1-1 CHAPTER 5 Determining How Costs Behave Dr. Hisham Madi

1-2  When managers make decisions, they need to compare the costs (and benefits) among alternative actions  Therefore, managers need to estimate the costs associated with each alternative.  Good decisions require good information about costs; the better these estimates, the better the decision managers will make. Basic Cost Behavior Patterns

1-3  The most important characteristic of costs for decision making is how they behave— how they vary with activity is the key distinction for decision making.  Therefore, the basic idea in cost estimation is to estimate the relation between costs and the variables affecting costs, the cost drivers  It is focused on the relation between costs and one important variable that affects them: activity level.  Activities can be measured by volume (for example, units of output, machine-hours, pages typed, miles driven), by complexity (for example, number of different products, number of components in a product), or by any other cost driver. Basic Cost Behavior Patterns

1-4 How to determine cost behaviour  understanding how costs change with changes in activity levels, units of products produced, and so on.  Knowing how costs vary by identifying the drivers of costs and by distinguishing fixed from variable costs is frequently the key to making considered management decisions.  Many managerial functions such as planning and control rely on knowing how costs will behave  Should a component part be made or purchased?

1-5 How to determine cost behaviour  Should we make the item or buy it?  What effect will a 20% increase in units sold have on operating profit ?

1-6  A cost function is a mathematical function describing cost behaviour patterns – how costs change with changes in the cost driver  Cost functions can be plotted on graph paper by measuring the cost driver on the x-axis and the corresponding amount of total costs on the y-axis Basic assumptions and examples of cost functions

1-7 Basic assumptions and examples of cost functions Two assumptions are frequently made when estimating cost functions: 1.Variations in the total costs of a cost-object are explained by variations in a single cost driver. 2.Cost behavior is approximated by a linear cost function within the relevant range.  a relevant range is the range of the activity in which there is a relationship between total cost and the level of activity.

1-8 Cost Terminology Variable costs  Costs that change in total in relation to some chosen activity or output Fixed costs  Costs that do not change in total in relation to some chosen activity or output Mixed costs  Costs that have both fixed and variable components; also called semivariable costs.

1-9 y = a + bX Linear Cost Function The dependent variable: the cost that is being predicted The intercept: fixed costs The slope of the line: variable cost per unit The independent variable: the cost driver

1-10 Bridging Accounting and Statistical Terminology

1-11 Linear Cost Functions Illustrated

1-12 Criteria for Classifying Variable and Fixed Components of a Cost Choice of cost object—  A particular cost item could be variable with respect to one cost object and fixed with respect to another.  For example, annual van registration and licence costs would be a variable cost with respect to the number of vans owned and operated by PLUS Company.  But registration and licence costs for a particular van are a fixed cost with respect to the number of kilo/meters that the van covered during the year.

1-13 Time span  The longer the period, the more likely the cost will be variable  For example, inspection costs at Boeing Company are typically fixed in the short run with respect to inspection-hours used because inspectors earn a fixed salary in a given year regardless of the number of inspection-hours of work done  But, in the long run, Boeing’s total inspection costs will vary with the inspection-hours required: More inspectors will be hired if more inspection-hours are needed, and some inspectors will be reassigned to other tasks Criteria for Classifying Variable and Fixed Components of a Cost

1-14 Criteria for Classifying Variable and Fixed Components of a Cost Relevant range  Behavior is predictable only within this band of activity.  Outside the relevant range, variable and fixed cost-behavior patterns change, causing costs to become nonlinear

1-15 Cause and Effect as It Relates to Cost Drivers  The most important issue in estimating a cost function is determining whether a cause-and-effect relationship exists between the level of an activity and the costs related to that level of activity.  Without a cause-and-effect relationship, managers will be less confident about their ability to estimate or predict costs.

1-16 The Cause-and-Effect Criterion The cause-and-effect relationship may arise as a result of:  A physical relationship between the level of activity and costs. There is a physical relationship between direct materials and the number of units produced  A contractual arrangement. For example, in a car rental contract that charges by the mile, miles driven is specified in the contract as the activity that affects the rental cost  Knowledge of operations. A product with many parts will incur higher ordering costs than a product with few parts. If the company is measuring ordering costs, the activity driver could be number of parts

1-17 The Cause-and-Effect Criterion  Managers must be careful not to interpret a high correlation, or connection, in the relationship between two variables to mean that either variable causes the other  Be careful not to interpret a high correlation, or connection, between two variables to mean that either variable causes the other  A high correlation between two variables, u and v, indicates merely that the two variables move together  It is possible that u may cause v; v may cause u; u and v may interact; both may be affected by a third variable z; or the correlation may be due to chance

1-18 The Cause-and-Effect Criterion  No conclusions about cause and effect are warranted by high correlations.  For example, higher production generally results in higher materials costs and higher labour costs. Materials costs and labour costs are highly correlated, but neither causes the other.

