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Identify potential problems with regression data. 7. Evaluate the advantages and disadvantages of alternative cost estimates. 8. (Appendix A) Use Microsoft Excel to perform a regression analysis. 9. (Appendix B) Understand the mathematical relationship describing the learning phenomenon. Why Estimate Costs? Managers make decisions and need to compare costs and benefits among alternative actions. Good decision requires good information about costs, the better these estimates, the better the decision managers will make (Lanen, 2008).. Key Question What adds value to the firm? Good decisions. You saw in Chapters 3 and 4 that good decisions require good information about costs. Cost estimates are important elements in helping managers make decisions that add value to the company (Lanen, 2008). Learning Objective One: Understand the reasons for estimating fixed and variable costs The reasons for estimating fixed and variable costs The basic idea in cost estimation is to estimate the relation between costs and the variables affecting costs, the cost drivers. We focus on the relation between costs and one important variable that affect them: activity (Lanen, 2008). Basic Cost Behavior Patterns By now you understand the importance of cost behavior. Cost behavior is the key distinction for decision making. Costs behave as either fixed or variable (Lanen, 2008). Fixed costs are fixed in total, variable costs vary in total. On a per-unit basis, fixed costs vary inversely with activity and variable costs stay the same. Are you getting the idea? Cost behavior is critical for decision making. The formula that we use to estimate costs is similar cost equation: Total costs = fixed costs + {variable cost per unit} number of units T c = f + {v} x |With a change in Activity |In Total |Per Unit | |Fixed Cost |Fixed |Vary | |Variable |Vary |Fixed | What Methods are used to Estimate Cost Behavior? Three general methods used to estimate the do my homework relationship between cost behavior and activity levels that are commonly used in practice: Engineering estimates, Account analysis & Statistical methods (Such as regression analysis) (Lanen, 2008). Results are likely to differ from method to method. Consequently, it’s a good idea to use more than one method so that results can be compared. These methods, therefore, should be seen as ways to help management arrive at the best estimates possible. Their weakness and strengths require attention. Learning Objective Two: Estimate costs using engineering estimates. Engineering Estimates Cost estimates are based on measuring and then pricing the work involved in a task. This method based on detailed plans and is frequently used for large projects or new products. This method often omits inefficiencies, such as downtime for unscheduled maintenance, absenteeism and other miscellaneous random events that affect the entire firm (Lanen, 2008). Identify the activities involved Labor |Rent |Insurance |Time |Cost | Advantages of engineering estimates |Details each step required to perform an operation |Permits comparison of other centers with similar operations | |Identifies strengths and weaknesses. | | Disadvantages of engineering estimates 1. Can be quite expensive to use. Learning Objective Three: Estimate costs using account analysis. Account Analysis Estimating costs using account analysis involves a review of each account making up the total costs being analyzed and identifying each cost as either fixed or variable, depending on the relation between the cost and some activity. Account analysis relies heavily on personal judgment. This method is often based on last period’s cost along and is subject to managers focusing on specific issues of the previous period even though these might be unusual and infrequent(Lanen, 2008) . Example: Account Analysis (Exhibit 5. 1) |3C Cost Estimation Using Account Analysis | |Costs for 360 Repair Hours | |Account |Total |Variable Cost |Fixed Cost | |Office Rent $3,375 |$1,375 |$2,000 | |Utilities |310 |100 |210 | |Administration |3,386 |186 |3,200 | |Supplies |2,276 |2,176 |100 | |Training |666 |316 |350 | |Other |613 |257 |356 | |Total |$10,626 |$4,410 |$6,216 | |Per Repair Hour |$12. 25 ($4,410 divided by 360 repair-hours) | 3C Cost Estimation Using Account Analysis (Costs at 360 Repair-Hours. A unit is a repair- hour) Total costs = fixed costs + {variable cost per unit} number of units T c = f + {v} x |$10,626 = $6,216 + $12. 25 (360) |$10,626 = $6,216 + $$4,410 | Costs at 520 Repair-Hours Total costs = fixed costs + {variable cost per unit} number of units |Tc = $6,216 + {$12. 