The break even point can be expressed as sales in

Cost-Volume-Profit Analysis

Cost-Volume-Profit

 CHAPTER PREVIEW 

As the Feature Story indicates, to manage any size business you must understand how costs respond to changes in sales volume and the effect of costs and revenues on profits. A prerequisite to understanding cost‐volume‐profit (CVP) relationships is knowledge of how costs behave. In this chapter, we first explain the considerations involved in cost behavior analysis. Then, we discuss and illustrate CVP analysis.

Don't Worry—Just Get Big

It wasn't that Jeff Bezos didn't have a good job. He was a vice president at a Wall Street firm. But, he quit his job, moved to Seattle, and started an online retailer, which he named Amazon.com. Like any good entrepreneur, Jeff strove to keep his initial investment small. Operations were run out of his garage. And, to avoid the need for a warehouse, he took orders for books and had them shipped from other distributors' warehouses.

By its fourth month, Amazon was selling 100 books a day. In its first full year, it had $15.7 million in sales. The next year, sales increased eightfold. Two years later, sales were $1.6 billion.

Although its sales growth was impressive, Amazon's ability to lose money was equally amazing. One analyst nicknamed it Amazon.bomb, while another, predicting its demise, called it Amazon.toast. Why was it losing money? The company used every available dollar to reinvest in itself. It built massive warehouses and bought increasingly sophisticated (and expensive) computers and equipment to improve its distribution system. This desire to grow as fast as possible was captured in a T‐shirt slogan at its company picnic, which read “Eat another hot dog, get big fast.” This buying binge was increasing the company's fixed costs at a rate that exceeded its sales growth. Skeptics predicted that Amazon would soon run out of cash. It didn't.

In the fourth quarter of 2010 (only 15 years after its world headquarters was located in a garage), Amazon reported quarterly revenues of $12.95 billion and quarterly income of $416 million. But, even as it announced record profits, its share price fell by 9%. Why? Because although the company was predicting that its sales revenue in the next quarter would increase by at least 28%, it predicted that its operating profit would fall by at least 2% and perhaps by as much as 34%. The company made no apologies. It explained that it was in the process of expanding from 39 distribution centers to 52. As Amazon's finance chief noted, “You're not as productive on those assets for some time. I'm very pleased with the investments we're making and we've shown over our history that we've been able to make great returns on the capital we invest in.” In other words, eat another hot dog.

Sources: Christine Frey and John Cook, “How Amazon.com Survived, Thrived and Turned a Profit,” Seattle Post (January 28, 2008); and Stu Woo, “Sticker Shock Over Amazon Growth,” WallStreet Journal Online (January 28, 2011).

LEARNING OBJECTIVE 1

Explain variable, fixed, and mixed costs and the relevant range.

Cost behavior analysis is the study of how specific costs respond to changes in the level of business activity. As you might expect, some costs change, and others remain the same. For example, for an airline company such as Southwest or United, the longer the flight, the higher the fuel costs. On the other hand, Massachusetts General Hospital's costs to staff the emergency room on any given night are relatively constant regardless of the number of patients treated. A knowledge of cost behavior helps management plan operations and decide between alternative courses of action. Cost behavior analysis applies to all types of entities.

The starting point in cost behavior analysis is measuring the key business activities. Activity levels may be expressed in terms of sales dollars (in a retail company), miles driven (in a trucking company), room occupancy (in a hotel), or dance classes taught (by a dance studio). Many companies use more than one measurement base. A manufacturer, for example, may use direct labor hours or units of output for manufacturing costs, and sales revenue or units sold for selling expenses.

For an activity level to be useful in cost behavior analysis, changes in the level or volume of activity should be correlated with changes in costs. The activity level selected is referred to as the activity (or volume) index. The activity index identifies the activity that causes changes in the behavior of costs. With an appropriate activity index, companies can classify the behavior of costs in response to changes in activity levels into three categories: variable, fixed, or mixed.

VARIABLE COSTS

Variable costs are costs that vary in total directly and proportionately with changes in the activity level. If the level increases 10%, total variable costs will increase 10%. If the level of activity decreases by 25%, variable costs will decrease 25%. Examples of variable costs include direct materials and direct labor for a manufacturer; cost of goods sold, sales commissions, and freight‐out for a merchandiser; and gasoline in airline and trucking companies. A variable cost may also be defined as a cost that remains the same per unit at every level of activity.

To illustrate the behavior of a variable cost, assume that Damon Company manufactures tablet computers that contain $10 cameras. The activity index is the number of tablet computers produced. As Damon manufactures each tablet, the total cost of cameras used increases by $10. As part (a) of Illustration 18-1 shows, total cost of the cameras will be $20,000 if Damon produces 2,000 tablets, and $100,000 when it produces 10,000 tablets. We also can see that a variable cost remains the same per unit as the level of activity changes. As part (b) of Illustration 18-1 shows, the unit cost of $10 for the cameras is the same whether Damon produces 2,000 or 10,000 tablets.

ILLUSTRATION 18-1 Behavior of total and unit variable costs

Companies that rely heavily on labor to manufacture a product, such as Nike or Reebok, or to perform a service, such as Hilton or Marriott, are likely to have many variable costs. In contrast, companies that use a high proportion of machinery and equipment in producing revenue, such as AT&T or Duke Energy Co., may have few variable costs.

▼ HELPFUL HINT

Variable costs per unit remain constant at all levels of activity.

FIXED COSTS

Fixed costs are costs that remain the same in total regardless of changes in the activity level. Examples include property taxes, insurance, rent, supervisory salaries, and depreciation on buildings and equipment. Because total fixed costs remain constant as activity changes, it follows that fixed costs per unit vary inversely with activity: As volume increases, unit cost declines, and vice versa.

To illustrate the behavior of fixed costs, assume that Damon Company leases its productive facilities at a cost of $10,000 per month. Total fixed costs of the facilities will remain constant at every level of activity, as part (a) of Illustration 18-2 shows. But, on a per unit basis, the cost of rent will decline as activity increases, as part (b) of Illustration 18-2 shows. At 2,000 units, the unit cost per tablet computer is $5 ($10,000÷2,000)$5 ($10,000÷2,000). When Damon produces 10,000 tablets, the unit cost of the rent is only $1 per tablet ($10,000÷10,000)($10,000÷10,000).

ILLUSTRATION 18-2 Behavior of total and unit fixed costs

The trend for many manufacturers is to have more fixed costs and fewer variable costs. This trend is the result of increased use of automation and less use of employee labor. As a result, depreciation and lease charges (fixed costs) increase, whereas direct labor costs (variable costs) decrease.

 PEOPLE, PLANET, AND PROFIT INSIGHT 

BrightFarms

Gardens in the Sky

© Jani Bryson/iStockphoto

Because of population increases, the United Nations' Food and Agriculture Organization estimates that food production will need to increase by 70% by 2050. Also, by 2050, roughly 70% of people will live in cities, which means more food needs to be hauled further to get it to the consumer. To address the lack of farmable land and reduce the cost of transporting produce, some companies, such as New York‐based BrightFarms, are building urban greenhouses.

This sounds great, but do the numbers work? Some variable costs would be reduced. For example, the use of pesticides, herbicides, fuel costs for shipping, and water would all drop. Soil erosion would be a non‐issue since plants would be grown hydroponically (in a solution of water and minerals), and land requirements would be reduced because of vertical structures. But, other costs would be higher. First, there is the cost of the building. Also, any multistory building would require artificial lighting for plants on lower floors.

Until these cost challenges can be overcome, it appears that these urban greenhouses may not break even. On the other hand, rooftop greenhouses on existing city structures already appear financially viable. For example, a 15,000 square‐foot rooftop greenhouse in Brooklyn already produces roughly 30 tons of vegetables per year for local residents.

Sources: “Vertical Farming: Does It Really Stack Up?” The Economist (December 9, 2010); and Jane Black, “BrightFarms Idea: Greenhouses That Cut Short the Path from Plant to Grocery Shelf,” The Washington Post (May 7, 2013).

What are some of the variable and fixed costs that are impacted by hydroponic farming? (Go to WileyPLUS for this answer and additional questions.)

