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**Cost Behavior and Cost-Volume-Profit Analysis**

Chapter 18 Cost Behavior and Cost-Volume-Profit Analysis This chapter shows how information on both costs and sales behavior is useful to managers in performing cost-volume-profit analysis. This analysis is an important part of successful management and sound business decisions.

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**Conceptual Learning Objectives**

C1: Describe different types of cost behavior in relation to production and sales volume. C2: Identify assumptions in cost-volume profit analysis and explain their impact. C3: Describe several applications of cost-volume-profit analysis. In this chapter, you will learn the following conceptual objectives: C1: Describe different types of cost behavior in relation to production and sales volume. C2: Identify assumptions in cost-volume profit analysis and explain their impact. C3: Describe several applications of cost-volume-profit analysis.

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**Analytical Learning Objectives**

A1: Compare the scatter diagram, high-low, and regression methods of estimating costs. A2: Compute contribution margin and describe what it reveals about a company’s cost structure. A3: Analyze changes in sales using the degree of operating leverage. In this chapter, you will learn the following analytical objectives: A1: Compare the scatter diagram, high-low, and regression methods of estimating costs. A2: Compute contribution margin and describe what it reveals about a company’s cost structure. A3: Analyze changes in sales using the degree of operating leverage.

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**Procedural Learning Objectives**

P1: Determine cost estimates using three different methods. P2: Compute the break-even point for a single product company. P3: Graph costs and sales for a single product company. P4: Compute break-even point for a multiproduct company. In this chapter, you will learn the following procedural objectives: P1: Determine cost estimates using three different methods. P2: Compute the break-even point for a single product company. P3: Graph costs and sales for a single product company. P4: Compute break-even point for a multiproduct company.

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**Questions Addressed by Cost-Volume-Profit Analysis**

CVP (BE) analysis is used to answer questions such as: What sales volume is needed to break-even? What sales volume is needed to earn a target income? What is the change in income if selling prices decline and sales volume increases? How much does income increase if we install a new machine to reduce labor costs? What is the income effect if we change the sales mix of our products or services? Cost-volume-profit analysis will allow us to answer many questions and make important decisions involving the relationships between the volume of activity and costs and revenues. Before we can answer these questions using cost-volume-profit analysis, we must first study cost behavior.

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**Total fixed costs + Total variable Costs**

Total Cost Total Costs = Total fixed costs + Total variable Costs We begin our study of cost behavior with fixed costs. Your basic land-line telephone has a monthly connect charge that remains constant regardless of the number of local calls that you might make. The monthly charge that is independent of call activity is a fixed cost..

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**Total Fixed Cost (Exhibit 18.1, Page 757)**

Total fixed costs remain unchanged when activity (units) changes. Monthly Basic Telephone Bill We begin our study of cost behavior with fixed costs. Your basic land-line telephone has a monthly connect charge that remains constant regardless of the number of local calls that you might make. The monthly charge that is independent of call activity is a fixed cost.. Your monthly basic telephone bill probably does not change when you make more local calls. Number of Local Calls

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**Monthly Basic Telephone Bill per Local Call**

Fixed Cost Per Unit C1 Fixed costs per unit decline as activity (units) increases. Monthly Basic Telephone Bill per Local Call Fixed costs per unit decline as activity increases. Dividing your monthly connect fee by more local calls reduces the cost per call by spreading the fixed amount over a higher number of calls. For example, if your monthly connect charge is twenty dollars and you make forty local calls in a month, your cost per local call is fifty cents. If you make one hundred local calls in a month, your cost per local call is twenty cents. Your average cost per local call decreases as more local calls are made. Number of Local Calls

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**Total Variable Cost (Exhibit 18.1, Page 757)**

Total variable costs change when activity (units) changes. Total Long Distance Telephone Bill Total variable costs increase as activity increases. For most people, the total land-line long distance telephone bill is based on the number of minutes talked. So there’s a direct relationship between the number of minutes talked and your total bill. You can see a graph of that relationship in the lower left-hand part of your screen. Your total long distance telephone bill is based on how many minutes you talk. Minutes Talked

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**Per Minute Telephone Charge**

