1. III. COST BEHAVIOR

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1 Chapter 3 Cost Behavior Page 1 1. III. COST BEHAVIOR In this chapter we discuss the manner in which costs behave. We will discuss fixed and variable costs. As part of this discussion, we will discuss learning curves. We will also discuss using past data to estimate a company s cost function. As part of this discussion, we will discuss the High- Low Method of generating a cost function from past data. In addition we will discuss using an OLS regression to generate such a function. As part of this discussion, we will use Microsoft Excel to generate a cost function from past data. When dealing with costs, it helps for you to determine what drives the cost in question. A Cost Driver (also called Cost Base) is an activity that is associated with, or related to, changes in the cost in question. For example, assume that Redford, Inc. produces classic, wood baseball bats. The cost of the wood materials used in the production of these baseball bats is closely associated with the number of bats produced. In this case, the number of units is a good Cost Driver for the material cost in Redford s production of bats. In fact, the number of units produced is often used as the Cost Driver for costs. For purposes of this discussion, we will assume that the Cost Driver is the number of units produced, but Cost Drivers actually can be a number of different things. For example, the cost of custodial services is driven by the amount of floor space maintained. Thus, floor space is often used to allocate custodial costs between plant departments. Another popular Cost Driver is the number of labor hours that are used to make a product. Variable Costs change as their associated Cost Drivers change. On the other hand, some costs do not change regardless of changes in production or other Cost Drivers. These costs are referred to as Fixed Costs. Fixed Costs A graphical depiction of a Fixed Cost is shown below. Regardless of the number of units produced (or changes in other typical Cost Drivers), the Fixed Cost remains unchanged.

2 Chapter 3 Cost Behavior Page 2 Graphical Representation of a Fixed Cost This definition of Fixed Costs is possible because two assumptions have been made. First, the time horizon being discussed is relatively short. Second, the range of production in question is limited. The time horizon is important. In making decisions, we typically assume a relatively short time horizon. For example, we might be considering a time horizon of one year. Over that year, our rent is likely to remain unchanged regardless of a change in the level of our production. Over a long enough time horizon, however, all costs become variable. For example, with a longer time horizon, our monthly rental expense is likely to increase due to the expiration of our lease, an expansion of our operations, and/or the need to increase and modernize our production capacity. In addition to the time horizon, we also typically assume that we will be operating within a range of activity (Relevant Range). For example, assume that our baseball bat manufacturer normally produces and sells between 10,000 and 20,000 bats in a year, and it has the capacity to make up to 40,000 bats in its current facilities. In this case, it is unlikely that it will be called upon to make more than 40,000 bats, and it is unlikely that its Fixed Costs will change within this Relevant Range of production (10,000 20,000 bats). Without the assumption regarding Relevant Range, the Fixed Cost function could become a step cost. It remains fixed for a given range of production (or other Cost Driver), but it eventually changes. A graphical depiction of the cost to rent a factory appears below:

3 Chapter 3 Cost Behavior Page 3 Graphical Representation of a Step Cost As long as you assume that the Relevant Range of production (the circle) can be handled by two factories, then factory rent is a Fixed Cost. Variable Costs As noted above, Variable Costs change with changes in their associated Cost Drivers. A graphical depiction of a Variable Cost appears below. Graphical Representation of a Variable Cost The linear representation of a Variable Cost with a constant slope is again an over simplification of the behavior of Variable Costs. For example, the existence of Economies Of Scale would make a Variable Cost function appear more like the following:

4 Chapter 3 Cost Behavior Page 4 Graphical Depiction of a Non-Linear Variable Cost When only the Relevant Range is considered, the non-linear cost (within the circle) appears more linear. This fact makes the assumption that the Variable Cost function is linear becomes more realistic. Mixed Costs Mixed Costs are partially fixed and partially variable. For example, if the cost of renting a car is $50 a day plus 20 a mile, then the rental cost has a fixed component (daily charge) and a variable component (mileage charge). Mixed costs can be represented as follows: Graphical Representation of a Mixed Cost Total Costs are a Mixed Cost because they include both Fixed Costs and Variable Costs. If a cost can be divided into a fixed component and a variable component, then: Total Cost = Variable Cost + Fixed Cost