RELEVANT RANGE

In Illustration 18-1 part (a) (page 884), a straight line is drawn throughout the entire range of the activity index for total variable costs. In essence, the assumption is that the costs are linear. If a relationship is linear (that is, straight‐line), then changes in the activity index will result in a direct, proportional change in the variable cost. For example, if the activity level doubles, the cost doubles.

It is now necessary to ask: Is the straight‐line relationship realistic? In most business situations, a straight‐line relationship does not exist for variable costs throughout the entire range of possible activity. At abnormally low levels of activity, it may be impossible to be cost‐efficient. Small‐scale operations may not allow the company to obtain quantity discounts for raw materials or to use specialized labor. In contrast, at abnormally high levels of activity, labor costs may increase sharply because of overtime pay. Also, at high activity levels, materials costs may jump significantly because of excess spoilage caused by worker fatigue.

As a result, in the real world, the relationship between the behavior of a variable cost and changes in the activity level is often curvilinear, as shown in part (a) of Illustration 18-3 . In the curved sections of the line, a change in the activity index will not result in a direct, proportional change in the variable cost. That is, a doubling of the activity index will not result in an exact doubling of the variable cost. The variable cost may more than double, or it may be less than double.

ILLUSTRATION 18-3 Nonlinear behavior of variable and fixed costs

Total fixed costs also do not have a straight‐line relationship over the entire range of activity. Some fixed costs will not change. But it is possible for management to change other fixed costs. For example, in some instances, salaried employees (fixed) are replaced with freelance workers (variable). Illustration 18-3 , part (b), shows an example of the behavior of total fixed costs through all potential levels of activity.

▼ HELPFUL HINT

Fixed costs that may be changeable include research, such as new product development, and management training programs.

For most companies, operating at almost zero or at 100% capacity is the exception rather than the rule. Instead, companies often operate over a somewhat narrower range, such as 40–80% of capacity. The range over which a company expects to operate during a year is called the relevant range of the activity index. Within the relevant range, as both diagrams in Illustration 18-4 show, a straight‐line relationship generally exists for both variable and fixed costs.

ILLUSTRATION 18-4 Linear behavior within relevant range

As you can see, although the linear (straight‐line) relationship may not be completely realistic, the linear assumption produces useful data for CVP analysis as long as the level of activity remains within the relevant range.

ALTERNATIVE TERMINOLOGY

The relevant range is also called the normal or practical range.

MIXED COSTS

Mixed costs are costs that contain both a variable‐ and a fixed‐cost element. Mixed costs, therefore, change in total but not proportionately with changes in the activity level.

The rental of a U‐Haul truck is a good example of a mixed cost. Assume that local rental terms for a 17‐foot truck, including insurance, are $50 per day plus 50 cents per mile. When determining the cost of a one‐day rental, the per day charge is a fixed cost (with respect to miles driven), whereas the mileage charge is a variable cost. The graphic presentation of the rental cost for a one‐day rental is shown in Illustration 18-5 (page 888).

ILLUSTRATION 18-5 Behavior of a mixed cost

In this case, the fixed‐cost element is the cost of having the service available. The variable‐cost element is the cost of actually using the service. Utility costs such as for electricity are another example of a mixed cost. Each month the electric bill includes a flat service fee plus a usage charge.

DO IT! 1

Types of Costs

Helena Company reports the following total costs at two levels of production.

10,000 Units

20,000 Units

Direct materials

$20,000

$40,000

Maintenance

  8,000

 10,000

Direct labor

 17,000

 34,000

Indirect materials

  1,000

  2,000

Depreciation

  4,000

  4,000

Utilities

  3,000

  5,000

Rent

  6,000

  6,000

Classify each cost as variable, fixed, or mixed.

Action Plan

✓ Recall that a variable cost varies in total directly and proportionately with each change in activity level.

✓ Recall that a fixed cost remains the same in total with each change in activity level.

✓ Recall that a mixed cost changes in total but not proportionately with each change in activity level.

SOLUTION

Direct materials, direct labor, and indirect materials are variable costs.

Depreciation and rent are fixed costs.

Maintenance and utilities are mixed costs.

Related exercise material: BE18-1, BE18-2, E18-1, E18-2, E18-4, E18-6, and DO IT! 18-1.

LEARNING OBJECTIVE 2

Apply the high‐low method to determine the components of mixed costs.

For purposes of cost‐volume‐profit analysis, mixed costs must be classified into their fixed and variable elements. How does management make the classification? One possibility is to determine the variable and fixed components each time a mixed cost is incurred. But because of time and cost constraints, this approach is rarely followed. Instead, the usual approach is to collect data on the behavior of the mixed costs at various levels of activity. Analysts then identify the fixed‐ and variable‐cost components. Companies use various types of analysis. One type of analysis, called the high‐low method, is discussed next.

HIGH‐LOW METHOD

The high‐low method uses the total costs incurred at the high and low levels of activity to classify mixed costs into fixed and variable components. The difference in costs between the high and low levels represents variable costs, since only the variable‐cost element can change as activity levels change.

The steps in computing fixed and variable costs under this method are as follows.

1. Determine variable cost per unit from the following formula.

Change in Total Costs÷High minus Low Activity Level=Variable Cost per UnitChange in Total Costs÷High minus Low Activity Level=Variable Cost per Unit

ILLUSTRATION 18-6 Formula for variable cost per unit using high‐low method

To illustrate, assume that Metro Transit Company has the following maintenance costs and mileage data for its fleet of buses over a 6‐month period.

 Month 

Miles Driven

Total Cost

January

20,000

$30,000

February

40,000

 48,000

March

35,000

 49,000

April

50,000

$63,000

May

30,000

 42,000

June

43,000

 61,000

ILLUSTRATION 18-7 Assumed maintenance costs and mileage data

The high and low levels of activity are 50,000 miles in April and 20,000 miles in January. The maintenance costs at these two levels are $63,000 and $30,000, respectively. The difference in maintenance costs is $33,000 ($63,000−$30,000)$33,000 ($63,000−$30,000), and the difference in miles is 30,000 (50,000−20,000)30,000 (50,000−20,000). Therefore, for Metro Transit, variable cost per unit is $1.10, computed as follows.

$33,000÷30,000=$1.10$33,000÷30,000=$1.10

2. Determine the fixed costs by subtracting the total variable costs at either the high or the low activity level from the total cost at that activity level.

For Metro Transit, the computations are shown in Illustration 18-8 .

ILLUSTRATION 18-8 High‐low method computation of fixed costs

Maintenance costs are therefore $8,000 per month of fixed costs plus $1.10 per mile of variable costs. This is represented by the following formula:

Maintenance costs=$8,000+($1.10×Miles driven)Maintenance costs=$8,000+($1.10×Miles driven)

For example, at 45,000 miles, estimated maintenance costs would be $8,000 fixed and $49,500 variable ($1.10×45,000)($1.10×45,000) for a total of $57,500.

The graph in Illustration 18-9 plots the 6‐month data for Metro Transit Company. The red line drawn in the graph connects the high and low data points, and therefore represents the equation that we just solved using the high‐low method. The red, “high‐low” line intersects the y‐axis at $8,000 (the fixed‐cost level), and it rises by $1.10 per unit (the variable cost per unit). Note that a completely different line would result if we chose any two of the other data points. That is, by choosing any two other data points, we would end up with a different estimate of fixed costs and a different variable cost per unit. Thus, from this scatter plot, we can see that while the high‐low method is simple, the result is rather arbitrary. A better approach, which uses information from all the data points to estimate fixed and variable costs, is called regression analysis. A discussion of regression analysis is provided in a supplement on the book's companion website.

ILLUSTRATION 18-9 Scatter plot for Metro Transit Company

 MANAGEMENT INSIGHT 

Tempur Sealy International

Skilled Labor Is Truly Essential

Bloomberg/Getty Images

The recent recession had devastating implications for employment. But one surprise was that for some manufacturers, the number of jobs lost was actually lower than in previous recessions. One of the main explanations for this was that in the years preceding the recession, many companies, such as Tempur Sealy International, adopted lean manufacturing practices. This meant that production relied less on large numbers of low‐skilled workers and more on machines and a few highly skilled workers. As a result of this approach, a single employee supports far more dollars in sales. Thus, it requires a larger decline in sales before an employee would need to be laid‐off in order for the company to continue to break even. Also, because the employees are highly skilled, employers are reluctant to lose them. Instead of lay‐offs, many manufacturers now resort to cutting employees' hours when necessary.