Variable Cost Per Unit C1 Variable costs per unit do not change as activity (unit) increases. Per Minute Telephone Charge The cost per land-line long distance minute talked is normally constant. For example, for your service, it may be seven cents per minute. Talking more or less minutes will not change the per minute charge. So, on a per unit basis, variable costs remain unchanged. You can see the graph of that in the lower right-hand side of your screen. The cost per long distance minute talked is constant. For example, 7 cents per minute. Minutes Talked

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**Cost Behavior Summary C1**

We know that some of the language we use to differentiate fixed and variable costs in total and per unit can be very confusing when you first see it. So we’ve prepared this chart to help you identify how those costs behave.

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**Mixed Costs (Exhibit 18.1, Page 757)**

Mixed costs contain a fixed portion that is incurred even when the facility is unused, and a variable portion that increases with usage. Example: monthly electric utility charge Fixed service fee Variable charge per kilowatt hour used Many costs are mixed in nature. That is, they have both a fixed and variable component. Think about your utility bill. You have a fixed monthly charge for the hook-up, and the variable portion of your bill depends upon the number of kilowatt hours you consume. The more the kilowatt hours you use, the higher your total utility bill will be.

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**Step-Wise Costs Exhibit 18.2 (page 758)**

Total cost remains constant within a narrow range of activity. Another type of cost is referred to as a step cost. Step costs remain constant in total within a relatively narrow range of activity. Cost Activity

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**Curvilinear Costs Exhibit 18.2 (page 758)**

1. Increase at a non-constant rate as volume increases. 2. Substantial gains in efficiency at low volume; Smaller gains in efficiency at higher volume. 3. When volume and costs are graphed, curvilinear costs appear as a curved line that starts at intersection point of cost axis and volume axis (total cost is zero when volume is zero) and increases at different rates. Another type of cost is referred to as a step cost. Step costs remain constant in total within a relatively narrow range of activity.

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Cost Behavior Exercise 2

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**Measuring Cost Behavior**

P1 The objective is to classify all costs as either fixed or variable. When presented with a mixed cost, we will separate the variable portion of the cost from the fixed portion of the cost. There are number of ways to do this. We will use a scatter diagram and the high-low method. A more sophisticated method, the least squares regression model, is also available, but we will not use it here.

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**Measuring Cost Behavior**

After establishing that cost data are reliable and useful in predicting future costs, three methods commonly used to analyze past cost behavior. -Scatter Diagrams -High-Low Method -Least-Squares Regression When presented with a mixed cost, we will separate the variable portion of the cost from the fixed portion of the cost. There are number of ways to do this. We will use a scatter diagram and the high-low method. A more sophisticated method, the least squares regression model, is also available, but we will not use it here.

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**Total Cost in 1,000’s of Dollars**

Scatter Diagram Exhibit 18.3: Data Unit Variable Cost = Slope = Δin cost Δin units * Total Cost in 1,000’s of Dollars 10 20 Activity, 1,000’s of Units Produced Vertical distance is the change in cost. A scatter diagram is a plot of cost data points on a graph. It is almost always helpful to plot cost data to be able to observe a visual picture of the relationship between cost and activity. We begin by plotting the data points on our graph. The vertical axis is cost and the horizontal axis is activity. Next, we draw a straight line through the data points with about an equal number of observations above and below the line. We continue the line past the observed points until it intersects with the vertical axis. The intercept in this case is our fixed cost, which is estimated to be ten thousand dollars. Next, we determine the slope of the line. The slope of the line is the change in cost divided by the change in activity. The slope, the amount of change in cost for a one unit change in activity, is the variable cost per unit of activity. Horizontal distance is the change in activity.

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Scatter Diagram Exercise 1

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The High-Low Method The following relationships between units produced and costs are observed: Using these two levels of activity, compute: the variable cost per unit. the total fixed cost. Now let’s look at the high-low method. In our example, we’re going to look at a company’s relationship between cost and sales activity. During the year, the company reports sales and costs on a monthly basis. The month with the high level of sales shows sales of sixty seven thousand five hundred dollars and a corresponding cost of $29,000, and the month with the low level of sales show sales of $17,500 with a corresponding cost of $20,500. We will use this information to compute the variable cost per dollar of sales and the total fixed cost.