5 Chapter 3 Cost Behavior Page 5 Since Variable Costs are driven by the number of units produced (or some other Cost Driver), Variable Cost is made up of two components, the Variable Cost per unit, V, and the number of units produced (or other Cost Driver), x. Fixed Costs can be represented by the single variable, F. Units produced (x) are not included because Fixed Costs do not change with the number of units produced. Using these variables, we can represent the linear cost function as follows: Total Cost = Vx + F As you will recall (remember High School?), the formula for a line is y = mx + b The y-axis is the total cost in question. The slope of the line is the Variable Cost per unit (V), and the y-intercept, b, is the total Fixed Costs (F). Deriving the Cost Function From Past Behavior Most books emphasize objective techniques that can be used to derive the cost function from a firm s past cost experience. There are other approaches that also include subjective analysis. One of the benefits of using more subjective techniques is that you can incorporate changes and events that are not reflected in past data. These more subjective techniques include: Engineering Method. With this method, you make a detailed step-by-step analysis of the manufacturing process and the costs involved in each step. From this analysis, you decide how much time and materials are needed. The same analysis decides how much Manufacturing Overhead is needed for the entire manufacturing process, and this Manufacturing Overhead can then be allocated to the production. From your analysis, you estimate the cost function. Conference Method. With this method, different departments and employees give their opinions as to the costs (and the likely Cost Drivers) involved in their operations. A consensus cost function is derived from these opinions. Account Analysis Method. With this method, you examine all of the accounts of the business in order to determine an operation s Variable Costs (and their Cost Drivers) and Fixed Costs. With this information you estimate the firm s cost function. Objective methods to derive a cost function from the past behavior range from a very low tech approach, the High-Low Method, which can be done with simple Geometry and Algebra, to the use of an OLS Regression, which can be done using Excel.

6 Chapter 3 Cost Behavior Page 6 Before using either of these approaches, it is important for you to do a scattergraph, in which you plot the past history of the cost in question. The reason that you do the scattergraph is to visually confirm that you are dealing with a linear relationship, and to determine whether there are outlying points that can throw off your analysis. High-Low Method Scattergraph A simple way to estimate a linear cost function from your past costs, is the High-Low Method. As you will recall, only one line runs through two points. Thus, you need only two points to define the cost formula. The High-Low Method says that the two points that define the cost formula are: (i) the highest activity level, and (ii) the lowest activity level. (If either or both of these points were outlying points, you should select others.) High-Low Method Cost Function With the High-Low Method, you first start by estimating the Variable Cost per unit (the slope of the cost formula). As you will recall, the slope of a line is derived from the following formula:

7 Chapter 3 Cost Behavior Page 7 V = m = y 1 - y 0 x 1 - x 0 Now that you know the Variable Cost per unit, you can figure out the Fixed Cost. Take your cost function: Total Cost = Vx + F Plug in: (i) The Variable Cost per unit, (ii) the Total Costs for one of the two points (either the high or the low point), and (iii) the activity level associated with the Total Costs; and solve for the Fixed Cost. Example of High-Low Method Assume that Redford, Inc. makes baseball bats, and the highest activity level last year was 40,000 baseball bats and the cost to make those bats during that month was $500,000. The lowest activity level last year was 20,000 baseball bats, and the cost to make these bats during that month was $300,000. If you were to use the High-Low Method, you would calculate the Variable Cost per unit (the slope of the linear cost function): Variable Cost per Unit = m = V = V = y 1 - y 0 x 1 - x 0 $500,000 - $300,000 40,000-20,000 $200,000 20,000 V = $10 per bat Now that you know the Variable Cost per unit, you can figure out the Fixed Cost: Take the generic cost formula (Total Cost = Vx + F), and plug in: (i) the $10 Variable Cost per unit, (ii) the Total Costs for one of the two points that you used to determine the Variable Cost per unit (either the high or the low point), and (iii) the activity level for that point. Then, solve for the Fixed Cost. Either point will give you the same Fixed Cost. Using the High Point: Using the Low Point: Total Cost = Vx + F Total Cost = Vx + F 500,000 = 10 (40,000) + F 300,000 = 10 (20,000) + F 500,000 = 400,000 + F 300,000 = 200,000 + F 500, ,000 = F 300, ,000 = F 100,000 = F 100,000 = F So Redford, Inc. s cost formula is: TC = $100,000 + [$10 x (number of bats)] or TC = 10x + 100,000

8 Chapter 3 Cost Behavior Page 8 [In Peggy Sue Got Married, Peggy Sue goes back in time to her High School Algebra class on the day of an examination. Having forgotten her Algebra, she turns in a blank answer sheet.] TEACHER: What's the meaning of this, Peggy Sue? PEGGY SUE: (patiently) Mr. Snelgrove, I happen to know that in the future, I will never have the slightest use for Algebra. And I speak from experience. Apparently, Peggy Sue never took Cost Accounting. OLS Regression Analysis Ordinary Least Squares (OLS) Regression analysis also involves estimating linear cost relationships from past data. Rather than merely drawing a line between two points, we use the computer to calculate the line that best fits the data. With OLS Regression, the computer squares the distances between a proposed cost function line and the actual cost data. The computer finds the line that produces the lowest sum of the squared distances. In the figure that appears below, the line in the center produces the lowest sum of these squared distances. You can run a Regression using Excel. With a Regression, you have independent variables and a dependent variable. The dependent variable is the variable whose behavior you are trying to estimate (cost). Independent variables are the explanatory variables (e.g., number of units). If you only