Source: Timothy Aeppel and Justin Lahart, “Lean Factories Find It Hard to Cut Jobs Even in a Slump,” Wall Street Journal Online (March 9, 2009).

Would you characterize labor costs as being a fixed cost, a variable cost, or something else in this situation? (Go to WileyPLUS for this answer and additional questions.)

IMPORTANCE OF IDENTIFYING VARIABLE AND FIXED COSTS

Why is it important to segregate mixed costs into variable and fixed elements? The answer may become apparent if we look at the following four business decisions.

1. If American Airlines is to make a profit when it reduces all domestic fares by 30%, what reduction in costs or increase in passengers will be required?

Answer: To make a profit when it cuts domestic fares by 30%, American Airlines will have to increase the number of passengers or cut its variable costs for those flights. Its fixed costs will not change.

2. If Ford Motor Company meets workers' demands for higher wages, what increase in sales revenue will be needed to maintain current profit levels?

Answer: Higher wages at Ford Motor Company will increase the variable costs of manufacturing automobiles. To maintain present profit levels, Ford will have to cut other variable costs or increase the price of its automobiles.

3. If United States Steel Corp.'s program to modernize plant facilities through significant equipment purchases reduces the work force by 50%, what will be the effect on the cost of producing one ton of steel?

Answer: The modernizing of plant facilities at United States Steel Corp. changes the proportion of fixed and variable costs of producing one ton of steel. Fixed costs increase because of higher depreciation charges, whereas variable costs decrease due to the reduction in the number of steelworkers.

4. What happens if Kellogg's increases its advertising expenses but cannot increase prices because of competitive pressure?

Answer: Sales volume must be increased to cover the increase in fixed advertising costs.

DO IT! 2

High‐Low Method

Byrnes Company accumulates the following data concerning a mixed cost, using units produced as the activity level.

Units Produced

Total Cost

March

9,800

$14,740

April

8,500

 13,250

May

7,000

 11,100

June

7,600

 12,000

July

8,100

 12,460

(a) Compute the variable‐cost and fixed‐cost elements using the high‐low method.

(b) Estimate the total cost if the company produces 8,000 units.

Action Plan

✓ Determine the highest and lowest levels of activity.

✓ Compute variable cost per unit as Change in total costs÷(High−low activity level)=Variable cost per unitChange in total costs÷(High−low activity level)=Variable cost per unit.

✓ Compute fixed cost as Total cost−(Variable cost per unit×Units produced)=Fixed costTotal cost−(Variable cost per unit×Units produced)=Fixed cost.

SOLUTION

(a) Variable cost: ($14,740−$11,100)÷(9,800−7,000)=$1.30 per unit($14,740−$11,100)÷(9,800−7,000)=$1.30 per unit

Fixed cost: $14,740−$12,740*=$2,000$14,740−$12,740*=$2,000 or $11,100−$9,100**=$2,000$11,100−$9,100**=$2,000

* $1.30×9,800 units$1.30×9,800 units

** $1.30×7,000 units$1.30×7,000 units

(b) Total cost to produce 8,000 units: $2,000+$10,400 ($1.30×8,000 units)=$12,400$2,000+$10,400 ($1.30×8,000 units)=$12,400

Related exercise material: BE18-3, BE18-4, BE18-5, E18-3, E18-5, and DO IT! 18-2.

LEARNING OBJECTIVE 3

Prepare a CVP income statement to determine contribution margin.

Cost‐volume‐profit (CVP) analysis is the study of the effects of changes in costs and volume on a company's profits. CVP analysis is important in profit planning. It also is a critical factor in such management decisions as setting selling prices, determining product mix, and maximizing use of production facilities.

BASIC COMPONENTS

CVP analysis considers the interrelationships among the components shown in Illustration 18-10 .

ILLUSTRATION 18-10 Components of CVP analysis

The following assumptions underlie each CVP analysis.

1. The behavior of both costs and revenues is linear throughout the relevant range of the activity index.

2. Costs can be classified accurately as either variable or fixed.

3. Changes in activity are the only factors that affect costs.

4. All units produced are sold.

5. When more than one type of product is sold, the sales mix will remain constant. That is, the percentage that each product represents of total sales will stay the same. Sales mix complicates CVP analysis because different products will have different cost relationships. In this chapter, we assume a single product. In Chapter 19 , however, we examine the sales mix more closely.

When these assumptions are not valid, the CVP analysis may be inaccurate.

CVP INCOME STATEMENT

Because CVP is so important for decision‐making, management often wants this information reported in a cost‐volume‐profit (CVP) income statement format for internal use. The CVP income statement classifies costs as variable or fixed and computes a contribution margin. Contribution margin (CM) is the amount of revenue remaining after deducting variable costs. It is often stated both as a total amount and on a per unit basis.

We will use Vargo Video Company to illustrate a CVP income statement. Vargo Video produces a high‐definition digital camcorder with 15× optical zoom and a wide‐screen, high‐resolution LCD monitor. Relevant data for the camcorders sold by this company in June 2017 are as follows.

Unit selling price of camcorder

$500

Unit variable costs

$300

Total monthly fixed costs

$200,000

Units sold

1,600

ILLUSTRATION 18-11 Assumed selling and cost data for Vargo Video

The CVP income statement for Vargo therefore would be reported as follows.

VARGO VIDEO COMPANY

CVP Income Statement

For the Month Ended June 30, 2017

  Total  

Sales (1,600 camcorders)

$ 800,000

Variable costs

  480,000

Contribution margin

 320,000

Fixed costs

  200,000

Net income

$120,000

ILLUSTRATION 18-12 CVP income statement, with net income

A traditional income statement and a CVP income statement both report the same net income of $120,000. However, a traditional income statement does not classify costs as variable or fixed, and therefore it does not report a contribution margin. In addition, sometimes per unit amounts and percentage of sales amounts are shown in separate columns on a CVP income statement to facilitate CVP analysis. Homework assignments specify which columns to present.

In the applications of CVP analysis that follow, we assume that the term “cost” includes all costs and expenses related to production and sale of the product. That is, cost includes manufacturing costs plus selling and administrative expenses.

DECISION TOOLS

The unit contribution margin indicates by how much every unit sold will increase income.

Unit Contribution Margin

The formula for unit contribution margin and the computation for Vargo Video are as follows.

Unit Selling Price−Unit Variable Costs=Unit Contribution Margin$500−$300=$200Unit Selling Price−Unit Variable Costs=Unit Contribution Margin$500−$300=$200

ILLUSTRATION 18-13 Formula for unit contribution margin

Unit contribution margin indicates that for every camcorder sold, the selling price exceeds the variable costs by $200. Vargo generates $200 per unit sold to cover fixed costs and contribute to net income. Because Vargo has fixed costs of $200,000, it must sell 1,000 camcorders ($200,000÷$200)($200,000÷$200) to cover its fixed costs.

At the point where total contribution margin exactly equals fixed costs, Vargo will report net income of zero. At this point, referred to as the break‐even point , total costs (variable plus fixed) exactly equal total revenue. Illustration 18-14 shows Vargo's CVP income statement at the point where net income equals zero. It shows a contribution margin of $200,000, and a unit contribution margin of $200 ($500−$300)$200 ($500−$300).

VARGO VIDEO COMPANY

CVP Income Statement

For the Month Ended June 30, 2017

  Total  

Per Unit

Sales (1,000 camcorders)

$  500,000

$ 500 

Variable costs

  300,000

  300 

Contribution margin

  200,000

$200 

Fixed costs

  200,000

Net income

$  –0–  

ILLUSTRATION 18-14 CVP income statement, with zero net income

It follows that for every camcorder sold above the break‐even point of 1,000 units, net income increases by the amount of the unit contribution margin, $200. For example, assume that Vargo sold one more camcorder, for a total of 1,001 camcorders sold. In this case, Vargo reports net income of $200, as shown in Illustration 18-15 .

