Homework answers / question archive / During week eight we will be focused on cost volume profit analysis

During week eight we will be focused on cost volume profit analysis. We will be looking at the ways that cost, volume, and profit interact. This can be critical for a business to understand. Failure to understand these items can lead to a business failing. For our discussion board post in week four please be sure to read chapter 7. Then locate a news article about a store or business that has shut down and provide a link to the article. Then provide a summary of the article in your own words and brainstorm why this business or store may have failed. Then answer the question "What are some aspects of cost volume profit that may have been at play that led to the closure of this business?" Be sure to integrate the concepts of cost volume profit that you are learning about this week into your post.

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THIS CHAPTER’S

FOCUS is on the

Seattle Contemporary Theater. This non

profit enterprise was formed to bring

contemporary drama

to the Seattle area. The

theater operates in a

historic theater building

owned by the city, for

which Seattle Contem

porary Theater pays the city a fixed monthly

rental charge and a portion of the price of each

ticket sold. The theater must cover its operat

ing expenses with ticket revenue in order to

break even. Using the Seattle Contemporary

Theater as an illustration, we will explore a

technique called costvolumeprofit (or CVP)

analysis, which the theater’s managing director

and business manager use to better under

stand the relationships between the theater’s

costs, ticket sales volume, and revenue.

FOCUS COMPANY >>>

7 Cost-Volume-Profit Analysis

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In contrast to the non

profit, entertainment

service setting of the Seattle Contemporary

Theater, we explore the use of costvolume

profit analysis by Digital Time Company.

The management of this manufacturer of

digital clocks uses CVP analysis to better

understand the relationships between the

company’s costs, sales volume, and profit.

The company’s management also analyzes

the firm’s cost structure, which refers to

the relative proportion of fixed and

vari able costs.

<<< IN CONTRAST

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nd riy

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What effect on profit can United Airlines expect if it adds a flight on the Chicago to New York route? How will NBC’s profit change if the ratings increase for its evening news program? How many patient days of care must Massachusetts General Hospital provide to break even for the year? What happens to this break-even patient load if the hospital leases a new computerized system for patient records?

Each of these questions concerns the effects on costs and revenues when the orga- nization’s activity changes. The analytical technique used by managerial accountants to address these questions is called cost-volume-profit analysis. Often called CVP analysis for short, this technique summarizes the effects of changes in an organization’s volume of activity on its costs, revenue, and profit. Cost-volume-profit analysis can be extended to cover the effects on profit of changes in selling prices, service fees, costs, income-tax rates, and the organization’s mix of products or services. What will happen to profit, for example, if the New York Yankees raise ticket prices for stadium seats? In short, CVP analysis provides management with a comprehensive overview of the effects on revenue and costs of all kinds of short-run financial changes.

Although the word profit appears in the term, cost-volume-profit analysis is not con- fined to profit-seeking enterprises. Managers in nonprofit organizations also routinely use CVP analysis to examine the effects of activity and other short-run changes on rev- enue and costs. For example, as the State of Florida gains approximately 1,000 people a day in population, the state’s political leaders must analyze the effects of this change on sales-tax revenues and the cost of providing services, such as education, transportation,

7-1 Compute a break-even point using the contribution-margin approach and the equation approach.

7-2 Compute the contribution-margin ratio and use it to find the break-even point in sales dollars.

7-3 Prepare a cost-volume-profit (CVP) graph and explain how it is used.

7-4 Apply CVP analysis to determine the effect on profit of changes in fixed expenses, variable expenses, sales prices, and sales volume.

7-5 Compute the break-even point and prepare a profit-volume graph for a multiprod- uct enterprise.

7-6 List and discuss the key assumptions of CVP analysis.

7-7 Prepare and interpret a contribution income statement.

7-8 Explain the role of cost structure and operating leverage in CVP relationships.

7-9 Understand the implications of activity-based costing for CVP analysis.

7-10 Be aware of the effects of advanced manufacturing technology on CVP relationships.

7-11 Understand the effect of income taxes on CVP analysis (appendix).

After completing this chapter, you should be able to:

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and police protection. Managers at such diverse nonprofit institutions as Massachusetts General Hospital, Stanford University, and the United Way all use CVP analysis as a routine operational tool.

Illustration of Cost-Volume-Profit Analysis

To illustrate the various analytical techniques used in cost-volume-profit analysis, we will focus on a performing arts organization. The Seattle Contemporary Theater was recently formed as a nonprofit enterprise to bring contemporary drama to the Seattle area. The organization has a part-time, unpaid board of trustees comprised of local professional people who are avid theater fans. The board has hired the following full-time employees.

Managing director: Responsibilities include overall management of the organiza- tion; direction of six plays per year. Artistic director: Responsibilities include hiring of actors and production crews for each play; direction of six plays per year. Business manager and producer: Responsibilities include managing the organiza- tion’s business functions and ticket sales; direction of the production crews, who handle staging, lighting, costuming, and makeup. The board of trustees has negotiated an agreement with the city of Seattle to hold per-

formances in a historic theater owned by the city. The theater has not been used for 30 years, but the city has agreed to refurbish it and to provide lighting and sound equipment. In return, the city will receive a rental charge of $10,000 per month plus $8 for each theater ticket sold.