9 Chapter 3 Cost Behavior Page 9 have one independent variable, this is called a Simple Regression. If you have more than one independent variable, this is called a Multiple Regression. When you run a Regression using any statistical package (including Excel), the Regression will provide you with: (i) the coefficients that go before the independent variable (e.g. Variable Cost per unit), and (ii) the y-intercept value (for Fixed Cost). With a Simple Regression, this gives you the linear cost function: Total Cost = [Coefficient x Independent Variable] + Y-Intercept Coefficient With a Multiple Regression, you are no longer in a two dimensional world [total cost (y) & 1 independent variable (x) as the two axis]. Instead, you are now in a greater than two dimensional world. The number of dimensions is equal to the number of dependent and of independent variables in your cost function. The cost function given by the Regression reflects the increased number of dimensions. When running a Regression, a key statistic given in the Regression output is the R 2. The R 2 is referred to as the Coefficient of Determination. This statistic gives the Goodness Of The Fit of the model (or the percentage of the dependent variable s behavior that is explained by the model). The higher the R 2, the better the model fits the data. The best R 2 would be That means 100% of the data is explained by the model. When you have a Multiple Regression, then the Adjusted R 2 is looked at because it adjusts the R 2 value for the number of explanatory variables. The Regression output also gives you the statistical significance (t-statistic) for the coefficient(s) of the explanatory variable(s) and the y-intercept. This gives the likelihood that the coefficient or y-intercept is significantly different than zero. Usually, people want these coefficients to be significant at the 99%, 95%, or 90% level. If you ever see a Multiple Regression with a high Adjusted R 2, but low t-statistics for the independent variable coefficients, this tells you that the model is good, but you have chosen related independent variables. Having correlated independent variables is called Multicollinearity. The program is saying that your model is explaining the cost behavior, but the model can not figure out how much each variable is contributing to the explanatory power of the model. If you see this, try dropping one of the independent variables. OLS Regression Analysis Using Excel In order to run an OLS Regression using Excel, you need to have Data Analysis added as a Tool. Click on Tools on the main Menu Bar, and check to see if you have Data Analysis as an option. If not, click on Add Ins and then check the Analysis ToolPak box, and then click OK. You will now have Analysis ToolPak as an option under the Tools Menu item.

10 Chapter 3 Cost Behavior Page 10 You need to set up the data so that you can run the Regression. You need to input the cost (the dependent variable) and the independent variables. We will use two independent variables, hours and units: Now, click on Tools on the main Menu Bar, and then click on Data Analysis. The Data Analysis Dialog Box will open, and you will click on Regression. Now, the Regression Dialog Box will open. Click on the Input Y Range Box. Then, highlight the O/H Cost information on the spreadsheet (D2:D13). Next, Click on the Input X Range Box. Then, highlight the information under Hours (B2:B13). Now, click on OK. A new worksheet should open that has the Regression output: The Coefficients column gives you the OLS Regression s formula for your cost function: O/H Costs = [$3.814 x (Number of Hours)] + $219,385 Using this formula, you can estimate that if you had 69,000 hours, then your Manufacturing Overhead would be: ($3.814 x 69,000) + $219,385 = $482,551 The R 2 (R square) gives you the Goodness Of The Fit of this model. In real life, 99.07% is superb. The t-statistics that are reported for each coefficient are also great. You can tell this from the P-value that is also reported, which gives the significance level of the t- Statistic. [The Confidence Level related to the t-statistic is 1-(P-value).] We are happy

11 Chapter 3 Cost Behavior Page 11 if it is significant to the 90% level (less than.10); the 95% level (less than.05) and the 99% level (less than.01). Here the t-statistic of is significant beyond the 99% level ( ), and the t-statistic of 32.6 is also significant beyond the 99% level ( ). What if you ran an OLS Regression using Units as the independent variable? The OLS Regression s formula for your cost function is now: O/H Costs = [$18.03 x (Number of Units)] + $379,984 Using this formula, we can estimate that if we had 6,000 units, then our Manufacturing Overhead would be: ($18.03 x 6,000) + $379,985 = $488,165 The R 2 and t-statistics reported for this Regression are also very significant; although the R 2 (98.4%) is slightly lower than that of the preceding regression (99.07%). What if you ran an OLS Regression using both Hours (X1) and Units (X2) as the independent variable? This would be a Multiple Regression because you have more than one independent variable:

