Mixed Cost Analysis

3 Fixed And Variable Costs Cost Behavior – Mixed Costs y x Cost Activity level y x Cost Activity level a y x Cost Activity level a y = a y = bx y = a + bx Fixed cost y = a + bx since b = 0 y = a Fixed cost y = a + bx since b = 0 y = a Variable cost y = a + bx since a = 0 y = bx Variable cost y = a + bx since a = 0 y = bx Mixed cost y = a + bx Mixed cost y = 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) * Total Cost in 1,000’s of Dollars * * * * * * * * * Activity, 1,000’s of Units Produced X Y Scatter Graph Method

* Total Cost in 1,000’s of Dollars * * * * * * * * * Activity, 1,000’s of Units Produced X Y Scatter Graph Method Intercept is the estimated fixed cost = $10,000 Draw a line through the data points with about an equal 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 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.

Scatter Graph Example ,000 11,000 24,000 30,000 31,000 26,000 20,000 1,200 1,000 1, ,000 2,000 $2,000 $1,600 $2,200 $2,400 $2,600 $2,200 $2,000 Truck Number Miles Driven Packages Delivered Maintenance Cost

Scatter Graph Example Estimated Line

Scatter Graph Example Y = a + bx $15,000= ($1,100 x 7) + bx Total Miles Driven (x) = 157,000 Total Miles Driven (x) = 157,000 b = $7,300 / 157,000 = $ 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

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 ,000 11,000 24,000 30,000 31,000 26,000 20,000 1,200 1,000 1, ,000 2,000 $2,000 $1,600 $2,200 $2,400 $2,600 $2,200 $2,000 Truck Number Miles Driven Packages Delivered Maintenance Cost

High-Low Method Example What is the fixed cost element? $1,00020,000 = $0.05 ($2,600 – $1,600) (31,000 – 11,000) =

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 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 Analysis