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III. The analysis of mixed costs
a. Account analysis and the engineering approach
i. In account analysis, each account under
consideration is classified as variable or fixed
based on the analyst’s prior knowledge about how
costs behave.
1. This approach is limited in value in the
sense that it glosses over the fact that some
accounts may have both fixed and variable
components.
ii. The engineering approach classifies costs based
upon an industrial engineer’s evaluation of
production methods, material specifications, labor
requirements, equipment usage, power
consumption, and so on.
1. This approach is particularly useful when no
past experience is available concerning
activity and costs.
b. Diagnosing cost behavior with a scattergraph plot
Learning Objective 5: Analyze a mixed cost using a
scattergraph plot and the high-low method.
i. Before analyzing a mixed cost you should plot the
data on a scattergraph. For illustrative purposes,
assume the following information, which would
be plotted as follows:
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1. The maintenance cost, which is known as
the dependent variable, is plotted on the Y
(vertical) axis.
2. The activity (hours of maintenance), which
is known as the independent variable, is
plotted on the X (horizontal) axis.
ii. After plotting the data, examine the dots on the
scattergraph to see if they are linear, such that a
straight line can be drawn that approximates the
relation between cost and activity.
1. If the dots are not linear, do not analyze the
data any further. Instead, search for another
independent variable that bears a stronger
linear relationship with the dependent
variable.
2. In this example, the dots are linear so we can
proceed to the high-low method.
c. The high-low method
i. This method can be used to analyze mixed costs if
a scattergraph plot reveals a linear relationship
between the X and Y variables. Let’s continue
with our data from the scattergraph plot.
ii. The first step is to choose the data points
pertaining to the highest and lowest activity levels
(high = 850 units; low = 450 units).
1. Notice, this method relies on two data points
to estimate the fixed and variable portions of
a mixed cost.
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iii. The second step is to determine the total costs
associated with the two chosen points (high =
$9,800; low = $7,400).
Helpful Hint: Emphasize that the high and low points
are identified by the level of activity and not by the level
of the cost.
iv. The third step is to calculate the change in cost
between the two data points ($2,400) and divide it
by the change in activity level between the two
data points (400 units).
1. The quotient represents an estimate of
variable cost per unit of activity ($6.00 per
unit).
v. The fourth step is to take the total cost at either
activity level (in this case, $9,800) and deduct the
variable cost component ($5,100). The residual
represents the estimate of total fixed costs
($4,700).
1. The variable cost component ($5,100) is
determined by multiplying the level of
activity (850 units) by the estimated variable
cost per unit of the activity ($6.00 per unit).
vi. The fifth step is to construct an equation that can
be used to estimate the total cost at any activity
level (Y = $4,700 + $6.00X).
Quick Check
−
the high-low method
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d. The least-squares regression method
i. This method can be used to analyze mixed costs if
a scattergraph plot reveals an approximately linear
relationship between the X and Y variables.
ii. This method uses all of the data points to
estimate the fixed and variable cost components
of a mixed cost. This method is superior to the
high-low method that uses only two data points to
estimate the fixed and variable cost components
of a mixed cost.
iii. The basic goal of this method is to fit a straight
line to the data that minimizes the sum of the
squared errors. The regression errors are the
vertical deviations from the data points to the
regression line.
iv. The formulas that are used for least-squares
regression are complex. Fortunately, computers
can perform the calculations quickly. The
observed values of the X and Y variables are
entered into the computer and the software does
the rest.
1. The output from the regression analysis can
be used to create an equation that enables
you to estimate total costs at any activity
level.
v. The high-low and least-squares regression
methods provide different estimates of the fixed
and variable cost components of a mixed cost.
This is to be expected because each method uses
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differing amounts of the data points to provide
estimates. Least-squares regression provides the
most accurate estimates because it uses all of the
data points.
IV. Traditional and contribution format income statements
Learning Objective 6: Prepare income statements for a
merchandising company using the traditional and
contribution formats.
a. The traditional and contribution formats differ as
follows:
i. The traditional approach separates product costs
as required for external reporting purposes from
selling and administrative expenses. It does not
focus on cost behavior.
ii. The contribution approach separates costs into
fixed and variable categories. Sales − variable
costs = contribution margin. The contribution
margin − fixed costs = net operating income.
iii. The contribution approach is used as an internal
planning and decision-making tool. For example,
this approach is useful for:
1. Cost-volume-profit analysis (Chapter 5).
2. Budgeting (Chapter 8).
3. Segmented reporting of profit data (Chapter
6).
4. Special decisions such as pricing and make
or buy analysis (Chapter 12).
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Helpful Hint: The income statement from the annual
report of a well-known local manufacturing firm can be
used to illustrate the functional income statement. Ask if
the various expense categories on the income statement
contain both fixed and variable costs. Also ask how to
estimate the increase in profit that would result from a
4% increase in sales using the functional statement.
There is no way to do this with reasonable accuracy,
since there is no way to tell on a functional income
statement what costs would increase.
V. Cost classifications for decision making
Learning Objective 7: Understand cost classifications
used in making decisions: differential costs, opportunity
costs, and sunk costs.
A. It is important to realize that every decision involves a
choice between at least two alternatives. The goal of
making decisions is to identify those costs that are either
relevant or irrelevant to the decision. To make
decisions, it is essential to have a grasp on three
concepts:
i. Differential costs (or incremental costs) − A
difference in cost between any two
alternatives (a difference in revenue between
two alternatives is called differential
revenue).
1. Differential costs can be either fixed or
variable.
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ii. Opportunity cost − The potential benefit that
is given up when one alternative is selected
over another.
1. These costs are not usually entered into the
accounting records of an organization, but
must be explicitly considered in all
decisions.
Helpful Hint: Ask students what opportunity costs they
incur by attending class. Their opportunity cost is the
value to them of the activity they would be doing
otherwise (e.g., working, sleeping, partying, studying,
etc.)
iii. Sunk cost − A cost that has already been
incurred and that cannot be changed now or in
the future.
Helpful Hint: Ask students: “Suppose you had
purchased gold for $400 an ounce, but now it is selling
for $250 an ounce. Should you wait for the gold to
reach $400 an ounce before selling it?” Many students
will say “yes” even though the $400 purchase is a sunk
cost.
Quick Check
−
relevant costs
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