12 Chapter 3 Cost Behavior Page 12 Does the use of the two variables really improve the model? The R 2 of this Multiple Regression is as high as the Hours Regression. But look at the t-statistics that are reported for each coefficient. The t-statistic for the y-intercept is significant, but not to the level that we saw in the Simple Regressions, and the t-statistics for the coefficients for the two independent variables are not significant at all. What is going on? You have Multicollinearity. The two independent variables are correlated. The model still does a great job explaining cost behavior, but the Regression cannot tell which independent variable is doing the explaining. You should also note that the Multiple Regression s Adjusted R 2 ( ) declined from the Adjusted R 2 produced from the Simple Regression using Hours as the independent variable ( ). This suggests that you do not add additional explanatory power to the model by including Units as an additional independent variable in a Multiple Regression. Learning Curves Up until now, we have assumed that cost formulas are linear. This is probably true over the Relevant Range, however, when you first start to produce a product, the cost drops as you learn how to make the product. For example, if you were to buy three bookcases that you needed to assemble, then it is likely that the first bookcase would take longer to assemble because you read the directions very carefully and study the parts involved. The second bookcase will probably takes less time because you don't have to read the instructions all over again. Instead, you can skim the instructions. When you assemble the third bookcase, you don't even have to look at the instructions, and it takes you even less time to assemble. This phenomenon is referred to as a Learning Curve. Learning Curves acknowledge that manufacturing costs drop as the firm makes more units. Understanding this phenomenon is important in start-up situations. For example, in 1960, no company dominated the ball point pen industry. BIC, a French pen company, entered the U.S. ballpoint pen market by selling its now classic, BIC Crystal ballpoint pen. At the time, common, everyday ballpoint pens cost around 29. BIC understood the Learning Curve, and it knew that as it made more pens, the manufacturing cost of each pen would drop. BIC, therefore, offered the BIC Crystal ballpoint pen at a price of 10, which was below its then manufacturing cost. BIC correctly assumed that the lower price would result in more sales. The increased sales would, in turn, result in cheaper production costs through the Learning Curve phenomenon. The end result would be that the price charged would be higher than the eventual production cost. BIC's assumptions were correct, and it quickly dominated the ballpoint pen market. Today, 14 billion BIC Crystal ballpoint pens are sold throughout the world each day. Anticipating the Learning Curve is referred to as Riding Down the Learning Curve.

13 Chapter 3 Cost Behavior Page 13 Learning Curves can be caused by such things as: Labor Efficiency; Methods Improvements; Changes in the Resource Mix; and Product Redesign. Learning Curves are closely related to Economies of Scale. Economies of Scale are a function of volume, and Learning Curves are a function of experience. These two effects tend to mirror each other because the growth of experience often coincides with increased production. Economies of Scale were certainly part of the reason for the decline in BIC s per unit manufacturing costs. The two effects, however, are not identical. For example a doubling of annual production could lead to both Economies of Scale and Learning Curve effects. Producing the same amount each year, however, would not lead to Economies of Scale, but it could still produce Learning Curve effects (because of the doubling of your experience over time). The availability of volume discounts when large amounts of raw materials are purchased is an Economy of Scale. It does not reflect a Learning Curve effect. The cost savings that result from switching from individual production to assembly line production would be another example of Economies of Scale. Except for Henry Ford, the existence of assembly lines is not learned; it is an option that available to everyone one if circumstances permit (e.g. sufficient volume of a standard product). In fact, switching to assembly line operations could cause prior Learning Curve effects (related to the individual production) to be lost, and a new Learning Curve (related to the assembly line) to be started. The cost savings from learning that we can replace our current titanium parts with plastic parts without a reduction in product quality would be a function of time and experience; not the scale of our operations. Similarly, learning that we can reduce the time it takes to make a given amount of units if we produce the units in smaller batches would be a function of our experience (not the scale of our production). The Learning Curve Calculation This Learning Curve was first quantified in 1925 at Wright-Patterson Air Force Base in the United States, where it was determined that every time aircraft production doubled, the required labor time decreased by 10 to 15 percent. Subsequent empirical studies from other industries have yielded different values ranging from only a couple of percent up to 30 percent. Technically, Learning Curves report improvements in labor time that result from experience. On the other hand, Experience Curves report reductions in all costs that result from experience. We will refer to both types of curves as Learning Curves. Learning Curves have been reported in the following industries:

14 Chapter 3 Cost Behavior Page 14 Aerospace 85% Shipbuilding 80-85% Complex Machine Tools For New Models 75-85% Repetitive Electronics Manufacturing 90-95% Repetitive Machining Or Punch-Press Operations 90-95% Repetitive Electrical Operations 75-85% Repetitive Welding Operations 90% Raw Materials 93-96% Purchased Parts 85-88% As noted above, the Learning Curve reflects the fact that every time you double your production, the Learning Curve Item being measured (e.g., cost or time) drops to a percentage (the Learning Curve Percentage) of what it was before the production was doubled (Doubling Rule). For example, assuming an 80% Learning Curve: Units Produced Learning Curve Item Calculation (80% x 1250) (80% x 1000) (80% x 800) This reduction in the Learning Curve Item can be represented graphically: Graphical Representation of the Learning Curve Item We will discuss the meaning of the Learning Curve Item shortly. If you need to know the Learning Curve Item for 3 units, then you need to rely on the following formula, which will give you the Learning Curve Item for any given production level:

