Chapter 7 - Cost-Volume-Profit Analysis

COST-VOLUME-PROFIT ANALYSIS What effect on profit can United Airline 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 Generals Hospital provide to break even for the year? What happens to this break-even point patient load if the hospital leases a new computerized system for patient records? Each of these questions concerns the effect on costs and revenues when the organization activity changes. The analytical technique used by managerial accountants to address these questions is called cost-volume-profit analysis, often called CVP for short. CVP 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. CVP is also in non-profit organizations. E.g. 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, and police protection. Illustration of Cost-Volume-Profit Analysis Projected Expenses and Revenue Fixed expenses per month: Theater rental ---------------------------------------------------$ 10,000 Employees’ salaries and fringe benefit ---------------------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 & 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 ------------------Other miscellaneous expenses (e.g. printing of playbills and tickets, variable portion of utilities) --------Total variable cost per ticket sold ----------------------------Revenue: Price per ticket ------------------------------------------

$8 2 $ 10

$ 16

Note the importance of cost behavior in cost categorization: fixed and variable.

The Break-even Point Break-even point is the volume of activity where the organization’s revenues and expenses are equal. Total contribution margin is the total sales revenue minus total variable expenses. This is the amount of revenue that is available to contribute to covering fixed expenses after all variable expenses have been covered. Break-even volume of tickets as follows: Fixed ExpensesUnit contribution margin =Break-even point (in units) Fixed ExpensesContribution-margin ratio =Break-even point in sales dollars

Contribution-margin ratio = the unit contribution margin divided by the unit sales price. 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 activity, a CVP graph is commonly used. The graph shows relevant range, which is the range of activity within which management expects the theater to operate.

If the theater building seats 450 people, the agreement calls for 20 performances expensesof for tickets that can be sold during each play’s one-month run, thus, the maximum Total number 8,000 tickets, $ 128,000 each month is 450 × 20 = 9,000. The organization’s break-even point is quite close to the maximum possible sales volume. This could be a cause of concern in a nonprofit organization operating on limited resources. What could the management do to improve thisTotal situation? One possibility is to fixed expense However, this might not be renegotiate with the city to schedule additional performances. 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. The CVP graph will not resolve this potential problemRelevant for the management of this Range theater. However, the graph will direct management’s attention to the situation. Target Net Profit The 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 space at a local college. No variable expenses would be incurred. If the theater could make a profit of $ 3,600 per month on its performances, the

workshop could be opened. How many theater tickets must be sold during each play’s onemonth run to make a profit of $3,600? The desired profit level of $ 3,600 is called a target net profit (or income). Contribution margin approach: Fixed expense +Target net profitUnit contribution margin=Number of sales unit required to earn target net profit $ 48,000 +$ 3,600$ 6=8,600 tickets $ 48,000 +$ 3,600.375=$ 137,600, Where the contributing margin ratio =

$ 6$ 16= .375

Applying CVP Analysis Safety Margin of an enterprise is the difference between budgeted sales revenue and the break-even sales revenue. Suppose theater’s business manager expects every performance of each play to be sold out. Then budgeted monthly sales revenue is $ 144,000 (450 seats x 20 performances of each play x $ 16 per ticket). Since breakeven 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. Changes in Fixed Expense: 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 estimate of fixed expenses has increased by 2.5 percent, since $ 1,200 is 2.5 percent of $ 48,000. Notice that break-even point also increased by 2.5 percent (200 tickets is 2.5 percent of 8,000 tickets). This relationship will always exist. 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. Suppose that various people pledge donations amounting to $ 6,000 per month. The new break-even point is ($ 48,000 - $ 6,000)/$ 6 = 7,000 tickets. Changes in the Unit Contribution Margin: What would happen to 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? Changes in Unit variable expenses:

Unit contribution margin reduces from $ 6 to $ 5, break-even point increases from 8,000 tickets to 9,600 tickets or from $ 128,000 to $ 153,600. 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 x 20 performances). Once again, CVP analysis will not solve this problem for management, but it will direct management’s attention to potentially serious difficulties. Changes in Sales Price: 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 $ 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 performance. 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 fundamental goals of 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. Prediction Profit Given Expected Volume: Suppose the management theater expects fixed monthly expense of $ 48,000 and unit variable expenses of $10 per ticket. The organization’s board of trustee is considering two different ticket prices, and the business manager has forecast monthly demand at each price. Ticket Price

Forecast Monthly Demand

$ 16

9,000

$ 20

6,000

The difference in expected profit at the two tickets 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 Expected total contribution margin at $ 20 ticket price: 6,000 x ($20 --------------------------------------------------

-

$10)

$ 60,000

Expected total contribution margin at $ 16 ticket price: 9,000 x ($16 -------------------------------------------------Difference in total contribution margin

-

$10)

54,000

$ 6,000

Interdependent Changes In Key Variables: 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 theater if the board wills set the ticket price at $ 16. The actress is interested in making the theater’s performances affordable by as many people as possible. The facts are now as follows: 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

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 The theater will make $ 4,000 more in profit at the $16 price ($10,000 - $6,000). CVP Analysis with Multiple Products Most firms have a sales mix consisting come complexity to their CVP analyses. Suppose 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: Seat Type

Ticket Price

Unit Variable Expense

Unit Margin

Contribution

Seats Theater

in

Seats Available month (20 performance)

Regular

$ 16

$ 10

$6

450

9,000

Box

20

10

10

50

1,000

Weighted-average unit contribution margin = ($6 x 90%) + ($10 x 10%) = $ 6.40 Break-even point = Fixed expensesWeighted-average unit contribution margin = $ 48,000$ 6.40

per

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

Break-even sales in units

Regular seats: 7,500 x 90%

6,750 tickets

Box seats:

750 tickets

7,500 x 10%

Total

7,500 tickets

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.

