Cost behavior and cvs analysis M.A CHAPTER II.pptx

Chapter II
Cost Behavior and CVP Analysis
2/14/2024 1

Basics of Cost Behavior
• Is the relationship between cost and activity
• Is nothing more than the sensitivity of costs to changes in
production or sales volume.
• Is the foundation upon which managerial accounting is built.
• Cost behavior is not required for external reporting under
U.S. GAAP.
• However, the understanding of cost behavior is very
important for management's efforts to plan and control its
organization's costs.
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Continued
• The behavior of costs is useful to managers for a variety of
reasons.
• To create a budget,
• Prepare a forecast,
• Determine how much profit a new product will
generate, and
• Determine which of two alternatives should be
selected.
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Continued
• Costs can be
• Variable
• step-variable
• Fixed
• Step-fixed
• Mixed and
• Curvilinear cost
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Variable costs
• Variable costs are costs that vary in proportion to changes in
the activity base.
Example: Direct material and direct labor costs.
• Variable costs can also be represented by a linear equation.
• This relationship can be described by the following equation
or graph:
Total variable costs = Variable rate x Amount of output
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Continued
• Variable costs have the following characteristics:-
 Cost per unit remains the same regardless of changes in the activity
base
 Total cost changes in proportion to changes in the activity base
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Examples:
variable costs and their related activity bases
Type of Business Cost Activity Base
University Instructor salaries Number of classes
Passenger airline Fuel Number of miles
flown
Manufacturing Direct materials Number of units
produced
Hospital Nurse wages Number of patients
Bank Teller wages Banking transactions
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Step-variable cost
• A cost that is nearly variable, but increases in small steps
instead of continuously.
• Example: direct labor cost of bakers, restaurant counter
service personnel, delivery truck drivers. Many of these
employees are part-time workers.
• If a step cost has relatively narrow steps, it means that the
cost changes in response to fairly small changes in output.
• May be approximated by a variable cost function without
much loss in accuracy
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Fixed Cost
• Fixed costs are costs that in total are constant within the
relevant range as the level of output increases or decreases.
• When the activity base is units produced, many factory
overhead costs such as straight-line depreciation are classified
as fixed costs.
• Fixed costs have the following characteristics:
 Cost per unit changes inversely to changes in the activity base
 Total cost remains the same regardless of changes in the activity base
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Some examples of fixed costs and their related activity bases
Type of Business Fixed Cost Activity Base
University Building (straight-line)
depreciation
Number of students
Passenger airline Airplane (straight-line)
depreciation
Number of miles flown
Manufacturing Plant manager salary Number of units produced
Hospital Property insurance Number of patients
Hotel Property taxes Number of guests
Bank Branch manager salary Number of customer
accounts
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Discretionary Fixed Costs and Committed Fixed Costs
• Two types of fixed costs are commonly recognized:
– Discretionary fixed costs and
– Committed fixed costs.
Discretionary fixed costs
– Fixed costs that can be changed or avoided relatively
easily at management discretion.
– Example:
• Advertising and promotion,
• Research and development
• Contribution to charitable organizations.
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Cont’d
Committed fixed costs
• Fixed costs that cannot be easily changed by management
decisions.
• Example:
– Lease cost
– Property tax
– Depreciation on building and equipment
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Step fixed cost
• Remain fixed over a wide range of activity but jump to a
different amount for activity levels outside that range.
• For example,
– A company may have to lease production machinery. If the
machine can only produce 1,000 units and the company
grows, they will have to lease additional machines for each
1,000 units of production needed (resulting in the wide
steps shown in the graph).
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Mixed Costs
• Are costs that have characteristics of both a variable and a fixed
cost.
• Are sometimes called semi-variable or semifixed costs.
• A salesperson’s compensation can be a mixed cost comprised of
a salary (fixed portion) plus a commission as a percent of sales
(variable portion).
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Measures of Output and the Relevant Range
• Fixed and variable costs have meaning only when related to
some output measure.
• A cost driver is a causal factor that measures the output of
the activity that leads (or causes) costs to change.
• Identifying and managing drivers helps managers better
predict and control costs.
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Relevant Range and Cost Relationships
• The relevant range is the range of output over which the
assumed cost relationship is valid for the normal operations
of a firm.
• The relevant range limits the cost relationship to the range of
operations that the firm normally expects to occur.
