AbstractCost estimation is the process of determining how the cost changes in relation to variations in a particular cost driver. Cost estimation aims at developing a numerical relationship between a cost and the main factor which causes the cost to be incurred. This numeric relationship is presented through a cost function. In addition, an understanding of cost behavior is necessary to plan and control costs. Four models of cost estimation: industrial engineering, account analysis, conference and quantitative analysis method can be used to estimate the cost. Engineering analysis method develops cost function using relationships between inputs and outputs. Study of the accounts in the general ledger is used to determine the fixed and variable cost in account analysis method. Conference method uses the opinion of different departments. Several quantitative analysis methods are used to estimate a cost function according to the past data observations. In scattergraph method, a regression line is developed on the basis of the data plotted on the graph. The high-low method estimates the cost function by determining the line that connects the highest and lowest values for the cost driver in the relevant range. Regression analysis estimates the cost function by using a statistical model that relates the average change in the dependent variables to a unit change in the cost driver(s).

1.0 IntroductionCost estimation is the process of developing a well-defined relationship between a cost object and its cost driver for the purpose of predicting the cost. A manager should consider the cost behavior before estimating the cost function. Understanding cost behavior patterns is important to managers as they plan, control, and make decisions in the operation of their organizations. A manager must understand how costs behave across various levels of activity before approaching to cost estimation. This report describes the different methods which can be used to analyse and estimate cost behaviour patterns and thus enable the prediction of future costs. We will also consider the problems associated with the different cost estimation methods that can be used. Four models of cost estimation: engineering analysis method, account analysis method, conference method and quantitative analysis method have been described along with the inherent limitations of the method. In the next part of the report, several quantitative analysis method like Scattergraph method, high-low techniques and least square regression method have been described with appropriate illustrations. A company can use a combination of these methods to develop its cost function. A particular method can provide the best estimation for a particular situation. On the other hand, another method may be best suited to another situation.

2.0 Cost Behavior AnalysisCost behavior is the manner in which a cost changes as some related activity changes. Thus, cost behavior analysis is associated with the determination of how costs behave when business activity such as production volume, sales volume changes. This section describes some common patterns of cost behavior. This analysis is important because knowledge of them can enable predictions of future cost amounts and also the use of decision-making techniques. There are three main types of costs according to their behavior: Fixed cost Variable cost Mixed costThey have been described below:i) Fixed costsFixed costs are those costs which do not change with the level of activity within the relevant range. These costs will incur even if no units are produced. For example rent expense, straight-line depreciation expense, etc. The wages paid to a production supervisor or a factory manager would also be a fixed amount per annum provided that they are not paid extra for working overtime. These costs are all based on time and not on some measure of activity or output. Fixed cost per unit decreases with increase in production. In addition, they are costs that do not change in response to changes in activity levels. Because the total amount of a fixed cost remains constant, it means that as production volume increases fixed cost per unit decreases.

ii) Variable costsVariable costs change in direct proportion to the level of production. This means that total variable cost increase when more units are produced and decreases when less units are produced. Thus, if activity increases by 10 percent, variable costs are assumed to increase by 10 percent. Some common variable costs are direct and indirect materials, direct labor, energy, and sales commissions. Variable cost behavior pattern specifies that variable costs have a linear relationship to the level of activity; that is, when the level of activity increases, total variable costs rise at a directly proportional rate. Although variable in total, these costs are constant per unit. On a per unit basis, however, a variable cost remains constant while the activity level is within the relevant range. If activity increases or decreases significantly, cost relationships will probably change.

iii) Mixed costsMixed costs are costs that contain both a variable cost element and a fixed cost element. These costs are sometimes referred to as semi variable costs. For example, a salesperson may be paid Tk 80,000 per year (fixed amount) plus commissions equal to 1 percent of sales (variable amount). In this case, the salespersons total compensation is a mixed cost. Note especially that total production cost is also a mixed cost since it is composed of material, labor, and both fixed and variable overhead cost items. Another example may be electricity bill. An electricity bill will usually include a fixed supply charge for a certain time period as well as a charge for the total amount of electricity consumed during that period. Even if production lines had been completely shut down for the whole of the billing period, and no electricity had been used, the fixed supply charge must be paid. This is the minimum cost of keeping electric power available for the factory. It represents the fixed component of total electricity cost.