VARGO VIDEO COMPANY

CVP Income Statement

For the Month Ended June 30, 2017

  Total  

Per Unit

Sales (1,001camcorders)

$500,500

$500

Variable costs

 300,300

 300

Contribution margin

 200,200

$200

Fixed costs

 200,000

Net income

$    200

ILLUSTRATION 18-15 CVP income statement, with net income and per unit data

Contribution Margin Ratio

Some managers prefer to use a contribution margin ratio in CVP analysis. The contribution margin ratio is the contribution margin expressed as a percentage of sales, as shown in Illustration 18-16 .

VARGO VIDEO COMPANY

CVP Income Statement

For the Month Ended June 30, 2017

  Total  

Per Unit

Sales (1,001 camcorders)

$500,500

100%

Variable costs

 300,300

 60 

Contribution margin

200,200

 40%

Fixed costs

 200,000

Net income

$    200

ILLUSTRATION 18-16 CVP income statement, with net income and percent of sales data

DECISION TOOLS

The contribution margin ratio indicates by how much every dollar of sales will increase income.

Alternatively, the contribution margin ratio can be determined by dividing the unit contribution margin by the unit selling price. For Vargo Video, the ratio is as follows.

Unit Contribution Margin÷Unit Selling Price=Contribution Margin Ratio$200÷$500=40%Unit Contribution Margin÷Unit Selling Price=Contribution Margin Ratio$200÷$500=40%

ILLUSTRATION 18-17 Formula for contribution margin ratio

The contribution margin ratio of 40% means that Vargo generates 40 cents of contribution margin with each dollar of sales. That is, $0.40 of each sales dollar (40%×$1)(40%×$1) is available to apply to fixed costs and to contribute to net income.

This expression of contribution margin is very helpful in determining the effect of changes in sales on net income. For example, if Vargo's sales increase $100,000, net income will increase $40,000 (40%×$100,000)$40,000 (40%×$100,000). Thus, by using the contribution margin ratio, managers can quickly determine increases in net income from any change in sales.

We can also see this effect through a CVP income statement. Assume that Vargo’s current sales are $500,000 and it wants to know the effect of a $100,000 (200‐unit) increase in sales. Vargo prepares a comparative CVP income statement analysis as follows.

VARGO VIDEO COMPANY

CVP Income Statements

For the Month Ended June 30, 2017

No Change

With Change

Total

Per Unit

Percent of Sales

Total

Per Unit

Percent of Sales

Sales

$ 500,000

$500

100%

$600,000

$500

100%

Variable costs

 300,000

 300

 60  

 360,000

 300

 60  

Contribution margin

200,000

$200

 40%

240,000

$200

 40%

Fixed costs

 200,000

 200,000

Net income

$  –0–  

$40,000

ILLUSTRATION 18-18 Comparative CVP income statements

The $40,000 increase in net income can be calculated on either a unit contribution margin basis (200 units×$200 per unit)(200 units×$200 per unit) or using the contribution margin ratio times the increase in sales dollars (40%×$100,000)(40%×$100,000). Note that the unit contribution margin and contribution margin as a percentage of sales remain unchanged by the increase in sales.

Study these CVP income statements carefully. The concepts presented in these statements are used extensively in this and later chapters.

DO IT! 3

CVP Income Statement

Ampco Industries produces and sells a cell phone‐operated thermostat. Information regarding the costs and sales of thermostats during September 2017 are provided below.

Unit selling price of thermostat

$85

Unit variable costs

$32

Total monthly fixed costs

$190,000

Units sold

4,000

Prepare a CVP income statement for Ampco Industries for the month of September. Provide per unit values and total values.

Action Plan

✓ Provide a heading with the name of the company, name of statement, and period covered.

✓ Subtract variable costs from sales to determine contribution margin. Subtract fixed costs from contribution margin to determine net income.

✓ Express sales, variable costs and contribution margin on a per unit basis.

SOLUTION

AMPCO INDUSTRIES

CVP Income Statement

For the Month Ended September 30, 2017

 Total 

Per Unit

Sales

$340,000

$85

Variable costs

 128,000

 32

Contribution margin

212,000

$53

Fixed costs

 190,000

Net income

$ 22,000

Related exercise material: BE18-6, BE18-7, E18-7, and DO IT! 18-3.

LEARNING OBJECTIVE 4

Compute the break‐even point using three approaches.

A key relationship in CVP analysis is the level of activity at which total revenues equal total costs (both fixed and variable)—the break‐even point. At this volume of sales, the company will realize no income but will suffer no loss. The process of finding the break‐even point is called break‐even analysis. Knowledge of the break‐even point is useful to management when it considers decisions such as whether to introduce new product lines, change sales prices on established products, or enter new market areas.

The break‐even point can be:

1. Computed from a mathematical equation.

2. Computed by using contribution margin.

3. Derived from a cost‐volume‐profit (CVP) graph.

The break‐even point can be expressed either in sales units or sales dollars.

DECISION TOOLS

Break‐even analysis indicates the amount of sales units or sales dollars that a company needs to cover its costs.

MATHEMATICAL EQUATION

The first line of Illustration 18-19 shows a common equation used for CVP analysis. When net income is set to zero, this equation can be used to calculate the break‐even point.

Required Sales−Variable Costs−Fixed Costs=Net Income$500Q−$300Q−$200,000=$0Required Sales−Variable Costs−Fixed Costs=Net Income$500Q−$300Q−$200,000=$0

ILLUSTRATION 18-19 Basic CVP equation

As shown in Illustration 18-14 (page 893), net income equals zero when the contribution margin (sales minus variable costs) is equal to fixed costs.

To reflect this, Illustration 18-20 rewrites the equation with contribution margin (sales minus variable costs) on the left side, and fixed costs and net income on the right. We can compute the break‐even point in units by using unit selling prices and unit variable costs. The computation for Vargo Video is as follows.

Required Sales−Variable Costs−Fixed Costs=Net Income$500Q −$300Q−$200,000=$0$500Q −$300Q=$200,000+$0$200Q=$200,000Required Sales−Variable Costs−Fixed Costs=Net Income$500Q −$300Q−$200,000=$0$500Q −$300Q=$200,000+$0$200Q=$200,000 Q=$200,000$200=Fixed CostsUnit Contribution MarginQ=1,000 unitswhereQ=sales volume in units$500=selling price$300=variable costs per unit$200,000=total fixed costsQ=$200,000$200=Fixed CostsUnit Contribution MarginQ=1,000 unitswhereQ=sales volume in units$500=selling price$300=variable costs per unit$200,000=total fixed costs

ILLUSTRATION 18-20 Computation of break‐even point in units

Thus, Vargo must sell 1,000 units to break even.

To find the amount of sales dollars required to break even, we multiply the units sold at the break‐even point times the selling price per unit, as shown below.

1,000×$500=$500,000 (break‐even sales dollars)1,000×$500=$500,000 (break‐even sales dollars)

CONTRIBUTION MARGIN TECHNIQUE

Many managers employ the contribution margin to compute the break‐even point.

Contribution Margin in Units

The final step in Illustration 18-20 divides fixed costs by the unit contribution margin (highlighted in red). Thus, rather than walk through all of the steps of the equation approach, we can simply employ this formula shown in Illustration 18-21 .

Fixed Costs÷Unit Contribution Margin=Break-Even Point in Units$200,000÷$200=1,000 unitsFixed Costs÷Unit Contribution Margin=Break-Even Point in Units$200,000÷$200=1,000 units

ILLUSTRATION 18-21 Formula for break‐even point in units using unit contribution margin

Why does this formula work? The unit contribution margin is the net amount by which each sale exceeds the variable costs per unit. Every sale generates this much money to pay off fixed costs. Consequently, if we divide fixed costs by the unit contribution margin, we know how many units we need to sell to break even.

Contribution Margin Ratio

As we will see in the next chapter, when a company has numerous products, it is not practical to determine the unit contribution margin for each product. In this case, using the contribution margin ratio is very useful for determining the break‐even point in total dollars (rather than units). Recall that the contribution margin ratio is the percentage of each dollar of sales that is available to cover fixed costs and generate net income. Therefore, to determine the sales dollars needed to cover fixed costs, we divide fixed costs by the contribution margin ratio, as shown in Illustration 18-22 .

