Mixed Cost Analysis Fixed And Variable Costs Cost

Mixed Cost Analysis

Fixed And Variable Costs Cost Behavior – Mixed Costs y Cost y=a a Activity level x Fixed cost y = a + bx since b = 0 y=a y y x b = Activity level a = y Cost y x b + a x Variable cost y = a + bx since a = 0 y = bx Activity level x Mixed cost y = a + bx 3

Methods of Analysis p Scatter diagram p High-low method p 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 p One of the principal advantages of this method is that it lets us “see” the data. p Shows the correlation between costs and volume of activity p 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, 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

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 p 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 Variable Cost = in units per Unit in cost Volume of Activity 20

High-low method ~ step 5 Select one of the two points (highest/lowest done separately) p Substitute into y = bx + a, where p n n n p y = total cost x = # of units b = step 4 calculations; variable cost per unit Find a, total fixed costs n 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, 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 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 p Simple p Easy to use to understand p Analysis based of easily accessible data (expenses and activity levels)

Weaknesses of High-Low p Rather unreliable, only two data points are used in the analysis. p Can be problematic if either (or both) high or low are extreme (i. e. , Outliers). p Number of steps, where each additional step increases the potential for errors.

End of Mixed Cost Analysis