Projected Expenses and Revenue The theater’s business manager and producer, Andrew Lloyd, has made the following projections for the first few years of operation.

“Accounting is changing. You’re no longer sitting behind a desk just working on a computer, just crunching the numbers. You’re actually getting to be a part of the day-to-day functions of the business.” (7a)

Abbott Laboratories

Fixed expenses per month:

Theater rental ................................................................................................................................................. $10,000

Employees’ salaries and fringe benefits ......................................................................................................... 8,000

Actors’ wages ................................................................................................................................................. 15,000

(to be supplemented with local volunteer talent)

Production crew’s wages ............................................................................................................................... 5,600

(to be supplemented with local volunteers)

Playwrights’ royalties for use of plays ............................................................................................................. 5,000

Insurance ........................................................................................................................................................ 1,000

Utilities—fixed portion .................................................................................................................................... 1,400

Advertising and promotion ............................................................................................................................. 800

Administrative expenses ................................................................................................................................ 1,200

Total fixed expenses per month ...................................................................................................................... $48,000

Variable expenses per ticket sold:

City’s charge per ticket for use of theater ...................................................................................................... $ 8

Other miscellaneous expenses (for example, printing of playbills and tickets,

variable portion of utilities) ........................................................................................................................ 2

Total variable cost per ticket sold ................................................................................................................... $10

Revenue:

Price per ticket ............................................................................................................................................... $16

Importance of Cost Behavior Notice that the theater’s expenses have been cate- gorized according to their cost behavior: fixed or variable. Analyzing an organization’s cost behavior, the topic of Chapter 6, is a necessary first step in any cost-volume-profit analysis. As we proceed through this chapter, the data pertaining to Seattle Contemporary Theater will be an important part of our cost-volume-profit analysis.

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The Break-Even Point

As the first step in the CVP analysis for Seattle Contemporary Theater, we will find the break-even point. The break-even point is the volume of activity where the organiza- tion’s revenues and expenses are equal. At this amount of sales, the organization has no profit or loss; it breaks even.

Suppose Seattle Contemporary Theater sells 8,000 tickets during a play’s one-month run. The following income statement shows that the profit for the month will be zero; thus, the theater will break even.

Sales revenue (8,000 × $16) ......................................................................................................... $128,000

Less variable expenses (8,000 × $10) .......................................................................................... 80,000

Total contribution margin ................................................................................................................ $ 48,000

Less fixed expenses ........................................................................................................................ 48,000

Profit ................................................................................................................................................ $ 0

“Break-even analyses figure prominently in any discussion of new programs. Although we have programs that operate at a loss because of their importance educationally, overall our cash inflows have to be sufficient to support our total program.” (7b)

Cornell University

Learning Objective 7-1

Compute a break-even point using the contribution-margin approach and the equation approach.

Notice that this income statement highlights the distinction between variable and fixed expenses. The statement also shows the total contribution margin, which is defined as total sales revenue minus total variable expenses. This is the amount of rev- enue that is available to contribute to covering fixed expenses after all variable expenses have been covered. The contribution income statement will be covered in more depth later in the chapter. At this juncture, it provides a useful way to think about the meaning of breaking even.

How could we compute Seattle Contemporary Theater’s break-even point if we did not already know it is 8,000 tickets per month? This is the question to which we turn our attention next.

Contribution-Margin Approach Seattle Contemporary Theater will break even when the organization’s revenue from ticket sales is equal to its expenses. How many tickets must be sold during one month (one play’s run) for the organization to break even?

Whether running a small business or a worldwide enterprise, understanding cost-volume-profit relationships is crucial in managing any organization. © Jack Hollingsworth/Getty Images RF © Ken James/Bloomberg/Getty Images

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Each ticket sells for $16, but $10 of this is used to cover the variable expense per ticket. This leaves $6 per ticket to contribute to covering the fixed expenses of $48,000. When enough tickets have been sold in one month so that these $6 contributions per ticket add up to $48,000, the organization will break even for the month. Thus, we may compute the break-even volume of tickets as follows:

Fixed expenses ____________________________________________________ Contribution of each ticket toward covering fixed expenses

= $48,000 _______ $6

= 8,000

Seattle Contemporary Theater must sell 8,000 tickets during a play’s one-month run to break even for the month.

The $6 amount that remains of each ticket’s price, after the variable expenses are covered, is called the unit contribution margin. The general formula for computing the break-even sales volume in units is given below.

Fixed expenses _____________________ Unit contribution margin

= Break-even point (in units) (1)

Contribution-Margin Ratio Sometimes management prefers that the break-even point be expressed in sales dollars rather than units. Seattle Contemporary Theater’s break-even point in sales dollars is computed as follows.

Learning Objective 7-2

Compute the contribution- margin ratio and use it to find the break-even point in sales dollars.

“Delta Air Lines computes a break-even load factor, which is the average percentage of available passenger seats that need to be occupied on our flights in order for the company to break even.” (7c)

Delta Air Lines

Break-even point in units (tickets) ...................................................................................................................... 8,000

Sales price per unit ............................................................................................................................................. × $16

Break-even point in sales dollars ....................................................................................................................... $128,000

The following computation provides an alternative way to determine the break-even point in sales dollars.

