Mixed Costs 3d1y2m
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Mixed Cost Analysis
y=a a Activity level
Fixed cost y = a + bx since b = 0 y=a
y
y Cost
Cost
y
Cost
Fixed And Variable Costs Cost Behavior – Mixed Costs
a x
Activity level
Variable cost y = a + bx since a = 0 y = bx
x
Activity level
x
Mixed cost y = a + bx
3
Methods of Analysis Scatter
diagram High-low method Linear regression analysis
4
Scatter Graph Method Plot the data points on a graph (total cost vs. activity)
Total Cost in 1,000’s of Dollars
Y 20
10
0
* * * *
* ** * ** X
0 1 2 3 4 Activity, 1,000’s of Units Produced
Scatter Graph Method Draw a line through the data points with about an equal numbers of points above and below the line.
Total Cost in 1,000’s of Dollars
Y 20
10
* ** * **
* * * * Intercept is the estimated fixed cost = $10,000
0
X
0 1 2 3 4 Activity, 1,000’s of Units Produced
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
Accuracy
- apply with caution because it does not provide and objective test that the line drawn is the most accurate.
Linear Relationship Activity Cost
* * * 0
*
*
* Activity Output
Nonlinear Relationship Activity Cost
* * 0
*
*
* Activity Output
Presence of Outliers Activity Cost
*
* *
* 0
*
* Activity Output
Scatter Graph Example The sales manager for Hinds Wholesale Supply Company needs to estimate the expected delivery vehicle operating cost (maintenance) for 2014 (for a specific mileage).
Scatter Graph Example Truck Number 202 204 205 301 422 460 520
Miles Packages Maintenance Driven Delivered Cost 15,000 1,200 $2,000 11,000 1,000 $1,600 24,000 1,500 $2,200 30,000 1,500 $2,400 31,000 500 $2,600 26,000 1,000 $2,200 20,000 2,000 $2,000
Scatter Graph Example Estimated Line Maintenance Cost
$3,000 $2,500 $2,000 $1,500 $1,000 $500 $0 0
10,000
20,000 Miles
30,000
40,000
Scatter Graph Example
Y = a + bx $15,000= ($1,100 x 7) + bx Total Miles Driven (x) = 157,000 b = $7,300 / 157,000 = $0.0465 or 4.7 cents per mile
Scatter Graph Example
Vehicle maintenance cost (y) = $1,100 (a) + $0.047 (b) per mile driven (x) What is the estimated maintenance cost for a truck that will be driven 28,000 miles? $1,100 + ($0.047 × 28,000) = $2,416
High Low Method
The high-low method involves taking the two observations with the highest and lowest level of activity to calculate the cost function
16
High-low method ~ step 1 Cost
Identify the highest and lowest activity levels.
Volume of Activity 17
High-low Method ~ step 2 Cost
Determine the differences between the high and low points coordinates.
Volume of Activity 18
High-low method ~ step 3 Cost
Variable cost per unit = slope of the line between the two points (which reflect total mixed costs). Variable Cost = in units per Unit in cost
Volume of Activity 19
High-low method ~ step 4 Cost
To find fixed costs, use slope and coordinates of one point in y = bx + a
in cost
Variable Cost = in units per Unit Volume of Activity 20
High-low method ~ step 5 Select one of the two points (highest/lowest done separately) 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
21
High-Low Method Example Truck Number 202 204 205 301 422 460 520
Miles Packages Maintenance Driven Delivered Cost 15,000 1,200 $2,000 11,000 1,000 $1,600 24,000 1,500 $2,200 30,000 1,500 $2,400 31,000 500 $2,600 26,000 1,000 $2,200 20,000 2,000 $2,000
High-Low Method Example
($2,600 – $1,600) $1,000 = = $0.05 (31,000 – 11,000) 20,000 What is the fixed cost element?
High-Low Method Example
$2,600 = Fixed cost + (31,000 × $0.05) Fixed cost = $2,600 – $1,550 = $1,050 $1,050 is the fixed cost element.