Fixed Costs÷Contribution Margin Ratio=Break-Even Point in Dollars$200,000÷40%=$500,000Fixed Costs÷Contribution Margin Ratio=Break-Even Point in Dollars$200,000÷40%=$500,000

ILLUSTRATION 18-22 Formula for break‐even point in dollars using contribution margin ratio

To apply this formula to Vargo Video, consider that its 40% contribution margin ratio means that for every dollar sold, it generates 40 cents of contribution margin. The question is, how many dollars of sales does Vargo need in order to generate total contribution margin of $200,000 to pay off fixed costs? We divide the fixed costs of $200,000 by the 40 cents of contribution margin generated by each dollar of sales to arrive at $500,000 ($200,000÷40%)$500,000 ($200,000÷40%). To prove this result, if we generate 40 cents of contribution margin for each dollar of sales, then the total contribution margin generated by $500,000 in sales is $200,000 ($500,000÷40%)$200,000 ($500,000÷40%).

 SERVICE COMPANY INSIGHT

Flightserve

Charter Flights Offer a Good Deal

Digital Vision/Getty Images

The Internet is wringing inefficiencies out of nearly every industry. While commercial aircraft spend roughly 4,000 hours a year in the air, chartered aircraft are flown only 500 hours annually. That means that they are sitting on the ground—not making any money—about 90% of the time. One company, Flightserve, saw a business opportunity in that fact. For about the same cost as a first‐class ticket, Flightserve matches up executives with charter flights in small “private jets.” The executive gets a more comfortable ride and avoids the hassle of big airports. Flightserve noted that the average charter jet has eight seats. When all eight seats are full, the company has an 80% profit margin. It breaks even at an average of 3.3 full seats per flight.

Source: “Jet Set Go,” The Economist (March 18, 2000), p. 68.

How did Flightserve determine that it would break even with 3.3 seats full per flight? (Go to WileyPLUS for this answer and additional questions.)

GRAPHIC PRESENTATION

An effective way to find the break‐even point is to prepare a break‐even graph. Because this graph also shows costs, volume, and profits, it is referred to as a cost‐volume‐profit (CVP) graph .

As the CVP graph in Illustration 18-23 shows, sales volume is recorded along the horizontal axis. This axis should extend to the maximum level of expected sales. Both total revenues (sales) and total costs (fixed plus variable) are recorded on the vertical axis.

ILLUSTRATION 18-23 CVP graph

The construction of the graph, using the data for Vargo Video, is as follows.

1. Plot the sales line, starting at the zero activity level. For every camcorder sold, total revenue increases by $500. For example, at 200 units, sales are $100,000. At the upper level of activity (1,800 units), sales are $900,000. The revenue line is assumed to be linear through the full range of activity.

2. Plot the total fixed costs using a horizontal line. For the camcorders, this line is plotted at $200,000. The fixed costs are the same at every level of activity.

3. Plot the total‐cost line. This starts at the fixed‐cost line at zero activity. It increases by the variable costs at each level of activity. For each camcorder, variable costs are $300. Thus, at 200 units, total variable costs are $60,000 ($300×200)$60,000 ($300×200) and the total cost is $260,000 ($60,000+$200,000)$260,000 ($60,000+$200,000). At 1,800 units, total variable costs are $540,000($300×1,800)$540,000($300×1,800) and total cost is $740,000 ($540,000+$200,000)$740,000 ($540,000+$200,000). On the graph, the amount of the variable costs can be derived from the difference between the total‐cost and fixed‐cost lines at each level of activity.

4. Determine the break‐even point from the intersection of the total‐cost line and the sales line. The break‐even point in dollars is found by drawing a horizontal line from the break‐even point to the vertical axis. The break‐even point in units is found by drawing a vertical line from the break‐even point to the horizontal axis. For the camcorders, the break‐even point is $500,000 of sales, or 1,000 units. At this sales level, Vargo will cover costs but make no profit.

The CVP graph also shows both the net income and net loss areas. Thus, the amount of income or loss at each level of sales can be derived from the sales and total‐cost lines.

A CVP graph is useful because the effects of a change in any element in the CVP analysis can be quickly seen. For example, a 10% increase in selling price will change the location of the sales line. Likewise, the effects on total costs of wage increases can be quickly observed.

DO IT! 4

Break‐Even Analysis

Lombardi Company has a unit selling price of $400, variable costs per unit of $240, and fixed costs of $180,000. Compute the break‐even point in units using (a) a mathematical equation and (b) unit contribution margin.

Action Plan

✓ Apply the formula: Sales−Variable costs−Fixed costs=Net incomeSales−Variable costs−Fixed costs=Net income.

✓ Apply the formula: Fixed costs÷Unit contribution margin=Break‐even point in unitsFixed costs÷Unit contribution margin=Break‐even point in units.

SOLUTION

(a) The equation is $400Q−$240Q−$180,000=$0;($400Q−$240Q)=$180,000$400Q−$240Q−$180,000=$0;($400Q−$240Q)=$180,000. The break‐even point in units is 1,125.

(b) The unit contribution margin is $160 ($400−$240)$160 ($400−$240). The formula therefore is $180,000÷$160$180,000÷$160, and the break‐even point in units is 1,125.

Related exercise material: BE18-8, BE18-9, E18-8, E18-9, E18-10, E18-11, E18-12, E18-13, E18-16, and DO IT! 18-4..

LEARNING OBJECTIVE 5

Determine the sales required to earn target net income and determine margin of safety.

TARGET NET INCOME

Rather than simply “breaking even,” management usually sets an income objective often called target net income . It then determines the sales necessary to achieve this specified level of income. Companies determine the sales necessary to achieve target net income by using one of the three approaches discussed earlier.

Mathematical Equation

We know that at the break‐even point no profit or loss results for the company. By adding an amount for target net income to the same basic equation, we obtain the following formula for determining required sales.

Required Sales−Variable Costs−Fixed Costs=Target Net IncomeRequired Sales−Variable Costs−Fixed Costs=Target Net Income

ILLUSTRATION 18-24 Formula for required sales to meet target net income

Recall that once the break‐even point has been reached so that fixed costs are covered, each additional unit sold increases net income by the amount of the unit contribution margin. We can rewrite the equation with contribution margin (required sales minus variable costs) on the left‐hand side, and fixed costs and target net income on the right. Assuming that target net income is $120,000 for Vargo Video, the computation of required sales in units is as shown in Illustration 18-25 (page 900).

Required Sales−Variable Costs−Fixed Costs=Target Net Income$500Q−$300Q−$200,000=$120,000$500Q−$300Q=$200,000+$120,000Required Sales−Variable Costs−Fixed Costs=Target Net Income$500Q−$300Q−$200,000=$120,000$500Q−$300Q=$200,000+$120,000 $200Q=$200,000+120,000Q=$200,000+120,000$200=Fixed Costs+Target Net IncomeUnit Contribution MarginQ=1,600whereQ=sales volume$500=selling price$300=variable costs per unit$200,000=total fixed costs$120,000=target net income$200Q=$200,000+120,000Q=$200,000+120,000$200=Fixed Costs+Target Net IncomeUnit Contribution MarginQ=1,600whereQ=sales volume$500=selling price$300=variable costs per unit$200,000=total fixed costs$120,000=target net income

ILLUSTRATION 18-25 Computation of required sales

Vargo must sell 1,600 units to achieve target net income of $120,000. The sales dollars required to achieve the target net income is found by multiplying the units sold by the unit selling price [(1,600×$500)=$800,000][(1,600×$500)=$800,000].

Contribution Margin Technique

As in the case of break‐even sales, we can compute in either units or dollars the sales required to meet target net income. The formula to compute required sales in units for Vargo Video using the unit contribution margin can be seen in the final step of the equation approach in Illustration 18-25 (shown in red). We simply divide the sum of fixed costs and target net income by the unit contribution margin. Illustration 18-26 shows this for Vargo.

(Fixed Costs+Target Net Income)÷Unit Contribution Margin=Required Sales in Units($200,000+$120,000)÷$200=1,600 units(Fixed Costs+Target Net Income)÷Unit Contribution Margin=Required Sales in Units($200,000+$120,000)÷$200=1,600 units

ILLUSTRATION 18-26 Formula for required sales in units using unit contribution margin

To achieve its desired target net income of $120,000, Vargo must sell 1,600 camcorders.

The formula to compute the required sales in dollars for Vargo using the contribution margin ratio is shown below.