Fixed expenses ___________________ Unit contribution margin ___________________

Unit sales price

= $48,000 _______ $6 ___ $16

= $48,000 _______

.375 = $128,000

The unit contribution margin divided by the unit sales price is called the contribution- margin ratio. This ratio also can be expressed as a percentage, in which case it is called the contribution-margin percentage. Seattle Contemporary Theater’s contribution- margin ratio is .375 (in percentage form, 37.5%). Thus, the organization’s break-even point in sales dollars may be found by dividing its fixed expenses by its contribution-margin ratio. The logic behind this approach is that 37.5 percent of each sales dollar is available to make a contribution toward covering fixed expenses. The general formula is given below.

Fixed expenses _____________________ Contribution-margin ratio

= Break-even point in sales dollars (2)

Equation Approach An alternative approach to finding the break-even point is based on the profit equation. Income (or profit) is equal to sales revenue minus expenses. If expenses are separated into variable and fixed expenses, the essence of the income (profit) statement is captured by the following equation.

Sales revenue – Variable expenses – Fixed expenses = Profit

This equation can be restated as follows:

Unit sales price

Sales volume in units

Unit variable expense

Sales volume in units

Fixed expenses

Profit (3)

––× ×

=

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To find Seattle Contemporary Theater’s break-even volume of ticket sales per month, we define profit in equation (3) to be zero.

($ 0$48,000($1016 X )X )

Unit variablle expense

Sales volume in units

Fixed expenses

Break-even profit (zero) (4)

Unit sales price

Sales volume in units

– –

––

× ×

××

=

=

where

X denotes the number of sales units (tickets) required to break even.

Equation (4) can be solved for X as shown below.

$16X − $10X − $48,000 = 0 $6X = $48,000

X = $48,000 _______ $6

= 8,000

Using the equation approach, we have arrived at the same general formula for computing the break-even sales volume (formula (1).

The contribution-margin and equation approaches are two equivalent techniques for finding the break-even point. Both methods reach the same conclusion, and so personal preference dictates which approach should be used.

Graphing Cost-Volume-Profit Relationships

While the break-even point conveys useful information to management, it does not show how profit changes as activity changes. To capture the relationship between profit and volume of activity, a cost-volume-profit (CVP) graph is commonly used. The follow- ing steps are used to prepare a CVP graph for Seattle Contemporary Theater. The graph is displayed in Exhibit 7–1. Notice that the graph shows the relevant range, which is the range of activity within which management expects the theater to operate.

Step 1: Draw the axes of the graph. Label the vertical axis in dollars and the horizontal axis in units of sales (tickets).

Step 2: Draw the fixed-expense line. It is parallel to the horizontal axis, since fixed expenses do not change with activity.

Step 3: Compute total expense at any convenient volume. For example, select a volume of 6,000 tickets.

Learning Objective 7-3

Prepare a cost-volume-profit (CVP) graph and explain how it is used.

Variable expenses (6,000 × $10 per ticket) ..................................................................... $ 60,000

Fixed expenses ................................................................................................................... 48,000

Total expenses (at 6,000 tickets) ........................................................................................ $108,000

Plot this point ($108,000 at 6,000 tickets) on the graph. See point A on the graph in Exhibit 7–1.

Step 4: Draw the total-expense line. This line passes through the point plotted in step 3 (point A) and the intercept of the fixed-expense line on the vertical axis ($48,000).

Step 5: Compute total sales revenue at any convenient volume. We will choose 6,000 tickets again. Total revenue is $96,000 (6,000 × $16 per ticket). Plot this point ($96,000 at 6,000 tickets) on the graph. See point B on the graph in Exhibit 7–1.

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Step 6: Draw the total revenue line. This line passes through the point plotted in step 5 (point B) and the origin.

Step 7: Label the graph as shown in Exhibit 7–1.

Interpreting the CVP Graph Several conclusions can be drawn from the CVP graph in Exhibit 7–1.

Break-Even Point The break-even point is determined by the intersection of the total- revenue line and the total-expense line. Seattle Contemporary Theater breaks even for the month at 8,000 tickets, or $128,000 of ticket sales. This agrees with our calculations in the preceding section.

Profit and Loss Areas The CVP graph discloses more information than the break- even calculation. From the graph, a manager can see the effects on profit of changes

Exhibit 7–1 Cost-Volume-Profit Graph: Seattle Contemporary Theater

$000 (per month)

10

2,000 Volume (tickets sold in one month)

Relevant range

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

Total variable expenses for 8,000 tickets (at $10 per ticket), $80,000

4,000 6,000 8,000 10,000 12,000

Loss area

Total fixed expenses per month, $48,000

Total fixed expenses

Total expenses

Profit area

Total expenses for 8,000 tickets, $128,000

Break-even point: 8,000 tickets or $128,000 of sales

A

B

Total revenue from ticket sales

Learning Objective 7-3

Prepare a cost-volume-profit (CVP) graph and explain how it is used.

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in volume. The vertical distance between the lines on the graph represents the profit or loss at a particular sales volume. If Seattle Contemporary Theater sells fewer than 8,000 tickets in a month, the organization will suffer a loss. The magnitude of the loss increases as ticket sales decline. The theater organization will have a profit if sales exceed 8,000 tickets in a month.

