Slides calculate total cost and incremental costs

Calculate Total Cost And
Incremental Costs
Principles of Cost Analysis and
Management

© Dale R. Geiger 2011

1


What if?
• Relationship between cost and unit of output
is neither fixed nor variable?
• There are multiple elements that affect the
cost of an output?
• A different type of cost relationship is relevant
to the decision at hand?

© Dale R. Geiger 2011

2


Terminal Learning Objective
• Task: Calculate Total Cost And Incremental Costs Given
Various Production Volumes
• Condition: You are a cost advisor technician with access to
all regulations/course handouts, and awareness of
Operational Environment (OE)/Contemporary Operational
Environment (COE)
• Standard: With at least 80% accuracy:

•
•
•
•

Describe multivariate (mixed) and incremental costs
Express total multivariate cost in an equation
Graph total multivariate cost over a relevant range
Express incremental cost in an equation
© Dale R. Geiger 2011

3


Cost Definitions
• Mixed Costs - A combination of fixed and
variable costs
Total Cost =
Variable Cost + Fixed Cost

• Also known as multivariate costs

© Dale R. Geiger 2011

4


Multivariate Cost Expressions
• Variable component:
• Variable $Cost per Unit * # Units

-Plus• Fixed component:
• Sum of relevant costs that remain the same
regardless of units of output

© Dale R. Geiger 2011

5


Multivariate Cost Example
• Relevant cost of transporting a unit for onlocation training is $350,000.
• Cost of training operations on-location runs
$20,000 per day.
• What is the unit of output?
• Days of training

© Dale R. Geiger 2011

6


Multivariate Cost Example
• Relevant cost of transporting a unit for onlocation training is $350,000.
• Cost of training operations on-location runs
$20,000 per day.
• What is the unit of output?
• Days of training

© Dale R. Geiger 2011

7


Multivariate Cost Example
• Relevant cost of transporting a unit for onlocation training is $350,000.
• Cost of training operations on-location runs
$20,000 per day.
• What is the cost expression for Fixed cost?
• Fixed cost = $350,000

© Dale R. Geiger 2011

8


Multivariate Cost Example
• Relevant cost of transporting a unit for onlocation training is $350,000.
• Cost of training operations on-location runs
$20,000 per day.
• What is the cost expression for Fixed cost?
• Fixed cost = $350,000

© Dale R. Geiger 2011

9


Multivariate Cost Example
• Relevant cost of transporting a unit for onlocation training is $350,000.
• Cost of training operations on-location runs

$20,000 per day.
• What is the cost expression for Variable Cost?
• Variable cost = $20,000/day * # of days

© Dale R. Geiger 2011

10


Multivariate Cost Example
• Relevant cost of transporting a unit for onlocation training is $350,000.
• Cost of training operations on-location runs
$20,000 per day.
• What is the cost expression for Variable Cost?
• Variable cost = $20,000 per day * # of days

© Dale R. Geiger 2011

11


Multivariate Cost Example
• Relevant cost of transporting a unit for onlocation training is $350,000.
• Cost of training operations on-location runs
$20,000 per day.
• What is the cost expression for Total Cost of
on-location training?

© Dale R. Geiger 2011

12


Multivariate Cost Example
• Relevant cost of transporting a unit for onlocation training is $350,000.
• Cost of training operations on-location runs
$20,000 per day.
• What is the cost expression for Total Cost of
on-location training?
• Total Cost = Variable cost + Fixed Cost
• Total Cost = $20,000 per day * #days +
$350,000
© Dale R. Geiger 2011

13


Graph of Mixed Cost
$K 700
600
500
400
$350K

Fixed Cost

300
200
100
0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

X Axis = Number of Days
As Number of Days increases, Fixed Cost does not change
© Dale R. Geiger 2011

14


Graph of Mixed Cost
$K 700

Variable cost
for 10 days =
$20K per day * 10 days
= $200K

600
500
400

Fixed Cost
Variable Cost

300
200
100
0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

X Axis = Number of Days
As Number of Days increases, Variable Cost increases
© Dale R. Geiger 2011

15


Graph of Mixed Cost
Total cost for 10 days =
$20K per day * 10 days +
$350K
or $550K

$K 700
600
$550K
500
400

Fixed Cost
Variable Cost
Total Cost

300
200
100
0

0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

X Axis = Number of Days
As Number of Days increases, both Variable Cost and Total Cost increase 16
© Dale R. Geiger 2011

Questions
•  What is the cost expression for Cost per Day?

• How would the graph of Cost per Day look?
• It should be a downward sloping curve that will
level out above $20K

© Dale R. Geiger 2011

17


Cost Definitions
• Semi-variable Cost - Costs that Increase as
Unit of Output increases, but not in Direct
Proportion
• Examples:
• Hours worked by an employee
• Miles driven
• Students in a course

© Dale R. Geiger 2011

18


Semi-Variable Cost Example
• Sometimes the Variable Cost per unit
remains the same only for a Relevant Range
• Example: Employee Wages

• Employee’s base wage is $15 per hour
• If the employee works more than 40 hours in a
week we must pay time and a half

© Dale R. Geiger 2011

19


Cost Expression for Semi Variable
• The cost expression for Total Wage Cost is:
1.5
Straight * Straight Time + Overtime *
*
Time Hours
$ per Hour
Hours
Straight Time
$ per Hour

© Dale R. Geiger 2011

20


Cost Expression for Semi Variable
• If the total number of hours worked is 30 and
straight-time rate is $15 per hour then:
1.5
30

0
*
Straight * $15 per Hour + Overtime * Straight
Time
Time Hours
Hours
$ per Hour

= $450
© Dale R. Geiger 2011

21


Cost Expression for Semi Variable
• If the total number of hours worked is 44 and
straight-time rate is $15 per hour then:
40
4
Straight * $15 per Hour + Overtime *
Time Hours
Hours

1.5
*
$15
per Hour

= $690
© Dale R. Geiger 2011

22


Graph for Total Wage Cost
1000
800
600
400
200
0

0

3

6

9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60

X Axis = # of Hours Worked
As # Hours Worked increases, total Wage Cost increases, but not uniformly
© Dale R. Geiger 2011

23


Graph for Wage Cost per Hour
25
20

15
10
5

This is known as a Step Function.
Cost per Hour for Hours 0-40 = $15
Cost per Hour for Hours 41-60 = $22.50

0

X Axis = # of Hours Worked
As # Hours Worked increases, Wage Cost per Hour remains the same for the relevant range
24
© Dale R. Geiger 2011


Questions for Thought
• What about a volume discount?
• Units 1-20 cost $10 per unit
• Units 21-50 cost $9 per unit
• Units 51-100 cost $8 per unit

• How would you express this cost relationship
• In total? On a per-unit basis?

• How would the graph of each look?
• What is the cost of 16 units? Of 67 units?
© Dale R. Geiger 2011

25