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**The High-Low Method Δin cost Δin units $8,500 $50,000**

Unit variable cost = = = $0.17 /unit Fixed cost = Total cost – Total variable cost Fixed cost = $29,000 – ($0.17 per unit × 17,500) Fixed cost = $29,000 – $11,475 = $17,525 Δin cost Δin units $8,500 $50,000 To determine the variable costs per unit of activity, we divide the change in cost by the change in activity, sales dollars in this example. In our case, the change in cost is $8,500 and the change in sales dollars is $50,000. The result is a variable cost rate of $0.17 per dollar of sales. 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 sales levels, we must choose either the high level or the low level for our computations. Let’s choose the high level of activity, sixty seven thousand five hundred dollars in sales. Our first step is to calculate the total variable cost. At sixty seven thousand, five hundred dollars of sales, the total variable cost is point one seven per dollar of sales times sixty seven thousand, five hundred dollars, resulting in a total variable cost of eleven thousand, four hundred seventy five dollars. Next, we subtract eleven thousand, four hundred seventy-five dollars from the total cost at the high sales activity, to get the fixed cost, seventeen thousand, five hundred twenty-five dollars. You will obtain the same result if you select the low level of activity to compute fixed cost. Why don’t you compute fixed cost using the low level of sales activity before advancing to the next screen. You should wind up with the exact same result.

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High-Low Method Exercise 7

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**Least-Squares Regression**

P1 Least-squares regression is usually covered in advanced cost accounting courses. It is commonly used with spreadsheet programs or calculators. The objective of the cost analysis remains the same: determination of total fixed cost and the variable unit cost. If we have a large number of observations, we’ll probably want to use computer software that can do regression analysis to determine cost volume relationships. Excel is a wonderful tool to carry out this computation. You can review the chapter’s appendix if this of interest to you.

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**Computing Break-Even Point**

The break-even point (expressed in units of product or dollars of sales) is the sales level at which a company earns neither a profit nor incurs a loss. @ BEP => Total Sales = TC = TFC + TVC Now that we have improved our knowledge of cost behavior, we are ready to apply the concepts to break-even analysis. The break-even point is the level of sales where a company’s income is exactly equal to zero. At breakeven, total costs equal total revenues.

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**Computing Break-Even Point (Contribution Margin)**

We’re going to concentrate exclusively on the contribution format income statement for our break-even analysis. Contribution margin is the amount remaining after we deduct all our variable expenses from sales revenue. Contribution margin can be expressed as a total amount, sixty thousand dollars in this example, or as an amount per unit, thirty dollars in this example. Each unit sold contributes twenty dollars toward covering fixed costs and providing for profits. Contribution margin is amount by which revenue exceeds the variable costs of producing the revenue.

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**Computing Break-Even Point**

Part I Contribution margin goes to cover our fixed costs. If all our fixed costs are covered, the company will operate in the profit area. If we fail to cover our fixed expenses, we will operate in the loss area. How much contribution must this company have to cover its fixed costs? Part II Fixed costs are twenty-four thousand dollars, so this company must generate twenty-four thousand dollars in contribution margin to cover its fixed costs. When contribution margin is exactly twenty-four thousand dollars, the company’s sales are at breakeven as its income will be zero. How much contribution margin must this company have to cover its fixed costs (break even)? Answer: $24,000

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**Computing Break-Even Point**

Part I This company is earning thirty-six thousand dollars income by selling two thousand units. The breakeven point will obviously occur at a sales volume less than two thousand units. If each unit contributes thirty dollars to covering fixed costs, can you compute the number of units that must be sold to cover the twenty four thousand dollars in fixed costs and allow the company to breakeven? Part II We compute the break-even sales volume in units by dividing fixed costs by the unit contribution margin. How many units must this company sell to cover its fixed costs (break even)? Answer: $24,000 ÷ $30 per unit = 800 units

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**Computing Break-Even Point**