Implications of the Break-Even Point The position of the break-even point within an organization’s relevant range of activity provides important information to manage- ment. The Seattle Contemporary Theater building seats 450 people. The agreement with the city of Seattle calls for 20 performances during each play’s one-month run. Thus, the maximum number of tickets that can be sold each month is 9,000 (450 seats × 20 performances). The organization’s break-even point is quite close to the maxi- mum possible sales volume. This could be cause for concern in a nonprofit organiza- tion operating on limited resources.

Exhibit 7–2 Alternative Format for CVP Graph: Seattle Contempo- rary Theater

$000 (per month)

10

2,000 Volume (tickets sold in one month)

Relevant range

20

30

40

50

60

70

80

90

100

110

120

130

140

150

160

Total variable expenses for 8,000 tickets (at $10 per ticket), $80,000

4,000 6,000 8,000 10,000 12,000

Loss area

Total fixed expenses per month, $48,000

Profit area

Total expenses for 8,000 tickets, $128,000

Total expenses

Break-even point: 8,000 tickets or $128,000 of sales

A

B

Total revenue from ticket sales

Total variable expenses

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What could management do to improve this situation? One possibility is to rene- gotiate with the city to schedule additional performances. However, this might not be feasible, because the actors need some rest each week. Also, additional performances would likely entail additional costs, such as increased theater-rental expenses and increased compensation for the actors and production crew. Other possible solutions are to raise ticket prices or reduce costs. These kinds of issues will be explored later in the chapter.

The CVP graph will not resolve this potential problem for the management of Seattle Contemporary Theater. However, the graph will direct management’s attention to the situation.

Alternative Format for the CVP Graph An alternative format for the CVP graph, preferred by some managers, is displayed in Exhibit 7-2 . The key difference is that fixed expenses are graphed above variable expenses, instead of the reverse as they were in Exhibit 7–1.

Profit-Volume Graph

Yet another approach to graphing cost-volume-profit relationships is displayed in Exhibit 7–3. This format is called a profit-volume graph, since it highlights the amount of profit or loss. Notice that the graph intercepts the vertical axis at the amount equal to fixed expenses at the zero activity level. The graph crosses the horizontal axis at the break-even point. The vertical distance between the horizontal axis and the profit line, at a particular level of sales volume, is the profit or loss at that volume.

Exhibit 7–3 Profit-Volume Graph: Seattle Contemporary Theater

$000 (per month)

50

2,000

Volume (tickets sold in one month)

40

30

20

10

0

10

20

30

40

50

4,000 6,000 8,000 10,000

Loss area

Profit

Total fixed expenses per month, $48,000

Break-even point: 8,000 tickets

Total profit

Loss

Profit area

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Target Profit

The board of trustees for Seattle Contemporary Theater would like to run free workshops and classes for young actors and aspiring playwrights. This program would cost $3,600 per month in fixed expenses, including teachers’ salaries and rental of space at a local college. No variable expenses would be incurred. If Seattle Contemporary Theater could make a profit of $3,600 per month on its performances, the Seattle Drama Workshop could be opened. The board has asked Andrew Lloyd, the organization’s business man- ager and producer, to determine how many theater tickets must be sold during each play’s one-month run to make a profit of $3,600.

The desired profit level of $3,600 is called a target profit (or income). The problem of computing the volume of sales required to earn a particular target profit is very similar to the problem of finding the break-even point. After all, the break-even point is the num- ber of units of sales required to earn a target profit of zero.1

Contribution-Margin Approach Each ticket sold by Seattle Contemporary Theater has a unit contribution margin of $6 (sales price of $16 minus unit variable expense of $10). Eight thousand of these $6 con- tributions will contribute just enough to cover fixed expenses of $48,000. Each additional ticket sold will contribute $6 toward profit. Thus, we can modify formula (1) given earlier in the chapter as follows:

1Remember that Seattle Contemporary Theater is a nonprofit enterprise. CVP analysis in a for-profit enterprise, including the effect of income taxes, is covered in the appendix to this chapter.

Learning Objective 7-4

Apply CVP analysis to determine the effect on profit of changes in fixed expenses, variable expenses, sales prices, and sales volume.

Fixed expenses + Target profit ________________________ Unit contribution margin

= Number of sales units required (5) to earn target profit

$48,000 + $3,600 ______________ $6

= 8,600 tickets

If Seattle Contemporary Theater sells 8,600 tickets during each play’s one-month run, the organization will make a monthly profit of $3,600 on its performances. This profit can be used to fund the Seattle Drama Workshop. The total dollar sales required to earn a target profit is found by modifying formula (2) given previously.

Fixed expenses + Target profit _________________________ Contribution-margin ratio

= Dollar sales required to earn

target profit (6)

$48, 000 + $3,600 _______________ .375

= $137,600

where the contribution margin ratio = $6 ____ $16

= .375

This dollar sales figure also can be found by multiplying the required sales of 8,600 tickets by the ticket price of $16 (8,600 × $16 = $137,600).