Mixed costs or semi-variable costs have properties of both fixed and variable costs due to presence of both variable and fixed components in them. Since mixed cost figures are not useful in their raw form, therefore they are split into their fixed and variable components by using cost behavior analysis techniques.

3.0 Some Issues regarding Cost EstimationThis is the process of determining how the cost changes in relation to variations in a particular cost driver or, in some cases, with variations in multiple cost drivers. In many cases, an examination of past cost behaviour can enable accurate predictions of future costs. The process of using data on past costs, and the corresponding levels of activity; to construct meaningful relationships between them is called cost estimation. The aim of this process is to establish a numerical relationship between a cost and the main factor which causes the cost to be incurred. Such a factor is called the cost driver. For example, an assembly labour cost for a given time period may vary with the number of units assembled during that period. Likewise, for a bakery the cost of electricity consumed may vary with the number of batches of bread baked. The number of units assembled and the number of batches baked are cost drivers which are output measures. To be able to predict future costs accurately there should be a strong correlation between a cost and the chosen cost driver, but we also need to be able to predict future changes in the cost driver easily. When there are semi-variable or mixed costs we need to be able to determine how much of each one is fixed and how much is variable. We also need to know how the variable component of such a cost will change in response to changes in the principal cost driver. Some important issues regarding cost estimation have been discussed below:

Cost FunctionCost behavior is identified by estimating cost functions. Cost function is mathematical relationship between cost and the level of an activity. Examples of activities used in cost accounting to develop cost functions are units of output, direct manufacturing labor hours, machine hours etc. Most costs are assumed to behave in a linear (straight line) manner. The assumption that most costs are linear means that it is easy to calculate the relevant cost function. This is a mathematical description of how a cost changes with changes in the level of its cost driver.

The general form of a linear cost function is simply the formula for a straight line:y = a + bxwhere: y = the estimated total cost amount (y is called the dependent variable)a = constant which represents the component of total cost that does not change as the level of activity changesb = the slope coefficient i.e. the amount by which the total cost amount increases for a one unit increase in the level of activity.x = the actual (or expected future) level of activity (x is called the independent variable)

There are two basic assumptions regarding the function:i. Variations in the cost under consideration are explained by variations in the level of a single activity. Thus, single activity is sufficient to capture the variation in the cost.ii. Cost behavior is adequately approximated by a linear function within the relevant range. Even though the function is shown on the graph from zero to infinity, the decision maker knows that the graph is valid only between some range and not from zero to infinity.It should be noted that assumptions about cost behaviour are usually valid only within a restricted range of activity called the relevant range. If the planned level of activity falls outside the relevant or normal range, caution is needed if past cost data is used to predict future costs.

Relevant RangeThe relevant range is the range of activity for which estimates and predictions are expected to be accurate. Outside the relevant range, the estimates of fixed and variable costs may not be very useful. Beyond the relevant range the cost estimation may not give good result. In order to design a cost function, it is assumed that there is linear relationship of costs. Outside the relevant range, the cost behavior becomes nonlinear. When companies produce unusually large quantities, for example, production may not be efficient, resulting in costs increasing more rapidly than the rate implied by a straight line. This may not be a serious limitation for a straight-line approach as long as the predictions and estimates are restricted to the relevant range.

Time horizonTime horizon is also an important issue to determine whether a particular cost is variable or fixed. The cost behavior patterns identified are true only over a specified period of time. Beyond this, the cost may show a different cost behavior pattern. A final, but important, point: determining whether a cost is fixed or variable depends on the time horizon. The longer the time period, the more likely it is that a cost will be variable. The so-called short run is a period of time for which at least one cost remains fixed. In the long run, all costs are variable.

