Please see attachment. All three question need to be answered in narrative format. If you have questions, just let me know. Normal requirement for references are 2 outside our course text.

edm10890_ch02_054-105.indd Page 54 6/18/10 5:03 PM user-f497 /Users/user-f497/Desktop/MHBR165 CHAPTER 2 Cost Behavior, Operating Leverage, and Profitability Analysis LEARNING OBJECTIVES R O B E R T S , After you have mastered the material in this chapter, B you will be able to: 1 2 3 4 5 6 7 Identify and describe fixed, variable, and mixed cost Ebehavior. Demonstrate the effects of operating leverage on profitability. N Prepare an income statement using the contribution margin approach. 2 Demonstrate how the relevant range and decision 6 context affect cost behavior. 5 average cost per unit. Select an appropriate time period for calculating the 7 analysis to estimate fixed and variable costs. Use the high-low method, scattergraphs, and regression B U CHAPTER OPENING Calculate the magnitude of operating leverage. Three college students are planning a vacation. One of them suggests inviting a fourth person along, remarking that four can travel for the same cost as three. Certainly, some costs will be the same whether three or four people go on the trip. For example, the hotel room costs $800 per week, regardless of whether three or four people stay in the room. In accounting terms the cost of the hotel room is a fixed cost. The total amount of a fixed cost does not change when volume changes. The total hotel room cost is $800 whether 1, 2, 3, or 4 people use the room. In contrast, some costs vary in direct proportion with changes in volume. When volume increases, total variable cost increases; when volume decreases, total variable cost decreases. For example, the cost of tickets to a theme park is a variable cost. The total cost of tickets increases proportionately with each vacationer who goes to the theme park. Cost behavior (fixed versus variable) can significantly impact profitability. This chapter explains cost behavior and ways it can be used to increase profitability. 54 edm10890_ch02_054-105.indd Page 55 6/18/10 5:03 PM user-f497 /Users/user-f497/Desktop/MHBR165 The Curious Accountant News flash! On April 29, 2009, Eastman Kodak, Inc., announced that its first quarter's revenues decreased 29 percent compared to the same quarter in 2008, yet its earnings had decreased by 213 percent. On May 4, 2009, Walt Disney announced that a decrease in R O same quarter in 2008. On April 12, 2009, Apple computer reported that its revenue for the quarter had increased B by 9 percent compared to the previous year, but its earnings E increased by 15 percent. Can you explain why such relatively small changes in Rthese companies' revenues resulted in such relatively large changes in their earnings or losses? In other words, T if a company's sales increase 10 percent, why do its earnings not also increase 10 percent? (Answer on pageS60.) , revenue of 7 percent for the just-ended quarter would cause its earnings to decrease 46 percent compared to the B E N 2 6 5 7 B U 55 edm10890_ch02_054-105.indd Page 56 6/18/10 5:04 PM user-f497 56 /Users/user-f497/Desktop/MHBR165 Chapter 2 FIXED COST BEHAVIOR LO 1 Identify and describe fixed, variable, and mixed cost behavior. How much more will it cost to send one additional employee to a sales meeting? If more people buy our products, can we charge less? If sales increase by 10 percent, how will profits be affected? Managers seeking answers to such questions must consider cost behavior. Knowing how costs behave relative to the level of business activity enables managers to more effectively plan and control costs. To illustrate, consider the entertainment company Star Productions, Inc. (SPI). SPI specializes in promoting rock concerts. It is considering paying a band $48,000 to play a concert. Obviously, SPI must sell enough tickets to cover this cost. In this example, the relevant activity base is the number of tickets sold. The cost of the band is a fixed cost because it does not change regardless of the number of tickets sold. Exhibit 2.1 illustrates the fixed cost behavior pattern, showing the total cost and the cost per unit at three different levels of activity. Total versus per-unit fixed costs behave differently. The total cost for the band remains constant (fixed) at $48,000. In contrast, fixed cost per unit decreases as volume (number of tickets sold) increases. The term fixed cost is consistent with the behavior of total cost. Total fixed cost remains R constant (fixed) when activity changes. However, there is a contradiction between the term fixed cost per unit and the per-unit behavior O pattern of a fixed cost. Fixed cost per unit is not fixed. It changes with the number of tickets sold. This contradiction B in terminology can cause untold confusion. Study carefully the fixed cost behavior patterns in Exhibit 2.2. E R TEXHIBIT 2.2 SFixed Cost Behavior , When Activity EXHIBIT 2.1 Fixed Cost Behavior Number of tickets sold (a) Total cost of band (b) Cost per ticket sold (b 4 a) 2,700 $48,000 $17.78 3,000 $48,000 $16.00 3,300 $48,000 $14.55 BTotal fixed