25} 520 |Total costs = $6,216 + $ $6,370 |$12,586 = $6,216 + $ $6,370 | Advantage of Account Analysis 1. Managers and accountants are familiar with company operations and the way costs react to changes in activity levels. Disadvantages of Account Analysis 1. Managers and accountants may be biased. 2. Decisions often have major economic consequences for managers and accountants. Learning Objective Four: Estimate costs using statistical analysis. The statistical analysis deals with both random and unusual events is to use several periods of operation or several locations as the basis for estimating cost relations . We can do this by applying statistical theory, which allows for random events to be separated from the underlying relation between costs and activities. A statistical cost analysis analyzes costs within the relevant range using statistics. Do you remember how we defined relevant range? A relevant range is the range of activity where a cost estimate is valid. The relevant range for cost estimation is usually between the upper and lower limits of past activity levels for which data is available (Lanen, 2008). Example: Overhead Costs for 3C ( Exhibit 5. 2) The following information is used throughout this chapter: Here we have the overhead costs data for 3C for the last 15 months. Let’s use this data to estimate costs using a statistical analysis. |Month |Overhead Costs |Repair-Hours |Month |Overhead Costs |Repair-Hours | |1 |$9,891 |248 |8 |$10,345 |344 | |2 $9,244 |248 |9 |$11,217 |448 | |3 |$13,200 |480 |10 |$13,269 |544 | |4 |$10,555 |284 |11 |$10,830 |340 | |5 |$9,054 |200 |12 |$12,607 |412 | |6 |$10,662 |380 |13 |$10,871 |384 | |7 |$12,883 |568 |14 |$12,816 |404 | | | | |15 |$8,464 |212 | A. Scattergraph Plot of cost and activity levels Does it look like a relationship exists between repair-hours and overhead costs? We will start with a scatter graph. A scatter graph is a plot of cost and activity levels. This gives us a visual representation of costs. Does it look like a relationship exists between repair-hours and overhead cost? We use “eyeball judgment” to determine the intercept and slope of the line. Now we “eyeball” the scatter graph to determine the intercept and the slope of a line through the data points. Do you remember graphing our total cost in Chapter 3? Where the total cost line intercepts the horizontal or Y axis represents fixed cost. What we are saying is the intercept equals fixed costs. The slope of the line represents the variable cost per unit. So we use “eyeball judgment” to determine fixed cost and variable cost per unit to arrive at total cost for a given level of activity. As you can imagine, preparing an estimate on the basis of a scatter graph is subject to a high level of error. Consequently, scatter graphs are usually not used as the sole basis for cost estimates but to illustrate the relations between costs and activity and to point out any past data items that might be significantly out of line. B. High-Low Cost Estimation A method to estimate costs based on two cost observations, usually at the highest and lowest activity level. Although the high-low method allows a computation of estimates of the fixed and variable costs, it ignores most of the information available to the analyst. The high-low method uses two data points to estimate costs (Lanen, 2008). Another approach: Equations V = Cost at highest activity – Cost at lowest activity Highest activity – Lowest activity F = Total cost at highest activity level – V (Highest activity) Or F = Total cost at lowest activity level – V (Lowest activity) Let’s put the numbers in the equations | | | |V = $12,883 – $9,054 |V = $10. 0/RH | |568 – 200 | | F = Total cost at highest activity level – V (Highest activity) F = $12,883 – $10. 40 (568), F= $6,976 Or F = Total cost at lowest activity level – V (Lowest activity) F = $9,054 – $10. 40 (200) Rounding Difference C. Statistical Cost Estimation Using Regression Analysis Statistical procedure to determine the relationship between variables High-Low Method: Uses two data points. Regression analysis Regression is a statistical procedure that uses all the data points to estimate costs. [pic] Regression Analysis Regression statistically measures the relationship between two variables, activities and costs. Regression techniques are designed to generate a line that best fits a set of data points. In addition, regression techniques generate information that helps a manager determine how well the estimated regression equation describes the relations between costs and activities (Lanen, 2008). We recommend that users of regression (1) fully understand the method and its limitations (2) specify the model, that is the hypothesized relation between costs and cost predictors (3) know the characteristics of the data being tested (4) examine a plot of the data . For 3C, repair-hours are the activities, the independent