Chapter 2: Cost Behavior and Cost Estimation

Summary of Scattergraph, High-Low, and Regression Methods

The three estimation techniques use different combinations of data points to arrive at a cost equation for deliveries. As a result, their estimated costs differ. Although none of the three techniques yields a correct answer (remember, they are estimations), most statisticians would agree that *regression* gives the best estimate because it calculates the line of best fit for all data points, not just one or two.

Discretionary Vs. Committed Fixed Costs

*Discretionary Fixed Costs* = Fixed costs that can be changed over the short run. ex: the cost of an annual contract for television advertising is a fixed cost; however, a company may choose to cut such advertising costs to improve profits *Committed Fixed Costs* = Fixed costs that cannot be changed over the short run. ex: a company may have signed a 10-year lease on an office building. Until the lease period ends, nothing can be done to change the amount of rent the company pays

Fixed Costs

*Fixed Costs* = A cost that does not change in total with changes in activity, but per unit cost varies indirectly with changes in activity. - The higher the level of activity, the lower the fixed cost per unit. - Two Main Characteristics: 1) The total cost remains fixed, regardless of changes in the level of activity. 2) The cost per unit varies inversely with changes in the level of activity.

Contribution Format Income Statement

*Contribution Format Income Statement* = An income statement that classifies costs by behavior. *Variable Cost Ratio* = Total variable costs divided by total sales or 1 minus the contribution margin ratio. Ex: Remember that Universal sold 10% fewer jerseys than it expected, so how many jerseys had it planned to sell? First, we need to know the current sales volume, and we can calculate that amount by dividing total sales dollars by sales price per unit: Shirts sold = 1,039,500/$20 = 51,975 jerseys - Based on actual sales of 51,975 jerseys, Universal's original sales projection was 57,750 jerseys (51,975/0.9). Therefore, Universal would need to sell 5,775 additional jerseys to reach that goal. So how much more income would these 5,775 additional jerseys generate? - Each jersey generates $4 in contribution margin - Additional Contribution Margin = Additional Sales Revenue x Contribution Margin ratio - ($20 x 5,775 jerseys) x 0.20 = $23,100

High Low Method

*High-Low Method* = A cost estimation technique that uses the equation of a line y = mx + b and a data set's highest and lowest volume points to separate a mixed cost into its fixed and variable components - Unlike the scattergraph, the high-low method requires only two data points—the lowest point of activity and the highest point of activity. - Like the scattergraph, the high-low method does have some limitations. Because it is based on only two extreme points, the high and low activity levels, the cost equation may not be truly representative of the cost relationship. Be careful not to use an obvious outlier as either the high or the low point, or it will greatly skew your cost estimate.

Mixed Costs

*Mixed Costs* = A cost that has both fixed and variable components. - Since a mixed cost has both a fixed and a variable component, both the total cost and the unit cost will vary with changes in the level of activity. ex: Think about the natural gas bill you might receive for heating your apartment. To receive service, you pay a base charge of $10 per month, regardless of how much gas you use. Then you pay an additional charge of $0.06 per cubic foot for the gas you use. The $10 monthly charge is the fixed component, and the $0.06 charge per cubic foot is the variable component. So the total cost can be expressed as: Total Gas Cost = $10($0.06 x cubic feet of gas used)

Regression Analysis

*Regression Approach* = A statistical technique that separates a mixed cost into its fixed and variable components by identifying the line of best fit for the points in a data set. - spreadsheet software such as Microsoft Excel makes regression analysis easy. After entering the data points in the spreadsheet, use the INTERCEPT and SLOPE functions to determine the fixed cost and variable cost per unit, respectively.

Cost Estimation and the Relevant Range

*Relevant Range* = The normal or expected range of operating activity - Cost behaviors and estimates are valid only within the relevant range - Beyond the relevant range, cost relationships are likely to change, and with them, cost estimates - Note that the cost relationships on either side of the shaded relevant range differ markedly from the highlighted portion of the curves. - While these graphs represent curvilinear cost relationships, within the relevant range the cost relationships approximate a linear relationship. Thus, the estimation techniques you have learned, which are based on a linear relationship, are valid, but only over the relevant range.

Scattergraphs

*Scattergraphs* = A graph of individual data points showing total costs in relation to volume, or activity level. - A graph of individual data points showing total costs in relation to volume, or activity level. - Once you have plotted the individual points, draw a line through them to estimate the cost relationship ex: Based on a visual inspection of the scattergraph, a linear relationship appears to exist between the number of deliveries and delivery cost. - To estimate the fixed and variable cost components using a scattergraph, it is necessary to visually "fit" a line to the plotted points. You need to draw the line so that it appears to fit the data well, minimizing the distance between the line and the data points.

