Chapter 3 Cost Behaviour COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Learning Objectives Explain cost behaviour, define fixed and variable costs Define mixed and step costs Separate mixed costs into fixed and variable components using the following methods: High-Low Sattergraph Least Squares (Appendix) Use a computer spreadsheet program to perform the method of least squares 3-2 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. OBJECTIVE  1 Explain the meaning of cost and behaviour, define fixed and variable costs COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cost Behaviour Cost Behaviour: The way costs change as the related activity changes Output Total Cost Increase No change Decrease A cost that does not change in total as output changes Fixed Cost = 3-4 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Cost Behaviour Cost Behaviour: The way costs change as the related activity changes Output Total Cost Increase Decrease A cost that changes in total as output changes Variable Cost = 3-5 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Measures of Output To determine if a cost is fixed or variable, we must first determine the underlying business activity and ask… “What causes the cost of this particular activity to go up/down?” In other words, we are trying to identify its driver 3-6 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Relevant Range The range of output over which the assumed cost relationship is valid for the normal operations of a firm Avoids extremely high levels of activity Avoids extremely low levels of activity Let’s take a closer look at fixed, variable, and mixed costs, in light of the relevant range 3-7 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example SyBan Computers Inc. wants to look at the cost relationship between supervision cost and the number of computers processed per year It process up to 50,000 computers per year Production-line manager is paid $32,000 per year Factory produces 40,000 to 50,000 computers per year Production has never fallen below 20,000 computers in a year Reminder: Fixed Costs are costs that in total are constant within the relevant range as the level of output increases or decreases Let’s look at the cost of supervision at several production levels 3-8 COPYRIGHT © 2012 Nelson Education Ltd.

Fixed Cost Example Fixed Costs = Costs that in total are constant within the relevant range as the level of output increases or decreases # of Computers Produced Total Cost of Supervision Unit Cost 20,000 $32,000 30,000 40,000 50,000 $1.60 We know the total cost of supervision, but what about cost per computer? Unit cost changes! As production increases, the per unit amount of a fixed cost decreases $1.07 $0.80 $0.64 3-9 COPYRIGHT © 2012 Nelson Education Ltd.

Discretionary vs. Committed Fixed Costs Fixed costs that can be changed relatively easily at management discretion Discretionary Fixed Costs = Fixed costs that can not be easily changed Often these involve a long-term contract Committed Fixed Costs = 3-10 COPYRIGHT © 2012 Nelson Education Ltd.

Variable Cost Behaviour Example Expanding our SyBan Computers example…. Each computer requires one DVD-ROM drive costing $40 The cost of DVD-ROM drives for various levels of production is as follows: Let’s look at the cost of DVD-ROM’s at several production levels 3-11 COPYRIGHT © 2012 Nelson Education Ltd.

Variable Cost Example Variable Costs = Costs that in total vary in direct proportion to changes in output within the relevant range # of Computers Produced Total Cost of DVD-ROM Drives Unit Cost 20,000 $800,000 30,000 $1,200,000 40,000 $1,600,000 50,000 $2,000,000 $40 We know the cost increases as production increases, but what about cost per computer? Unit cost stays the same! The per unit variable cost of DVD-ROM drives is always $40 per computer $40 $40 $40 3-12 COPYRIGHT © 2012 Nelson Education Ltd.

Variable Cost Relationship Total Variable Cost Variable Rate Amount of output = × $40 per computer 50,000 computers $2,000,000 = × Let’s look at the DVD-ROM’s cost for 50,000 computers 3-13 COPYRIGHT © 2012 Nelson Education Ltd.

