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## Cost Estimation

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**11**Cost Estimation**Costprediction**Costestimation Introduction Costbehavior Existingrelationshipbetweencost andactivity. Process ofestimating relationship between costsand cost driveractivities that cause those costs. Using results ofcost estimationto forecast alevel of cost ata particularactivity. Focusis on the future.**How muchwill costs increaseif sales increase10 percent?**What will mycosts be if I introducethe new model in aforeign market? Reasons for Estimating Costs Management needsto know the costs thatare likely to beincurred for eachalternative.**Reasons for Estimating Costs**More accurate cost estimates Increasedcompanyvalue • Better informed decisions about: • efficient business processes • alternative courses of action • performance standards • financial forecasts**Exh.**11-1 Reasons for Estimating Costs Relationship between activities and costs • First identify this 3. To reduce these Costs • We estimate costs to: • manage costs • make decisions • plan and set standards. 2. Then manage these Activities**Basic Cost Behavior Patterns**Total Costs = Fixed costs + Variable costs TC = F + VX Vis the variable cost per cost driver unit (cost driver rate). X is the number of cost driver units.**Exh.**11-2 One Cost Driver and Fixed/Variable Cost Behavior Slope = Cost Driver Rate $.16 Intercept = Fixed Cost**Multiple Cost Drivers and Complex Cost Behavior**In cases of complex cost behavior and multiple cost drivers, the cost-benefit test should be considered when developing a cost estimation model.**Step Costs**• Step Cost • A cost that increases in steps as the amount of the cost driver volume increases. • Also called a “semifixed cost” Cost Activity Total cost remains unchanged over a narrow range of activity. As activity increases to the next range, total cost steps up to the next level.**Step Costs**Example: Office space is available at a rental rate of $30,000 per year in increments of 1,000 square feet. As the business grows more space is rented, increasing the total cost. Continue**Step Costs**Rent Cost $90,000 Total cost remains unchanged for arange of activity, then jumps to a higher cost for the next range of activity. $60,000 $30,000 0 1,000 2,000 3,000 Rented Area (Square Feet)**Relevant Range of Activity**Unit variable costsremain unchanged. The activity limits within which acost projection may be valid is the relevant range of activity. Total fixed costsremain unchanged.**Mixed Costs**A mixed cost is one that has both a fixed and a variable component. For example, a cellular phone plan that charges $40 for the first 600 minutes and $0.10 per minute thereafter.**A nonlinear cost pattern (e.g. changes in unit variable**cost) may often approximate a straight line (when the unit variable cost is constant) within the relevant range. Total Cost Relevant Range Nonlinear Costs CurvilinearCost Function Activity**Methods of Estimating Costs**Scattergraph and high-low estimates Statistical methods (regression analysis) Account analysis Engineering method**The Scattergraph**Simply plotting past cost behavior on a graph may be a helpful first step in analyzing costs regardless of the estimation method ultimately chosen. It can reveal outlier data points and suggest possible relationships between the variables.**The Scattergraph**The Scattergraph Plot the data points on a graph (total cost vs. activity). Total cost $20,000 * * * * * * * * * * $10,000 0 0 1 2 3 4 Activity: Units produced (‘000)**The Scattergraph*** * * * * * * * * * Estimated fixed cost = $10,000 0 0 1 2 3 4 The Scattergraph Draw a line through the plotted data points so that about an equal amount of points falls above and below the line. Total Cost $20,000 $10,000 Activity: Units produced (‘000)**The Scattergraph*** * Vertical distance is the change in cost. * * * * * * * * Horizontal distance is the change in activity. 0 0 1 2 3 4 The Scattergraph The slope of this line is the unit variable cost. (Slope is the change in total cost for a one-unit change in activity). Total Cost $20,000 $10,000 Activity: Units produced (‘000)**The High-Low Method**The high-low method uses two data points to estimate the general cost equation TC = F VX TC = the estimated total cost F = a fixed quantity that represents the value of Y when X = zero V = the slope of the line (equivalent to the unit variable cost) X= units of the cost driver activity**The High-Low Method**The high-low method uses two data points to estimate the general cost equation TC = F + VX Total Cost $20,000 * * * * * * * * * * $10,000 The two points should be representative ofthe cost and activity relationship over the rangeof activity for which the estimation is made. 0 0 1 2 3 4 Activity: Units produced (‘000)**The High-Low Method**WiseCo recorded the following production activity and maintenance costs for two months: Using these two levels of activity, compute: • the variable cost per unit; • the fixed cost; and then • express the costs in equation form TC = F + VX.**The High-Low Method**The High-Low Method • Unit variable cost = $3,600 ÷ 4,000 units = $.90 per unit • Fixed cost = Total cost – Total variable cost • Fixed cost = $9,700 – ($.90 per unit × 9,000 units) • Fixed cost = $9,700 – $8,100 = $1,600 • Total cost = Fixed cost + Variable cost (TC = F + VX) TC = $1,600 + $0.90X**Regression Analysis**A statistical method used to create an equation relating dependent (or Y) variables to independent (or X) variables. Data from the past are used to estimate relationships between costs and activities. Before doing the analysis, take time to determine if a logical relationship between the variables exists. Independent variables are the cost drivers that drive the variation in dependent variables.