cost Fixed cost per unit E N Increases When Activity Decreases Remains constant Decreases Remains constant Increases The fixed cost data in Exhibit 2.1 help SPI's management decide whether to sponsor the concert. For example, the information influences potential pricing choices. The 2 per-unit costs represent the minimum ticket prices required to cover the fixed cost at various levels of activity. SPI could compare these per-unit costs to the prices of com6 peting entertainment events (such as the prices of movies, sporting events, or theater 5 tickets). If the price is not competitive, tickets will not sell and the concert will lose money. Management must also7consider the number of tickets to be sold. The volume data in Exhibit 2.1 can be compared to the band's track record of ticket sales at previous concerts. A proper analysisBof these data can reduce the risk of undertaking an unprofitable venture. U OPERATING LEVERAGE LO 2 Demonstrate the effects of operating leverage on profitability. Heavy objects can be moved with little effort using physical leverage. Business managers apply operating leverage to magnify small changes in revenue into dramatic changes in profitability. The lever managers use to achieve disproportionate changes between revenue and profitability is fixed costs. The leverage relationships between revenue, fixed costs, and profitability are displayed in Exhibit 2.3. When all costs are fixed, every sales dollar contributes one dollar toward the potential profitability of a project. Once sales dollars cover fixed costs, each EXHIBIT 2.3 Operating Leverage Small percentage change in revenue $ Dramatic percentage change in profitability $ Fixed costs $ edm10890_ch02_054-105.indd Page 57 6/18/10 5:04 PM user-f497 /Users/user-f497/Desktop/MHBR165 Cost Behavior, Operating Leverage, and Profitability Analysis 57 FOCUS ON INTERNATIONAL ISSUES FIXED COSTS BRING INTERNATIONAL INTRIGUE INTO THE AUTOMOBILE INDUSTRY The major advantage of fixed costs is that as output increases, cost per unit decreases. Of course fixed costs can be a disadvantage if output is falling. Due to the nature of the industry automobile manufacturers have high fixed costs. It takes a lot of land, buildings, and machinery to mass produce cars and trucks. In 2007 the worldwide production of autos was 73.3 million units;* in 2008 it had fallen to 70.5 million units due to the global recession. Not surprisingly, this had an adverse effect on companies that were already struggling, such as GM, Ford, and Chrysler, but it also affected the strongest company inRthe industry, Toyota. In its fiscal year ended March 31, 2008, Toyota O produced 8.5 million vehicles and had a profit of $17.1 billion. In B fallen to 7.1 million vehicles, and it had a net loss of $4.0 billion. its fiscal year ended March 31, 2009, the company's output had A company with high fixed costs suffers on two fronts during E a recession. First, the lower production causes its cost per unit to rise. Second, the weak economy puts pressure on it, and its competitors, to lower prices, or at least not to raise them. In Toyota's R profits for many years suddenly had a significant loss. case, this meant that a company that had been reporting growing T S , *Sources of data: International Organization of Motor Vehicle Manufactures and Toyota's annual reports. additional sales dollar represents pure profit. As a result, a small change in sales volume can significantly affect profitability. To illustrate, assume SPI estimates it will sell 3,000 tickets for $18 each. A 10 percent difference in actual sales Bvolume will produce a 90 percent difference in profitability. Examine the data in Exhibit 2.4 to verify this result.1 E N EXHIBIT 2.4 Effect of Operating Leverage on Profitability Number of tickets sold Sales revenue ($18 per ticket) Cost of band (fixed cost) Gross margin 2,700 $48,600 (48,000) $ 600 210% 290% Calculating Percentage Change 2 63,000 $54,000 5 (48,000) $7 6,000 B U 110% 190% 3,300 $59,400 (48,000) $11,400 The percentages in Exhibit 2.4 are computed as follows: (Alternative measure 2 Base measure) 4 Base measure 5 % change The base measure is the starting point. To illustrate, compute the percentage change in gross margin when moving from 3,000 units (base measure) to 3,300 units (the alternative measure). (Alternative measure 2 Base measure) 4 Base measure 5 % change ($11,400 2 $6,000) 4 $6,000 5 90% 1 Do not confuse operating leverage with financial leverage. Companies employ financial leverage when they use debt to profit from investing money at a higher rate of return than the rate they pay on borrowed money. Companies employ operating leverage when they use proportionately more fixed costs than variable costs to magnify the effect on earnings of changes in revenues. edm10890_ch02_054-105.indd Page 58 6/18/10 5:04 PM user-f497 58 /Users/user-f497/Desktop/MHBR165 Chapter 2 The percentage decline in profitability is similarly computed: (Alternative measure 2 Base measure) 4 Base measure 5 % change ($600 2 $6,000) 4 $6,000 5 (90%) Risk and Reward Assessment Risk refers to the possibility that sacrifices may exceed