variable or predictor variable. In regression, the independent variable or predictor variable is identified as the X term. An overhead cost is the dependent variable or Y term. What we are saying is; overhead costs are dependent on repair-hours, or predicted by repair-hours. The Regression Equation |Y = a + bX |Y = Intercept + (Slope) X |OH = Fixed costs + (V) Repair-hours | You already know that an estimate for the costs at any given activity level can be computed using the equation TC = F + VX. The regression equation, Y= a + bX represents the cost equation. Y equals the intercept plus the slope times the number of units. When estimating overhead costs for 3C, total overhead costs equals fixed costs plus the variable cost per unit of repair-hours times the number of repair-hours. We leave the description of the computational details and theory to computer and statistics course; we will focus on the use and interpretation of regression estimates. We describe the steps required to obtain regression estimates using Microsoft Excel in Appendix A to this chapter. Learning Objective Five: Interpret the results of regression output. Interpreting Regression [pic] Interpreting regression output allows us to estimate total overhead costs. The intercept of 6,472 is total fixed costs and the coefficient, 12. 52, is the variable cost per repair-hours. Correlation coefficient “R” measures the linear relationship between variables. The closer R is to 1. 0 the closer the points are to the regression line. The closer R is to zero, the poorer the regression line (Lanen, 2008). Coefficient of determination “R2” The square of the correlation coefficient. The proportion of the variation in the dependent variable (Y) explained by the independent variable(s)(X). T-Statistic The t-statistic is the value of the estimated coefficient, b, divided by its standard error. Generally, if it is over 2, then it is considered significant. If significant, the cost is NOT totally fixed. The significant level of the t-statistics is called the p-value. Continuing to interpret the regression output, the Multiple R is called the correlation coefficient and measures the linear relationship between the independent and dependent variables. R Square, the square of the correlation cost efficient, determines and identifies the proportion of the variation in the dependent variable, in this case, overhead costs, that is explained by the independent variable, in this case, repair-hours. The Multiple R, the correlation coefficient, of . 91 tells us that a linear relationship does exist between repair-hours and overhead costs. The R Square, or coefficient of determination, tells us that 82. 8% of the changes in overhead costs can be explained by changes in repair-hours. Can you use this regression output to estimate overhead costs for 3C at 520 repair-hours? Multiple Regressions Multiple regressions are used when more than one predictor (x) is needed to adequately predict the value (Lanen, 2008). For example, it might lead to more precise results if 3C uses both repair hours and the cost of parts in order to predict the total cost. Let’s look at this example. |Predictors: |X1: Repair-hours |X2: Parts Cost | 3C Cost Information | |Month |Overhead Costs |Repair-Hours ( X1) |Parts ( X2) | |1 |$9,891 |248 |$1,065 | |2 |$9,244 |248 |$1,452 | |3 |$13,200 |480 |$3,500 | |4 |$10,555 |284 |$1,568 | |5 |$9,054 |200 |$1,544 | |6 |$10,662 |380 |$1,222 | |7 |$12,883 |568 |$2,986 | |8 |$10,345 |344 |$1,841 | |9 |$11,217 |448 |$1,654 | |10 |$13,269 |544 |$2,100 | |11 |$10,830 |340 |$1,245 | |12 |$12,607 |412 |$2,700 | |13 |$10,871 |384 |$2,200 | |14 |$12,816 |404 |$3,110 | |15 |$8,464 |212 |$ 752 | In multiple regressions, the Adjusted R Square is the correlation coefficient squared and adjusted for the number of independent variables used to make the estimate. Reading this output tells us that 89% of the changes in overhead costs can be explained by changes in repair-hours and the cost of parts. Remember 82. % of the changes in overhead costs were explained when one independent variable, repair-hours, was used to estimate the costs. Can you use this regression output to estimate overhead costs for 520 repair-hours and $3,500 cost of parts? Learning Objective Six: Identify potential problems with regression data. Implementation Problems It’s easy to be over confident when interpreting regression output. It all looks so official. But beware of some potential problems with regression data. We already discussed in earlier chapters that costs are curvilinear and cost estimations are only valid within the relevant range. Data may also include outliers and the relationships may be spurious. Let’s talk a bit about each. Curvilinear costs |Outliers |Spurious relations |Assumptions | 1. Curvilinear costs Problem: Attempting to fit a linear model to nonlinear data. Likely to occur near full-capacity. Solution: Define a more limited relevant range (example: from 25 – 75% capacity) or design a nonlinear model. If the cost function is curvilinear, then a linear model contains weaknesses. This generally occurs when the firm is at or near capacity. The leaner cost estimate understates the slope of the cost line in the ranges close capacity. This situation is shown in exhibit 5. 