1-19 The industrial engineering method,  This is also called the work-measurement method, estimates cost functions by analyzing the relationship between inputs and outputs in physical terms.  This is a thorough and detailed method, but can be very time- consuming.  For example, a carpet manufacturer that uses inputs of cotton, wool, dyes, direct labour, machine time and power. Production output is square metres of carpet  Time-and-motion studies analyse the time and materials required to perform the various operations to produce the carpet Cost Estimation Methods

1-20  A time-and-motion study may conclude that to produce 20 square metres of carpet requires 2 kilograms of cotton and 3 litres of dye  The result is an estimated cost function relating total manufacturing costs to the cost driver, square metres of carpet  Many organizations, however, find it too costly for analyzing their entire cost structure.  More frequently, organizations use this approach for direct-cost categories such as materials and labour but not for indirect-cost categories such as manufacturing overhead  Cost Estimation Methods

1-21 Cost Estimation Methods Conference method  The conference method estimates cost functions on the basis of analysis and opinions about costs and their drivers gathered from various departments of an organization (purchasing, process engineering, manufacturing, employee relations, and so on)  Because it does not require detailed analysis of data, it can be used to develop cost functions very quickly.  However, the emphasis on opinions rather than systematic estimation can make this a less accurate method.

1-22 Cost Estimation Methods Account analysis method  The account analysis method estimates cost functions by classifying various cost accounts as variable, fixed, or mixed with respect to the identified level of activity.  Consider indirect manufacturing labour costs for a small production area (or cell) at Møre-Teppe.  These costs include maintenance, quality control and set-up costs for the machines  Møre-Teppe worked the machines in the cell for a total of 862 hours and incurred total indirect manufacturing labour costs of €12 501

1-23  Management wants the cost analyst to use the account analysis method to estimate a linear cost function for indirect manufacturing labour costs with machine-hours as the cost driver.  The cost analyst decides to separate total indirect manufacturing labour costs (€12 501) into costs that are fixed (€2157) and costs that are variable (€10 344) with respect to the number of machine-hours worked  Variable costs per machine-hour are € ÷ 862 = €12.  The general cost equation, y = a + bX, is indirect manufacturing labour costs = € (€12 × number of machine-hours). The indirect manufacturing labour cost per machine-hour is € ÷ 862 = € Cost Estimation Methods

1-24 Cost Estimation Methods  Management at Møre-Teppe can use the cost function to estimate the indirect manufacturing labour costs of using 950 machine-hours to produce carpet in the next 12 week period.  Using the cost function, estimated costs = € (950 × 12) = €  The indirect manufacturing labour costs per machine-hour decrease to € ÷ 950 = €14.27,  Organizations must take care to ensure that individuals thoroughly knowledgeable about the operations make the cost- classification decisions, to obtain reliable estimates of the fixed and variable components of cost

1-25 Cost Estimation Methods Quantitative Analysis Method  The quantitative analysis method uses formal mathematical models to fit cost functions to past data observations. The most common quantitative analysis methods are the high-low method and regression analysis.

1-26 Steps in estimating a cost function Using Quantitative Analysis Step 1 Choose the dependent variable (cost being estimated or predicted). The dependent variable is the cost being estimated (y in the equation) and depends on the cost function being estimated. For example,  if the purpose is to determine indirect manufacturing costs for a production line, then the dependent variable should incorporate all costs that are classified as indirect with respect to the production line

1-27 Steps in estimating a cost function Using Quantitative Analysis Step 2 Identify the independent variable, or cost driver. The independent variable is the factor used to predict the cost function.  This is the cost driver, otherwise referred to as X in the equation, or the slope.  The cost driver should be measurable and have an cause-effect relationship to the dependent variable.  Consider several types of fringe benefit paid to employees and their cost drivers:

1-28 Steps in estimating a cost function Using Quantitative Analysis  The costs of health benefits and cafeteria meals can be combined into one cost pool because they both have the same cost driver, number of employees. Pension benefits and life insurance costs have a different cost driver, salaries of employees Step 3 Collect data on the dependent variable and the cost driver. This is usually the most difficult step, as the data comes from a number of sources, and managers need to be concerned about the validity of the data  Time-series data pertain to the same entity (organisation, plant, activity area, and so on) over a sequence of past time periods

1-29  Weekly observations of indirect manufacturing labour costs and machine- hours in the Møre-Teppe illustration are an example of time-series data.  The ideal time-series database would contain numerous observations for a firm whose operations have not been affected by economic or technological change.  Stable technology ensures that data collected in the estimation period represent the same underlying relationship between the dependent variable and the cost driver  Cross-sectional data pertain to different entities for the same time period.  For example, studies of personnel costs and loans processed at 50 individual branches of a bank during March would produce cross-sectional data for March. Steps in estimating a cost function Using Quantitative Analysis

1-30 Steps in estimating a cost function Using Quantitative Analysis Step 4 Plot the data. By plotting the data on a scattergraph it can be determined if a linear relationship exists. Also, this alerts the manager to any extreme observations.