Equation Approach The equation approach also can be used to find the units of sales required to earn a target profit. We can modify the profit equation given previously as follows:

Unit sales price

Sales volume required to earn target

profit

Sales volume required to earn target

profit

Unit variable expense

Fixed expenses Target profit

–

–

× ×

=

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Learning Objective 7-4

Apply CVP analysis to determine the effect on profit of changes in fixed expenses, variable expenses, sales prices, and sales volume.

“Basically the role of the [accountant] on the team [is] analyzing the financial impact of the business decision and providing advice. Does this make sense financially or not?” (7d)

Abbott Laboratories

Filling in the values for Seattle Contemporary Theater, we have the following equation.

($16 × X) − ($10 × X) − $48,000 = $3,600 (7)

where X denotes the sales volume required to earn the target profit

Equation (7) can be solved for X as follows:

$16X − $10X − $48,000 = $3,600 $6X = $51,600

X = $51,600 _______ $6

= 8,600

Graphical Approach The profit-volume graph in Exhibit 7–3 also can be used to find the sales volume required to earn a target profit. First, locate Seattle Contemporary Theater’s target profit of $3,600 on the vertical axis. Then move horizontally until the profit line is reached. Finally, move down from the profit line to the horizontal axis to determine the required sales volume.

Applying CVP Analysis

The cost-volume-profit relationships that underlie break-even calculations and CVP graphs have wide-ranging applications in management. We will look at several common applications illustrated by Seattle Contemporary Theater.

Safety Margin The safety margin of an enterprise is the difference between the budgeted sales rev- enue and the break-even sales revenue. Suppose Seattle Contemporary Theater’s busi- ness manager expects every performance of each play to be sold out. Then budgeted monthly sales revenue is $144,000 (450 seats × 20 performances of each play × $16 per ticket). Since break-even sales revenue is $128,000, the organization’s safety margin is $16,000 ($144,000 − $128,000). The safety margin gives management a feel for how close projected operations are to the organization’s break-even point. We will further discuss the safety margin concept later in the chapter.

Changes in Fixed Expenses What would happen to Seattle Contemporary Theater’s break-even point if fixed expenses change? Suppose the business manager is concerned that the estimate for fixed utilities expenses, $1,400 per month, is too low. What would happen to the break-even point if fixed utilities expenses prove to be $2,600 instead? The break-even calculations for both the original and the new estimate of fixed utilities expenses are as follows:

Original Estimate New Estimate

Fixed utilities expenses ............................................................................................... $ 1,400 $ 2,600

Total fixed expenses .................................................................................................... $48,000 $49,200

Break-even calculation ...............................................................................................

(Fixed expenses ÷ unit contribution margin)

$48,000 ÷ $6 $49,200 ÷ $6

Break-even point (units) .............................................................................................. 8,000 tickets 8,200 tickets

Break-even point (dollars) ........................................................................................... $128,000 $131,200

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The estimate of fixed expenses has increased by 2.5 percent, since $1,200 is 2.5 percent of $48,000. Notice that the break-even point also increased by 2.5 percent (200 tickets is 2.5 percent of 8,000 tickets). This relationship will always exist.

Original Estimate New Estimate

Miscellaneous variable expenses .................................................................................. $2 per ticket $3 per ticket

Unit contribution margin ................................................................................................ $6 $5

Break-even calculation ...................................................................................................

(Fixed expenses ÷ unit contribution margin)

$48,000 ÷ $6 $48,000 ÷ $5

Break-even point (units) ................................................................................................. 8,000 tickets 9,600 tickets

Break-even point (dollars) .............................................................................................. $128,000 $153,600

Fixed expenses _____________________ Unit contribution margin

= Break-even point (in units)

Fixed expenses × 1.025 _____________________ Unit contribution margin

= (Break-even point in units) × 1.025

Donations to Offset Fixed Expenses Nonprofit organizations often receive cash donations from people or organizations desiring to support a worthy cause. A donation is equivalent to a reduction in fixed expenses, and it reduces the organization’s break-even point. In our original set of data, Seattle Contemporary Theater’s monthly fixed expenses total $48,000. Suppose that various people pledge donations amounting to $6,000 per month. The new break-even point is computed as follows:

Fixed expenses − Donations ________________________ Unit contribution margin

= Break-even point (in units)

$48, 000 - $6, 000 _______________ $6

= 7, 000 tickets

Changes in the Unit Contribution Margin What would happen to Seattle Contemporary Theater’s break-even point if miscellaneous variable expenses were $3 per ticket instead of $2? Alternatively, what would be the effect of raising the ticket price to $18?

Change in Unit Variable Expenses If the theater organization’s miscellaneous vari- able expenses increase from $2 to $3 per ticket, the unit contribution margin will fall from $6 to $5. The original and new break-even points are computed as follows:

If this change in unit variable expenses actually occurs, it will no longer be possible for the organization to break even. Only 9,000 tickets are available for each play’s one- month run (450 seats × 20 performances), but 9,600 tickets would have to be sold to break even. Once again, CVP analysis will not solve this problem for management, but it will direct management’s attention to potentially serious difficulties.

Change in Sales Price Changing the unit sales price will also alter the unit contribu- tion margin. Suppose the ticket price is raised from $16 to $18. This change will raise the unit contribution margin from $6 to $8. The new break-even point will be 6,000 tickets ($48,000 ÷ $8).