15 Chapter 3 Cost Behavior Page 15 Where: Y = ax b Y = The Learning Curve Item a = The Learning Curve Item for the first unit X = The number of units produced b = natural log (Learning Curve Percentage) / natural log (2) Using this formula we can find the Learning Curve Item for 3 units: b = ln(.80)/ ln(2) b = /.6931 b = Y = (1250)(3) Y = (1250) (.70205) Y = Once you know the Learning Curve Item for 3 units, then you can use the Doubling Rule to find the Learning Curve Item for 6 units (.80 x = 702). Learning Curve Item As noted above, Learning Curves can be used to measure: (i) the time needed to for a given operation, or (ii) cost incurred by that operation. Thus, the Learning Curve Item can represent either cost or hours. The Learning Curve Item (whether cost or hours) can be thought of in one of two ways: Incremental Learning Curve. With an Incremental Learning Curve, the Learning Curve Item represents the incremental (or marginal) cost or hours needed to produce the last unit if a given number of units are produced; or Average Learning Curve. With an Average Learning Curve, the Learning Curve Item represents the average cost or hours needed to produce each unit produced assuming that a given number of units are produced Regardless of whether you are employing an Incremental or Average Learning Curve, the Learning Curve Item is calculated the same way. Only the interpretation of the Learning Curve Item changes with the type of Learning Curve being used. Let us examine the meaning of an 80% Learning Curve where it takes 1250 hours to make the first unit. The Learning Curve Items for this Learning Curve were calculated in the above discussion. The Learning Curve Item is the same for both the Average and the Incremental Learning Curves, but the interpretations of the Learning Curve Item are different.

16 Chapter 3 Cost Behavior Page 16 Units LC Item Incremental Interpretation Average Interpretation It takes 1250 hours to make the first unit It takes 1000 hours to make the second unit It takes 800 hours to make the fourth unit It takes 640 hours to make the eighth unit. It takes 1250 hours to make the first unit. It takes an average of 1000 hours to make each unit if you make 2 units. It takes an average of 800 hours to make each unit if you make 4 units. It takes an average of 640 hours to make each unit if you make 8 units. These different interpretations affects the total hours needed to produce a given number of units: Incremental Learning Curve Average Learning Curve Units LC Item Total Hours To Make All Units Total Hours To Make All Units ( ) (1000x2) ( ) (877.6x3) ( ) (800x4) With the Incremental Learning Curve, you know the time/cost to make the next unit, but with the Average Learning Curve this calculation only gives you the average time/cost to make all of the units in question. If you want to know the incremental time/cost to make the last unit, then you have to calculate it yourself. An easy way to do this is to look at the total time/cost for each level of production. The difference between the totals is the time/cost that the last unit added to the total. For example, in the above chart, the total time to make one unit with the Average Learning Curve was 1250 hours, and the total time to make two units was 2000 hours. So, you know that the second unit took 750 hours ( ). The total time to make three units was hours and time to make two units is 2000 hours. So, the time to make the third unit was hours ( ). If you look at the incremental times that you calculate with this method, you can see that there is a large learning effect (60% from 1 to 2 units) that drops as more units are made (75.62% from 2 to 4 units). Units LC Item Total Hours To Make All Units Time to Make Last Unit % Decline With Doubling (1250 x1) (1000 x2) % (877.6 x3) (800 x 4) %

17 Chapter 3 Cost Behavior Page 17 You can see that the initial marginal learning effect is greater for the Average Learning Curve than is the case for the Incremental Learning Curve when you compare the marginal time it takes to make each unit for each type of Learning Curve: Time It Takes To Make Each Unit Units Incremental Curve Average Curve 1 st nd rd th Total There are no rigid rules when it comes to Learning Curves. It is up to you to pick the Learning Curve that best describes the learning phenomenon that occurs in your operation. Remember you are using Learning Curves to describe a phenomenon that occurs naturally in your production process. Most researchers use the Average Learning Curve to describe situations because it is easier to calculate production time when large numbers of units are produced. For example, if you made 2,000,000 units, you could calculate the total production time with one calculation (ax b a(2,000,000) b ). With the Incremental Learning Curve, you would need to make 2,000,000 calculations in order to obtain the total production time. Questions E3-1. If the level of activity increases within the relevant range: A) variable cost per unit and total fixed costs also increase. B) fixed cost per unit and total variable cost also increase. C) total cost will increase and fixed cost per unit will decrease. D) variable cost per unit and total cost also increase. E3-2. In describing the cost equation, Y = a + bx, "a" is: A) the dependent variable, cost. B) the independent variable, the level of activity. C) the total fixed costs. D) the variable cost per unit of activity.