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• As this graph shows, the concept of the relevant range
allows managerial accountants to assume a linear cost
relationship.
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Accounting Records and Need for Cost Separation
• Can all costs be classified into the appropriate cost behavior
categories?
• If mixed costs are a very small percentage of total costs,
• In this case, mixed costs could be assigned to either the fixed
or variable cost category without much concern for the
classification error or its effect on decision making.
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Continued
• Alternatively, the total mixed cost could be arbitrarily divided
between the two cost categories.
(This is rarely done and not a good option.)
• Typically, mixed costs for many firms are large enough to call
for separation.
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Methods for Separating Mixed Costs into Fixed and
Variable Components
• Three common methods of separating a mixed cost into its
fixed and variable components are:
– The high-low method
– The scatter graph/ Visual fit/ method
– Least square regression
• Each method requires the simplifying assumption of a linear
cost relationship.
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Continued
• Recall the expression of cost as an equation for a straight line
is:
Total cost = Fixed cost + (Variable rate x Output)
• The dependent variable is a variable whose value depends on
the value of another variable.
• In the previous equation, total cost is the dependent variable;
it is the cost we are trying to predict.
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Continued
• The independent variable is a variable that measures output
and explains changes in the cost or other dependent variable.
– A good independent variable is one that causes or is closely associated
with the dependent variable.
– Therefore, many managers refer to an independent variable as a cost
driver.
• The intercept corresponds to fixed cost.
• The slope of the cost line corresponds to the variable rate.
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The High-Low Method
• Given two points, the slope and the intercept can be
determined.
• The high-low method is method of separating mixed costs into
fixed and variable components by using just the high and low
data points.
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Continued
• Four steps must be taken in the high-low method:
– Step 1: Find the high point and the low point for a given data set.
– Step 2: Using the high and low point, calculate the variable rate.
• Variable rate = (High point cost - Low point cost) ÷ (High point output -
Low point output)
– Step 3: Calculate the fixed cost using the variable rate (from Step 2)
and either the high point or low point.
• Fixed cost = Total cost at high point - (Variable rate x Output at high point)
– Step 4: Form the cost formula based on the high-low method.
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Example
• Company A wants to determine the cost-volume relation between
its factory overhead cost and number of units produced. Use the
high-low method to split its factory overhead (FOH) costs into fixed
and variable components and create a cost volume formula. The
volume and the corresponding total cost information of the factory
for past eight months are given below:
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Month Units FOH
1 1,520 $36,375
2 1,250 38,000
3 1,750 41,750
4 1,600 42,360
5 2,350 55,080
6 2,100 48,100
7 3,000 59,000
8 2,750 56,800

Solution:
We have,
• At lowest activity: X1 = 1,250; Y1 = $38,000
• At highest activity: X2 = 3,000; Y2 = $59,000
• Variable Cost per Unit
= ($59,000 − $38,000) ÷ (3,000 − 1,250)
= $12 per unit
• Total Fixed Cost
= $59,000 − ($12 × 3,000) = $38,000 − ($12 × 1,250)
= $23,000
• Cost Volume Formula:
Y = $23,000 + 12X
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Scatter graph Method
• A method of separating mixed costs into fixed and variable
components by fitting a line to a set of data using two points
that are selected by judgment.
• The scatter graph method is a way to see the cost relationship
by plotting the data points on a graph.
• The first step in applying the scatter graph method is to plot
the data points so that the relationship between costs and
activity output can be seen.
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Continued
• Finally, we can use the scatter graph to visually fit a line to
the data points on the graph.
• Of course, the manager or cost analyst will choose the line
that appears to fit the points the best, and perhaps that
choice will take into account past experience with the
behavior of the cost item.
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Continued
• Unfortunately, the scatter graph method suffers from the lack
of any objective criterion for choosing the best-fitting line.
• The quality of the cost formula depends on the quality of the
subjective judgment of the analyst.
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Example
• Company A decides to use scatter graph method to split its
factory overhead (FOH) into variable and fixed components.
Following is the data which is provided for the analysis.
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Month Units FOH
1 1,520 $36,375
2 1,250 38,000
3 1,750 41,750
4 1,600 42,360
5 2,350 55,080
6 2,100 48,100
7 3,000 59,000
8 2,750 56,800

Solution:
• Fixed Cost = y-intercept = $18,000
• Variable Cost per Unit = Slope of Regression Line
• To calculate slop we will take two points on line: (0,18000)
and (3500,68000)
• Variable Cost per Unit = (68000 − 18000) ÷ (3500 − 0) =
$14.286
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The Method of Least Squares
• The method of least squares (regression) is a statistical way to
find the best-fitting line through a set of data points.