A $2 increase in the ticket price will lower the break-even point from 8,000 tickets to 6,000 tickets. Is this change desirable? A lower break-even point decreases the risk of operating with a loss if sales are sluggish. However, the organization may be more likely to at least break even with a $16 ticket price than with an $18 ticket price. The reason is that the lower ticket price encourages more people to attend the theater’s performances.

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It could be that break-even sales of 8,000 tickets at $16 are more likely than break-even sales of 6,000 tickets at $18. Ultimately, the desirability of the ticket-price increase depends on management’s assessment of the likely reaction by theater patrons.

Management’s decision about the ticket price increase also will reflect the funda- mental goals of Seattle Contemporary Theater. This nonprofit drama organization was formed to bring contemporary drama to the people of Seattle. The lower the ticket price, the more accessible the theater’s productions will be to people of all income levels.

The point of this discussion is that CVP analysis provides valuable information, but it is only one of several elements that influence management’s decisions.

Predicting Profit Given Expected Volume So far, we have focused on finding the required sales volume to break even or achieve a particular target profit. Thus, we have asked the following question.

Ticket Price Forecast Monthly Demand

$16 ............................................................................................................................................ 9,000

$20 ............................................................................................................................................ 6,000

Ticket Price

$16 $20

Sales revenue:

9,000 × $16 ......................................................................................................... $144,000

6,000 × $20 ......................................................................................................... $120,000

Less variable expenses:

9,000 × $10 ......................................................................................................... 90,000

6,000 × $10 ......................................................................................................... 60,000

Total contribution margin .......................................................................................... $ 54,000 $ 60,000

Less fixed expenses .................................................................................................. 48,000 48,000

Profit $ 6,000 $ 12,000

Given: {

Fixed expenses

Unit contribution margin Target profit

}

, Find: {required sales volume}

We also can use CVP analysis to turn this question around and make the following query.

Given: {

Fixed expenses

Unit contribution margin Expected sales volume

}

, Find: {expected profit}

Suppose the management of Seattle Contemporary Theater expects fixed monthly expenses of $48,000 and unit variable expenses of $10 per ticket. The organization’s board of trustees is considering two different ticket prices, and the business manager has forecast monthly demand at each price.

Expected profit may be calculated at each price as shown in the following table. In these profit calculations, the total contribution margin is the difference between total sales revenue and total variable expenses. This use of the term contribution margin is a “total” concept rather than the “per unit” concept used earlier in the chapter. The total contribution margin is the total amount left to contribute to covering fixed expenses after total variable expenses have been covered.

The difference in expected profit at the two ticket prices is due to two factors:

1. A different unit contribution margin, defined previously as unit sales price minus unit variable expenses.

2. A different sales volume.

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Incremental Approach Rather than presenting the entire income statement under each ticket price alternative, we can use a simpler incremental approach. This analysis focuses only on the difference in the total contribution margin under the two prices. Thus, the combined effect of the change in unit contribution margin and the change in sales volume is as follows:

Expected total contribution margin at $20 ticket price:

6,000 × ($20 − $10) ......................................................................................................................... $60,000

Expected total contribution margin at $16 ticket price:

9,000 × ($16 − $10) ......................................................................................................................... 54,000

Difference in total contribution margin .................................................................................................. $ 6,000

Ticket Price Unit Contribution

Margin Forecast Monthly

Demand Net Fixed Expenses

(after subtracting donation)

$16 ................ $ 6 ................. 9,000 .............. $38,000 ($48,000 − $10,000)

20 ................ 10 ................. 6,000 .............. 48,000

Ticket Price

$16 $20

Sales revenue:

9,000 × $16 ....................................................................................................... $144,000

6,000 × $20 ....................................................................................................... $120,000

Less variable expenses:

9,000 × $10 ....................................................................................................... 90,000

6,000 × $10 ....................................................................................................... 60,000

Total contribution margin ........................................................................................ $ 54,000 $ 60,000

Less net fixed expenses (net of donation) .............................................................. 38,000 48,000

Profit ........................................................................................................................ $ 16,000 $ 12,000

The $6,000 difference in expected profit, at the two ticket prices, is due to a $6,000 difference in the total contribution margin. The board of trustees will consider these pro- jected profits as it decides which ticket price is best. Even though Seattle Contemporary Theater is a nonprofit organization, it may still have legitimate reasons for attempting to make a profit on its theater performances. For example, the board might use these prof- its to fund a free drama workshop, provide scholarships for local young people to study drama in college, or produce a free outdoor play for Seattle’s residents.

Interdependent Changes in Key Variables Sometimes a change in one key variable will cause a change in another key variable. Suppose the board of trustees is choosing between ticket prices of $16 and $20, and the business manager has projected demand as shown in the preceding section. A famous retired actress who lives in Seattle has offered to donate $10,000 per month to Seattle Contemporary Theater if the board will set the ticket price at $16. The actress is inter- ested in making the theater’s performances affordable for as many people as possible. The facts are now as follows:

The organization’s expected profit at each price is computed as follows:

Now the difference in expected profit at the two ticket prices is due to three factors:

1. A different unit contribution margin. 2. A different sales volume. 3. A difference in the net fixed expenses, after deducting the donation.