High-Low Method Example
$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
Strengths of High-Low Method Simple Easy
to use
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 Analysis
y=a a Activity level
Fixed cost y = a + bx since b = 0 y=a
y
y Cost
Cost
y
Cost
Fixed And Variable Costs Cost Behavior – Mixed Costs
a x
Activity level
Variable cost y = a + bx since a = 0 y = bx
x
Activity level
x
Mixed cost y = a + bx
3
Methods of Analysis Scatter
diagram High-low method Linear regression analysis
4
Scatter Graph Method Plot the data points on a graph (total cost vs. activity)
Total Cost in 1,000’s of Dollars
Y 20
10
0
* * * *
* ** * ** X
0 1 2 3 4 Activity, 1,000’s of Units Produced
Scatter Graph Method Draw a line through the data points with about an equal numbers of points above and below the line.
Total Cost in 1,000’s of Dollars
Y 20
10
* ** * **
* * * * Intercept is the estimated fixed cost = $10,000
0
X
0 1 2 3 4 Activity, 1,000’s of Units Produced
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
Accuracy
- apply with caution because it does not provide and objective test that the line drawn is the most accurate.
Linear Relationship Activity Cost
* * * 0
*
*
* Activity Output
Nonlinear Relationship Activity Cost
* * 0
*
*
* Activity Output
Presence of Outliers Activity Cost
*
* *
* 0
*
* Activity Output
Scatter Graph Example The sales manager for Hinds Wholesale Supply Company needs to estimate the expected delivery vehicle operating cost (maintenance) for 2014 (for a specific mileage).
Scatter Graph Example Truck Number 202 204 205 301 422 460 520
Miles Packages Maintenance Driven Delivered Cost 15,000 1,200 $2,000 11,000 1,000 $1,600 24,000 1,500 $2,200 30,000 1,500 $2,400 31,000 500 $2,600 26,000 1,000 $2,200 20,000 2,000 $2,000
Scatter Graph Example Estimated Line Maintenance Cost
$3,000 $2,500 $2,000 $1,500 $1,000 $500 $0 0
10,000
20,000 Miles
30,000
40,000
Scatter Graph Example
Y = a + bx $15,000= ($1,100 x 7) + bx Total Miles Driven (x) = 157,000 b = $7,300 / 157,000 = $0.0465 or 4.7 cents per mile
Scatter Graph Example
Vehicle maintenance cost (y) = $1,100 (a) + $0.047 (b) per mile driven (x) What is the estimated maintenance cost for a truck that will be driven 28,000 miles? $1,100 + ($0.047 × 28,000) = $2,416
High Low Method
The high-low method involves taking the two observations with the highest and lowest level of activity to calculate the cost function
16
High-low method ~ step 1 Cost
Identify the highest and lowest activity levels.
Volume of Activity 17
High-low Method ~ step 2 Cost
Determine the differences between the high and low points coordinates.
Volume of Activity 18
High-low method ~ step 3 Cost
Variable cost per unit = slope of the line between the two points (which reflect total mixed costs). Variable Cost = in units per Unit in cost
Volume of Activity 19
High-low method ~ step 4 Cost
To find fixed costs, use slope and coordinates of one point in y = bx + a
in cost
Variable Cost = in units per Unit Volume of Activity 20
High-low method ~ step 5 Select one of the two points (highest/lowest done separately) 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
21
High-Low Method Example Truck Number 202 204 205 301 422 460 520
Miles Packages Maintenance Driven Delivered Cost 15,000 1,200 $2,000 11,000 1,000 $1,600 24,000 1,500 $2,200 30,000 1,500 $2,400 31,000 500 $2,600 26,000 1,000 $2,200 20,000 2,000 $2,000
High-Low Method Example
($2,600 – $1,600) $1,000 = = $0.05 (31,000 – 11,000) 20,000 What is the fixed cost element?
High-Low Method Example
$2,600 = Fixed cost + (31,000 × $0.05) Fixed cost = $2,600 – $1,550 = $1,050 $1,050 is the fixed cost element.
High-Low Method Example
$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
Strengths of High-Low Method Simple Easy
to use
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 Analysis
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