We have just seen one of the basic CVP relationships => the break-even computation. Break-even point in units = Fixed costs Contribution margin per unit The results of the previous question can be expressed in equation form as seen on your screen. The break-even point in units is equal to fixed costs divided by the unit contribution margin. Unit sales price less unit variable cost ($30 in previous example)

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**The break-even formula may also be expressed in sales dollars.**

Computing Break-Even Point P2 The break-even formula may also be expressed in sales dollars. Break-even point in dollars = Fixed costs Contribution margin ratio The break-even point in sales dollars is equal to fixed costs divided by the contribution margin ratio. The contribution margin ratio is equal to the the unit contribution divided by the unit sales price. In the earlier example, the contribution margin ratio is thirty percent, resulting from dividing the thirty dollars unit contribution margin by the one hundred dollars unit sales price. You might want to refer back to the example to verify these numbers. The contribution margin ratio tells us that thirty cents of each sales dollar contributes to covering fixed costs and providing for income. Unit contribution margin Unit sales price

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CVP Analysis Exercise 9

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**Preparing a CVP Chart (Exhibit 18.14, Page 764)**

Plot total fixed costs on the vertical axis. Total fixed costs Total costs Draw the total cost line with a slope equal to the unit variable cost. Costs and Revenue in Dollars The relationships between cost, volume and profit can also be shown in a graph. In this graph, we have plotted costs and revenues on the vertical axis and volume in units on the horizontal axis. The total cost line has a slope equal to the variable cost per unit and intercepts the vertical cost axis at the fixed cost. Volume in Units

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**Preparing a CVP Chart (Exhibit 18.14, Page 764)**

Starting at the origin, draw the sales line with a slope equal to the unit sales price. Sales Total fixed costs Costs and Revenue in Dollars Total costs When we add the sales line to our graph, we see the break even point where the sales line crosses the total cost line. The sales line begins at the origin and has a slope equal to the unit sales price. The sales line is steeper, that is increases at a faster rate than the total cost line, because because the unit sales price is greater than the unit variable cost. Break-even Point Volume in Units

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CVP Chart Exercise 9

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**Assumptions of CVP Analysis**

A limited range of activity called the relevant range, where CVP relationships are linear. Unit selling price remains constant. Unit variable costs remain constant. Total fixed costs remain constant. Production = sales (no inventory changes). There are some basic assumptions related to cost volume profit analysis that we are studying in this chapter. Some of these assumptions may be very restrictive. First, costs and revenues are assumed to be linear in nature, meaning that the selling price is assumed to be constant, the unit variable cost is assumed to be constant, and total fixed costs are assumed to be constant. Also, for manufacturing companies, inventories don’t increase or decrease during the period. All units produced, are sold.

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**Computing Income from Expected Sales**

Income (pretax) = Sales – Variable costs – Fixed costs We have seen what it takes for a company to breakeven, but we are not in business just to breakeven. Hopefully our business will earn an income. The break-even relationships that we have studied can be slightly altered to include income.

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**Computing Sales for a Target Income**

Break-even formulas may be adjusted to show the sales volume needed to earn any amount of income. Fixed costs + Target income Unit sales = We can adjust the break-even formulas that we used earlier to incorporate income. Recall that we calculated breakeven by dividing fixed costs by contribution. When we incorporate income, contribution must cover the fixed cost as well as provide for income. To adapt the break-even formulas for income, we add the desired amount of income to the numerator. Contribution margin per unit Fixed costs + Target income Dollar sales = Contribution margin ratio

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Exercise 10

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**Computing Sales (Dollars) for a Target Net Income**

Target net income is income after income tax. But we can use target income before tax in our calculations. Fixed Target income costs before tax + Our previous formulas allowed us to solve for sales necessary to earn a target income used pretax income. Pretax income which has two components, net income (after tax) and the income taxes paid on the pretax income are shown on your screen. Dollar sales = Contribution margin ratio

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**Computing Sales (Dollars) for a Target Net Income**

To convert target net income to before- tax income, use the following formula: Target net income Before-tax income = 1 - tax rate Net Income = Income before Tax - Tax Expense Tax Expense = Income before Tax * Tax Rate Therefore; Net Income = Income before Tax ( 1 - Tax Rate) => Income before Tax = Net Income / ( 1- Tax Rate) If our target income is stated as after-tax net income, we can covert to pretax income by dividing the target after-tax net income by one minus the tax rate.