5. 2. Outliers Problem: Outlier moves the regression line. Solution: Prepare a scatter-graph, analyze the graph and eliminate highly unusual observations before running the regression. Because regression calculates the line that best fits the data points, observations that lie a significant distance away from the line could have an overwhelming effect on the regression estimate. Here we see the effect of one significant outlier. The computed regression line is a substantial distance from most of the points. The outlier moves the regression line. Please refer exhibit 5. 6. 3. Spurious or false relations Problem: Using too many variables in the regression. For example, using direct labor to explain materials costs. Although the association is very high, actually both are driven by output. Solution: Carefully analyze each variable and determine the relationship among all elements before using in the regression. 4. Assumptions Problem: If the assumptions in the regression are not satisfied then the regression is not reliable. Solution: No clear solution. Limit time to help assure costs behavior remains constant, yet this causes the model to be weaker due to less data. Learning Objective Seven: Evaluate the advantages and disadvantages of alternative cost estimation methods. Statistical Cost Estimation Advantages 1. Reliance on historical data is relatively inexpensive. 2. Computational tools allow for more data to be used than for non-statistical methods. Disadvantages 1. Reliance on historical data may be the only readily available, cost-effective basis for estimating costs. 2. Analysts must be alert to cost-activity changes. Choosing an Estimation Method Each cost estimation method can yield a different estimate of the costs that are likely to result from a particular management decision. This underscores the advantage of using more than one method to arrive at a final estimate. Which method is the best? Management must weigh the cost-benefit related to each method (Lanen, 2008). Estimated manufacturing overhead with 520 repair-hours and $3,500 parts costs *. The more sophisticated methods yield more accurate cost estimates than the simple methods. |Account Analysis = $12,586 |High-Low = $12,384 |Regression= $12,982 |Multiple Regression= $13,588* | Data Problems Missing data Outliers Allocated and discretionary costs Inflation Mismatched time periods No matter what method is used to estimate costs, the results are only as good as the data used. Collecting appropriate data is complicated by missing data, outliers, allocated and discretionary costs, inflation and mismatched time periods. Learning Objective Eight: (Appendix A) Use Microsoft Excel to perform a regression analysis. Appendix A: Microsoft as a Tool Many software programs exist to aid in performing regression analysis. In order to use Microsoft Excel, the Analysis Tool Pak must be installed. There are software packages that allow users to easily generate a regression analysis. The analyst must be well schooled in regression in order to determine the meaning of the output! Learning Objective Nine: (Appendix B) Understand the mathematical relationship describing the learning phenomenon. Learning Phenomenon Leaning phenomenon refers to the systematic relationship between the amount of experience in performing a task and the time required to perform it. The learning phenomenon means that the variable costs tend to decrease per unit as the volume increase. Example: | |Unit |Time to Produce |Calculation of Time | |First Unit |100 hours |(assumed) | |Second Unit |80 hours |(80 percent x 100 hours | |Fourth Unit |64 hours |(80 percent x 80 hours | |Eighth Unit |51. hours |(80 percent x 64 hours | |Impact: Causes the unit price to decrease as production increases. This implies a nonlinear model. | Another element that can change the shape of the total cost curve is the notion of a learning phenomenon. As workers become more skilled they are able to produce more output per hour. This will impact the total cost curve since it leads to a lower per unit cost, the higher the output. Chapter 5: END!! COURSE WORK EXERCISE 5-25 – A& B PROBLEM 5-47 -A& B REFERENCES Lanen , N. W. , Anderson ,W. Sh. & Maher ,W. M. ( 2008). Fundamentals of cost accounting. New York : McGraw-Hill Irwin. [pic] 568