benefits. A fixed cost represents a commitment to an economic sacrifice. It represents the ultimate risk of undertaking a particular business project. If SPI pays the band but nobody buys a ticket, the company will lose $48,000. SPI can avoid this risk by substituting variable costs for the fixed cost. VARIABLE COST BEHAVIOR LO 1 Identify and describe fixed, variable, and mixed cost behavior. To illustrate variable cost behavior, assume SPI arranges to pay the band $16 per ticket sold instead of a fixed $48,000. Exhibit 2.5 shows the total cost of the band and the cost per ticket sold at three different levels of activity. R EXHIBIT 2.5 O B Variable Cost Behavior E Number of tickets sold (a) 2,700 3,000 3,300 Total cost of band (b)R $43,200 $48,000 $52,800 Cost per ticket sold (b 4 a) $16 $16 $16 T S Since SPI will pay the band $16 for each ticket sold, the total variable cost increases , of tickets sold. If SPI sells one ticket, total band cost in direct proportion to the number will be $16 (1 3 $16); if SPI sells two tickets, total band cost will be $32 (2 3 $16); and so on. The total cost of the band increases proportionately as ticket sales move from B cost per ticket remains $16, however, regardless of 2,700 to 3,000 to 3,300. The variable whether the number of tickets sold E is 1, 2, 3, or 3,000. The behavior of variable cost per unit is contradictory to the word variable. Variable cost per unit remains constant Nare sold. Study carefully the variable cost behavior regardless of how many tickets patterns in Exhibit 2.6. 2 6 Variable Cost Behavior 5 7 Activity Increases When B proportionately Total variable cost Increases Variable cost per unit Remains U constant EXHIBIT 2.6 When Activity Decreases Decreases proportionately Remains constant Risk and Reward Assessment LO 2 Demonstrate the effects of operating leverage on profitability. Shifting the cost structure from fixed to variable enables SPI to avoid the fixed-cost risk. Recall that under the fixed cost structure, SPI was locked into a $48,000 cost for the band regardless of how many tickets are sold. If no tickets are sold, SPI will have to report a $48,000 loss on its income statement. The risk of incurring this loss is eliminated by the variable cost structure that requires SPI to only pay the band $16 per ticket sold. If SPI sells zero tickets then the cost of the band is zero. For each ticket sold, SPI earns a $2 profit ($18 ticket sales price 2 $16 fee paid to band). Shifting the cost structure from fixed to variable reduces not only the level of risk but also the potential for profits. Managers cannot avoid the risk of fixed costs without also sacrificing the benefits. Variable costs do not offer operating leverage. Exhibit 2.7 shows edm10890_ch02_054-105.indd Page 59 6/18/10 5:04 PM user-f497 /Users/user-f497/Desktop/MHBR165 Cost Behavior, Operating Leverage, and Profitability Analysis 59 EXHIBIT 2.7 Variable Cost Eliminates Operating Leverage Number of tickets sold Sales revenue ($18 per ticket) Cost of band ($16 variable cost) Gross margin 2,700 $48,600 (43,200) $ 5,400 210% 210% 3,000 $54,000 (48,000) $ 6,000 110% 110% 3,300 $59,400 (52,800) $ 6,600 that a variable cost structure produces a proportional relationship between sales and profitability. A 10 percent increase or decrease in sales results in a corresponding 10 percent increase or decrease in profitability. While the variable cost structure reduces risk, Exhibit 2.7 demonstrates that it also limits the opportunity to benefit from operating leverage. The risk versus reward trade-off of cost structure is widespread in business practice. For example, borrowing money to buy an office building may require a company to commit to a fixed monthly principal and interest payment. R If the company's revenue stream unexpectedly declines, the company still has to make its monthly payment. O Indeed, many companies are forced into bankruptcy because they cannot satisfy their B cost risks by renting their fixed debt commitments. Many companies avoid these fixed office space instead of purchasing buildings. If revenue E dips, the company simply reduces the amount of office space it rents, thereby reducing its rental cost. Other realRtemporary employees instead world examples of fixed-cost risk avoidance include using of hiring for permanent positions and paying a variableTretainer fee to an independent law firm instead of creating a legal department within the company. These examples S associated with cost strucdemonstrate the widespread applicability of the trade-offs ture. Managers continually apply professional judgment,to assess the risks of locking in costs with the opportunities provided by operating leverage. CHECK YOURSELF 2.1 B E N Suppose that you are sponsoring a political rally at which Ralph Nader will speak. You estimate that approximately 2,000 people will buy tickets to hear Mr. Nader's speech. The tickets are expected to be priced at $12 each. Would you prefer 2 a contract that agrees to pay Mr. Nader $10,000 or one that agrees to pay him $5 per ticket purchased? 