DSS-ESTIMATING COSTS Cost estimation is the process of estimating the relationship between costs and cost driver activities. We estimate costs for three reasons: to manage costs, to make decisions, and to plan and set standards. In this chapter, we will focus on several tools that will enable us to develop cost estimation relationships.

Existing relationship between cost and activity. Introduction Cost behavior Cost estimation Cost prediction Existing relationship between cost and activity. Process of estimating relationship between costs and cost driver activities that cause those costs. Using results of cost estimation to forecast a level of cost at a particular activity. Focus is on the future. Cost behavior is an existing relationship between an activity (cost driver) and a cost. Cost estimation is the process of estimating the relationship between the cost driver activity and the cost. Cost prediction is the use of the cost estimation to forecast a cost at a particular level of activity.

Reasons for Estimating Costs How much will costs increase if sales increase 10 percent? What will my costs be if I introduce the new model in a foreign market? Management needs to know the costs that are likely to be incurred for each alternative. Managers control costs by managing activities. Better knowledge of the relationships between costs and activities means better managed costs.

Reasons for Estimating Costs Accurate Cost Estimates Better Decisions Add Value Accurate cost estimates lead to improved decision making, and improved decision making adds value. Improved Decision Making

Reasons for Estimating Costs Exh. 11-1 Reasons for Estimating Costs Relationship between activities and costs 1. First, identify this 3. To reduce these Costs We estimate costs to: manage costs make decisions plan & set standards We determine the relationship between costs and activities and then manage those activities to control costs. We estimate costs for three primary reasons: To manage and control costs. To make better decisions. To plan and set standards. 2. Then manage these Activities

One Cost Driver and Fixed/Variable Cost Behavior Exh. 11-2 One Cost Driver and Fixed/Variable Cost Behavior Slope = Cost Driver Rate $.16 Here we see a graph of the relationship between miles driven and cost. Miles driven is the independent variable and is plotted on the horizontal axis. Cost is the dependent variable and is plotted on the vertical axis. Total cost is equal to the fixed cost of one hundred ninety dollars plus sixteen cents per mile. Notice that the fixed cost at all miles, even at zero, is one hundred ninety dollars. The variable cost, which rises as more miles are driven is added to the fixed cost to obtain the total cost. You could think about these relationships in terms of your car. The fixed cost is your car payment that remains the same, even if you do not drive the car. The variable cost is the cost of gasoline that increase as you drive more miles. Intercept = Fixed Cost

Nonlinear Costs Total Cost Curvilinear Cost Function A straight-Line (constant unit variable cost) often closely approximates a nonlinear line within the relevant range. Relevant Range Not all variable costs are linear as shown in our previous examples. Over a range of activity from zero to extremely high levels, most variable costs are curvilinear. However, in the range of activity that a company is likely to operate (relevant range), costs are either linear, or very close to linear. Activity

The High-Low Method The high-low method uses two points to estimate the general cost equation TC = F  VX TC = the value of the estimated total cost F = a fixed quantity that represents the value of Y when X = zero The high-low method uses two data points to estimate a linear cost equation in the form: Total costs equals total fixed costs plus total variable costs. Variable costs are a function of activity, so the total variable cost is the variable cost per unit (cost driver rate) times the number of cost driver units. V = the slope of the line, the unit variable cost . X = units of the cost driver activity.

Total Cost in 1,000s of Dollars The High-Low Method The high-low method uses two points to estimate the general cost equation TC = F + VX 20 * * * * * * Total Cost in 1,000s of Dollars * * * * 10 We can use any two data points with the high-low method, but we should plot the data and select two points that are representative of the cost and activity relationship over the range of activity for which the estimation is made. The two points should be representative of the cost and activity relationship over the range of activity for which the estimation is made. 0 1 2 3 4 Activity, 1,000s of Units Produced

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. In our high-low example, we’re going to look at a company’s relationship between maintenance cost and units of production . During the year, the company reports production and maintenance costs on a monthly basis. The month with the high level of production shows nine thousand units and a corresponding maintenance cost of nine thousand seven hundred dollars, and the month with the low level of production shows five thousand units with a corresponding cost of six thousand one hundred dollars. We will use this information to compute the variable maintenance cost per unit of production and the total fixed cost. Then we will write a linear equation to describe the cost behavior.

