid to a sales person
– Fuel used by a transportation company
• A variable cost remains constant if expressed on a per unit basis
• For a cost to be variable, it must be variable with respect to an
activity base. An activity base is a measure of whatever causes the
incurrence of the variable cost. Also known as the cost driver

4
 Example of Variable Costs
• ABC Company provides meals to its customers. The meals are
purchased from a caterer for ¢30 a customer.
• If we look at the cost of the meal on a customer basis, it remains
constant at ¢30. This ¢30 cost per customer will not change,
regardless of how many customers ABC feeds.
• On a total basis, the cost varies per number of customers

• The table below illustrates the behaviour of the variable cost

Number of Cost of meal Total cost

Customers per customer of meals
250 ¢30 ¢7,500
500 ¢30 ¢15,000
750 ¢30 ¢22,500
1,000 ¢30 ¢30,000
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 Fixed Costs
• Total fixed costs remain constant within the relevant range of activity.
• Some costs do not vary, whatever the level of activity. These are called
fixed costs.
• Since fixed costs remain constant in total, the fixed cost per unit becomes
progressively smaller as the level of activity increases
• Most capacity-related costs (such as depreciation on factory equipment)
since they result from investments in building, equipment, skilled
professional employees needed to provide the basic capacity for sustained
operations.
• Committed Fixed Costs – these are costs that are the result of
commitments made previously and can not be reduced or changed
without making fundamental changes to the company’s production
facilities or labour requirements - depreciation, insurance, real estate
taxes, salaries of top management.
• Discretionary Fixed Costs – (or managed) arise from annual decisions by
management to spend on certain fixed cost items – advertising, research,
public relations, management development programs, travels, internships.

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 Semi-Variable or Mixed Costs
• A mixed cost contains both variable and fixed cost
elements. Mixed costs are also known as semi-variable
costs. Examples include a salespersons compensation
which has a salary and a commission components,
maintenance and repairs, utilities etc.
• From the levels of activity perspective, total cost is
composed of Fixed Cost and Variable Cost.
• Therefore Total cost (TC) = Fixed cost (FC) + Variable
cost (VC).
• Graphically, the Variable cost curve can be
superimposed on to the Fixed cost curve to give the
Total cost curve.

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 Mixed Cost Behaviour

6
C
5
O
S 4 Variable cost
T
3
FC
(

0 2 TC
0 Fixed cost
1
0
)

0
0 100 200 300 400 500 600
UNITS

8
 Cost Function Analysis

• The Total Cost function can be stated as:

• y = a + bx
• Where y = total cost
• a = Total fixed cost
• b = variable cost per unit
• x = number of units or activity level
• bx = total variable cost for x units.
• Note: the slope of the total cost curve (the variable cost curve
as well) is measured as:
• ∆y/∆x = b

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 Segregation of Cost

• Methods used to segregate the total cost into

its fixed and variable components include:
• High/Low method
• Scatter graph and
• Regression analysis.

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 High/Low Method
• It estimates fixed and variable costs by comparing the cost of
the highest and lowest activity levels.
• The differences are analysed.
• The high-low method is explained, step by step, as follows.
• Step 1 - Select the highest pair and the lowest pair.
• Step2 - Compute the variable rate, b, using the formula
Difference in cost y
Difference in activity x
• Step 3 Compute the fixed cost portion as:
Fixed cost portion = Total cost -Variable cost

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 High/Low Method
• Example
• Production costs for the six months to 31 December, 2009
were as follows:
Month Units Costs
GH¢
• July 340 2,260
• August 300 2,160
• September 380 2,320
• October 420 2,400
• November 400 2,300
• December 360 2,266

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 High/Low Method
• Solution
• Month Units Cost
• GH¢
• Highest Month 420 2,400
• Lowest Month 300 2,160
• Difference 120 240

• The additional cost per unit between the highest and lowest
months is GH¢240 / 120Units = GH¢2 per unit.
• This is the variable cost per unit.
• The total variable cost for the highest month is 420units x
GH¢2 = GH¢840.
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 High/Low Method
• Total cost = total variable cost + fixed cost
• Fixed cost = total cost – total variable cost
• Fixed cost = 2,400 – 840 = 1,560 or
• 2,160 – (300 x 2) = 1,560.
• The cost function is y = 1,560 + 2x

• Limitations:
• It relies on historical data, assuming that (i) activity is the only
factor affecting cost and (ii) historical costs reliably predict
future cost.
• It uses only two values, the highest and the lowest, which
means that the results may be distorted due to random
variations in these values.