OBJECTIVE  2 Define and describe mixed and step costs COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Mixed Costs Costs that have both a fixed and a variable component Total Fixed Cost Total Variable Cost Total Cost = + Let’s look at an example from the SyBan Computers 15 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example SyBan Computers has 10 sales representatives Each earns a salary of $30,000 per year And a commission of $25 per computer sold Each sales rep sells up to 50,000 computers per year Let’s plug this into our mixed cost formula 3-16 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Mixed Cost Example Total Fixed Cost Total Variable Cost Total Cost = + ($25 × # of computers sold) Total Cost = $30,000 + Example: ($25 × 4,000 computers sold) = $30,000 + $130,000 3-17 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Step Costs Display a constant cost for a range of output Then jumps to a new cost level for a different range $15 per unit Example: $10 per unit 1,000 + $5 per unit 500 to 1,000 1 to 500 units 3-18 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. OBJECTIVE  3 Separate mixed costs into their fixed and variable components using the high-low method, the scattergraph method, and the method of least squares COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Separating Costs Accounting records typically show only total cost and associated amount of activity of a mixed cost item Therefore it is necessary to separate the total cost into its fixed and variable components Three methods: How do we separate the costs? High-Low method Scattergraph method Method of Least Squares 3-20 COPYRIGHT © 2012 Nelson Education Ltd.

Dependent Variable in the Cost Formula Total Cost Total Fixed Cost Total Variable Cost = + Total Cost Total Fixed Cost Variable Rate × Output = + Dependent Variable is a variable whose value depends on the value of another variable 3-21 COPYRIGHT © 2012 Nelson Education Ltd.

Independent Variable in the Cost Formula Total Cost Total Fixed Cost Total Variable Cost = + Total Cost Total Fixed Cost Variable Rate × Output = + Independent Variable is a variable that measures output and explains changes in the cost 3-22 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Intersect & Slope Intersect: Point at which the cost line intercepts the cost (vertical) axis Slope: Corresponds to variable rate (variable cost per unit of output) Slope of the cost line Let’s look at the formula Intercept 3-23 COPYRIGHT © 2012 Nelson Education Ltd.

Intercept & Slope in the Cost Formula Total Cost Total Fixed Cost Total Variable Cost = + Total Cost Total Fixed Cost Variable Rate = + × Output Intercept Slope 3-24 COPYRIGHT © 2012 Nelson Education Ltd.

Example: Cornerstone 3-1 How to Create and Use a Cost Formula Information: College art and graphics department decided to equip each faculty office with an inkjet colour printer Printers had monthly depreciation of $250 Department purchased paper in boxes of 10,000 sheets for $35 per box Ink cartridges cost $30 and will print, on average, 300 sheets Required: Create a formula for the monthly cost of inkjet printing If the department expects to print 4,400 pages next month, what is… Expected fixed cost? Total variable cost? Total printing cost? 3-25 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example Continued Total Cost = Total Fixed Cost + Total Variable Cost Total Cost = $250 + ($0.1035 × No. of pages) Using 4,400 as the # of pages…. ($0.1035 × 4,400) $455.40 Depreciation per month of $250 is a fixed cost Paper is $0.0035 per sheet and ink is $0.10 per sheet = $0.1035 per sheet Paper and ink are the two variable costs $705.40 = $250 + Total Costs for 4,400 pages Total Fixed Costs Total Variable Cost 3-26 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. High-Low Method A method of separating mixed costs into fixed & variable components by using just the high and low data points Step 1: Find the high point and low point Step 2: Using the high and low points, calculate the variable rate High point cost – Low point cost Variable rate = High point output – Low point output 3-27 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. High-Low Method Step 3: Calculate the fixed cost using the variable rate and either the high point or the low point Total cost at high point (Variable rate x Output at high point) Fixed Cost = - Or Low Point Step 4: Form the cost formula based on the high-low method Cornerstone 3-2 will walk us through an example 3-28 COPYRIGHT © 2012 Nelson Education Ltd.