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Exercise 11

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**Computing the Margin of Safety**

Margin of safety is the amount by which sales can drop before the company incurs a loss. Margin of safety equals excess of expected sales over sales at break-even sales level. Margin of safety may be expressed as a percentage of expected sales: Margin of safety Expected sales - Break-even sales percentage Expected sales = The margin of safety is the excess of expected sales (or actual sales) over the breakeven sales. It’s the amount by which expected sales can drop before the company begins to incur losses. We can also express the margin of safety as a percent of sales. The margin of safety percentage is equal to the margin of safety in dollars divided by the expected sales in dollars. Exhibit 18.24, page 768

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**Contribution margin Income Statement**

Exhibit 18.19, page 767: Pretax Exhibit 18.20, page 767: After tax

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Sensitivity Analysis The basic CVP relationships may be used to analyze a number of situations such as: -changing sales price, -changing variable cost, or -changing fixed cost. Exercise 12 Our basic assumptions related to cost volume profit analysis such as the selling price is assumed to be constant, the unit variable cost is assumed to be constant, and total fixed costs are assumed to be constant, can be restrictive.

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**Computing Multiproduct Break-Even Point**

The CVP formulas may be modified for use when a company sells more than one product: The unit contribution margin is replaced with the contribution margin for a composite unit. A composite unit is composed of specific numbers of each product in proportion to the product sales mix. Sales mix is the ratio of the volumes of the various products. To this point, we’ve assumed that a company sells a single product. We can extend the cost-volume-profit relationships to cover multiproduct companies. Instead of unit contribution margin for one unit, we will have a composite unit contribution for all units. The composite unit contribution margin is dependent on the sales mix of the products sold. .

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**Computing Multiproduct Break-Even Point**

The resulting break-even formula for composite unit sales is: Fixed costs Contribution margin per composite unit Break-even point in composite units = Note that the break-even formula looks the same for a multiproduct company. The only difference is the denominator. The unit contribution margin for one unit is replaced by a composite unit contribution for all units. A composite unit is composed of specific numbers of each product in proportion to the product sales mix.

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**Computing Multiproduct Break-Even Point**

To apply multiproduct CVP analysis, estimate break-even point by using a composite unit. -Determine sales mix of various products. -Using sales mix, determine the selling price of a composite unit by multiplying the sales mix ratio times the selling price of each product and then adding the totals for all of the products. -Compute the variable price of a composite unit in the same manner, and then determine the CM per composite unit. -Compute Break-even point in composite units; BEP equals total fixed costs divided by CM per composite unit. -To determine how many units of each product must be sold to break even, multiply the number of units of each product in the composite unit by the break-even point in composite units.

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Exercises 15 & 17

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**A measure of how a percentage change in sales will affect profits.**

Operating Leverage A measure of the extent to which fixed costs are being used in an organization. A measure of how a percentage change in sales will affect profits. Degree of operating leverage (DOL) is defined as total CM (in dollars) divided by pretax income. Operating leverage is an important concept for managers to understand. It’s a measure of how sensitive operating income is to changes in sales. When operating leverage is high, a small percentage increase in sales can result in a much larger percentage increase in operating income. The degree of operating leverage is equal to contribution margin divided by net income. Contribution margin Pretax income = Degree of operating leverage

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**Exercises 19 3 Steps: DOL is used to measure**

the effect of changes in the level of sales on pretax income by multiplying DOL by the percentage change in sales. A high DOL firm will experience a higher increase in pretax income due to increase in the level of sales. Exercises 19 3 Steps: -Prepare a CM Income Statement & calculate DOL for Co. A; -Prepare a CM Income Statement & calculate DOL for Co. B; -Analyze & interpret which company benefits more from a 20% sales increase; These cost, volume, profit analyses are some of the basic concepts and principles of managerial accounting. They are important ones for you to understand.

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McGraw-Hill/Irwin1 © The McGraw-Hill Companies, Inc., 2006 22-1 Cost-Volume- Profit Analysis Chapter 22.

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