Chapter 5
The Nature of Costs
Topics to be Discussed
Introduction
The Behavior of Fixed and Variable
Costs
The Cost Equation
Cost Behavior and Decision Making
Introduction
What is the nature of costs and how
are they used in decision making?
Do they increase or decrease as
production volume changes?
Do they remain stable?
Introduction
Key Concept
Costs behave in predictable ways.
The concept of predictable cost behavior
based on volume is very important to the
effective use of accounting information
for managerial decision making.
The Behavior of Fixed Costs
Fixed Costs remain the same in total, but may vary per
unit when production volume changes.
Examples: Rent, Depreciation, Salary of a Plant Manager,
Insurance, Property Taxes
Fixed Cost Per Unit
Total Fixed Costs
$
$
Volume
Volume
The Behavior of Variable Costs
Variable Costs vary in direct proportion to changes in
production volume, but are fixed when expressed as perunit amounts.
Examples: Direct material, direct labor, and other unitlevel costs like factory supplies
Total Variable Costs
$
Variable Cost Per Unit
$
Volume
Volume
Curvilinear Costs and the Relevant Range
Relevant Range
Cost
Straight-Line
Approximation
Volume
Curvilinear
Function
The Cost Equation
Y = a + bx
Y = total costs
a = fixed costs
b = slope of line (variable costs)
x = units produced
Cost Behavior and Decision Making
Last month, 2,100 pizzas cost $15,750
Amount
Per Unit
$4,200
$2.00
Direct labor
3,150
1.50
Overhead
8,400
4.00
$15,750
$7.50
Direct materials
Total
If all costs are variable, how much
would 2,600 pizzas cost?
Cost Behavior and Decision Making
Cost of Goods Sold for 2,600
pizzas:
2,600 x $7.50 = $19,500
Assume that the direct materials,
direct labor, and overhead of
$1.00 per pizza are variable
costs, and that $6,300 is fixed.
What would be the cost of goods
sold for 2,600 pizzas?
Cost Behavior and Decision Making
Direct materials
$2.00 x 2,600 =
$5,200
Direct labor
$1.50 x 2,600 =
3,900
Variable overhead
$1.00 x 2,600 =
2,600
=
6,300
Fixed costs
Total cost of goods sold
y = a+bx
y = 6,300 + 4.50x
$18,000
More Cost Topics
Step Costs
Mixed Costs
Separating Mixed Costs into Their
Fixed and Variable Components
Regression Analysis
Step Costs
Step Costs remain constant within a
relevant range of production.
Example: Janitorial services within a
company that manufactures desks
0-7,500 desks
7,501-15,000 desks
1 Janitor
2 Janitors
$25,000
$50,000
Mixed Costs
Fixed and Variable Components
Fixed: lease payment each month
Variable: Gas, oil, maintenance costs, etc.,
that vary with the number of deliveries made
(and miles driven)
Mixed Costs
Pause and Reflect
Can you think of other common
examples of mixed costs?
Separating Mixed Costs into their
Fixed and Variable Components
Key Concept
Within the relevant range, fixed costs
are constant in total and vary per unit,
variable costs vary in total and are
constant per unit, and mixed costs
vary in total and vary per unit.
Separating Mixed Costs into their
Fixed and Variable Components
Regression Analysis: A statistical technique
used to estimate the fixed and variable
components of a mixed cost is called least
squares regression.
Regression analysis uses statistical methods to
fit a cost line (regression line) through a set of
points which minimizes the sum of the squared
distance from each data point to the line (hence
the name least squares regression).
Regression Analysis
Regression Line =
Total Overhead Cost
Costs
Slope of Regression
Line = Variable Cost
per unit
Fixed Cost
Using a Spreadsheet Program to
Perform Regression Analysis
Using the actual values of the mixed
costs (dependent variable) and the
volume of production (independent
variable) and a spread sheet
program such as Excel, you can
compute the regression line using
least squares regression.
See Exhibits 5-6, 5-8, 5-9 in the text.
