In cost volume profit analysis the unit contribution margin is

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.