4.0 Cost Estimation ApproachesThere are four approaches which can be used to estimate the cost. These methods use different approaches to estimate the cost function. Before choosing a method, the managers should consider the expenses, technical expertise required for each method. They are not mutually exclusive and thus, a company can choose a cost model by combining these methods. The four cost estimation approaches have been discussed below:

4.1 Industrial Engineering MethodThe aim of this method is to identify the relationships which should exist between inputs and outputs. This method is also termed as the work-measurement method. Industrial engineers could conduct time and motion studies or task analyses which involve observing employees as they undertake work tasks and establish a normal time for each type of task. These times are then costed using the wage rates for the various types of worker. By analysing the sequence of tasks or activities needed to make a particular product or to provide a certain type of service, a normal or standard labour cost can be estimated. The engineers can then determine from design specifications the types and quantities of material required for each unit of the product or service and how much these materials should cost. An estimated amount of overhead cost will be added to the material and labour costs and this gives a standard unit cost which can then be used to predict future costs based on planned levels of activity. The industrial engineering method relies for its accuracy on the skills and experience of trained engineers. It is time-consuming and expensive, but it has to be used when estimating costs for a completely new product because there is no historical data to rely upon. This method is most useful for estimating the costs of repetitive processes where input-output relationships for material and labour are clearly defined.

The major limitation of this method is that it requires a through and detailed way to determine the cost functions. Moreover, it is time consuming to use this method. On the other hand, this method can be used to determine the direct manufacturing cost but it is difficult to determine the indirect manufacturing cost using this method. For example, it is difficult to determine research and development cost by this method.

4.2 Account Analysis MethodIn this method, each account is classified as either fixed or variable based on experience and judgment of accounting and other qualified personnel in the organization. The account classification method requires a study of an account in the general ledger. The experienced analysts use the account information as well as their own judgment to determine how costs will behave in the future. Using this method requires the management accountant to review past cost behaviour patterns as shown in the organizations ledger accounts and other accounting records. Then management use judgment and knowledge of operations to classify each cost as either fixed, variable or semi-variable.

This method requires that the manager use professional judgment to classify costs as either fixed or variable. The total of the costs classified as variable can then be divided by a measure of activity to calculate the variable cost per unit of activity. The total of the costs classified as fixed provides the estimate of fixed cost. We can use an illustration to show how the costs are allocated under this method. Let, ABC Co. is a manufacturing company. The activities of ABC Co. during the month August, 2013 are shown below:

Production in units 5,000

Production Cost Component cost Assembly labour cost Utilities Office Rent Depreciation of equipmentTotal production costTK 1,50,000 30,000 40,000 1,30,000 80,000 TK 4,30,000

Using professional judgment and analysis of the accounts, management of ABC Co. has decided that component cost, assembly labour cost and 50% of utilities are variable costs and all other items are fixed costs.

So, the fixed and variable cost can be estimated as follows:

Variable Cost Estimate

Component costAssembly labour cost50% of Utilities Total variable costProduction in unitsVariable cost per unitTK 1,50,000 30,000 20,000 TK 200,000 5,000 TK 40

Fixed Cost estimate

50% of utilitiesOffice RentDepreciation of equipment Total fixed cost

TK 20,000 1,30,000 80,000TK 2,30,000

So, here the fixed cost is TK 2,30,000 and variable cost is TK 40 per unit produced. So, we can write the cost function as:Total production cost = TK 2,30,000 + TK 40 Production in units

Thus, if the production is 10,000 units, the total cost of production is Total production cost for 10,000 units = TK 2,30,000 + TK 40 10,000 = TK 6,30,000

The account analysis method is subjective in that different managers viewing the same set of facts may reach different conclusions regarding which costs are fixed and which costs are variable. Despite this limitation, most managers consider it an important tool for estimating fixed and variable costs.

