Mixed Cost Analysis

3

Fixed And Variable CostsCost Behavior – Mixed Costs

y

x

Cost

Activity level

y

x

Cost

Activity level

a

y

x

Cost

Activity level

a

y = a

y = bxy = a + bx

Fixed costy = a + bx

since b = 0 y = a

Fixed costy = a + bx

since b = 0 y = a

Variable costy = a + bx

since a = 0 y = bx

Variable costy = a + bx

since a = 0 y = bx

Mixed costy = a + bx

Mixed costy = a + bx

4

Methods of Analysis Scatter diagram High-low method Linear regression analysis

Plot the data points on a graph (total cost vs. activity)

Plot the data points on a graph (total cost vs. activity)

0 1 2 3 4

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10

20

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**

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*

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Activity, 1,000’s of Units Produced

X

Y

Scatter Graph Method

0 1 2 3 4

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Activity, 1,000’s of Units Produced

X

Y

Scatter Graph Method

Intercept is the estimated fixed cost = $10,000

Intercept is the estimated fixed cost = $10,000

Draw a line through the data points with about anequal numbers of points above and below the line.

Draw a line through the data points with about anequal numbers of points above and below the line.

Advantages and Disadvantages

One of the principal advantages of this method is that it lets us “see” the data.

Shows the correlation between costs and volume of activity

Apply with caution because it does not provide and objective test that the line drawn is the most accurate.

Linear Relationship

ActivityCost

0 Activity Output

* **

**

*

Nonlinear Relationship

ActivityCost

0 Activity Output

**

* **

Presence of Outliers

ActivityCost

0 Activity Output*

**

*

**

Scatter Graph Example

The sales manager for Hinds WholesaleThe sales manager for Hinds WholesaleSupply Company needs to estimate theSupply Company needs to estimate the

expected delivery vehicle operatingexpected delivery vehicle operatingcost (maintenance) for 2014.cost (maintenance) for 2014.

Scatter Graph Example

202204205301422460520

15,00011,00024,00030,00031,00026,00020,000

1,2001,0001,5001,500 5001,0002,000

$2,000$1,600$2,200$2,400$2,600$2,200$2,000

TruckNumber

MilesDriven

PackagesDelivered

MaintenanceCost

Scatter Graph Example

$0

$500

$1,000

$1,500

$2,000

$2,500

$3,000

0 10,000 20,000 30,000 40,000

Miles

Mai

nte

nan

ce C

ost

Estimated Line

Scatter Graph Example

Y = a + bxY = a + bx$15,000= ($1,100 x 7) + bx$15,000= ($1,100 x 7) + bx

Total Miles Driven (x) = 157,000Total Miles Driven (x) = 157,000

b = $7,300 / 157,000b = $7,300 / 157,000= $0.0465 or 4.7 cents per mile= $0.0465 or 4.7 cents per mile

Scatter Graph Example

Vehicle maintenance cost (y)Vehicle maintenance cost (y)= $1,100 (a) + $0.047 (b) per mile driven (x)= $1,100 (a) + $0.047 (b) per mile driven (x)

What is the estimated maintenance cost forWhat is the estimated maintenance cost fora truck that will be driven 28,000 miles?a truck that will be driven 28,000 miles?

$1,100 + ($0.047 × 28,000) = $2,416$1,100 + ($0.047 × 28,000) = $2,416

16

The high-low method involves taking the two observations with the highest and lowest level of activity to calculate the cost function

High Low Method

17

Cost

Volume of Activity

Identify the highest and lowest activity levels.

High-low method ~ step 1

18

Cost

Volume of Activity

Determine the differences between the high and low points coordinates.

High-low Method ~ step 2

19

Cost

Volume of Activity

Variable Cost

per Unit =

Variable cost per unit = slope of the line between the two points (which reflect total mixed costs).

High-low method ~ step 3

in cost

in units

20

Cost

Volume of Activity

Variable Cost

per Unit=

To find fixed costs, use slope and co-ordinates of one point in

y = bx + a

High-low method ~ step 4

in cost

in units

21

High-low method ~ step 5 Select one of the two point Substitute into y = bx + a, where

y = total cost x = # of units b = step 4 calculations; variable cost per unit

Find a, total fixed costs a = y-bx

High-Low Method Example

202204205301422460520

15,00011,00024,00030,00031,00026,00020,000

1,2001,0001,5001,500 5001,0002,000

$2,000$1,600$2,200$2,400$2,600$2,200$2,000

TruckNumber

MilesDriven

PackagesDelivered

MaintenanceCost

High-Low Method Example

What is the fixedWhat is the fixedcost element?cost element?

$1,000$1,00020,00020,000

= $0.05$0.05($2,600 – $1,600)($2,600 – $1,600)(31,000 – 11,000)(31,000 – 11,000)

=

High-Low Method Example

$2,600 = Fixed cost + (31,000 × $0.05)$2,600 = Fixed cost + (31,000 × $0.05)Fixed cost = $2,600 – $1,550 = Fixed cost = $2,600 – $1,550 = $1,050$1,050

$1,050 is the fixed cost element.$1,050 is the fixed cost element.

High-Low Method Example

$1,600 = Fixed cost + (11,000 × $0.05)$1,600 = Fixed cost + (11,000 × $0.05)Fixed cost = $1,600 – $550 = Fixed cost = $1,600 – $550 = $1,050$1,050

What is the estimated maintenance costWhat is the estimated maintenance costfor a truck to be driven 28,000 miles?for a truck to be driven 28,000 miles?

$1,050 + (28,000 × $0.05) = $2,450$1,050 + (28,000 × $0.05) = $2,450

Strengths of High-Low Method

Simple to use

Easy to understand

Analysis based of easily accessible data (expenses and activity levels)

Weaknesses of High-Low

Rather unreliable, only two data points are used in the analysis.

Can be problematic if either (or both) high or low are extreme (i.e., Outliers).

Number of steps, where each additional step increases the potential for errors.

End of Mixed Cost AnalysisEnd of Mixed Cost Analysis