Cost Behavior Analysis and Use UAA ACCT 202

Cost Behavior: Analysis and Use UAA – ACCT 202 Principles of Managerial Accounting Dr. Fred Barbee

$ Volume (Activity Base) As the volume of activity goes up How does the cost react?

Why do I need to know this information? Good question. Here are some examples of when you would want to know this.

$ Volume (Activity Base) For decision making purposes, it’s important for a manager to know the cost behavior pattern and the relative proportion of each cost.

Knowledge of Cost Behavior Setting Sales Prices Make-or-Buy decisions Entering new markets Introducing new products Buying/Replacing Equipment 5

Total Variable Costs $ Volume (Activity Base) 6

Per Unit Variable Costs $ Volume (Activity Base) 7

Variable Costs - Example A company manufacturers microwave ovens. Each oven requires a timing device that costs $30. The per unit and total cost of the timing device at various levels of activity would be: # of Units 1 10 100 200 Cost/Unit Total Cost $30 30 30 3, 000 30 6, 000 Linearity is assumed

Variable Costs The equation for total VC: TVC = VC x Activity Base Thus, a 50% increase in volume results in a 50% increase in total VC. 9

Step-Variable Costs Step Costs are constant within a range of activity. $ But different between ranges of activity Volume (Activity Base) 10

Total Fixed Costs $ Volume (Activity Base) 11

Per-Unit Fixed Costs $ Volume (Activity Base) 12

Fixed Costs - Example A company manufacturers microwave ovens. The company pays $9, 000 per month for rental of its factory building. The total and per unit cost of the rent at various levels of activity would be: # of Units Monthly Cost Average Cost 1 $9, 000 10 9, 000 900 100 9, 000 90 200 9, 000 45

Curvilinear Costs & the Relevant Range Economist’s Curvilinear Cost Function $ Accountant’s Straight-Line Approximation Relevant Range Volume (Activity Base) 14

Mixed Costs $ Variable costs Volume (Activity Base) Fixed costs 15

Intercept Slope This is probably how you learned this equation in algebra. 17

Total Costs Fixed Cost (Intercept) VC Per Unit (Slope) Level of Activity 18

Dependent Total Costs Variable Fixed Cost (Intercept) VC Per Unit (Slope) Independent Level of Variable Activity 19

Methods of Analysis • Account Analysis • Engineering Approach • High-Low Method • Scattergraph Plot • Regression Analysis 20

Account Analysis Each account is classified as either – variable or – fixed based on the analyst’s prior knowledge of how the cost in the account behaves.

Engineering Approach Detailed analysis of cost behavior based on an industrial engineer’s evaluation of required inputs for various activities and the cost of those inputs.

The Scattergraph 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 23

Quick-and-Dirty 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 24

Quick-and-Dirty Method The slope is the estimated variable cost per unit. Slope = Change in cost ÷ Change in units Total Cost in 1, 000’s of Dollars Y 20 10 0 * *Horizontal distance is the change in activity. * ** Vertical distance is the change in cost. X 0 1 2 3 4 Activity, 1, 000’s of Units Produced 25

Advantages • One of the principal advantages of this method is that it lets us “see” the data. • What are the advantages of “seeing” the data?

Nonlinear Relationship Activity Cost * * * 0 Activity Output 27

Upward Shift in Cost Relationship Activity Cost * * * 0 * * * Activity Output 28

Presence of Outliers Activity Cost * * * 0 * Activity Output 29

Brentline Hospital Patient Data Month Activity Level: Patient Days Maintenance Cost Incurred January 5, 600 $7, 900 February 7, 100 8, 500 March 5, 000 7, 400 April 6, 500 8, 200 May 7, 300 9, 100 June 8, 000 9, 800 July 6, 200 7, 800 Textbook Example

From Algebra. . . • If we know any two points on a line, we can determine the slope of that line.

High-Low Method • A non-statistical method whereby we examine two points out of a set of data. . . – The high point; and – The low point

High-Low Method • Using these two points, we determine the equation for that line. . . – The intercept; and – The Slope parameters

High-Low Method • To get the variable costs. . . – We compare the difference in costs between the two periods to – The difference in activity between the two periods.