4.3 Conference MethodUnder this approach, costs are classified based on opinions from various company departments such as purchasing, process engineering, manufacturing, employee relations and so on. Here, cost function is developed on the opinion given by the departments. Here opinions are gathered from the supervisors and managers of several departments to determine the cost drivers and variable-fixed cost classification. Thus, efficiency of the cost function depends on the skills and expertise of the department managers and supervisors. The main features of this method can be stated as: This method doesnt require so much analysis of the data and investigation like engineering method. So, the cost function can be determined quickly. It is not time consuming like industrial engineering method. Thus, this can help to reduce the time needed to develop the cost classification and cost function. This method can increase the cooperation among different departments. The opinions from different departments are required to determine the cost behavior. Thus, this can increase the responsiveness of the employees. As this method develops cost function based on the inputs and opinions given by several departments. So, the efficiency and accuracy of cost estimation depends on the skills and expertise of the persons providing the inputs.

4.4 Quantitative Analysis MethodThis methods develops a mathematical model to estimate a cost function according to the past data observations. There are six steps of developing the cost function under this method. They are described below:i. Defining the cost to be estimated: At first, the dependent variable is determined. Here dependent variable means the cost that is to be predicted. The example of dependent variable is the total production cost during a particular period. ii. Determining the cost drivers: Here cost driver or dependent variable is used to predict the dependent variable. Cost driver is variable that causally affects the costs over a given time span. There should be an economically plausible relationship between the cost driver and dependent variable. For example, the direct labour hour can be the cost driver for determining the total manufacturing labour cost. iii. Collection of consistent and accurate data: Here data of both dependent and independent variable should be collected. Several sources like company documents, opinions of the managers, special studies may be used to collect relevant data. iv. Plotting the data: Then the data of dependent and independent variable can be plotted. This can show the graphical relationship between the cost driver and dependent variable. This can help in determining the extreme observations. This can also help in determining the relevant range of the data. v. Selection and use of the appropriate estimation method: In this step, several methods are used to develop the cost function. In this case, computer programme like Microsoft Excel can be used to plot the data and perform necessary calculation. vi. Assessment of the accuracy of the cost estimate: At this step the accuracy of the prediction can be judged. Moreover, the criteria for evaluating the cost driver of the estimated cost function can also be described in this step. The above mentioned steps are followed in quantitative analysis method to develop a cost function.

Three commonly used quantitative analysis methods are: Scattergraph/ Visual fit method High-low method Regression analysis

In Scattergraph Method, all observed costs at various activity levels are plotted on a graph. Based on sound judgment, a regression line is then fitted to the plotted points to represent the line function. The high-low method of approximating cost behavior considers only two points of data, the highest and lowest, for activity within the relevant range. Least-squares regression method is a statistical technique that investigates the association between dependent and independent variables. This method determines the line of best fit for a set of observations by minimizing the sum of the squares of the vertical deviations between actual points and the regression line. Cost estimation procedures using these three methods will be described with appropriate illustration in the next section.

5.0 Cost estimation using different quantitative methods

5.1 Scattergraph/ Visual Fit MethodScatter Graph ApproachCreating a scatter graph is another method of estimating fixed and variable costs. It provides a good visual picture of the costs at different activity levels. Many organizations prefer to use thescatter graph methodto estimate costs. Accountants who use this approach are looking for an approach that does not simply use the highest and lowest data points. However, it is often hard to visualize the line through the data points especially if the data is varied. This approach requires multiple data points and requires five steps:Step 1: Plot the data points for each period on a graph.Step 2: Visually fit a line to the data points and be sure the line touches one data point.Step 3: Estimate the total fixed costs (A).Step 4: Calculate the variable cost per unit (B).Step 5: State the results in equation form Y =A+BX.

Step 1: Plot the data points for each period on a graphThis step requires that each data point be plotted on a graph. Thex-axis (horizontal axis) reflects the level of activity (units produced in this example), and they-axis (vertical axis) reflects the total production cost.

Step 2: Visually fit a line to the data points and be sure the line touches one data pointOnce the data points are plotted as described in step 1, it is required to draw a line through the points touching one data point and extending to they-axis. The goal here is to minimize the distance from the data points to the line (i.e., to make the line as close to the data points as possible).