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Incremental Approach The combined effect of these factors is shown in the follow- ing analysis, which focuses on the effects of the price alternatives on the total contribu- tion margin and the net fixed expenses.

Expected total contribution margin at $20 ticket price:

6,000 × ($20 − $10) ................................................................................................................................................ $60,000

Expected total contribution margin at $16 ticket price:

9,000 × ($16 − $10) ................................................................................................................................................ 54,000

Difference in total contribution margin (higher with $20 ticket price) ......................................................................... $ 6,000

Net fixed expenses at $20 ticket price .......................................................................................................................... $48,000

Net fixed expenses at $16 ticket price .......................................................................................................................... 38,000

Difference in net fixed expenses (higher with $20 ticket price) ................................................................................... $10,000

The expected total contribution margin is $6,000 higher with the $20 ticket price, but net fixed expenses are $10,000 higher. Thus, Seattle Contemporary Theater will make $4,000 more in profit at the $16 price ($10,000 − $6,000).

CVP Information in Published Annual Reports Cost-volume-profit relationships are so important to understanding an organization’s operations that some companies disclose CVP information in their published annual reports. The following illustration is from the airline industry.

AIRLINES KEEP A CLOSE EYE ON BREAK-EVEN LOAD FACTORS

An airline’s break-even load factor is the percentage of available seats that must be filled in order for the airline’s revenues to equal its expenses. This is the point where the airline breaks even on its flight operations. Airlines pay close attention to their system-wide break- even load factors and often disclose them in their annual reports.

JetBlue, a successful discount airline founded in 1998, now serves over 70 cities in the USA in addition to a number of destinations in the Caribbean, Latin America, and South America. A recent airline industry analysis listed JetBlue’s break-even load factor as 81.79 percent. By comparison, the break-even load factors for a few other well-known air- lines were reported as follows: American, 83.14 percent; United, 88.6 percent; and Southwest, 79.6 percent.2

It is not necessarily valid, however, to compare operating statistics, such as break- even load factors, across airlines. According to industry analysts, the definition of operating expenses used in calculating the break-even load factor differs across airlines. For exam- ple, some airlines exclude fuel costs from the calculation of operating expenses, because oil prices fluctuate widely and are not under an airline management’s control. Given the disparity in the definition of the expenses used to calculate the break-even load factor, comparisons across airlines are suspect. However, it is worthwhile to track a particular airline’s break-even load factor across time periods.3

2“4Q 2012 Scorecard” www.theairlinewebsite.com. 3Based on the authors’ research.

anagement ccounting ractice

M

A

P

American Airlines, JetBlue Airways, Southwest Airlines, and United Airlines

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CVP Analysis with Multiple Products

Our CVP illustration for Seattle Con- temporary Theater has assumed that the organization has only one product, a theater seat at a dramatic performance. Most firms have a sales mix consisting of more than one product, and this adds some complexity to their CVP analyses.

As we have seen, Seattle Contempo- rary Theater’s monthly fixed expenses total $48,000, and the unit variable expense per ticket is $10. Now suppose that the city of Seattle has agreed to refurbish 10 theater boxes in the historic

theater building. Each box has five seats, which are more comfortable and afford a better view of the stage than the theater’s general seating. The board of trustees has decided to charge $16 per ticket for general seating and $20 per ticket for box seats. These facts are summarized as follows:

Learning Objective 7-5

Compute the break-even point and prepare a profit-volume graph for a multiproduct enterprise.

Seat Type Ticket Price Unit Variable

Expense

Unit Contribution

Margin Seats in Theater

Seats Available per Month

(20 performances)

Regular $16 $10 $ 6 450 9,000

Box 20 10 10 50 1,000

Regular seats: 90% × 5,000 .................................................................................................................................... 4,500

Box seats: 10% × 5,000 ..................................................................................................................................... 500

Total ............................................................................................................................................................ 5,000

Major airlines keep a close watch on the break-even passenger load factor.

Notice that 90 percent of the available seats are regular seats, and 10 percent are box seats. The business manager estimates that tickets for each type of seat will be sold in the same proportion as the number of seats available. If, for example, 5,000 tickets are sold during a month, sales will be as follows:

For any organization selling multiple products, the relative proportion of each type of product sold is called the sales mix. The business manager’s estimate of Seattle Contem- porary Theater’s sales mix is 90 percent regular seats and 10 percent box seats.

The sales mix is an important assumption in multiproduct CVP analysis. The sales mix is used to compute a weighted-average unit contribution margin. This is the average of the several products’ unit contribution margins, weighted by the relative sales propor- tion of each product. Seattle Contemporary Theater’s weighted-average unit contribution margin is computed below.

Weighted-average unit contribution margin = ($6 × 90 %) + ($10 × 10%) = $6.40

The organization’s break-even point in units is computed using the following formula.

Break-even point = Fixed expenses _____________________________ Weighted-average unit contribution _____________________________ margin

= $48,000 _______ $6.40

= 7,500 tickets

(8)

© Royalty-Free/Corbis

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The break-even point of 7,500 tickets must be interpreted in light of the sales mix. Seattle Contemporary Theater will break even for the month if it sells 7,500 tickets as follows:

Break-even ? ? ?