(Fixed Costs+Target Net Income)÷Contribution Margin Ratio=Required Sales in Dollars($200,000+$120,000)÷40%=$800,000(Fixed Costs+Target Net Income)÷Contribution Margin Ratio=Required Sales in Dollars($200,000+$120,000)÷40%=$800,000

ILLUSTRATION 18-27 Formula for required sales in dollars using contribution margin ratio

To achieve its desired target net income of $120,000, Vargo must generate sales of $800,000.

Graphic Presentation

We also can use the CVP graph in Illustration 18-23 (on page 898) to find the sales required to meet target net income. In the profit area of the graph, the distance between the sales line and the total‐cost line at any point equals net income. We can find required sales by analyzing the differences between the two lines until the desired net income is found.

For example, suppose Vargo Video sells 1,400 camcorders. Illustration 18-23 shows that a vertical line drawn at 1,400 units intersects the sales line at $700,000 and the total‐cost line at $620,000. The difference between the two amounts represents the net income (profit) of $80,000.

MARGIN OF SAFETY

Margin of safety is the difference between actual or expected sales and sales at the break‐even point. It measures the “cushion” that a particular level of sales provides. It tells us how far sales could fall before the company begins operating at a loss. The margin of safety is expressed in dollars or as a ratio.

The formula for stating the margin of safety in dollars is actual (or expected) sales minus break‐even sales. Assuming that actual (expected) sales for Vargo Video are $750,000, the computation is as follows.

Actual (Expected) Sales−Break-Even Sales=Margin of Safety in Dollars$750,000−$500,000=$250,000Actual (Expected) Sales−Break-Even Sales=Margin of Safety in Dollars$750,000−$500,000=$250,000

ILLUSTRATION 18-28 Formula for margin of safety in dollars

Vargo's margin of safety is $250,000. Its sales could fall $250,000 before it operates at a loss.

The margin of safety ratio is the margin of safety in dollars divided by actual (or expected) sales. Illustration 18-29 shows the formula and computation for determining the margin of safety ratio.

Margin of Safety in Dollars÷Actual (Expected) Sales=Margin of Safety Ratio$250,000÷$750,000=33%Margin of Safety in Dollars÷Actual (Expected) Sales=Margin of Safety Ratio$250,000÷$750,000=33%

ILLUSTRATION 18-29 Formula for margin of safety ratio

This means that the company's sales could fall by 33% before it operates at a loss.

The higher the dollars or the percentage, the greater the margin of safety. Management continuously evaluates the adequacy of the margin of safety in terms of such factors as the vulnerability of the product to competitive pressures and to downturns in the economy.

 SERVICE COMPANY INSIGHT

Rolling Stones

How a Rolling Stones' Tour Makes Money

Yael/Retna

Computations of break‐even and margin of safety are important for service companies. Consider how the promoter for the Rolling Stones' tour used the break‐even point and margin of safety. For example, say one outdoor show should bring 70,000 individuals for a gross of $2.45 million. The promoter guarantees $1.2 million to the Rolling Stones. In addition, 20% of gross goes to the stadium in which the performance is staged. Add another $400,000 for other expenses such as ticket takers, parking attendants, advertising, and so on. The promoter also shares in sales of T‐shirts and memorabilia for which the promoter will net over $7 million during the tour. From a successful Rolling Stones' tour, the promoter could make $35 million!

What amount of sales dollars are required for the promoter to break even? (Go to WileyPLUS for this answer and additional questions.)

DO IT! 5

Break‐Even, Margin of Safety, and Target Net Income

Zootsuit Inc. makes travel bags that sell for $56 each. For the coming year, management expects fixed costs to total $320,000 and variable costs to be $42 per unit. Compute the following: (a) break‐even point in dollars using the contribution margin (CM) ratio; (b) the margin of safety and margin of safety ratio assuming actual sales are $1,382,400; and (c) the sales dollars required to earn net income of $410,000.

Action Plan

✓ Apply the formula for the break‐even point in dollars.

✓ Apply the formulas for the margin of safety in dollars and the margin of safety ratio.

✓ Apply the formula for the required sales in dollars.

SOLUTION

(a) Contribution margin ratio=[($56−$42)÷$56]=25%Contribution margin ratio=[($56−$42)÷$56]=25%

Break‐even sales in dollars=$320,000÷25%=$1,280,000Break‐even sales in dollars=$320,000÷25%=$1,280,000

(b) Margin of safety=$1,382,400−$1,280,000=$102,400Margin of safety=$1,382,400−$1,280,000=$102,400

Margin of safety ratio=$102,400÷$1,382,400=7.4%Margin of safety ratio=$102,400÷$1,382,400=7.4%

(c) Required sales in dollars=($320,000+$410,000)÷25%=$2,920,000Required sales in dollars=($320,000+$410,000)÷25%=$2,920,000

Related exercise material: BE18-10, BE18-11, BE18-12, E18-14, E18-15, E18-17, and DO IT! 18-5.

USING DECISION TOOLS—AMAZON.COM

Amazon.com faces many situations where it needs to apply the decision tools presented in this chapter, such as calculating the break‐even point to determine a product's profitability. Amazon's dominance of the online retail space, selling other company's products, is well known. But not everyone may realize that Amazon also sells its own private‐label electronics, including USB cables, mice, keyboards, and audio cables, under the brand name AmazonBasics. Assume that Amazon's management was provided with the following information regarding the production and sales of Bluetooth keyboards for tablet computers.

Cost Schedules

Variable costs

 Direct labor per keyboard

$ 8.00

 Direct materials

4.00

 Variable overhead

  3.00

Variable cost per keyboard

$15.00

Fixed costs

 Manufacturing

$ 25,000

 Selling

40,000

 Administrative

  70,000

Total fixed costs

$135,000

Selling price per keyboard

$25.00

Sales, 2017 (20,000 keyboards)

$500,000

INSTRUCTIONS

(Ignore any income tax considerations.)

(a) What is the operating income for 2017?

(b) What is the unit contribution margin for 2017?

(c) What is the break‐even point in units for 2017?

(d) Assume that management set the sales target for the year 2018 at a level of $550,000 (22,000 keyboards). Amazon's management believes that to attain the sales target in 2018, the company must incur an additional selling expense of $10,000 for advertising in 2018, with all other costs remaining constant. What will be the break‐even point in sales dollars for 2018 if the company spends the additional $10,000?

(e) If the company spends the additional $10,000 for advertising in 2018, what is the sales level in dollars required to equal 2017 operating income?

SOLUTION

1. (a)

Sales

$500,000

Less:

 Variable costs (20,000 keyboards × $15)

300,000

 Fixed costs

  135,000

Operating income

$ 65,000

2. (b) 

Selling price per keyboard

$25

Variable cost per keyboard

 15

Unit contribution margin

$10

3. (c) Fixed costs÷Unit contribution margin=Break-even point in units: $135,000÷$10=13,500 unitsFixed costs÷Unit contribution margin=Break-even point in units: $135,000÷$10=13,500 units

4. (d) Fixed costs÷Contribution margin ratio=Break-even point in dollars: $145,000∗÷40%**=$362,500Fixed costs÷Contribution margin ratio=Break-even point in dollars: $145,000*÷40%**=$362,500

*Fixed costs

$135,000

 Additional advertising expense

 10,000

 Revised fixed costs

$145,000

**Contribution margin ratio = Unit contribution margin ÷ Unit selling price: 40% = $10 ÷ $25

5. (e)Required sales=(Fixed costs+Target net income)÷Contribution margin ratio$525,000=($145,000+$65,000)÷40%(e) Required sales=(Fixed costs+Target net income)÷Contribution margin ratio$525,000=($145,000+$65,000)÷40%

REVIEW AND PRACTICE

LEARNING OBJECTIVES REVIEW

1 Explain variable, fixed, and mixed costs and the relevant range. Variable costs are costs that vary in total directly and proportionately with changes in the activity index. Fixed costs are costs that remain the same in total regardless of changes in the activity index.

The relevant range is the range of activity in which a company expects to operate during a year. It is important in CVP analysis because the behavior of costs is assumed to be linear throughout the relevant range.

Mixed costs change in total but not proportionately with changes in the activity level. For purposes of CVP analysis, mixed costs must be classified into their fixed and variable elements.