Example: Cornerstone 3-2 How to use the High-Low Method Information: Blue Denim Company controller wants to calculate the fixed and variable costs associated with electricity used in the factory Required: Using the High-Low method, calculate: fixed cost of electricity the variable rate per machine hour construct the cost formula for total electricity cost 3-29 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Blue Denim Company Step 1: Identify the high and low points Month Electricity Costs Machine Hours January $3,255 450 February 3,485 500 March 4,100 600 April 3,300 470 May 3,312 470 June 2,575 350 July 3,910 570 August 4,200 590 3-30 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Blue Denim Company Month Electricity Costs Machine Hours January $3,255 450 February 3,485 500 March 4,100 600 April 3,300 470 May 3,312 470 June 2,575 350 July 3,910 570 August 4,200 590 High Point COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Blue Denim Company Month Electricity Costs Machine Hours January $3,255 450 February 3,485 500 March 4,100 600 April 3,300 470 May 3,312 470 June 2,575 350 July 3,910 570 August 4,200 590 Low Point 3-32 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. High-Low Method Step 2: Calculate the variable rate High point cost – Low point cost Variable rate = High point output – Low point output $4,100 – $2,575 Variable rate = 600 – 350 Variable rate = $6.10 per machine hour 3-33 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. High-Low Method Step 3: Calculate the fixed cost using the variable rate and either the high point or the low point Total cost at high point (Variable rate × Output at high point) Fixed Cost = – Fixed Cost = $4,100 – ($6.10 × 600) For this example we will chose the high point Fixed Cost = $4,100 – $3,660 Fixed Cost = $440 3-34 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. High-Low Method Step 4: Construct a cost formula Total electricity cost = $440 + ($6.10 x Machine hrs.) 3-35 COPYRIGHT © 2012 Nelson Education Ltd.

Example: Cornerstone 3-3 How to use the High-Low Method to Calculate Predicted Total Variable Cost and Total Cost for Budgeted Output Information: Blue Denim’s formula for monthly electrical cost: Total electricity cost = $440 + ($6.10 × Machine Hrs) Required: Assume that 550 machine hours are budgeted for the month of September. Using the formula calculate the following: Total variable electricity cost for October Total electricity cost for October 3-36 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example Monthly Electricity Cost Formula: Total electricity cost = $440 + ($6.10 × Machine hrs.) Total electricity cost = $440 ($6.10 × 550) + 550 machine hours Total electricity cost = $440 + $3,355 Total electricity cost = $3,795 Total variable electricity cost 3-37 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. High-Low Method Disadvantages: High and low points can be outliers and may represent atypical cost-activity relationships Even if these points are not outliers, other pairs of points may clearly be more representative The scattergraph method does a better job of separating the costs 3-38 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Scattergraph Method Purpose of the Method: To see whether a straight line reasonably describes the cost relationship To reveal one or more points that do not seem to fit the general pattern of behaviour 3-39 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Scattergraph Method Applying the Method: Draw a graph with units on the x-axis and cost on the y-axis Plot the data points on the graph Visually fit a line to the data points on the graph The intercept is the fixed cost Use the high-low method using the points from the graph to determine the variable rate We need a method that is objective and produces the best-fitting line Disadvantage: Lack of any objective criterion for choosing the best fitting line 3-40 COPYRIGHT © 2012 Nelson Education Ltd.

Method of Least Squares A statistical way to find the best-fitting line through a set of data points What does best fitting mean? The line is one in which the data points are closer to the line than to any other line Spreadsheet programs have packages to calculate the best-fitting line (called regression line) Steps: Measure distance from points to line Then square the differences Add up all the squared differences ▪ ▪ ▪ ▪ ▪ ▪ ▪ ▪ 3-41 COPYRIGHT © 2012 Nelson Education Ltd.

Example: Cornerstone 3-4 How to use the Regression Method to calculate fixed cost and variable rate, construct a cost formula and to determine budgeted cost Information: Blue Denim’s electricity cost and machine hours data for the past nine months Coefficients shown by regression program: Intercept 321 X Variable 6.38 (given in Cornerstone 3-2) Required: Using the results of regression, calculate: The fixed cost of electricity and the variable rate per machine hour Construct the cost formula for total electricity cost Calculate the budgeted cost for next month assuming 550 budgeted machine hours 3-42 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Example The fixed cost and the variable rate are given directly by regression Fixed Cost = $321 Variable Rate = $6.38 Intercept X Variable Total Electricity Cost = Fixed Cost + Variable Cost Total Electricity Cost = $321 + ($6.38 × 550) Budgeted machine hours Total Electricity Cost = $3,830 3-43 COPYRIGHT © 2012 Nelson Education Ltd.

COPYRIGHT © 2012 Nelson Education Ltd. Managerial Judgment Instead of the three methods previously discussed, many managers use their experience and past observation of cost relationships to determine fixed and variable costs Statistical techniques are highly accurate in depicting the past, but they cannot foresee the future 3-44 COPYRIGHT © 2012 Nelson Education Ltd.