1-31 Steps in estimating a cost function Using Quantitative Analysis  Plotting the data can also provide insight into whether the relation is approximately linear and what the relevant range of the cost function is. Step 5 Estimate the cost function. As mentioned, there are two primary methods of estimating a cost function—the high-low method and regression analysis.  By using the high–low method and regression analysis Step 6 Evaluate the cost driver of the estimated cost function

1-32 High–low method  Managers, at times, use very simple methods to estimate cost functions.  Using only the highest and lowest observed values of the cost driver within the relevant range.

1-33 High–low method

1-34 High–low method  To compute the constant, we can use either the highest or the lowest observation of the cost driver.

1-35 High–low method Advantages of the high-low method are that it is simple to compute and understand, and it can give a quick insight into cost-activity relationships. However, it utilizes only two data points, thus ignoring a great deal of valid data.

1-36 Regression analysis method  Regression analysis is a statistical method that measures the average amount of change in the dependent variable that is associated with a unit change in one or more independent variables.  Simple regression analysis estimates the relationship between the dependent variable and one independent variable.  Multiple regression analysis estimates the relationship between the dependent variable and multiple independent variables  Regression analysis is widely used because it helps managers understand why costs behave as they do and what managers can do to influence them

1-37 Regression analysis method  The difference between actual and predicted cost is called the residual term  The smaller the residual terms, the better the fit between predicted costs and actual cost observations

1-38 Regression analysis method  Goodness of fit indicates the strength of the relationship between the cost driver and costs  The estimate of the slope coefficient b indicates that the average indirect manufacturing labour costs vary at the rate of €10.31 for every machine-hour within the relevant range. Y = € €10.31X

1-39 Evaluating and choosing Cost Drivers  How does a company determine the best cost driver when estimating a cost function?  Is this the best cost driver to predict the behavior?  How good is this driver at predicting cost behavior?  Suppose Møre-Teppe wants to evaluate whether direct manufacturing labour-hours is a better cost driver than machine-hours for indirect manufacturing labour costs.

1-40 Evaluating and choosing Cost Drivers There are three criteria often used to evaluate cost drivers; they are:  Economic plausibility. Do the cost driver and the level of costs seem to be related? Does it make sense that an increase in the independent variable will cause an increase in the costs?  Highly automated production environment of Møre-Teppe, costs are likely to be more closely related to machine-hours than to direct manufacturing labour-hours.

1-41  Goodness of fit. Are the differences between the actual costs and predicted costs small? In a regression analysis, goodness of fit is measured by the r 2 statistic.  The vertical differences between actual and predicted costs are much smaller for machine-hours than for direct manufacturing labour-hours – machine-hours has a stronger relationship with indirect manufacturing labour costs.  Evaluating and choosing Cost Drivers

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1-43  Significance of independent variable. If the regression line (or total cost line) has a steep slope, this indicates a strong relationship between the cost driver and the costs incurred  The machine-hours regression line has a relatively steep slope while the direct manufacturing labour-hours regression line is relatively flat (small slope)  A relatively flat regression line indicates a weak or no relationship between indirect manufacturing labour costs and direct manufacturing labour-hours.  On average, changes in direct manufacturing labour-hours appear to have a minimal effect on indirect manufacturing labour costs. Evaluating and choosing Cost Drivers

1-44 Evaluating and choosing Cost Drivers Why is choosing the correct cost driver to estimate indirect manufacturing labor costs important?  Because identifying the wrong drivers or misestimating cost functions can lead management to incorrect (and costly) decisions  Management estimates 72 machine-hours and 21 direct manufacturing labor- hours would be required per week to produce new style of carpet. Machine-hours as the cost driver  Cost function y= € (€10.31 ×machine-hours) to predict future indirect manufacturing labour costs  Using this model, Møre-Teppe would predict costs of y=€ (€10.31 ×72) = €

1-45 Evaluating and choosing Cost Drivers labour-hours as the cost driver  Predicted cost is € (€7.72 ×21) = €906.79

1-46 Cost drivers and Activity-Based Costing  Estimating cost drivers in an activity-based costing system doesn’t differ in general from what’s been discussed.  However, since ABC systems have a great number and variety of cost drivers and cost pools, managers must estimate many cost relationships.  In estimating the cost function for each cost pool, the manager must pay careful attention to the cost hierarchy.  For example, if a cost is a batch-level cost such as setup cost, the manager must only consider batch-level cost drivers like number of setup-hours.