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 Scatter Graph Method
• Procedure:
• Plot the points in the example on a graph paper.
• Select a line of best fit through the points by visual inspection.
• Extend the line of best fit to the y-axis.
• The point of interception is the estimated Fixed cost.
• Calculate the variable cost per unit by selecting two points on
the graph and find the change in cost and output.
• Divide change in cost by the change in output to get the
variable cost per unit.

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 Scatter Graph Method

• Limitations:
• Method is subjective as line of best fit is fitted by visual
inspection.
• The line of best fit will probably differ depending on the
individual who chooses it by visual inspection.
• The total cost function may be different from that of the
high/low method.

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 Least Squares Regression Method
• A more scientific and accurate method of showing the line of best
fit. It makes use of all the data.
• The cost function y = a + bx will be used.
• To predict the total cost y from activity level x it is necessary to
calculate the values of a and b from the following equations:
• a = mean of y – b(mean of x) = ∑ y _ b∑x = Fixed Cost
• n n
• b = n∑xy – (∑x)(∑y) = Variable cost per unit
• n∑x² - (∑x)²
• Where n is the number of observations of x and y values, and ∑
represents the sum of the variables
• Solve for a and b and substitute the values into the equation y = a +
bx for the regression line.
• Visually, the vertical deviations are called the regression errors. The
line of best fit or regression line simply computes the regression
line that minimizes the sum of these squared errors.
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 Regression Analysis
• Procedure:
• Tabulate the data and determine which is the dependent variable, y and
the independent variable x.
• Calculate ∑x, ∑y, ∑x², ∑xy
• Substitute the values in the formulae in order to find b and a in that order.
• Substitute the values of a and b in the equation to get the regression line
for y on x.
• The formulas are complex and involve numerous computations but the
principle is simple.
• Fortunately, computers are used to carry out the computations fairly
easily.
• In addition to estimate of the intercept (fixed cost) and the slope (variable
cost per unit), the statistical software provides other useful statistics.
• One of these statistics is the R2, which is a measure of "goodness of fit."
The R2 tells us the percentage of the variation in the dependent variable
(cost) that is explained by variation in the independent variable (activity).
The R2 varies from 0% to 1 00%, and the higher the percentage, the better.

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 Regression Analysis Statistics – Coefficient of
Determination
• In addition to estimate of the intercept (fixed cost) and the
slope (variable cost per unit), the statistical software provides
other useful statistics.
• One of these statistics is the R2, which is called, coefficient of
determination, a measure of "goodness of fit." The R2 tells us
the percentage of the variation in the dependent variable
(cost) that is explained by variation in the independent
variable (activity). The R2 varies from 0% to 100%, and the
higher the percentage, the better.
• The R2 is computed using the following formula:
R2 = {n∑xy – (∑x)(∑y)}2
{n∑x2-(∑x)2}{n∑y2-(∑y)2}

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 Practice Question
• XYZ Company decides to relate total factory overhead costs to direct labor
hours (DLH) to develop a cost formula in the form of y = a + bx. Twelve
monthly observations are collected as follows:
Month Direct Labour Hours(x) Factory Overhead(y)
January 9 hours ¢15
February 19 20
March 11 14
April 14 16
May 23 25
June 12 20
July 12 20
August 22 23
September 7 14
October 13 22
November 15 18
December 17 18