Regular seats: 7,500 × 90% .......................................................................................... 6,750 tickets

sales in Box seats: 7,500 × 10% .......................................................................................... 750 tickets

units: Total .................................................................................................................................... 7,500 tickets

Sales revenue:

Regular seats: 6,750 × $16 ............................................................................................................................ $108,000

Box seats: 750 × $20 ..................................................................................................................................... 15,000

Total revenue: 7,500 seats in total .................................................................................................................. $123,000

Less variable expenses: 7,500 × $10 ................................................................................................................. 75,000

Total contribution margin ...................................................................................................................................... $ 48,000

Less fixed expenses .............................................................................................................................................. 48,000

Profit ...................................................................................................................................................................... $ 0

Exhibit 7–4 Profit-Volume Graph with Multiple Products: Seattle Contemporary Theater

$000 (per month)

50

2,000

Volume* (tickets sold in one month)

40

30

20

10

0

10

20

30

40

50

4,000 6,000 8,000 10,000

Loss area

Profit Break-even point: 7,500 tickets in total

Total profit

Loss

Profit area

* Sales mix assumption: 90% regular seats 10% box seats

The following income calculation verifies the break-even point.

The break-even point of 7,500 tickets per month is valid only for the sales mix assumed in computing the weighted-average unit contribution margin. If 7,500 tickets are sold in any other mix of regular and box seats, the organization will not break even.

Notice that break-even formula (8) is a modification of formula (1) given earlier in the chapter. The only difference is that formula (8) uses the weighted-average unit con- tribution margin.

Seattle Contemporary Theater’s business manager has constructed the profit-volume graph in Exhibit 7–4. The PV graph shows the organization’s profit at any level of total monthly sales, assuming the sales mix of 90 percent regular seats and 10 percent box seats. For example, if 9,000 tickets are sold in total, at the assumed sales mix, the PV graph indicates that profit will be $9,600.

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With multiproduct CVP analysis, a managerial accountant can investigate the impact on profit of changes in sales volume, prices, variable costs, fixed costs, or the sales mix itself. For example, what would be the effect on Seattle Contemporary The- ater’s break-even point if the sales mix were 95 percent regular seats and 5 percent box seats? With this sales mix, the weighted-average unit contribution margin is computed as follows:

Learning Objective 7-6

List and discuss the key assumptions of CVP analysis.

Weighted-average unit contribution margin = ($6 × 95 %) + ($10 × 5%) = $6.20

The break-even point increases from 7,500 tickets to approximately 7,742 tickets as a result of the lower proportion of expensive seats in the sales mix.

Break-even point = Fixed expenses ____________________________________ Weighted-average unit contribution margin

= $48, 000 ________ $6.20

= 7,742 tickets *

Assumptions Underlying CVP Analysis

For any cost-volume-profit analysis to be valid, the following important assumptions must be reasonably satisfied within the relevant range.

1. The behavior of total revenue is linear (straight-line). This implies that the price of the product or service will not change as sales volume varies within the rel- evant range.

2. The behavior of total expenses is linear (straight-line) over the relevant range. This implies the following more specific assumptions.

a. Expenses can be categorized as fixed, variable, or semivariable. Total fixed expenses remain constant as activity changes, and the unit variable expense remains unchanged as activity varies.

b. The efficiency and productivity of the production process and workers remain constant.

3. In multiproduct organizations, the sales mix remains constant over the relevant range.

4. In manufacturing firms, the inventory levels at the beginning and end of the period are the same. This implies that the number of units produced during the period equals the number of units sold.

Role of Spreadsheets and Computerized Planning Models Cost-volume-profit analysis is based on the four general assumptions listed above as well as specific estimates of all the variables used in the analysis. Since these variables are rarely known with certainty, it is helpful to run a CVP analysis many times with differ- ent combinations of estimates. For example, Seattle Contemporary Theater’s business manager might do the CVP analysis using different estimates for the ticket prices, sales mix for regular and box seats, unit variable expenses, and fixed expenses. This approach is called sensitivity analysis, since it provides the analyst with a feel for how sensitive the analysis is to the estimates upon which it is based. The widespread availability of per- sonal computers and spreadsheet software (such as Excel) has made sensitivity analysis relatively easy to do.

*Rounded

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- 7 Cost-Volume-Profit Analysis
- Illustration of Cost-Volume-Profit Analysis
- Projected Expenses and Revenue

- The Break-Even Point
- Contribution-Margin Approach

- Graphing Cost-Volume-Profit Relationships
- Interpreting the CVP Graph
- Alternative Format for the CVP Graph
- Profit-Volume Graph

- Target Profit
- Contribution-Margin Approach
- Equation Approach
- Graphical Approach

- Applying CVP Analysis
- Safety Margin
- Changes in Fixed Expenses
- Changes in the Unit Contribution Margin
- Predicting Profit Given Expected Volume
- Interdependent Changes in Key Variables
- CVP Information in Published Annual Reports
- M.A.P. Airlines Keep a Close Eye on Break-Even Load Factors

- CVP Analysis with Multiple Products
- Assumptions Underlying CVP Analysis
- Role of Spreadsheets and Computerized Planning Models

- Illustration of Cost-Volume-Profit Analysis