Regression Statistics
Exhibit 5-9 shows R2 of less than
1.0 which implies that other
independent variable might have an
impact on the dependent variable.
Examples: Outside temperature and
other environmental factors might
impact overhead costs incurred.
Regression Statistics
Pause and Reflect
Can you think of other variables
that might have an impact on
total overhead costs?
Regression Statistics
Uses in other managerial decision making
Marketing Managers predicting changes in sales
based on changes in advertising expenditures.
Production Managers interested in quality
control might collect data on overtime worked in
a factory vs. the number of defective items
produced.
Estimating Regression Results Using
the High-Low Method
1. Use only two data points, the high and low
level of activity and their related total overhead
costs.
2. Subtract the smallest from the largest for
each
3. Change in cost
= Variable cost per unit
Change in volume
Estimating Regression Results Using
the High-Low Method
4. Substitute the total cost of one of the points
for “y” in the equation y = a + bx
5. Substitute the variable cost found
previously for “b”
6. Substitute the number of activity units for “x”
7. Solve for fixed costs “a”
8. Determine the formula to use in estimating
the mixed costs at various levels
Estimating Regression Results Using
the High-Low Method
If the high point of activity was 2,500
units and $12,450 of overhead costs and
the low point of activity was 1,950 units
and $10,300 of overhead costs, what
would be the estimated total costs at
2,435 units of activity?
Estimating Regression Results Using
the High-Low Method
1. High Point = 2,500 units at $12,450
Low Point = 1,950 units at $10,525
2. 2,500 - 1,950 = 550 units
$12,450 - 10,525 = $1,925
3. $1,925 / 550 units = $3.50 var cost/unit
Estimating Regression Results Using
the High-Low Method
4,5,6,7.
Y = a + bx
$12,450 = a + $3.50 (2,500)
$12,450 = a + $8,750
$3,700 = a
Y = $3,700 + $3.50x
8. Y = $3,700 + $3.50 (2,435)
Y = $12,222.50 total overhead costs
More Cost Behavior Topics
CB, ABC and ABM
CB in Merchandising and Service
Companies
Relevant Costs and CB
Impact of Income Taxes on Costs and
Decision Making
The Time Value of Money and Decision
Making
CB, ABC and ABM
Regression Analysis can be used to help
identify the “best” cost drivers of activities for
use in ABC and ABM.
An activity such as processing customer
orders might vary with the number of orders
OR the number of customers.
Regression analysis can help identify which
best explains the dependent variable, costs of
placing customer orders.
Relevant Costs and Cost Behavior
Merchandising
Sales revenue is a common cost driver. Cost
of goods purchased is a variable cost.
Service
Airlines might look at the number of
passengers or passenger miles as cost
drivers.
Relevant Costs and Cost Behavior
Key Concept
It can be misleading to always view
variable costs as relevant and fixed
costs as non relevant.
Taxes and Decision Making
Three Tax Considerations:
1. Costs of operating businesses are deductible
for income tax and revenues are taxable.
2. Form of a transaction may impact the amount of
tax paid or whether cost is tax deductible
3. Payment of tax requires cash outflow, thus
reducing the amount of cash available for other
purposes.
Taxes and Decision Making
Key Concept
Managers must consider the
impact of taxes on decisions.
After-Tax Costs and Revenues
After-Tax Cost of a tax deductible cash
expenditure:
after-tax cost = pretax cost X (1-tax rate)
After Tax Benefit of a taxable cash receipt:
after-tax benefit = pretax receipts X
(1-tax rate)
Before and After-Tax Net Income
After-Tax Income = Pretax Income X (1-Tax Rate)
$700 = $1,000 x (1 -.30)
The Time Value of Money and
Decision Making
When cash flows are
received or paid in
different time periods,
they are commonly
discounted by finding
their present value.
The Time Value of Money and
Decision Making
Key Concept
Managers must consider the
time value of money when
making long-term decisions.
End of Chapter 5
Analyzing costs has
to be a continuous
process!