18 Chapter 3 Cost Behavior Page 18 E3-3. Quartz Manufacturing Company has developed the following overhead cost formulas: Overhead Cost Cost Formulas Insurance... $400 Depreciation... $900 Maintenance materials... $0.15 per machine hour Utilities... $600 plus $0.20 per machine hour Based on these cost formulas, the total overhead cost expected for Quartz Manufacturing Company if 1,500 hours are worked is: A) $1,825. B) $525. C) $1,900. D) $2,425. E3-4. Given the cost formula Y = $15,000 + $2X, total cost at an activity level of 8,000 units is expected to be: A) $23,000. B) $31,000. C) $15,000. D) $16,000. Use the following to answer questions E3-5 and E3-6: Frank Company operates a cafeteria for its employees. The number of meals served each week over the last seven weeks, along with the total costs of operating the cafeteria are given below: Week Meals served Cafeteria costs 1 1,500 $4, ,600 $5, ,800 $5, ,450 $4, ,200 $4, ,650 $5, ,900 $5,400 Assume that the relevant range includes all of the activity levels mentioned in this problem Using the high-low method of analysis, the variable cost per meal served in the cafeteria would be estimated to be: A) $1.50. B) $2.00. C) $2.80. D) $1.00.

19 Chapter 3 Cost Behavior Page 19 E3-6. Assume that the cafeteria expects to serve 1,850 meals during Week 8. Using the high-low method, the expected total cost of the cafeteria would be: A) $5,340. B) $5,180. C) $5,300. D) $4,375. E3-7. A disadvantage of the high-low method of cost analysis is that: A) it cannot be used when there are a very large number of observations. B) it is too time consuming to apply. C) it uses two extreme data points, which may not be representative of normal conditions. D) it relies totally on the judgment of the person performing the cost analysis. E3-8. To complete the first setup on a new machine took an employee 200 minutes. Using an 80% cumulative average-time learning curve indicates that the second setup on the new machine is expected to take A) 160 minutes. B) 120 minutes. C) 80 minutes. D) 60 minutes. E3-9. To complete the first setup on a new machine took an employee 200 minutes. Using an 80% incremental unit-time learning model indicates that the second setup on the new machine is expected to take A) 160 minutes. B) 120 minutes. C) 80 minutes. D) 60 minutes. E3-10. Craig's Cola was to manufacture 1,000 cases of cola next week. The accountant provided the following analysis of total manufacturing costs. Variable Coefficient Standard Error t-value Constant Independent variable R2 = 0.82 What is the estimated cost of producing the 1,000 cases of cola? A) $200,100 B) $142,071 C) $100,200 D). $9,000

20 Chapter 3 Cost Behavior Page 20 P3-1. Harrison Company has accumulated the following total Manufacturing Overhead costs for two levels of activity (within the Relevant Range): Low High Activity (Direct Labor Hours) 80, ,000 Total Manufacturing Overhead $468,000 $604,000 Using the High-Low Method of cost analysis, determine the cost formula for Harrison Company. P3-2. Adams Company has accumulated the following total Manufacturing Overhead costs for two levels of activity (within the Relevant Range): Low High Activity (Direct Labor Hours) 30,000 50,000 Total Manufacturing Overhead $270,000 $362,000 Using the High-Low Method of cost analysis, determine the cost formula for Adams Company. P3-3. General Corp. is planning its budget for next year. Its accountant is trying to develop a formula for General Corp.'s travel costs. For the past year, the travel bills were as set forth below. Using the High-Low Method, give the formula for travel costs. Month Cost Mileage January $1, February 2, March 1, April 1, May 1, June 1, July 1, August September 1, October 1, November 1, December 1,

21 Chapter 3 Cost Behavior Page 21 P3-4. Brandie Corp. used Regression analysis to predict the annual cost of Manufacturing Overhead. The results were as follows: Manufacturing Overhead Cost Explained by Units Produced Constant 8,320 Standard Error of Y Estimate 1,050 R-Squared No. of Observations 15 Degrees of Freedom 13 X Coefficient 4.25 Standard Error of Coefficients.4456 What is the linear cost function indicated by the Regression analysis? What is the Goodness Of The Fit of this model? P3-5. Apogee Electronics manufactures high-technology instruments for spacecraft. The company recorded the following costs subject to an Average Learning Curve: Number of Units Produced Cost per Unit (Average) Total Costs For All Units 1 $2,000 (1 x $2,000) $2,000 2 $1,500 (2 x $1,500) $3,000 4?? 8?? 16?? Complete the chart by filling in the cost amounts for volumes of 4, 8 and 16 units. What would the total costs be if four units were produced under an Incremental Learning Curve?