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 Part I To determine the variable costs per unit of activity, we divide the change in cost by the change in production activity. In our case, the change in maintenance cost is three thousand six hundred dollars and the change in units produced is four thousand. The result is a variable cost rate of ninety cents per unit produced. Part II Next, we calculate the fixed cost by subtracting the total variable cost from the total cost. Since total cost and total variable cost are different amounts at different activity levels, we must choose either the high level or the low level for our computations. Let’s choose the high level of activity, nine thousand units. Our first step is to calculate the total variable cost. At nine thousand units, the total variable cost is ninety cents per unit times nine thousand units resulting in a total variable cost of eight thousand one hundred dollars. Next, we subtract eight thousand one hundred dollars from the total cost at the high activity, to get the fixed cost, one thousand six hundred dollars. We will obtain the same result if using the low level of activity to compute fixed cost. Part III Now, we can write a linear equation using our variable cost of ninety cents per unit and our fixed cost of one thousand six hundred dollars. Total cost equals one thousand six hundred dollars plus ninety cents per unit for any number of units within the relevant range.

Regression Analysis A statistical method used to create an equation relating dependent (or Y) variables to independent (or X) variables. Past data is used to estimate relationships between costs and activities. If we have a large number of observations, we’ll probably want to use computer software that can do regression analysis to determine cost-activity relationships. Excel is a wonderful tool to carry out this computation. Independent variables are the cost drivers that drive the variation in dependent variables. Before doing the analysis, take time to determine if a logical relationship between the variables exists.

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 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 Using regression analysis our objective will be the same cost function, that is, Total cost equals fixed costs plus variable unit cost times activity. X = value of the independent variable, the cost driver

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 Regression analysis results in a unique line through data points that minimizes the sum of squared distances from the data points to the line. 50 100 150 200 Independent Variable

Regression Analysis V = the slope of the regression line or the coefficient of the independent variable, the increase in TC for each unit increase in X. 400 350 300 250 200 Dependent Variable The intercept is a fixed quantity, independent of activity. The coefficient of the independent variable is the slope of the regression line and tells us the change in total cost (dependent variable) for a one-unit change in activity (independent variable). F = a fixed quantity, the intercept 50 100 150 200 Independent Variable

Regression Analysis * * * * * * * * * * The correlation coefficient, r, is a measure of the linear relationship between variables such as cost and activity. 20 * * * * * * * * * * Total Cost 10 Regression analysis provides us with several measures that that are helpful in assessing the quality of the relationship between the variables. The correlation coefficient, r, is a measure of the linear relationship between variables such as cost and activity. The correlation coefficient is highly positive (close to plus one) if the data points are close to the regression line, and if the dependent variable increases as the independent variable increases. The correlation coefficient is highly positive (close to 1.0) if the data points are close to the regression line. 0 1 2 3 4 Activity

Regression Analysis * * * * * * * * * * The correlation coefficient, r, is a measure of the linear relationship between variables such as cost and activity. * * * * 20 * * * * * * Total Cost 10 The correlation coefficient is near zero if little or no relationship exists between the variables. The correlation coefficient is near zero if little or no relationship exists between the variables. 0 1 2 3 4 Activity

Regression Analysis * * * * * * * * * * The correlation coefficient, r, is a measure of the linear relationship between variables such as cost and activity. * * 20 * * * * * * * * Total Cost 10 The correlation coefficient is highly negative (close to minus one) if the data points are close to the regression line, and if the dependent variable decreases as the independent variable increases. This relationship has a negative correlation coefficient, approaching a maximum value of –1.0 0 1 2 3 4 Activity

Regression with high R2 (close to 1.0) Regression Analysis R2, the coefficient of determination, is a measure of the goodness of fit. R2 tells us the amount of the variation of the dependent variable that is explained by the independent variable. 400 350 300 250 200 Dependent Variable R-squared is the term used in least squares regression analysis to measure the goodness of the fit of the line. The closer that R-squared is to one hundred percent, the better the fit or description the line is of the data point observations. R-squared is also called the coefficient of determination. R-squared tells us the percentage of the variation of the dependent variable that is explained by the independent variable. Values of R-squared range from zero to one. The regression line on your screen has an R-squared value close to one as the data points lie close to the line. Regression with high R2 (close to 1.0) 50 100 150 200 Independent Variable

Regression with low R2 (close to 0) Regression Analysis The coefficient of determination, R2, is the correlation coefficient squared. 400 350 300 250 200 Dependent Variable The coefficient of determination, R-squared, is equal to the square of the correlation coefficient. The regression line on your screen has an R-squared value close to zero as the data points do not lie close to the line. Regression with low R2 (close to 0) 50 100 150 200 Independent Variable

Regression Analysis Uses all data points resulting in a better 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 is superior to the high-low method because it: Uses all data points, resulting in a better 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.