Assumptions Underlying CVP Analysis For any CVP 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 relevant 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 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 Computerized Planning Models and Electronic Spreadsheets Since these variables are rarely known with certainty, it is helpful to run a CVP analysis many times with different combinations of estimates. For example, 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. CVP Relationships and the Income Statement Contribution Income statement vs. traditional Income Statement Cost Structure and Operating Leverage The cost structure of an organization is the relative proportion of its fixed and variable costs.

An organization’s cost structure has significant effect on the sensitivity of its profit to changes in volumes. Operating Leverage The extent to which an organization uses fixed costs in its cost structure is called operating leverage. The operating leverage is the greatest in firms with a large proportion of fixed costs, low proportion of variable costs, and the resulting high contribution-margin ratio. To physical scientist, leverage refers to the ability of a small force to move a heavy weight. To the managerial accountant, operating leverage refers to the ability of the firm to generate an increase in net income when sales revenue increases. Operating Leverage = Contribution MarginNet Income

Break-even Point and Safety Margin Since a firm with relatively high operating leverage has proportionally high fixed expenses, the firm’s break-even point will be relatively high and the firm’s safety margin will be relatively lower. Labor-Intensive Production Processes versus Advanced Manufacturing Systems A movement toward an advanced manufacturing environment often results in a higher break-even point, lower safety margin, and higher operating leverage. However, high-technology manufacturing systems often have greater throughput, thus allowing greater potential for profitability. Along with the increased potential for profitability comes increased risk. In an economic recession, for example, a highly automated company with high fixed costs will be less able to adapt to lower consumer demand than will a firm with a more laborintensive production process. Cost Structure and Operating Leverage: A Cost-Benefit Issue An organization’s cost structure plays an important role in determining its cost-volumeprofit relationships. A firm with proportionally high fixed costs has relatively high operating leverage. The result of high operating leverage is that the firm can generate a large percentage increase in net income from a relatively small percentage increase in sales revenue. On the other hand, a firm with high operating leverage has a relatively high break-even point. This entails some risk to the firm. CVP Analysis, Activity-Based Costing, and Advanced Manufacturing System The contribution Income Statement: Sales Volume

20,000 Units

Sales Price

$ 25

Unit variable costs: Variable manufacturing

$ 14

Variable selling and administrative

1

Total unit variable cost

$ 15

Unit contribution margin

$10

Fixed costs: Fixed manufacturing

$ 100,000

Fixed selling and administrative Total fixed costs

50,000 $ 150,000

Break-even point = $ 150,000$ 10 =15,000 units Sales volume required to earn target net profit of $ 200,000 = $ 150,000+$ 200,000$ 10 = 35,000 units These focus on sales volume as the sole revenue and cost driver. The CVP analysis depends on a distinction between costs that are fixed and costs that are variable with respect to sales volume. The contribution Income Statement: Sales Price

$ 25

Unit variable costs: Variable manufacturing Variable selling and administrative Total unit variable cost Unit contribution margin

$ 14 1 $ 15 $10

Fixed costs (fixed with respect to sales volume): General factory overhead (including depreciation on plant and equipment) Setup (52 setups at $ 100 per setup)*

$ 60,000

5,200

Inspection [(52)(21) inspections at $ 20 per inspection]**

21,880

Material handling (1,080 hours at $12 per hour)

12,960

Total fixed manufacturing costs Fixed selling and administrative costs Total fixed costs

$ 100,000 50,000 $ 150,000

*One setup per week **Three inspections per day, seven days a week (52 weeks per year)

With the installation of a flexible manufacturing system and a move toward just-in-time production: Sales Price

$ 25

Unit variable costs: Variable manufacturing Variable selling and administrative Total unit variable cost Unit contribution margin

$9 1 $ 10 $15

Fixed costs (fixed with respect to sales volume): General factory overhead (including depreciation on plant and equipment) Setup (365 setups at $ 30 per setup)*

$ 184,000

10,950

Inspection [365 inspections at $ 10 per inspection]**

3,650

Material handling (100 hours at $14 per hour)

1,400

Total fixed manufacturing costs Fixed selling and administrative costs Total fixed costs

$ 200,000 50,000 $ 250,000

Break-even point = $ 250,000$ 15 =16,667 units Sales volume required to earn target net profit of $ 200,000 = $ 250,000+$ 200,000$ 15 = 30,000 units Note that the break-even point increased with the introduction of the advanced manufacturing system (from 15,000 to 16,667 units). However, the number of sales units required to earn a target net profit of $ 200,000 declined (from 35,000 to 30,000 units).