1-47 Cost drivers and Activity-Based Costing  ABC systems emphasise long-run relationships between the cost driver (level of activity) and cost.  Because in the short run, costs may be fixed and, therefore, will not vary with changes in the level of the cost driver  The long-run focus means that more costs are variable, which leads to a stronger cause-and-effect relationship between the cost driver and the corresponding cost  Hence, the ideal database to estimate cost driver rates will contain data over a longer time period

1-48 Cost drivers and Activity-Based Costing  If the time period used to estimate the cost relationship is short, the relationship between changes in the cost driver and changes in cost may be weak. Why  Because many costs are acquired in lump-sum amounts and hence are fixed in the short run while the levels of activity vary.

1-49 Nonlinear Cost Functions  cost functions are not always linear.  A non-linear cost function is a cost function where, within the relevant range, the graph of total costs versus the level of a single activity is not a straight line  Some examples of nonlinear cost functions follow

1-50 Nonlinear Cost Functions Economies of scale  Direct materials costs are not always linear variable costs.  Consider quantity discounts on direct materials purchases.

1-51 Nonlinear Cost Functions  the total direct materials costs rise, but they rise more slowly as the cost driver increases because of quantity discounts  b= €25 for 1–1000 units purchased; b = €15 for 1001–2000 units purchased; and b= €10 for 2001 or more units purchased (a= €0 for all ranges of the units purchased).

1-52 Nonlinear Cost Functions A step cost function  is a cost function in which the cost is constant over various ranges of the cost driver, but the cost increases by discrete amounts (that is, in steps) as the cost driver moves from one range to the next.  A step variable-cost function, a step cost function in which cost is constant over narrow ranges of the cost driver in each relevant range.  The pattern is a step cost function because set-up costs are incurred only when each production batch is started

1-53 Nonlinear Cost Functions Learning curve  A function that measures how labor-hours per unit decline as units of production increase because workers are learning and becoming better at their jobs.  Managers use learning curves to predict how labour-hours (or labour costs) will change as more units are produced  The aircraft-assembly industry first documented the effect that learning has on efficiency. As workers become more familiar with their tasks, their efficiency improves.

1-54 Nonlinear Cost Functions Learning curve  Managers are now extending the learning-curve notion to include other cost areas in the value chain, such as marketing, distribution and customer service  An experience curve is a function that shows how full product costs per unit (including manufacturing, marketing, distribution, and so on) decline as units of output increase.

1-55 Types of Learning Curves  Cumulative average time per unit declines by a constant percentage each time the cumulative quantity of units produced doubles.  Rayburn has an 80% learning curve.  The 80% means that when the quantity of units produced is doubled from X to 2X, cumulative average time per unit for 2Xunits is 80% of cumulative average time per unit for X units. Average time per unit has dropped by 20% (100% – 80%).

1-56 Types of Learning Curves

1-57 Types of Learning Curves Incremental Unit-Time Learning Model  Incremental time needed to produce the last unit declines by a constant percentage each time the cumulative quantity of units produced doubles.  80% learning curve  The 80% here means that when the quantity of units produced is doubled from X to 2X, the time needed to produce the last unit when 2Xtotal units are produced is 80% of the time needed to produce the last unit when X total units are produced

1-58 Types of Learning Curves

1-59 Types of Learning Curves  The incremental unit-time learning model predicts a higher cumulative total time to produce 2 or more units than the cumulative average-time learning model,  assuming the same learning rate for both models 80%.  If we compare the results, to produce 4 cumulative units,  the 80% incremental unit-time learning model predicts labor-hours versus labor-hours predicted by the 80% cumulative average-time learning model.  That’s because under the cumulative average-time learning model average labor-hours needed to produce produce unit 4 is much less than 64 hours—it is hours

1-60 Types of Learning Curves  Under the incremental unit-time learning model, the labor- hour amount needed to produce unit 4 is 64 hours, and the labor- hours needed to produce the first 3 units are more than 64 hours, so average time needed to produce all 4 units is more than 64 hours  How do managers choose which model and what percent learning curve to use?  Engineers, plant managers, and workers are good sources of information on the amount and type of learning actually occurring as production increases

1-61 Predicting Costs Using Alternative Time Learning Models How do companies use learning curves?  For example, a company might set an extremely low selling price on its product in order to generate high demand.  As the company’s production increases to meet this growing demand, costs per unit drop.  The company rides the product down the learning curve as it establishes a higher market share.  Although the company may have earned little on its first unit sold – it may actually have lost money – the company earns more profit per unit as output increases

1-62 Predicting Costs Using Alternative Time Learning Models Alternatively,  the company might set a low price on just the final 8 units. After all, the labour and related overhead costs per unit are predicted to be only€ for these final 8 units (€ – €20 480).  The per unit costs of €1536 on these final 8 units (€ ÷ 8) are much lower than the €5000 costs per unit of the first unit produced.

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