Brentline Hospital Patient Data Month Activity Level: Patient Days Maintenance Cost Incurred January 5, 600 $7, 900 February 7, 100 8, 500 March 5, 000 7, 400 April 6, 500 8, 200 May 7, 300 9, 100 June 8, 000 9, 800 July 6, 200 7, 800 Textbook Example

High/ Low Month Patient Days Maint. Cost High June 8, 000 $9, 800 Low March 5, 000 7, 400 3, 000 $2, 400 Difference

Change in Cost V = ---------Change in Activity (Y 2 - Y 1) V = ------(X 2 - X 1)

High/ Low Month High June Low March Divided by the Difference change in activity Patient Days Maint. Cost The Change 8, 000 $9, 800 in Cost 5, 000 7, 400 3, 000 $2, 400

Change in Cost V = ---------Change in Activity $2, 400 V = ------3, 000 = $0. 80 Per Unit

Total Cost (TC) = FC + VC - FC = - TC + VC FC = TC - VC

FC = $9, 800 - (8, 000 x $0. 80) = $3, 400

FC = $7, 400 - (5, 000 x $0. 80) = $3, 400

TC = $3, 400 + $0. 80 X

Month Activity Level: Patient Days Maintenance Cost Incurred January 5, 600 $7, 900 February 7, 100 8, 500 March 5, 000 7, 400 April 6, 500 8, 200 We have taken May 7, 300 “Total Costs” which June 8, 000 is a mixed cost and 6, 200 July we have separated it into its VC and FC components. 9, 100 9, 800 7, 800

So what? You say! Thank you for asking! Now I can use this formula for planning purposes. For example, what if I believe my activity level will be 6, 325 patient days in February. What would I expect my total maintenance cost to be? 49

What is the estimated total cost if the activity level for February is expected to be 6, 325 patient days? Y = a + bx TC = $3, 400 + 6, 325 x $0. 80 TC = $8, 460

Some Important Considerations • We have used historical cost to arrive at the cost equation. • Therefore, we have to be careful in how we use the formula. • Never forget the relevant range.

$ Relevant Range Volume (Activity Base)

Strengths of High-Low Method • Simple to use • Easy to understand

Weaknesses of High-Low • Only two data points are used in the analysis. • Can be problematic if either (or both) high or low are extreme (i. e. , Outliers).

Extreme values not necessarily representative . . . . Representative High/Low Values

Weaknesses of High-Low • Other months may not yield the same formula.

FC = $8, 500 - (7, 100 x $0. 80) = $2, 820

FC = $7, 800 - (6, 200 x $0. 80) = $2, 840

Regression Analysis • A statistical technique used to separate mixed costs into fixed and variable components. • All observations are used to fit a regression line which represents the average of all data points.

Regression Analysis • Requires the simultaneous solution of two linear equations • So that the squared deviations from the regression line of each of the plotted points cancel out (are equal to zero).

Cost Actual Y Error Estimated y The objective is to find values of a and b in the equation y = a + b. X that minimize Production

The equation for a linear function (straight line) with one independent variable is. . . y = a + b. X Where: y a b X = = The Dependent Variable The Constant term (Intercept) The Slope of the line The Independent variable

The equation for a linear The function (straight line) with Dependent Variable one independent variable is. . . y = a + b. X Where: The y = The Dependent Variable Independent a = The Constant term (Intercept) Variable b = The Slope of the line X = The Independent variable

Regression Analysis • With this equation and given a set of data. • Two simultaneous linear equations can be developed that will fit a regression line to the data.

Where: a b n X Y = = = Fixed cost Variable cost Number of observations Activity measure (Hours, etc. ) Total cost

Fixed Costs Variable Costs

R 2, the Coefficient of Determination is the percentage of variability in the dependent variable being explained by the independent variable. This is referred to as a “goodness of fit” measure.

R, the Coefficient of Correlation is square root of R 2. Can range from -1 to +1. Positive correlation means the variables move together. Negative correlation means they move in opposite directions.

Method Fixed Cost Variable Cost High-Low $3, 400 $0. 80 Scattergraph $3, 300 $0. 79 Regression $3, 431 $0. 76

Coefficient of Determination • R 2 is the percentage of variability in the dependent variable that is explained by the independent variable.

Coefficient of Determination • This is a measure of goodness-offit. • The higher the R 2, the better the fit.

Coefficient of Determination • The higher the R 2, the more variation (in the dependent variable) being explained by the independent variable.

Coefficient of Determination • R 2 ranges from 0 to 1. 0 • Good Vs. Bad R 2 s is relative. • There is no magic cutoff

Coefficient of Correlation • The relationship between two variables can be described by a correlation coefficient. • The coefficient of correlation is the square root of the coefficient of determination.

Coefficient of Correlation • Provides a measure of strength of association between two variables. • The correlation provides an index of how closely two variables “go together. ”

Machine Hours Utility Costs

Hours of Safety Training Industrial Accidents

Hair Length 202 Grade