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Chapter 5

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Chapter 5

Cost Behavior

Learning Objective 1

Describe the differences between fixed costs and variable costs.

Laura Jorgensen is planning a party.

She identifies two major costs:

1. Entertainment (a live band)

2. Food and drinks

$3,650 was spent last year on this party:

♫ $525 for entertainment

☺ $3,125 for food and drinks

The spending limit for this

event, this year, is $5,500.

Prices for entertainment and food and

drinks are expected to remain the same.

175 guests are expected to attend this

year’s party, compared to 125 last year.

Cost behavior is the reaction of costs to

changes in levels of business activity.

Fixed Costs

Fixed costs remain constant in total

regardless of the level of activity.

What is the fixed cost per guest?

125 Guests175 Guests

Total fixed cost: $525 $525

125 Guests

Cost per guest: $525 ÷ 125 = $4.20

175 Guests

Cost per guest: $525 ÷ 175 = $3.00

Variable Costs

Variable costs are costs that change in direct

proportion with changes in the level of activity.

What is the variable cost per guest?

Cost per guest: $3,125 ÷ 125 = $25.00

What is the total variable cost for 175 guests?

$25 × 175 = $4,375

Learning Objective 2

Classify costs by cost behavior.

The measure of activity is shown

on the horizontal axis (the x-axis).

The x-axis is the independent variable.

The type of cost is shown on

the vertical axis (the y-axis).

The y-axis is the dependent variable.

y

Cost of the Band

$525

x

Number of Guests

$4,375

175

y

Cost of Catering

x

Number of Guests

Total Costs

= Fixed Costs

+ Variable Costs

What is the total cost for 175 guests?

Total fixed cost = $525

Total variable cost: $25 × 175 = $4,375

Total cost: $525 + $4,375 = $4,900

y

$4,900

$525

x

175

Learning Objective 3

Explain the concept of relevant range and its effect on cost behavior information.

The range of activity within which

cost behavior assumptions are

valid is called the relevant range.

y

Relevant

Range

Fixed Cost

x

Activity

y

Relevant

Range

Variable Cost

x

Activity

Learning Objective 4

Describe the characteristics of a mixed cost and the four basic approaches to separating a mix cost into its fixed and variable components.

Mixed costs contain elements of both

fixed- and variable-cost behavior.

Variable

Component

y

Cost

Fixed

Component

x

Activity

The engineering approach

Scatter graphing

The high-low method

Regression analysis

This approach relies on engineers or

other professionals who are familiar

with the technical aspect of the

activity and the associated cost.

The engineering approach may employ

time-and-motion studies or other

aspects of scientific management.

The scatter graph plots historical activity

and cost data on a graph to see how a

cost relates to various levels of activity.

The analyst places a straight line through

the visual center of the points plotted on

the graph, so roughly half the dots are

above the line and half are below the line.

y

Cost

x

Activity

In the high-low method, only two

of the data points are used to

determine the fixed and

variable cost components.

The highest and lowest

observations are picked.

Regression analysis, also called the

least-squares method or linear

regression analysis, is a mathematical

approach to determining fixed and

variable cost with statistical accuracy.

The basic mathematical equation is:

Y = a + bX

Where:

Y =The dependent variable

a =The Y intercept, or the amount for Y

when X is zero

b =The slope coefficient

X = The independent variable

When applying regression analysis to

find the fixed and variable elements

of a mixed cost, the variables in

the regression equation are

defined as follows:

Y=total cost

a=fixed cost

b=unit variable cost

X=activity level

Microsoft Excel’s Chart Wizard uses

a four-step sequence to do the

graphing and mathematical

computations to approximate

costs at various levels of activity.

Learning Objective 5

Determine the fixed and variable components of a mixed cost using scatter graphs and the high-low method.

The sales manager for Hinds Wholesale

Supply Company needs to estimate the

expected delivery vehicle operating

cost (maintenance) for 2005.

Truck

Number

Miles

Driven

Packages

Delivered

Maintenance

Cost

202

204

205

301

422

460

520

15,000

11,000

24,000

30,000

31,000

26,000

20,000

1,200

1,000

1,500

1,500

500

1,000

2,000

$2,000

$1,600

$2,200

$2,400

$2,600

$2,200

$2,000

Vehicle Data for 2004:

Estimated Line

Maintenance Cost and Miles Driven

Maintenance Cost and Miles Driven

Total Cost

= Fixed Cost + Variable Cost

Total Mixed Cost

= Fixed Cost Element + Variable Cost Element

Total Mixed Cost

= $1,100 + Variable Cost Element

Maintenance Cost and Miles Driven

Maintenance Cost and Miles Driven

MilesCost

34,000$2,700

0 1,100

34,000$1,600

$1,600 ÷ 34,000

= $0.047059 or 4.7 cents per mile

Maintenance Cost and Miles Driven

Vehicle maintenance cost

= $1,100 + $0.047 per mile driven

What is the estimated maintenance cost for

a truck that will be driven 28,000 miles?

$1,100 + ($0.047 × 28,000) = $2,416

Truck

Number

Miles

Driven

Packages

Delivered

Maintenance

Cost

202

204

205

301

422

460

520

15,000

11,000

24,000

30,000

31,000

26,000

20,000

1,200

1,000

1,500

1,500

500

1,000

2,000

$2,000

$1,600

$2,200

$2,400

$2,600

$2,200

$2,000

Maintenance Cost and Packages Delivered

Maintenance Cost and Packages Delivered

Maintenance Cost and Miles Driven

Truck

Number

Miles

Driven

Packages

Delivered

Maintenance

Cost

202

204

205

301

422

460

520

15,000

11,000

24,000

30,000

31,000

26,000

20,000

1,200

1,000

1,500

1,500

500

1,000

2,000

$2,000

$1,600

$2,200

$2,400

$2,600

$2,200

$2,000

($2,600 – $1,600)

(31,000 – 11,000)

=

$1,000

20,000

=

$0.05

Maintenance Cost and Miles Driven

What is the fixed

cost element?

Maintenance Cost and Miles Driven:

High Observation

$2,600 = Fixed cost + (31,000 × $0.05)

Fixed cost = $2,600 – $1,550 = $1,050

$1,050 is the fixed cost element.

Maintenance Cost and Miles Driven:

Low Observation

$1,600 = Fixed cost + (11,000 × $0.05)

Fixed cost = $1,600 – $550 = $1,050

What is the estimated maintenance cost

for a truck to be driven 28,000 miles?

$1,050 + (28,000 × $0.05) = $2,450

End of Chapter 5