Step 3: Estimate the total fixed costs (A)The total fixed costs are simply the point at which the line drawn in step 2 meets they-axis. This is often called they-intercept. The line meets they-axis when the activity level (units produced in this example) is zero. Fixed costs remain the same in total regardless of level of production, and variable costs change in total with changes in levels of production. Since variable costs are zero when no units are produced, the costs reflected on the graph at they-intercept must represent total fixed costs.

Step 4: Calculate the variable cost per unit (B)After completing step 3, the equation to describe the line is partially complete and stated as Y = A +BX. The goal of step 4 is to calculate a value for variable cost per unit (B). Simply use the data point the line intersects, and fill in the data to solve for v.

Step 5: State the results in equation form Y =A+BX.We know from step 3 that the total fixed costs are A, and from step 4 that the variable cost per unit is B. Thus the equation used to estimate total costs looks like this:YC = A + BXNow it is possible to estimate total production costs given a certain level of production (X).

Alta Production Inc. reported the following production costs for the 12 months January through December.Reporting Period(Month)Total Production CostsLevel of Activity(Units Produced)

JanuaryTk. 460,000300

February300,000220

March480,000330

April550,000390

May570,000410

June310,000240

July440,000290

August455,000320

September530,000380

October250,000150

November700,000450

December490,000350

1. Using the information, we can perform the five steps of the scatter graph method to estimate costs and state your results in cost equation form YC =A+BX.2. Assume Alta Production, Inc. will produce 400 units next month. We can calculate total production costs for the month.

Step 1: Plot the data points for each period on a graph

Step 2: Visually fit a line to the data points and be sure the line touches on the data

Step 3: Estimate the total fixed costs (A)They-intercept represents total fixed costs. This is where the line meets they-axis. Total fixed costs in the graph appear to be approximately $5,000. You will likely get a different answer because the answer depends on the line that you visually fit to the data points. Remember you must draw the line through one data point. The line intersects the data point for March ($480,000 production costs; 330 units produced). This will be used in step 4.Step 4: Calculate the variable cost per unit (B)After completing step 3, the equation to describe the line is partially complete and stated as Y = $5,000 +BX. The goal of this step is to calculate a value for variable cost per unit (v). Use the data point the line intersects (for March, 330 units produced and $480,000 total costs), and fill in the data to solve forv(variable cost per unit):Step 5: State the results in equation form Y =A+BXWe know from step 3 that the total fixed costs are $5,000, and from step 4 that variable cost per unit is $1,439.39. Thus the equation used to estimate total production costs is stated as:It is evident from this information that this company has very little in fixed costs and relatively high variable costs. This is indicative of a company that uses a high level of labor and materials (both variable costs) and a low level of machinery (typically a fixed cost through depreciation or lease costs).

Advantage of Scatter Graph MethodThe key weakness of the high-low method is that it considers only two data points in estimating fixed and variable costs. The scatter graph method mitigates this weakness by considering all data points in estimating fixed and variable costs. The scatter graph method gives us an opportunity to review all data points in the data set when we plot these data points in a graph in step 1. If certain data points seem unusual, we can exclude them from the data set when drawing the best-fitting line. In fact, many organizations use a scatter graph to identify outliers and then useregression analysisto estimate the cost equation YC =A+BX.Although the scatter graph method tends to yield more accurate results than the high-low method, the final cost equation is still based on estimates. The line is drawn using our best judgment and a bit of guesswork, and the resultingy-intercept (fixed cost estimate) is based on this line. This approach is not an exact science.

5.2 High-Low Method

Scatter Graph ApproachCreating a scatter graph is another method of estimating fixed and variable costs. It provides a good visual picture of the costs at different activity levels. Many organizations prefer to use thescatter graph methodto estimate costs. Accountants who use this approach are looking for an approach that does not simply use the highest and lowest data points. However, it is often hard to visualize the line through the data points especially if the data is varied. This approach requires multiple data points and requires five steps:Step 1: Plot the data points for each period on a graph.Step 2: Visually fit a line to the data points and be sure the line touches one data point.Step 3: Estimate the total fixed costs (A).Step 4: Calculate the variable cost per unit (B).Step 5: State the results in equation form Y =A+BX.