22 Chapter 3 Cost Behavior Page 22 P3-6. Holte Manufacturing estimates the Variable Cost of producing each unit of a product as follows: Direct Materials: Direct Labor: Variable Manufacturing Overhead: $1500 per unit $30 per hour $200 per unit plus 75% of Direct Labor Costs The first unit requires 100 hours to make. Direct Labor Hours is subject to an 80 percent Average Learning Curve. What is the cost to make three units? P3-7. Bob wants to assemble four bookcases. The first bookcase will take 10 hours to assemble. If the time it takes Bob to assemble each bookcase is subject to an Incremental Learning Curve of 95%, how long will it take for Bob to assemble all four bookcases? What would the answer be if this were an Average Learning Curve? P3-8. General Corp. is planning its budget for next year. Its accountant is trying to develop a formula for General Corp.'s travel costs. For the past year, the travel bills were as set forth below. Using the High-Low Method, give the formula for travel costs. Month Cost Mileage January $1, February 2, March 1, April 1, May 1, June 1, July 1, August September 1, October 1, November 1, December 1,

23 Chapter 3 Cost Behavior Page 23 P3-9. Brandie Corporation used regression analysis to predict the annual cost of Indirect Materials. The results were as follows: Indirect Materials Cost Explained by Units Produced Constant 8,320 Standard error of Y estimate 1,050 R - squared.9282 No. of observations 15 Degrees of freedom 13 X coefficient(s) 4.25 Standard error of coefficient(s).4456 A. The linear cost function is? B. How much of the observations is explained by the model? P3-10. Each time Mayberry Nursery hires a new employee, it must wait for some period of time before the employee can meet production standards. Management is unsure of the Learning Curve in its operations but it knows the first job by a new employee takes 30 hours and the second job takes 24 hours. Assume all jobs to be equal in size. A. What is the Learning Curve Percentage, assuming the Average Learning Curve? What if it were an Incremental Learning Curve? B. What is the time for a new employee to build 16 units assuming an Average Learning Curve?

24 Chapter 3 Cost Behavior Page 24 Solutions E3-1 A is wrong. Neither variable cost per unit nor total fixed costs change. B is wrong. Fixed cost per unit decreases as you increase the number of units produced. C is correct. Total cost will increase because variable costs increase as production increases. Fixed costs per unit decrease as production increases. D is wrong. Variable cost per unit does not change. E3-2 The answer is C. A is the y-intercept and it represents total fixed costs. E3-3 The answer is D. The cost formula would have fixed costs of $1,900 ($ ). You also have the variable costs of 35 cents ( ) for each machine hour. The variable costs are $525 (.35 x 1500). So, the total overhead cost is $2,425 ($ ). E3-4. B is correct. The cost formula produces a total cost of $31,000 ($15,000 + ($2 x 8,000)). E3-5. The answer is B. The high point is 1900 meals, and the low point is 1200 meals. The activity level is used to determine the high and low points. Using these points, calculate the slope of the line that runs through these two points. This is the variable cost per unit: V = ( )/( ) = $1400/700 = $2 per meal E3-6. The answer is C. You know the variable cost per unit. Now, calculate the total fixed cost: TC = Vx + F TC = 2x + F $4,000 = $2 (1200) + F $4,000 = $ F $1,600 = F So, the cost function is TC = 2x + $1,600. Plug 1850 into the formula and solve for total costs: TC = (2 x 1850) + $1600. TC = $ $1600 TC = $5,300 E3-7. A is not true. It can applied no matter how many observations that you have. B is not true. It is easy to calculate. C is true.

25 Chapter 3 Cost Behavior Page 25 D is not true. There is no judgment. E3-8. B is correct. The learning curve would produce the following results. Unit Average Time Calculation minutes Given minutes.80 x 200 This question is checking to see if you understand the interpretation of the 160 minutes figure. The 160 minutes says that if you make two units, then the average time to make each is 160 minutes. If the first unit takes 200 minutes, then the second unit must take 120 minutes in order for the average time to be 160 minutes: (200 +?)/2 = ? = 160 x ? = 320? = 120 I prefer to look at the change in the total units. If you make one unit, the total time is 200 minutes, and if you make two units, the total time is 320 minutes (160 x 2). The production of the second unit added 120 minutes to the total production time ( ).

26 Chapter 3 Cost Behavior Page 26 E3-9. A is correct. The learning curve would produce the following results. Unit Time To Make Unit Calculation minutes Given minutes.80 x 200 This question is checking to see if you understand the interpretation of the 160 minute number. With an incremental learning curve the 160 minutes represents the time it takes to make the second unit. E3-10. A is correct. The cost formula from this regression is TC = $200x Plug 1,000 cases into the formula. TC = ($200 x 1,000) = $200,100. P3-1. Variable Cost per unit = V = $604,000 - $468, ,000-80,000 V = $136,000 / 40,000 V = $3.40 Using The High Point: Using The Low Point: Total Cost = Vx + F Total Cost = Vx + F 604,000 = 3.4 (120,000) + F 468,000 = 3.4 (80,000) + F 604,000 = 408,000 + F 468,000 = 272,000 + F 604, ,000 = F 468, ,000 = F 196,000 = F 196,000 = F TC = 3.4x + 196,000 P3-2. Variable Cost per unit = V = $362,000 - $270,000 50,000-30,000 V = $92,000 / 20,000 V = $4.60 Using The High Point: Using The Low Point: Total Cost = Vx + F Total Cost = Vx + F 362,000 = 4.6 (50,000) + F 270,000 = 4.6 (30,000) + F 362,000 = 230,000 + F 270,000 = 138,000 + F 362, ,000 = F 270, ,000 = F 132,000 = F 132,000 = F TC = 4.6x + 132,000