• One advantage of the method of least squares is that for a
given set of data, it will always produce the same cost
formula.
• Basically, the best-fitting line is the one in which the data
points are closer to the line than to any other line.
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Continued
• The squared deviations between the regression line and each
data point are, in total, smaller than the sum of the squared
deviations of the data points and any other line.
• Can find:-
– The one line with the smallest sum of squared deviations or
– The line which minimizes the cost prediction errors or
– Differences between predicted costs (i.e., on the regression line) and
actual costs (i.e., the actual data points).
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Using the Regression Programs
• Computing the regression formula manually is tedious, even
with only a few data points.
• As the number of data points increases, manual computation
becomes impractical.
• It requires a computer spreadsheet program (for example,
Excel) or calculator and uses all points of data instead of just
two points like the high‐low method.
• It also provides information that can be used to see how
reliable the cost equation is—a feature that is not available
for the scatter graph and high-low methods.
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Cont’d
• Assuming that the cost varies along y-axis and activity levels
along x-axis, the required cost line may be represented in the
form of following equation:
y = a + bx
Where
– a is the y-intercept of the line and it equals the approximate fixed cost
at any level of activity.
– b is the slope of the line and it equals the average variable cost per
unit of activity.
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Cont’d
Unit Variable Cost = 𝑏 =
nΣxy – Σx.Σy
nΣx2 − (Σx)2
Total Fixed Cost = a = Σy – bΣx
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Example
• Based on the following data of number of units produced and
the corresponding total cost, estimate the total cost of
producing 4,000 units. Use the least-squares linear regression
method.
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Month Units FOH
1 1,520 $36,375
2 1,250 38,000
3 1,750 41,750
4 1,600 42,360
5 2,350 55,080
6 2,100 48,100
7 3,000 59,000
8 2,750 56,800

Solution:
x Y x2 xy
1,520 $36,375 2,310,400 55,290,000
1,250 38,000 1,562,500 47,500,000
1,750 41,750 3,062,500 73,062,500
1,600 42,360 2,560,000 67,776,000
2,350 55,080 5,522,500 129,438,000
2,100 48,100 4,410,000 101,010,000
3,000 59,000 9,000,000 177,000,000
2,750 56,800 7,562,500 156,200,000
Σx = 16,320 Σy = 377,465 Σx2 = 35,990,400 Σxy = 807,276,500
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Solution
Calculating the average variable cost per unit:
𝑏 =
nΣxy – Σx.Σy
nΣx2 − (Σx)
2
=
8 X 807,276,500 − 16,320 X 377,465
8 X 35,990,400 – (16,320)2
= 13.8
Calculating the approximate total fixed cost:
Total Fixed Cost = a = Σy – bΣx
= 377,465 − 13.8078 X 16,320 = 19,015
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Solution
• The cost-volume formula now becomes:
y = a + bx
y = 19,015 + 13.8x
• At 4,000 activity level, the estimated total cost is $74,215
Y = 19,015 + 13.8 × 4,000
Y = 74,215
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Goodness of Fit
• Regression routines provide information on goodness of fit.
• Goodness of fit tells us how well the independent variable
predicts the dependent variable.
• The percentage of variability in the dependent variable
explained by an independent variable (in this case, a
measure of activity output) is called the coefficient of
determination (R-squared).
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Cont’d
• The higher the percentage of cost variability explained, the
better job the independent variable does of explaining the
dependent variable.
• Since R-squared is the percentage of variability explained, it
always has a value between 0 and 1.00.
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Comparison of Methods for Separating Mixed Costs
into Fixed and Variable Components
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COST-VOLUME-PROFIT (CVP) ANALYSIS
 CVP analysis looks at the relationship between selling price,
sales volumes, costs, and profits.
 It is a powerful tool in making managerial decisions including
marketing, production, investment, and financing decisions.
 To perform Cost-Volume-Profit-Analysis (C-V-P-A), you need
to know how costs behave when business activity
(production volume, sales volume…) changes.
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Cont’d
• That is, once the variable and fixed elements have been
determined using the tools discussed in the preceding slides,
we use the following profit equation:
Profit = SP(x) - VC(x) – TFC=Net Income
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Cont’d
• One of the primary purposes of C-V-P is to calculate the
Break-Even Point.