Step 1: Plot the data points for each period on a graphThis step requires that each data point be plotted on a graph. Thex-axis (horizontal axis) reflects the level of activity (units produced in this example), and they-axis (vertical axis) reflects the total production cost.

Step 2: Visually fit a line to the data points and be sure the line touches one data pointOnce the data points are plotted as described in step 1, it is required to draw a line through the points touching one data point and extending to they-axis. The goal here is to minimize the distance from the data points to the line (i.e., to make the line as close to the data points as possible).

Step 3: Estimate the total fixed costs (A)The total fixed costs are simply the point at which the line drawn in step 2 meets they-axis. This is often called they-intercept. The line meets they-axis when the activity level (units produced in this example) is zero. Fixed costs remain the same in total regardless of level of production, and variable costs change in total with changes in levels of production. Since variable costs are zero when no units are produced, the costs reflected on the graph at they-intercept must represent total fixed costs.

Step 4: Calculate the variable cost per unit (B)After completing step 3, the equation to describe the line is partially complete and stated as Y = A +BX. The goal of step 4 is to calculate a value for variable cost per unit (B). Simply use the data point the line intersects, and fill in the data to solve for v.

Step 5: State the results in equation form Y =A+BX.We know from step 3 that the total fixed costs are A, and from step 4 that the variable cost per unit is B. Thus the equation used to estimate total costs looks like this:YC = A + BXNow it is possible to estimate total production costs given a certain level of production (X).

Alta Production Inc. reported the following production costs for the 12 months January through December.Reporting Period(Month)Total Production CostsLevel of Activity(Units Produced)

JanuaryTk. 460,000300

February300,000220

March480,000330

April550,000390

May570,000410

June310,000240

July440,000290

August455,000320

September530,000380

October250,000150

November700,000450

December490,000350

1. Using the information, we can perform the five steps of the scatter graph method to estimate costs and state your results in cost equation form YC =A+BX.2. Assume Alta Production, Inc. will produce 400 units next month. We can calculate total production costs for the month.

Step 1: Plot the data points for each period on a graph

Step 2: Visually fit a line to the data points and be sure the line touches on the data

Step 3: Estimate the total fixed costs (A)They-intercept represents total fixed costs. This is where the line meets they-axis. Total fixed costs in the graph appear to be approximately $5,000. You will likely get a different answer because the answer depends on the line that you visually fit to the data points. Remember you must draw the line through one data point. The line intersects the data point for March ($480,000 production costs; 330 units produced). This will be used in step 4.Step 4: Calculate the variable cost per unit (B)After completing step 3, the equation to describe the line is partially complete and stated as Y = $5,000 +BX. The goal of this step is to calculate a value for variable cost per unit (v). Use the data point the line intersects (for March, 330 units produced and $480,000 total costs), and fill in the data to solve forv(variable cost per unit):Step 5: State the results in equation form Y =A+BXWe know from step 3 that the total fixed costs are $5,000, and from step 4 that variable cost per unit is $1,439.39. Thus the equation used to estimate total production costs is stated as:It is evident from this information that this company has very little in fixed costs and relatively high variable costs. This is indicative of a company that uses a high level of labor and materials (both variable costs) and a low level of machinery (typically a fixed cost through depreciation or lease costs).

Advantage of Scatter Graph MethodThe key weakness of the high-low method is that it considers only two data points in estimating fixed and variable costs. The scatter graph method mitigates this weakness by considering all data points in estimating fixed and variable costs. The scatter graph method gives us an opportunity to review all data points in the data set when we plot these data points in a graph in step 1. If certain data points seem unusual, we can exclude them from the data set when drawing the best-fitting line. In fact, many organizations use a scatter graph to identify outliers and then useregression analysisto estimate the cost equation YC =A+BX.Although the scatter graph method tends to yield more accurate results than the high-low method, the final cost equation is still based on estimates. The line is drawn using our best judgment and a bit of guesswork, and the resultingy-intercept (fixed cost estimate) is based on this line. This approach is not an exact science.