**Regression Analysis**Regression Analysis The objective of the regression method is still a linear equation to estimate costs TC = F + VX TC= value of the dependent variable (estimated total cost) F= a fixed quantity, the intercept, that represents the value of TC when X = 0 V= the unit variable cost, the coefficient of the independent variable measuring the increase in TC for each unit increase in X X= value of the independent variable, the cost driver**Regression Analysis**Regression Analysis A statistical procedure that finds the unique line through data points that minimizes the sum of squared distances from the data points to the line. 400 350 300 250 200 Dependent Variable 50 100 150 200 Independent Variable**Regression Analysis**Regression Analysis V= the slope of the regression line or the coefficient of the independent variable. Here it represents the increase in TC for each unit increase in X. 400 350 300 250 200 Dependent Variable F= a fixed quantity, the intercept 50 100 150 200 Independent Variable**Regression Analysis**Regression Analysis proper line, excluding the outlier improper line, influenced by outlier 400 350 300 250 200 Dependent Variable Outlier Outliers may be discarded toobtain a regression that is morerepresentative of the data. 50 100 150 200 Independent Variable**Regression Analysis**Thecorrelation coefficient (r)is a measure of the linear relationship between variables such as cost and activity. Total Cost $20,000 * * * * * * * * * * $10,000 The correlation coefficient is highly positive (close to 1.0) if the data points are close to the regression line. 0 0 1 2 3 4 Activity: Units produced (‘000)**Regression Analysis**Thecorrelation coefficient (r)is a measure of the linear relationship between variables such as cost and activity. Total Cost * * * * $20,000 * * * * * * $10,000 The correlation coefficient is near zero if little or no relationshipexists between the variables. 0 0 1 2 3 4 Activity: Units produced (‘000)**Regression Analysis**Thecorrelation coefficient (r)is a measure of the linear relationship between variables such as cost and activity. Total Cost * * $20,000 * * * * * * * * $10,000 This relationship has a negative correlation coefficient, approachinga maximum value of –1.0 0 0 1 2 3 4 Activity: Units produced (‘000)**Regression Analysis**Regression Analysis R2, the coefficient of determination, is a measureof the goodness of fit. R2 tellsus the amountof the variation of the dependent variable thatis explained by the independent variable. 400 350 300 250 200 Dependent Variable Regression withhigh R2 (close to 1.0) 50 100 150 200 Independent Variable**Regression Analysis**Regression Analysis The coefficient ofdetermination, R2,is the correlationcoefficient squared. 400 350 300 250 200 Dependent Variable Regression withlowR2 (close to 0) 50 100 150 200 Independent Variable**Regression Analysis**• Includes all data points, resulting in more thorough study of the relationship between the variables. • Generates statistical information that describes the relationship between variables. • Permits the use of more than one cost driver activity to explain cost behavior.**Regression Analysis**• Statistics courses deal with detailed regression computations using computer spreadsheet software. • Accountants and managers must be able to interpret and use regression estimates. • Let’s look at an example using Excel.**Simple Regression Example**Eagle Enterprises wants to analyze the relationship between units produced and total costs. Using the data to the right, let’s see how to do a regression using Excel.**Simple Regression Using Excel**• We will obtain three pieces • of information from our • regression analysis: • Estimated Variable Cost per Unit (line slope) • Estimated Fixed Costs (line intercept) • Goodness of fit, or R2 To get these three pieces of information we will need to find the following Excel functions: LINEST, INTERCEPT and RSQ.**Simple Regression Using Excel**After opening Excel and entering your data, click on “Insert” and “Function”**Simple Regression Using Excel**When the function box opens, click on “Statistical”, then on “LINEST”**Simple Regression Using Excel**By clicking on the buttons to the left, you can highlight the desired cells directly from the spreadsheet. 1. Enter the cell range for the cost amounts in the “Known_y’s” box. 2. Enter the cell range for the quantity amounts in the “Known_x’s” box.**Simple Regression Using Excel**The Slope, or estimated variable cost per unit, is identified here. Click OK to put this value on your spreadsheet.**Simple Regression Using Excel**Repeat the procedure using “Intercept”, to estimate fixed cost.**Simple Regression Using Excel**As previously, enter the appropriate cell ranges in their appropriate places. The estimated fixed cost per unit is identified here.**Simple Regression Using Excel**Finally, determine the “goodness of fit”, or R2, by using the RSQ function.**Simple Regression Using Excel**As previously, enter the appropriate cell ranges in their appropriate places. The estimated R2 for your estimated cost function is identified here.**Simple RegressionExample Summary**The objective of the regression method is a linear equation to estimate costs TC = F + VX We found the following linear equation for Eagle:TC = $2,618.72 + $2.768 per unit The high value for R2 tellsus that approximately93.26 percent of the variation in total costis explained by the variation in the number ofunits produced.**Multiple Regression Analysis**Multiple Regression is a regression that has more than one independent (X) variable. For example, demand for a product may be affected by factors such as inflation, interest rates and competitors’ prices. Can be very useful in situations where the dependent variable is impacted by several different independent variables.