3-1 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Activity Cost Behaviour 3 PowerPresentation® prepared by David J. McConomy, Queen’s University

3-2 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Learning Objectives l Define and describe cost behaviour for fixed, variable, and mixed costs. l Explain the role of the resource usage model in understanding cost behaviour. Learning Objectives

3-3 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. l Separate mixed costs into their fixed and variable components using the high-low method, the scatterplot method, and the method of least squares. Learning Objectives (continued)

3-4 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Learning Objectives (continued) l Evaluate the reliability of a cost equation. l Explain the role of multiple regression in assessing cost behaviour. l Describe the use of managerial judgment in determining cost behaviour.

3-5 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Cost Behaviour Cost Behaviour Fixed-Cost BehaviourVariable-Cost Behaviour $ $ Relevant Range Units Produced

3-6 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Mixed-Cost Behaviour Total Costs Cost Number of Units Produced Fixed Costs Variable Costs Linearity Assumption Total cost = Fixed cost + Total variable cost

3-7 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Activity Cost Behaviour Model Inputs: Materials Energy Labour Capital Cost Behaviour ActivitiesActivity Output Changes in Input CostChanges in Output

3-8 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Basic Terms The linearity assumption assumes that variable costs increase in direct proportion to the number of units produced (or activity units used). Practical capacity is the efficient level of activity performance.

3-9 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Types of Resources l Flexible Resources l Committed Resources l Discretionary Fixed Costs

3-10 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Flexible Resources l Flexible resources are supplied as used and needed. They are acquired from outside sources, where the terms of acquisition do not require any long- term commitment for any given amount of the resource

3-11 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Committed Resources l Committed resources are resources that are supplied in advance of usage. They are acquired by the use of either an explicit or implicit contract to obtain a given quantity of resource, regardless of whether the amount of the resource available is fully used or not. Committed resources may have unused capacity.

3-12 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Discretionary Fixed Costs l Discretionary fixed costs are shorter- term committed resources

3-13 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Step-Cost Function Cost Activity Output (units) Narrow Width

3-14 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Step-Fixed Costs Cost Activity Usage Normal Operating Range (Relevant Range)

3-15 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Resource Relationships The relationship between resources supplied and resources used is expressed by the following equation: Resources available = Resources used + Unused capacity

3-16 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Resource Relationships Example l Three engineers hired at $50,000 each l Each engineer is capable of processing 2,500 change orders l $90,000 was spent on supplies for the engineering activity l There were 6,000 orders processed

3-17 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Resource Relationships Example (continued) Available orders = Orders used + Orders unused 7,500 orders = 6,000 orders + 1,500 orders Fixed engineering rate = $150,000/7,500 = $20 per change order Variable engineering rate = $90,000/6,000 = $15 per change order

3-18 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Resource Relationships Example (continued) Cost of orders supplied = Cost of orders used + Cost of unused orders = [($20 + $15) x 6,000] + ($20 x 1,500) = $240,000 Of course, the $240,000 is precisely equal to the $150,000 spent on engineers and the $90,000 spent on supplies. The $30,000 of excess engineering capacity means that a new product could be introduced without increasing current spending on engineering.

3-19 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Methods for Separating Mixed Costs into Fixed and Variable Components l The High-Low Method l The Scatterplot Method l The Method of Least Squares

3-20 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Month Setup Costs Setup Hours January $1, February 1, March 2, April 2, May 3, High-Low Method: An Example

3-21 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. The High-Low Method (continued) Variable Rate (V)=Change in cost/Change in output V=(High cost - Low cost) / (High output - Low output) V=($3,750 - $1,000) / ( ) V=$2,750 / 400 V= $6.875 per setup hour

3-22 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. The High-Low Method (continued) 3,750 = Fixed costs + $6.875 (500) Fixed costs = $3, $3, Fixed costs = $ The cost formula using the high-low method is: Total cost = $ ($6.875 x setup hours)

3-23 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Activity Hours Activity Cost $4,000 3,000 2,000 1, Scatterplot Method.... Analyst can fit line based on his or her experience Important: Cost function is only relevant within relevant range

3-24 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Nonlinear Relationship` Activity Cost 0 Activity Output * * * * *

3-25 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Upward Shift in Cost Relationship Activity Cost 0 Activity Output * * * * * *

3-26 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Presence of Outliers Activity Cost 0 Activity Output * * * * * *

3-27 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Least Squares Constant 125 Standard Error of Y Est R squared No. of Observations5 Degrees of Freedom3 X Coefficient(s) 6.75 Standard Error of Coef

3-28 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Least Squares (continued) The results give rise to the following equation: Setup Costs = $125 + ($6.75 x # of setup hours) R 2 =.944, or 94.4 percent of the variation in setup costs is explained by the number of setup hours variable.

3-29 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. TC = b 0 + b 1 X 1 + b 2 X b 0 = the fixed cost or intercept b i = the variable rate for the ith independent variable X i = the ith independent variable Multiple Regression

3-30 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Multiple Regression (continued) Utility MonthMHrsSummerCost January1,3400$1,688 February1,29801,636 March1,37601,734 April1,40501,770 May1,50012,390 June1,43212,304 July1,32212,166 August1,41612,284 September1,37011,730 October1,58001,991 November1,46001,840 December1,45501,833

3-31 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Multiple Regression (continued) Constant Std Error of Y Est R squared No. of Observations 12 Degrees of Freedom 9 X Coefficient(s) Std Err of Coef

3-32 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Multiple Regression (continued) The results gives rise to the following equation: Utilities cost = $ $1.097(MH) + $510.49(Summer) R 2 =.967, or 96.7 percent of the variation in utilities cost is explained by the machine hours and summer variables.

3-33 Copyright © 2004 by Nelson, a division of Thomson Canada Limited. Cost Behaviour and Managerial Judgment l Use past experience l Try to confirm results with operating personnel l Use common sense to confirm statistical studies Some Tips