• It simply represents the number of units the firm must sell to
generate exactly zero net income– to earn neither profit nor
loss.
• Graphically, Break-Even is the point where the sales curve and
cost curve cross.
• It should be noted here that managers are seldom interested
in merely breaking even. But the Break-Even is an important
benchmark!
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Assumptions Underlying
CVP Analysis
1. The analysis assumes a linear revenue function and a linear
cost function.
2. The analysis assumes that price, total fixed costs, and unit
variable costs can be accurately identified and remain
constant over the relevant range.
3. The analysis assumes that what is produced is sold.
4. For multiple-product analysis, the sales mix is assumed to
be known.
5. The selling price and costs are assumed to be known with
certainty.
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Department of Accounting and Finance,
Sundaero College

CVP analysis with Multiple products
 For a company with more than one product, sales
mix is the relative combination in which a company’s
products are sold.
 Different products have different selling prices, cost
structures, and contribution margins.
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Sales mix break-even point calculation steps
• Step 1: Calculate the contribution margin per unit for each
product
• Step 2: Calculate the weighted-average contribution margin
per unit for the sales mix
• Step 3: Calculate total units of sales mix required to break-
even
• Step 4: Calculate number units for each product at break-even
point
• Step 5: Calculate Break-even Point in dollars
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CVP Relationships and the Income Statement
• The management functions of planning, control, and decision
making all are facilitated by an understanding of cost-volume-
profit relationships.
• These relationships are important enough to operating
managers that some businesses prepare income statements
in a way that highlights CVP issues.
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Traditional Income statement
• Contains several blocks of revenue and expense information:
Revenue Block, Cost of goods sold block, Gross margin line,
Selling and administrative block, Operating profit/loss line,
Non-operating expenses block and net income line.
• Its approach is the dominant format used by nearly all
companies, because it is required by the accounting
standards for the reporting of financial results to outside
parties.
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A. Traditional Format
Sales $500,000
Less: 380,000
Gross margin $120,000
Less: Operating expenses:
Selling expenses $35,000
Administrative expenses 35,000 70,000
Net income $50,000
ACCUTIME COMPANY
Income Statement
For the Year Ended December 31, 20x1
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Contribution Income statement
• Variable expenses are aggregated into what would have been
the cost of goods sold block in a traditional income statement.
• The contribution margin approach can be of use for internal
reporting, when a company wants better visibility into the
results of its operations and how its net income will vary in
response to different changes in revenue levels.
• Highlights the distinction between variable and fixed
expenses.
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B. Contribution Format
Sales $500,000
Less: Variable expenses:
Variable manufacturing $280,000
Variable selling 15,000
Variable administrative 5,000 300,000
Contribution margin $200,000
Less: Fixed expenses:
Fixed manufacturing $100,000
Fixed selling 20,000
Fixed administrative 30,000 150,000
Net income $50,000
Income Statement
For the Year Ended December 31, 20x1
ACCUTIME COMPANY
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Cost Structure and Operating
Leverage
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Cost Structure
• Its concept is a management accounting concept; it has no
applicability to financial accounting.
• Refers to the types and relative proportions of fixed and
variable costs that a business incurs.
• This concept can be defined in smaller units, such as by
product, service, product line, customer, division or
geographic region.
• Used as a tool to determine prices.
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OPERATING LEVERAGE
• The extent to which an organization uses fixed costs in cost
structure.
• Greatest in Firms with a large proportion of fixed costs, low
proportion of variable costs, and the resulting high
contribution-margin ratio
• The ability of the firm to generate an increase in net income
when sales revenue increases.
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Operating Leverage Factor
• The managerial accountant can measure a firm’s operating
leverage, at a particular sales volume, using the degree of
operating leverage.
• In Break even analysis, margin of safety is how much output
or sales level can fall before a business reaches its breakeven
point.
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Continued
• A firm with proportionately high fixed costs has relatively
high operating leverage.
• A firm with high operating leverage has a relatively high
break-even point.
• A company with higher DOL has more extreme fluctuations in
operating income than a company with a lower DOL when a
change in sales revenue occurs.
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Continued
• A high DOL implies a more risky operating structure because
of the volatility of the change in profit.
• Conversely, a lower DOL amount implies a less risky operating
structure.
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