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## Cost Behavior: Analysis and Use

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**Cost Behavior: Analysis and Use**UAA – ACCT 202 Principles of Managerial Accounting Dr. Fred Barbee**$**How does the cost react? Volume (Activity Base) As the volume of activity goes up ? ? Graphically ? ?**Why do I need to know this information?**Good question. Here are some examples of when you would want to know this.**?**? 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.**Knowledge of Cost Behavior**Setting Sales Prices Make-or-Buy decisions Entering new markets Introducing new products Buying/Replacing Equipment**$**Volume (Activity Base) Total Variable Costs**$**Volume (Activity Base) Per Unit Variable Costs**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**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.**Step-Variable Costs**Step Costs are constant within a range of activity. $ But different between ranges of activity Volume (Activity Base)**$**Volume (Activity Base) Total Fixed Costs**$**Volume (Activity Base) Per-Unit Fixed Costs**# of Units**Monthly Cost Average Cost 1 $9,000 $9,000 10 9,000 900 100 9,000 90 200 9,000 45 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:**Relevant**Range Curvilinear Costs & the Relevant Range Economist’s Curvilinear Cost Function $ Accountant’s Straight-Line Approximation Volume (Activity Base)**$**Volume (Activity Base) Mixed Costs Variable costs Fixed costs**The Analysis of . . .**Mixed Costs**Slope**Intercept y = a + bX This is probably how you learned this equation in algebra.**Total Costs**VC Per Unit (Slope) y = a + bX Fixed Cost (Intercept) Level of Activity**Total Costs**Dependent Variable VC Per Unit (Slope) y = a + bX Fixed Cost (Intercept) Level of Activity Independent Variable**Methods of Analysis**• Account Analysis • Engineering Approach • High-Low Method • Scattergraph Plot • Regression Analysis**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.**Y**20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced The Scattergraph Method Plot the data points on a graph (total cost vs. activity).**Quick-and-Dirty Method**Draw a line through the data points with about anequal numbers of points above and below the line. Y 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 Intercept is the estimated fixed cost = $10,000 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced**Quick-and-Dirty Method**The slope is the estimated variable cost per unit. Slope = Change in cost ÷ Change in units Y 20 * * * * * * * * Total Cost in1,000’s of Dollars * * 10 Horizontal distance is the change in activity. Vertical distance is the change in cost. 0 X 0 1 2 3 4 Activity, 1,000’s of Units Produced**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?**Activity**Cost * * * * * 0 Activity Output Nonlinear Relationship**Activity**Cost * * * * * * 0 Activity Output Upward Shift in Cost Relationship**Activity**Cost * * * * * * 0 Activity Output Presence of Outliers**Brentline Hospital Patient Data**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 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.**Brentline Hospital Patient Data**Low High Textbook Example**High/ Low**Month Patient Days Maint. Cost High June 8,000 $9,800 Low March 5,000 7,400 Difference 3,000 $2,400**Change in Cost**V = ------------------ Change in Activity (Y2 - Y1) V = ------------ (X2 - X1)**High/ Low**Month Patient Days Maint. Cost High June 8,000 $9,800 Low March 5,000 7,400 Difference 3,000 $2,400 Calculate the Variable Rate The Change in Cost Divided by the change in activity**Change in Cost**V = ------------------ Change in Activity $2,400 V = ------------ 3,000 = $0.80 Per Unit**Calculate Fixed Costs**Total Cost (TC) = FC + VC - FC = - TC + VC FC = TC - VC**Calculate Fixed Costs**Using June FC = TC - VC FC = $9,800 - (8,000 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**We have taken “Total Costs” which is a mixed cost and we**have separated it into its VC and FC components.**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