Required
Separate the factory overhead costs into fixed and variable components using a) the high-
low method and b) method of least squares. 20
 Solution
a) High-Low Method
DLH FOH
H 23 25
L 7 14
Diff 16 11
Variable rate b = diff in y/diff in x = 11/16 = ¢0.6875 per DLH
Fixed cost = TC-VC
= 25 – 0.6875(23) = ¢9.1875 OR
= 14 – 0.6875(7) = ¢9.1875
Cost formula for factory overhead costs is ¢9.1875 fixed, plus
¢0.6875 per DLH or alternatively Y= ¢9.1875 + ¢0.6875X

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 Practice Question cont’d
b) Method of Least Squares
Direct Labour Factory
Month
Hours(x) Overhead(y) XY X2 Y2
January 9 15 135 81 225
February 19 20 380 361 400
March 11 14 154 121 196
April 14 16 224 196 256
May 23 25 575 529 625
June 12 20 240 144 400
July 12 20 240 144 400
August 22 23 506 484 529
September 7 14 98 49 196
October 13 22 286 169 484
November 15 18 270 225 324
December 17 18 306 289 324
Total 174 225 3414 2792 4359

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 Solution Cont’d
∑x =174, ∑y = 225, ∑xy = 3,414, ∑x2 = 2,792, ∑y2 = 4359, mean of X = ∑x/12 =
174/12 = 14.5, mean of Y = ∑y/n = 225/12 = 18.75
b = n∑xy – (∑x)(∑y) = 12(2,414) –(174)(225) = 1,818 = 0.5632
n∑x² - (∑x)² 12(2792) – (174)2 3,228
a = mean of y – b(mean of x) = ∑ y _ b∑x = Fixed Cost
n n
a = 18.75 – 0.5632(14.5) = 10.5836
Therefore the cost formula is: Y = ¢10.5836 + ¢0.5632 per DLH

R2 = {n∑xy – (∑x)(∑y)}2
{n∑x2-(∑x)2}{n∑y2-(∑y)2}
R2 = (1,818)2 3,305,124 = 0.6084 or 60.84%
(3228){(12(4359)-(225)2} 5,432,724
Interpretation
• This means that about 60.84 percent of the total variation in total factory
overhead is explained by DLH and the remaining 39.16 percent is still
unexplained. Indication that DLH is not good enough to explain fully the
behaviour of factory overhead costs. There are other factors that are also
important in explaining the behaviour of factory overhead costs.

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 Question – High-Low
• A hospital’s records show that the cost of carrying out health checks in the
last five periods have been as follows:
Period # of Patients seen Total Cost (¢)
1 650 17,125
2 940 17,800
3 1,260 18,650
4 990 17,980
5 1,150 18,360

• Using the high-low method, calculate the estimated cost of carrying out
health checks on 850 patients during period 6.
• a) 17,515, b) 17,570 c) 17,625 d) 17,680

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 Solution
# of patients Costs
High 1,260 18,650
Low 650 17,125
Diff 610 1,525
VC per patient = 1525/610 = 2.50
FC = 17,125 – 650x2.50 = 15,500
Y = 15,500 + 2.50 x number of patients
Estimated cost = 15,500 + 2.50x850 = ¢17,625

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 Question: High-Low
• All variable costs of a particular service vary based on direct
labour costs. The following relationship pertains to a year’s
budgeted activity regarding this service:
Direct labour cost Total costs
GHC 30,000 GHC 129,000
GHC 40,000 GHC 154,000

• What are the budgeted fixed costs for the year?

a) GHC25,000
b) GHC29,000
c) GHC54,000
d) GHC75,000

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 Practice Question – High/Low
• ABC has the following machine hours and production costs for the
last six months of last year:
Month Machine Hours Production Cost
July 15,000 ¢12,330
August 13,500 ¢10,300
September 11,500 ¢9,580
October 15,500 ¢12,080
November 14,800 ¢11,692
December 12,100 ¢9,922

• If ABC expects to incur 14,000 machine hours in January, what will

be the total production cost estimate using the high-low method?

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