Step Costs

*Step Costs* = Costs that are fixed over only a small range of activity. Once that level of activity has been exceeded, total costs increase and remain constant over another small range of activity. ex: Suppose your cell phone company offers a plan under which you can buy airtime in blocks of 500 minutes. Every block of 500 minutes costs $40. If you use between 1 and 500 minutes, you will pay $40; if you use 501 minutes, you will pay $80. - With step costs, total cost remains constant over the step range, but unit cost decreases as usage within the step range increases. ex: So while the total cost of both 100 minutes and 500 minutes would be $40, the cost per minute of airtime would be $0.40 and $0.08, respectively.

Variable Costs

*Variable Cost* = Any cost whose total varies in proportion to a business activity. Variable cost per unit is constant over the relevant range. *Activity* = An event that consumes resources; any repetitive event that serves as a measure of output or usage, such as sales, production, phone calls made, or miles driven. - As the level of activity increases, the total cost increases by the same proportion - Conversely, as the level of activity decreases, the total cost decreases by the same proportion. - Two Main Characteristics 1) The total cost varies in proportion to changes in the level of activity. 2) The cost per unit remains constant, regardless of the level of activity. - If there is no activity, no cost is incurred

2.3 Contribution Margin Analysis

1) Define the term contribution margin. 2) What is the contribution margin ratio? How is it related to the variable cost ratio? 3) If a product's variable cost per unit increases while the selling price and fixed cost decrease, what will happen to the contribution margin per unit? 4) How can a company increase a product's contribution margin? *One of the basic tools for making business decisions is the contribution margin - In this unit you will learn how to calculate the contribution margin and how to construct a contribution format income statement to support business decision making.

Three Methods of Estimating Costs

1) Scattergraphs 2) High-Low Method 3) Regression Analysis

2.2 Cost Estimation

1. Express the relationship between total cost (TC), variable cost per unit (VC), volume (x), and fixed cost (FC) in equation form. 2. Explain how a scattergraph is used to separate a mixed cost into its fixed and variable components. 3. Explain how the high-low method is used to separate a mixed cost into its fixed and variable components for cost estimation. 4. Given a choice between the high-low method, a scattergraph, or regression analysis, which method would you prefer for separating a mixed cost into its fixed and variable components? Why? 5. Explain the concept of the relevant range. How does a company's relevant range differ from the steps found in a step cost? Total cost is a combination of fixed and variable costs. It can be predicted using the standard algebraic equation: y = mx + b where: m = the variable cost per unit x = the level of activity (such as number of units) b = total fixed cost y = total cost

2.1 Cost Behavior Patterns

1. Why is it important for managers to understand cost behavior patterns? 2. What is a variable cost? If the activity level increases, what happens to the total cost incurred? Give three examples of a variable cost. 3. What is a fixed cost? If the activity level increases, what happens to the total cost incurred? Give three examples of a fixed cost. 4. Distinguish between committed and discretionary fixed costs. 5. What is a mixed cost? If the activity level increases, what happens to the total cost incurred? Give three examples of a mixed cost. 6. What is a step cost? If the activity level increases, what happens to the total cost incurred? Give three examples of a step cost. *Cost Behavior* = The way total costs change in response to changes in the level of activity. 4 Common Cost Behavior Patterns 1) Variable Costs 2) Fixed Costs 3) Discretionary Vs. Committed Fixed Costs 4) Step Costs

Contribution Margin

If an organization wants to make a profit, it must generate more sales revenue than the expenses it incurs. - Operating Income = Sales Revenue - Total Expenses OR - Operating Income = Sales Revenue - Total Variable Expenses - Total Fixed Expenses Operating Income = (sales price per unit x # of units sold) - (variable cost per unit x # of units sold) - fixed expenses *Operating Income = [(sales price per unit - variable cost per unit) x # of units sold)] - fixed expenses* *Contribution Margin* = The difference between sales and variable costs—the amount that remains to cover fixed costs and provide a profit: 1) *Contribution Margin Per Unit = sales price per unit - variable cost per unit* OR 2) *Contribution Margin = sales revenue - total variable expenses* *Operating Income = [Contribution margin per unit x # of units sold] - Fixed Expenses* - As the number of units sold increases, total contribution margin increases, but fixed expenses remain the same. - Thus, as the number of units sold rises, profit increases by the additional contribution margin per unit. *Contribution Margin Ratio* = the ratio of the contribution margin to sales - Contribution margin ratio = (contribution margin / sales revenue) = (contribution margin per unit / sales price per unit) - The contribution margin ratio can be used to determine the increase in profits from a given dollar increase in sales revenue. With a 20% contribution margin ratio, each dollar in baseball jersey sales generates in contribution margin for Universal. So an additional $100 in jersey sales will generate $20 in additional contribution margin. *Cost vs. Expense* 1) *Cost* = is the cash or other value given up to obtain goods or services in the expectation that they will generate future benefits. A cost can be capitalized as an asset on the balance sheet, as in the purchase of inventory for resale. 2) *Expense* = Once the future benefits have been received, the cost becomes an expense on the income statement