2 Apply the high‐low method to determine the components of mixed costs. Determine the variable costs per unit by dividing the change in total costs at the highest and lowest levels of activity by the difference in activity at those levels. Then, determine fixed costs by subtracting total variable costs from the amount of total costs at either the highest or lowest level of activity.

3 Prepare a CVP income statement to determine contribution margin. The five components of CVP analysis are (1) volume or level of activity, (2) unit selling prices, (3) variable costs per unit, (4) total fixed costs, and (5) sales mix. Contribution margin is the amount of revenue remaining after deducting variable costs. It is identified in a CVP income statement, which classifies costs as variable or fixed. It can be expressed as a total amount, as a per unit amount, or as a ratio.

4 Compute the break‐even point using three approaches. The break‐even point can be (a) computed from a mathematical equation, (b) computed by using a contribution margin technique, and (c) derived from a CVP graph.

5 Determine the sales required to earn target net income and determine margin of safety. The general formula for required sales is Required sales −Variable costs−Fixed costs=Target net incomeRequired sales −Variable costs−Fixed costs=Target net income. Two other formulas are (1) Required sales in units=(Fixed costs+Target net income)÷Unit contribution marginRequired sales in units=(Fixed costs+Target net income)÷Unit contribution margin, and (2) Required sales in dollars=(Fixed costs+Target net income)÷Contribution margin ratioRequired sales in dollars=(Fixed costs+Target net income)÷Contribution margin ratio.

Margin of safety is the difference between actual or expected sales and sales at the break‐even point. The formulas for margin of safety are (1) Actual (expected) sales−Break‐even sales=Margin of safety in dollarsActual (expected) sales−Break‐even sales=Margin of safety in dollars, and (2) Margin of safety in dollars÷Actual (expected) sales=Margin of safety ratioMargin of safety in dollars÷Actual (expected) sales=Margin of safety ratio.

DECISION TOOLS REVIEW

DECISION CHECKPOINTS

INFO NEEDED FOR DECISION

TOOL TO USE FOR DECISION

HOW TO EVALUATE RESULTS

What was the contribution toward fixed costs and income from each unit sold?

Selling price per unit and variable cost per unit

Unit contribution margin=Unit selling price−Unit variable costUnit contribution margin=Unit selling price−Unit variable cost

Every unit sold will increase income by the contribution margin.

What would be the increase in income as a result of an increase in sales?

Unit contribution margin and unit selling price

Contribution margin ratio=Unit contribution margin÷Unit selling priceContribution margin ratio=Unit contribution margin÷Unit selling price

Every dollar of sales will increase income by the contribution margin ratio.

At what amount of sales does a company cover its costs?

Unit selling price, unit variable cost, and total fixed costs

Break-even point analysis

In units: Break-even point=Fixed costsUnit contribution marginBreak-even point=Fixed costsUnit contribution margin

In dollars: Break-even point=Fixed costsContribution margin ratioBreak-even point=Fixed costsContribution margin ratio

Below the break-even point, the company is unprofitable.

GLOSSARY REVIEW

Activity index The activity that causes changes in the behavior of costs.

Break-even point The level of activity at which total revenue equals total costs.

Contribution margin (CM) The amount of revenue remaining after deducting variable costs.

Contribution margin ratio The percentage of each dollar of sales that is available to apply to fixed costs and contribute to net income; calculated as unit contribution margin divided by unit selling price.

Cost behavior analysis The study of how specific costs respond to changes in the level of business activity.

Cost-volume-profit (CVP) analysis The study of the effects of changes in costs and volume on a company’s profits.

Cost-volume-profit (CVP) graph A graph showing the relationship between costs, volume, and profits.

Cost-volume-profit (CVP) income statement A statement for internal use that classifies costs as fixed or variable and reports contribution margin in the body of the statement.

Fixed costs Costs that remain the same in total regardless of changes in the activity level.

High-low method A mathematical method that uses the total costs incurred at the high and low levels of activity to classify mixed costs into fixed and variable components.

Margin of safety The difference between actual or expected sales and sales at the break-even point.

Mixed costs Costs that contain both a variable- and a fixed-cost element and change in total but not proportionately with changes in the activity level.

Relevant range The range of the activity index over which the company expects to operate during the year.

Target net income The income objective set by management.

Unit contribution margin The amount of revenue remaining per unit after deducting variable costs; calculated as unit selling price minus unit variable costs.

Variable costs Costs that vary in total directly and proportionately with changes in the activity level.

PRACTICE MULTIPLE-CHOICE QUESTIONS

(LO 1)

1. Variable costs are costs that:

(a) vary in total directly and proportionately with changes in the activity level.

(b) remain the same per unit at every activity level.

(c) Neither of the above.

(d) Both (a) and (b) above.

(LO 1)

2. The relevant range is:

(a) the range of activity in which variable costs will be curvilinear.

(b) the range of activity in which fixed costs will be curvilinear.

(c) the range over which the company expects to operate during a year.

(d) usually from zero to 100% of operating capacity.

(LO 2)

3. Mixed costs consist of a:

(a) variable‐cost element and a fixed‐cost element.

(b) fixed‐cost element and a controllable‐cost element.

(c) relevant‐cost element and a controllable‐cost element.

(d) variable‐cost element and a relevant‐cost element.

(LO 2)

4. Your cell phone service provider offers a plan that is classified as a mixed cost. The cost per month for 1,000 minutes is $50. If you use 2,000 minutes this month, your cost will be:

(a) $50.

(b) $100.

(c) more than $100.

(d) between $50 and $100.

(LO 2)

5. Kendra Corporation's total utility costs during the past year were $1,200 during its highest month and $600 during its lowest month. These costs corresponded with 10,000 units of production during the high month and 2,000 units during the low month. What are the fixed and variable components of its utility costs using the high‐low method?

(a) $0.075 variable and $450 fixed.

(b) $0.120 variable and $0 fixed.

(c) $0.300 variable and $0 fixed.

(d) $0.060 variable and $600 fixed.

(LO 3)

6. Which of the following is not involved in CVP analysis?

(a) Sales mix.

(b) Unit selling prices.

(c) Fixed costs per unit.

(d) Volume or level of activity.

(LO 3)

7. When comparing a traditional income statement to a CVP income statement:

(a) net income will always be greater on the traditional statement.

(b) net income will always be less on the traditional statement.

(c) net income will always be identical on both.

(d) net income will be greater or less depending on the sales volume.

(LO 3)

8. Contribution margin:

(a) is revenue remaining after deducting variable costs.

(b) may be expressed as unit contribution margin.

(c) is selling price less cost of goods sold.

(d) Both (a) and (b) above.

(LO 3)

9. Cournot Company sells 100,000 wrenches for $12 a unit. Fixed costs are $300,000, and net income is $200,000. What should be reported as variable expenses in the CVP income statement?

(a) $700,000.

(b) $900,000.

(c) $500,000.

(d) $1,000,000.

(LO 4)

10. Gossen Company is planning to sell 200,000 pliers for $4 per unit. The contribution margin ratio is 25%. If Gossen will break even at this level of sales, what are the fixed costs?

(a) $100,000.

(b) $160,000.

(c) $200,000.

(d) $300,000.

(LO 4)

11. Brownstone Company's contribution margin ratio is 30%. If Brownstone's sales revenue is $100 greater than its break‐even sales in dollars, its net income:

(a) will be $100.

(b) will be $70.

(c) will be $30.

(d) cannot be determined without knowing fixed costs.

(LO 5)

12. The mathematical equation for computing required sales to obtain target net income is Required sales =

(a) Variable costs+Target net incomeVariable costs+Target net income.

(b) Variable costs+Fixed costs+Target net incomeVariable costs+Fixed costs+Target net income.

(c) Fixed costs + Target net incomeFixed costs + Target net income.

(d) No correct answer is given.

(LO 5)

13. Margin of safety is computed as:

(a) Actual sales−Break−even salesActual sales−Break−even sales.

(b) Contribution margin−Fixed costsContribution margin−Fixed costs.

(c) Break‐even sales−Variable costsBreak‐even sales−Variable costs.

(d) Actual sales − Contribution marginActual sales − Contribution margin.

(LO 5)

14. Marshall Company had actual sales of $600,000 when break‐even sales were $420,000. What is the margin of safety ratio?