5.3 Regression AnalysisA parametric cost-estimating model consists of one or more functions or relationships between the cost as the dependent variable and the cost governing factors as the independent variables. Regression analysis (RA) represents one of the most widely used methods for parametric cost estimation during early project stages. Traditionally, cost-estimating relationships are developed by applying RA to historical project information. Linear regression is a process which fits the equation of a line in the form YC = A + BX, where B is the slope of the line and A is the YC intercept, to a given set of data. Linear regression calculates the equation for this line by minimizing the sum of the squared residuals between the actual data points and the predicted data points using the estimated lines slope and intercept. Once the slope and intercept have been calculated, it is fairly easy to substitute other values for X and predict a corresponding value for YC, or to substitute a value for YC and predict a value for X. Linear regression is often used to estimate the fixed and variable components from a companys or departments total costs. In these circumstances, the values for X are usually the cost driver for the organization or department. Examples might include units produced, hours worked, hours of machine time, and others. The values for YC are the total cost for that level of X input. The computed slope of the linear regression line will indicate the variable cost per unit of X, while the computed YC-intercept will indicate the fixed cost. In many or most circumstances, this type of cost analysis will generate slopes and YC-intercepts that make sense in the real world. It is sometimes possible, though, that the fixed cost component in particular may not make any sense. The generated YC-intercept (fixed cost) might be negative, for example, to make the linear regression line fit the observed cost data as closely as possible. Be aware, as well, that it is rarely a good idea to use such an equation to predict too far into the future from the actual data used, since circumstances can change rather quickly. In other words, if you fit a line using cost data for units produced from 500 to 1500 a month, making cost predictions using forecasted production levels of 5000 units a month may generate unreliable results. Also, since time is not a variable in these calculations, the order in which the costs are input as data points does not matter you may enter the data points in any order desired

Assumptions of the Regression ModelThe assumptions listed below enable us to calculate unbiased estimators of the population) and to use these in predicting values and regression function coefficients (of Y given X). You should be aware of the fact that violation of one or more of these assumptions reduces the efficiency of the model, but a detailed discussion of this topic is beyond the purview of this text. Assume that all these assumptions have been met. For each value of X there is an array of possible Y values which is normally distributed about the regression line. The mean of the distribution of possible Y values is on the regression line. That is, the expected value of the error term is zero. The standard deviation of the distribution of possible Y values is constant regardless of the value of X. The error terms are statistically independent of each other. That is, there is no serial correlation. The error term is statistically independent of X.

Developing and Using a Simple Regression EquationSimple Regression Model: The simple regression model is based on the equation for a straight line: YC = A + BXWhere,YC = the calculated or estimated value for the dependent (response) variableA = the Y intercept, the theoretical value of Y when X = 0X = the independent (explanatory) variableB = the slope of the line, the change in Y divided by the change in X, the value by which Y changes when X changes by one.For a given data set, A and B are constants. They do not change as the value of the independent variable changes. YC is a function of X. Specifically, the functional relationship between YC and X is that YC is equal to A plus the product of B times X.

The following figure graphically depicts the regression line:

Steps for Developing a 2-Variable Linear Regression EquationTo develop a regression equation for a particular set of data, use the following 5-step least-squares-best-fit (LSBF) process:

Step 1: Collect the historical data required for analysisIdentify the X and Y values for each observation. X = Independent variable Y = Dependent variable Step 2: Put the data in tabular formStep 3: Compute X bar and Y bar = =

Where,X bar = sample mean for the observations the independent variablesY bar = sample mean for the observations the dependent variables = Summation of all the variables that follow the symbol (e.g., X represents the sum of all X values) X = Observation value for the independent variable Y = Observation value for the dependent variable n = Total number of observations in the sample

Step 4: Compute the slope (B) and the Y intercept (A)A = - B

Step 5: Formulate the Estimating EquationYC = A + BX

2-Variable Linear Regression Equation Development ExampleAssume a relationship between a firm's direct labor hours and manufacturing overhead cost based on the use of direct labor hours as the allocation base for manufacturing overhead. Develop an estimating equation using direct labor hours as the independent variable and manufacturing overhead cost as the dependent variable. Estimate the indirect cost pool assuming that 2,100 manufacturing direct labor hours will be needed to meet 2008 production requirements.