27 Chapter 3 Cost Behavior Page 27 P3-3. Variable Cost per unit = V = $2,000 - $ V = $1,200 / 550 V = $ Using The High Point: Using The Low Point: Total Cost = Vx + F Total Cost = Vx + F 2,000 = 2.18 (750) + F 800 = 2.18 (200) + F 2,000 = 1, F 800 = F 2,000-1, = F = F = F = F TC = 2.18x P3-4 The linear cost function is Y=$8,320 + $4.25 x The model explains 92.82% of the data. P3-5. First, you must calculate the Learning Curve Percentage. When the number of units produced doubled from 1 to 2 units, the average cost dropped to 75% ($1,500/$2,000) of the average cost that existed before the production doubled. Thus, we are dealing with a 75% Learning Curve. No. of Units Cost per Unit (Average Cost) Total Costs For All Units 1 $2,000 (1 x $2,000) $2,000 2 $1,500 (2 x $1,500) $3,000 4 (1500 x.75) $1,125 (4 x $1,125) $4,500 8 (1125 x.75) $ (8 x $843.75) $6, ( x.75) $ (16 x $632.81) $10,125 If this were an Incremental Learning Curve (rather than an Average Learning Curve), then the Cost per unit reflects the incremental cost to make each unit. In order to obtain the total costs to make four units, you add the incremental cost to make up each of the four units. The above table provides the costs to produce the first, second and the fourth unit. You need to calculate the incremental cost to make the third unit.

28 Chapter 3 Cost Behavior Page 28 You can do this using the following formula: Y = a (X) b 3 rd LC Item = 2000 (3 ) 3 rd LC Item = 2000 (3) 3 rd LC Item = 2000 (3) rd LC Item = 2000 (.6338) 3 rd LC Item = 1268 ln(.75) / ln(2) /.6931 The total cost to make four units is $2,000 + $1,500 + $1,268 + $1,125 = $5,893 P3-6. Y = a (X) b Exponent (b): b = ln(.80)/ ln(2) b = /.6931 b = The cost to make 3 units: LC Item: a (X) b 3 rd LC Item = 100(3) rd LC Item = 100(.70205) 3 rd LC Item = 70.2 hours (average) Direct Materials 3 x 1500 $ 4, Direct Labor (3 x 70.2) x $30 $ 6, Variable Manufacturing Overhead (3 x 200) + (.75 x 6,318) $ 5, Cost to make 3 units: $16, P3-7. Incremental Learning Curve: Calculation This Unit Total Hours x (3) (ln.95/ln2) x You are given the hours to make the first unit. You can use the doubling rule to get the hours to make the second and fourth unit. You need to use the learning curve formula to get the time it takes to make the third unit:

29 Chapter 3 Cost Behavior Page 29 Time = Ax(ln.95/ln2) Time = 10 (3) ( / ) Time = 10 (3) Time = 10 x Time = 9.22 With the average learning curve, you would take the per unit time for the fourth unit. That represents the average time to make one unit if you make four units total. To get the total time, you would multiply the average time by the number of units made: x 4 = 36.1 hours P3-8. With the High-Low Method, you would take the highest activity level and the lowest activity level, and figure out the equation of the line that passes through both of the points. High = $2,000 for 750 miles Low = $800 for 200 miles Use the two points to calculate the slope of the line that passes through the two points. ($2,000 - $800)/( ) = $1,200/ 550 = $ Thus, the slope of the line is 2.18, which means that the variable cost per unit for each unit is $2.18 per unit. You now use the slope and one of the two points (high or low) to solve for the fixed costs: TC = 2.18x + F 800 = 2.18 (200) + F 2000 = 2.18 (750) + F 800 = F 2000 = F 364 = F 364 = F TC = 2.18x P3-9. A. Remember the slope of the line is given by the coefficient of X, and the fixed costs are given by the y-intercept or constant. TC = 4.25x

30 Chapter 3 Cost Behavior Page 30 B. Remember that the goodness of the fit is given by the R % P3-10. A. If you are doing an incremental learning curve, then the percentage of the learning curve would be the time it takes for the second unit divided by the time it take to do the first unit: Incremental Learning Curve Percentage = 24/30 = 80% If you are doing an average learning curve, you have to divide the average time to make a unit when you make two units by the average time to make a unit when you make one unit (the time to make one unit). Average time to make two units = ( )/2 = 54/2 = 27 Average Learning Curve Percentage = 27/30 = 90% B. Using the doubling rule: Unit Calculation Average Time x x x x This tells us that the average time to make a unit if you make 16 units is hours. To get the total time, multiply this average time by 16 units: 16 x = hours

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