(a) 25%.

(b) 30%.

(c) 331/3%3313%.

(d) 45%.

SOLUTIONS

1. (d) Variable costs vary in total directly and proportionately with changes in the activity level and remain the same per unit at every activity level. Choices (a) and (b) are correct, but (d) is the better and more complete answer. Since (a) and (b) are both true statements, choice (c) is incorrect.

2. (c) The relevant range is the range over which the company expects to operate during a year. The other choices are incorrect because the relevant range is the range over which (a) variable costs are expected to be linear, not curvilinear, and (b) the company expects fixed costs to remain the same. Choice (d) is incorrect because this answer does not specifically define relevant range.

3. (a) Mixed costs consist of a variable‐cost element and a fixed‐cost element, not (b) a controllable‐cost element, (c) a relevant‐cost element or a controllable‐cost element, or (d) a relevant‐cost element.

4. (d) Your cost will include the fixed‐cost component (flat service fee) which does not increase plus the variable cost (usage charge) for the additional 1,000 minutes which will increase your cost to between $50 and $100. Therefore, choices (a) $50, (b) $100, and (c) more than $100 are incorrect.

5. (a) Variable is $0.075 [($1,200−$600)÷(10,000−2,000)]$0.075 [($1,200−$600)÷(10,000−2,000)] and fixed is $450 [($1,200−($0.075×10,000)]$450 [($1,200−($0.075×10,000)]. Therefore, choices (b) $0.120 variable and $0 fixed, (c) $0.300 variable and $0 fixed, and (d) $0.060 variable and $600 fixed are incorrect.

6. (c) Total fixed costs, not fixed costs per unit, are involved in CVP analysis. Choices (a) sales mix, (b) unit selling prices, and (d) volume or level of activity are all involved in CVP analysis.

7. (c) Net income will always be identical on both a traditional income statement and a CVP income statement. Therefore, choices (a), (b), and (d) are incorrect statements.

8. (d) Contribution margin is revenue remaining after deducting variable costs and it may be expressed on a per unit basis. Choices (a) and (b) are accurate, but (d) is a better answer. Choice (c) is incorrect because it defines gross margin, not contribution margin.

9. (a) Contribution margin is equal to fixed costs plus net income ($300,000+$200,000=$500,000)($300,000+$200,000=$500,000). Since variable expenses are the difference between total sales ($1,200,000) and contribution margin ($500,000), $700,000 must be the amount of variable expenses in the CVP income statement. Therefore, choices (b) $900,000, (c) $500,000, and (d) $1,000,000 are incorrect.

10. (c) Unit contribution margin is $1 ($4×25%)$1 ($4×25%). Fixed costs÷Unit contribution margin=Break‐even point in unitsFixed costs÷Unit contribution margin=Break‐even point in units. Solving for fixed costs, 200,000 units×$1 per unit=$200,000200,000 units×$1 per unit=$200,000, not (a) $100,000, (b) $160,000, or (d) $300,000.

11. (c) If Brownstone's sales revenue is $100 greater than its break‐even sales in dollars, its net income will be $30 or ($100×30%)($100×30%), not (a) $100 or (b) $70. Choice (d) is incorrect because net income can be determined without knowing fixed costs.

12. (b) The correct equation is Required sales=Variable costs+Fixed costs+Target net incomeRequired sales=Variable costs+Fixed costs+Target net income. The other choices are incorrect because (a) needs fixed costs added, (c) needs variable costs added, and (d) there is a correct answer given.

13. (a) Margin of safety is computed as Actual sales−Break‐even salesActual sales−Break‐even sales. Therefore, choices (b) Contribution margin−Fixed costsContribution margin−Fixed costs, (c) Break‐even sales−Variable costsBreak‐even sales−Variable costs, and (d) Actual sales−Contribution marginActual sales−Contribution margin are incorrect.

14. (b) The margin of safety ratio is computed by dividing the margin of safety in dollars of $180,000 ($600,000−$420,000)$180,000 ($600,000−$420,000) by actual sales of $600,000. The result is 30% ($180,000÷$600,000)30% ($180,000÷$600,000), not (a) 25%, (c) 331/3%331/3%, or (d) 45%.

PRACTICE EXERCISES

Determine fixed and variable costs using the high‐low method and prepare graph.

(LO 1, 2)

1. The controller of Teton Industries has collected the following monthly expense data for use in analyzing the cost behavior of maintenance costs.

Month

Total Maintenance Costs

Total Machine Hours

January

$2,900

300

February

 3,000

400

March

 3,600

600

April

 4,300

790

May

 3,200

500

June

 4,500

800

INSTRUCTIONS

(a) Determine the fixed‐cost and variable‐cost components using the high‐low method.

(b) Prepare a graph showing the behavior of maintenance costs, and identify the fixed‐cost and variable‐cost elements. Use 200 unit increments and $1,000 cost increments.

SOLUTION

1. (a) Maintenance Costs:

   $4,500−$2,900800−300=$1,600500=$3.20$4,500−$2,900800−300=$1,600500=$3.20 variable cost per machine hour

800 Machine Hours

300 Machine Hours

Total costs

$4,500

$2,900

Less: Variable costs

  800 × $3.20

 2,560

  300 × $3.20

  960

Total fixed costs

$1,940

$1,940

Thus, maintenance costs are $1,940 per month plus $3.20 per machine hour.

Determine contribution margin ratio, break‐even point in dollars, and margin of safety.

(LO 3, 4, 5)

2. Zion Seating Co., a manufacturer of chairs, had the following data for 2017:

Sales

2,400 units

Sales price

$40 per unit

Variable costs

$15 per unit

Fixed costs

$19,500

INSTRUCTIONS

(a) What is the contribution margin ratio?

(b) What is the break‐even point in dollars?

(c) What is the margin of safety in units and dollars?

(d) If the company wishes to increase its total dollar contribution margin by 40% in 2018, by how much will it need to increase its sales if all other factors remain constant?

(CGA adapted)

SOLUTION

2. (a) Contribution margin ratio=Unit contribution margin÷Unit selling price ($40−$15)÷$40=62.5%Contribution margin ratio=Unit contribution margin÷Unit selling price ($40−$15)÷$40=62.5%

(b) Break‐even in dollars: $19,500÷62.5%=$31,200$19,500÷62.5%=$31,200

(c) Margin of safety=(2,400×$40)−$31,200=$64,800 Margin of safety=(2,400×$40)−$31,200=$64,800

  $64,800÷$40=1,620 units$64,800÷$40=1,620 units

(d) Current contribution margin is $40−$15=$25$40−$15=$25

Total contribution margin is $25×2,400=$60,000$25×2,400=$60,000

40% increase in contribution margin is $60,000×40%=$24,000$60,000×40%=$24,000

Total increase in sales required is $24,000÷62.5%=$38,400$24,000÷62.5%=$38,400

PRACTICE PROBLEM

Compute break‐even point, contribution margin ratio, margin of safety, and sales for target net income.

(LO 4, 5)

Mabo Company makes calculators that sell for $20 each. For the coming year, management expects fixed costs to total $220,000 and variable costs to be $9 per unit.

INSTRUCTIONS

(a) Compute break‐even point in units using the mathematical equation.

(b) Compute break‐even point in dollars using the contribution margin (CM) ratio.

(c) Compute the margin of safety percentage assuming actual sales are $500,000.

(d) Compute the sales required in dollars to earn net income of $165,000.

SOLUTION

(a) Required sales−Variable costs−Fixed costs=Net income$20Q−$9Q−$220,000=$0$11Q=$220,000Q=20,000 units(a) Required sales−Variable costs−Fixed costs=Net income$20Q−$9Q−$220,000=$0$11Q=$220,000Q=20,000 units

(b) Unit contribution margin=Unit selling price−Unit variable costs$11=$20−$9Contribution margin ratio=Unit contribution margin÷Unit selling price55%=$11÷$20Break-even point in dollars=Fixed costs÷Contribution margin ratio=$220,000÷55%=$400,000(b) Unit contribution margin=Unit selling price−Unit variable costs$11=$20−$9Contribution margin ratio=Unit contribution margin÷Unit selling price55%=$11÷$20Break-even point in dollars=Fixed costs÷Contribution margin ratio=$220,000÷55%=$400,000