Step 1: Collect the Historical Data Required for AnalysisHistorical Data

YearManufacturing Direct Labor HoursManufacturing Overhead

2002120073,000

2003150097,000

20042300128,000

20052700155,000

20063300175,000

20073400218,000

20082100 (est)

Step 2: Put the Data in Tabular FormX = Manufacturing direct labor hours in hundreds of hours (00s) Y = Manufacturing overhead in thousands of dollars ($000s)Tabular Presentation

XYXYX2Y2

12738761225329

159714552259409

23128294452916384

27155418572924025

33175577518930625

342187412115647524

Column TotalsX = 144Y = 846XY = 22647X2 = 3872Y2 = 133296

Step 3: Compute and = = = 24 = = = 141

Step 4: Compute the slope (B) and the Intercept (A)

= = = = 5.6322A = - B= 141 - 5.6322(24)= 141 - 135.1728= 5.8272

Step 5: Formulate the Estimating EquationSubstitute the calculated values for A and B into the equation:YC = A + BXYC = 5.8272 + 5.6322XWhere,YC = Manufacturing OverheadX = Manufacturing Direct labor Hours

Estimate manufacturing overhead given an estimate for manufacturing direct labor hours of 2100.YC = 5.8272 + 5.6322X= 5.8272 + 5.6322 21= 5.8272 + 118.2762= 124.1034 thousand takaRounded to the nearest taka, the estimate would be Tk. 124,103

The Contrast between Regression Analysis and High-Low Analysis Regression analysis estimates the cost function by using a statistical model that relates the average change in the dependent variables to a unit change in the cost driver(s). The high-low method estimates the cost function by determining the line that connects the highest and lowest values for the cost driver in the relevant range.

The Advantages of Using Regression Analysis Provides an estimation model with best fit (least squared error) to the data Provides measures of goodness of fit and of the reliability of the model which can be used to assess the usefulness of the specific model, in contrast to the other estimation methods which provide no means of self-evaluation Can incorporate multiple independent variables Can be adapted to handle non-linear relationships in the data, including trends, shifts and other discontinuities, seasonality, etc. Results in a model that is unique for a given set of data.

6.0 ConclusionCost estimation can help managers to make more accurate forecast about future costs. Better forecast can assist managers to make more informed planning and decision making. So, it is essential to use a model for developing a cost function that can help in estimating future costs. There are several methods of cost estimation. A company should consider the expertise and technology necessary for a particular cost estimation method. There are certain limitations of a particular method. So, an organization should consider them before choosing a particular method. For example, engineering analysis method can provide good estimation but it requires huge analysis and involves time consuming process. As account analysis method is based on the judgment of the account in the general ledger, this may be subjective because of the judgment of the managers. Conference method may increase cooperation among different departments and develop a cost function quickly. But efficiency and accuracy of cost estimation depends on the skills and expertise of the person providing the inputs. In scattergraph method, user fits the regression line through the data points is entirely subjective. The high-low method estimates the cost function by highest and lowest values for the cost driver in the relevant range. These two points may not be truly representative of the general relation between cost and activity. Though regression analysis requires complex calculation, this method provides quantitative and objective measures of the precision and reliability. Thus, it can provide better estimation in contrast to the other estimation methods which provide no means of self-evaluation.

ReferencesGarrison, RH, Noreen, EW & Brewer, PC 2008, Managerial Accouting, 12th edn, McGraw-Hill companies Inc.Horngren, CT, Datar, SM, Foster, G, Rajan, M & Ittner, C 2013, Cost Accounting- A Manegerial Emphais, 13th edn, Prentice-Hall Inc.Horngren, CT, Sundem, GL, Stratton, WQ, Burgstahler, D & Schatzberg, J 2009, Introduction to Management Accounting, 14th edn, Perason Education Inc.