Cost Behavior: Analysis and Use April 15, 2017 Cost Behavior: Analysis and Use UAA – ACCT 202 Principles of Managerial Accounting Dr. Fred Barbee Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 ? ? Graphically $ Volume (Activity Base) ? ? How does the cost react? As the volume of activity goes up Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Why do I need to know this information? Good question. Here are some examples of when you would want to know this. Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 ? ? Graphically $ ? ? 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. Dr. Fred Barbee

Knowledge of Cost Behavior Cost Behavior: Analysis and Use Knowledge of Cost Behavior April 15, 2017 Setting Sales Prices Make-or-Buy decisions Entering new markets Introducing new products Buying/Replacing Equipment Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Total Variable Costs $ Volume (Activity Base) Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Per Unit Variable Costs $ Volume (Activity Base) Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 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 Cost/Unit Total Cost 1 $30 $30 10 30 300 100 30 3,000 200 30 6,000 Linearity is assumed Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 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. Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Step-Variable Costs Step Costs are constant within a range of activity. $ But different between ranges of activity Volume (Activity Base) Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Total Fixed Costs $ Volume (Activity Base) Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Per-Unit Fixed Costs $ Volume (Activity Base) Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 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 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Curvilinear Costs & the Relevant Range Economist’s Curvilinear Cost Function Relevant Range $ Accountant’s Straight-Line Approximation Volume (Activity Base) Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Mixed Costs $ Volume (Activity Base) Variable costs Fixed costs Dr. Fred Barbee

Mixed Costs

This is probably how you learned this equation in algebra. Slope Intercept y = a + bX This is probably how you learned this equation in algebra.

Fixed Cost (Intercept) Total Costs VC Per Unit (Slope) y = a + bX Fixed Cost (Intercept) Level of Activity

Fixed Cost (Intercept) Dependent Variable Total Costs VC Per Unit (Slope) y = a + bX Fixed Cost (Intercept) Independent Variable Level of Activity

Cost Behavior: Analysis and Use April 15, 2017 Methods of Analysis Account Analysis Engineering Approach High-Low Method Scattergraph Plot Regression Analysis Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 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. Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 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. Dr. Fred Barbee

The Scattergraph Method Cost Behavior: Analysis and Use April 15, 2017 The Scattergraph Method Plot the data points on a graph (total cost vs. activity). 0 1 2 3 4 * Total Cost in 1,000’s of Dollars 10 20 Activity, 1,000’s of Units Produced X Y Dr. Fred Barbee

Quick-and-Dirty Method Cost Behavior: Analysis and Use April 15, 2017 Quick-and-Dirty Method Draw a line through the data points with about an equal numbers of points above and below the line. Y 20 * * * * * * * * Total Cost in 1,000’s of Dollars * * 10 Intercept is the estimated fixed cost = $10,000 X 0 1 2 3 4 Activity, 1,000’s of Units Produced Dr. Fred Barbee

Quick-and-Dirty Method Cost Behavior: Analysis and Use April 15, 2017 Quick-and-Dirty Method The slope is the estimated variable cost per unit. Slope = Change in cost ÷ Change in units Y 20 * * * * * * * * Total Cost in 1,000’s of Dollars * * 10 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 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 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? Dr. Fred Barbee

Nonlinear Relationship Activity Cost Activity Output *

Upward Shift in Cost Relationship Activity Cost Activity Output *

Presence of Outliers Activity Cost Activity Output *

Cost Behavior: Analysis and Use April 15, 2017 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 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Dr. Fred Barbee

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 y = a + bX

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.

Cost Behavior: Analysis and Use April 15, 2017 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 Low High Textbook Example Dr. Fred Barbee

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

(Y2 - Y1) V = ------------ (X2 - X1) Change in Cost Change in Activity (Y2 - Y1) V = ------------ (X2 - X1)

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

$2,400 V = ------------ 3,000 = $0.80 Per Unit Change in Cost Change in Activity $2,400 V = ------------ 3,000 = $0.80 Per Unit

Total Cost (TC) = FC + VC - FC = - TC + VC FC = TC - VC Calculate Fixed Costs Total Cost (TC) = FC + VC - FC = - TC + VC FC = TC - VC

FC = $9,800 - (8,000 x $0.80) = $3,400 Calculate Fixed Costs Using June FC = TC - VC FC = $9,800 - (8,000 x $0.80) = $3,400

FC = $7,400 - (5,000 x $0.80) = $3,400 Calculate Fixed Costs Using March FC = TC - VC FC = $7,400 - (5,000 x $0.80) = $3,400

The Cost Formula y = a + bx TC = $3,400 + $0.80X

Cost Behavior: Analysis and Use April 15, 2017 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 We have taken “Total Costs” which is a mixed cost and we have separated it into its VC and FC components. Dr. Fred Barbee

So what. You say. Thank you for asking 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?

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.

Cost Behavior: Analysis and Use April 15, 2017 5,000 8,000 Relevant Range $ 5,000 to 8,000 activity level Volume (Activity Base) Dr. Fred Barbee

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 Calculate Fixed Costs Using February FC = TC - VC FC = $8,500 - (7,100 x $0.80) = $2,820

FC = $7,800 - (6,200 x $0.80) = $2,840 Calculate Fixed Costs Using July FC = TC - VC 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.

Cost Behavior: Analysis and Use April 15, 2017 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). Dr. Fred Barbee

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

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

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

Cost Behavior: Analysis and Use April 15, 2017 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. Dr. Fred Barbee

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

Estimating the Regression Line

Fixed Costs Variable Costs

This is referred to as a “goodness of fit” measure. R2, 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 R2 R, the Coefficient of Correlation is square root of R2. Can range from -1 to +1. Positive correlation means the variables move together. Negative correlation means they move in opposite directions.

Cost Behavior: Analysis and Use April 15, 2017 Comparison of Methods Method Fixed Cost Variable Cost High-Low $3,400 $0.80 Scattergraph $3,300 $0.79 Regression $3,431 $0.76 Dr. Fred Barbee

Coefficient of Determination Cost Behavior: Analysis and Use April 15, 2017 Coefficient of Determination R2 is the percentage of variability in the dependent variable that is explained by the independent variable. Dr. Fred Barbee

Coefficient of Determination Cost Behavior: Analysis and Use April 15, 2017 Coefficient of Determination This is a measure of goodness-of-fit. The higher the R2, the better the fit. Dr. Fred Barbee

Coefficient of Determination Cost Behavior: Analysis and Use April 15, 2017 Coefficient of Determination The higher the R2, the more variation (in the dependent variable) being explained by the independent variable. Dr. Fred Barbee

Coefficient of Determination Cost Behavior: Analysis and Use April 15, 2017 Coefficient of Determination R2 ranges from 0 to 1.0 Good Vs. Bad R2s is relative. There is no magic cutoff Dr. Fred Barbee

Coefficient of Correlation Cost Behavior: Analysis and Use April 15, 2017 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. Dr. Fred Barbee

Coefficient of Correlation Cost Behavior: Analysis and Use April 15, 2017 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.” Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Positive Correlation Machine Hours Utility Costs Machine Hours Utility Costs r approaches +1 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 r approaches +1 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 r Equals +1 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Negative Correlation Hours of Safety Training Industrial Accidents Hours of Safety Training Industrial Accidents r approaches -1 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 r approaches -1 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 r Equals -1 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 No Correlation Hair Length 202 Grade Hair Length 202 Grade r ~ 0 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Dr. Fred Barbee

Cost Behavior: Analysis and Use April 15, 2017 Dr. Fred Barbee