6 Your answer would depend on how certain you are that 2,000 people will purchase 5be sold, you would be better tickets. If it were likely that many more than 2,000 tickets would off with a fixed cost structure, agreeing to pay Mr. Nader a flat7fee of $10,000. If attendance numbers are highly uncertain, you would be better off with a variable cost structure thereby B guaranteeing a lower cost if fewer people buy tickets. Answer U EFFECT OF COST STRUCTURE ON PROFIT STABILITY The preceding discussion suggests that companies with higher levels of fixed costs are more likely to experience earnings volatility. To illustrate, suppose three companies produce and sell the same product. Each company sells 10 units for $10 each. Furthermore, each company incurs costs of $60 in the process of making and selling its products. However, the companies operate under radically different cost structures. The entire $60 of cost incurred by Company A is fixed. Company B incurs $30 of fixed cost and $30 of variable cost ($3 per unit). All $60 of cost incurred by Company C is variable ($6 per unit). Exhibit 2.8 displays income statements for the three companies. LO 2 Demonstrate the effects of operating leverage on profitability. edm10890_ch02_054-105.indd Page 60 6/18/10 5:04 PM user-f497 60 /Users/user-f497/Desktop/MHBR165 Chapter 2 EXHIBIT 2.8 EXHIBIT 2.9 Income Statements Income Statements Company Name Variable cost per unit (a) Sales revenue (10 units 3 $10) Variable cost (10 units 3 a) Fixed cost Net income EXHIBIT 2.10 Income Statements Variable cost per unit (a) Sales revenue (9 units 3 $10) Variable cost (9 units 3 a) Fixed cost Net income Answers A B C $ 0 $100 0 (60) $ 40 $ 3 $100 (30) (30) $ 40 $ 6 $100 (60) 0 $ 40 Company Name Variable cost per unit (a) Sales revenue (11 units 3 $10) Variable cost (11 units 3 a) Fixed cost Net income A B C $ 0 $110 0 (60) $ 50 $ 3 $110 (33) (30) $ 47 $ 6 $110 (66) 0 $ 44 When sales change, the amount of the corresponding change in net income is directly influenced by the company's cost structure. The more fixed cost, the greater the R fluctuation in net income. To illustrate, assume sales increase by one unit; the resulting income statements are displayedOin Exhibit 2.9. Company A, with the highest level of fixed costs, experienced a $10 ($50 2 $40) B C, with the lowest level of fixed cost (zero), had increase in profitability; Company only a $4 ($44 2 $40) increase E in profitability. Company B, with a 50/50 mix of fixed and variable cost, had a mid-range $7 ($47 2 $40) increase in net income. The effect R to decreases as well as increases in sales volume. To of fixed cost on volatility applies illustrate, assume sales decrease by one unit (from 10 to T 9 units). The resulting income statements are displayed in S 2.10. Exhibit , Company A again experiences the largest variance in earnings ($10 decrease). Company B had a moderate deCompany Name cline of $7, and Company C had the least volatility with Ba $4 decline. only A B C EWhat cost structure is the best? Should a manager use $ 0 $ 3 $ 6 fixed or variable costs? The answer depends on sales N expectations. A manager who expects revenues to volume $90 $90 $90 0 (27) (54) increase should use a fixed cost structure. On the other (60) (30) 0 hand, if future sales growth is uncertain or if the manager 2 revenue is likely to decline, a variable cost struc$30 $33 $36 believes ture 6 makes more sense. 5 7 B to The Curious Accountant U TThe explanation for how a company's earnings can rise faster, as a percentage, than its revenue rises is operating leverage, and operating leverage is due entirely to fixed costs. As the chapter explains, when a company's output goes up, its fixed cost per unit goes down. As long as it can keep prices about the same, this lower unit cost will result in higher profit per unit sold. In real-world companies, the relationship between changing sales levels and changing earnings levels can be very complex, but the existence of fixed costs helps to explain why a 9 percent rise in revenue can cause a 15 percent rise in net earnings. Chapter 3 will investigate the relationships among an entity's cost structure, output level, pricing strategy, and profits earned in more depth. edm10890_ch02_054-105.indd Page 61 6/18/10 5:04 PM user-f497 /Users/user-f497/Desktop/MHBR165 Cost Behavior, Operating Leverage, and Profitability Analysis 61 CHECK YOURSELF 2.2 If both Kroger Food Stores and Delta Airlines were to experience a 5 percent increase in revenues, which company would be more likely to experience a higher percentage increase in net income? Delta would be more likely to experience a higher percentage increase in net income because a large portion of its cost (e.g., employee salaries and depreciation) is fixed, while a large portion of Kroger's cost is variable (e.g., cost of goods sold). Answer AN INCOME STATEMENT UNDER THE CONTRIBUTION MARGIN APPROACH The impact of cost structure on profitability is so significant that managerial accounR costs according to their betants frequently construct income statements that classify havior patterns. Such income statements first subtract variable costs from revenue; the O resulting subtotal is called the contribution margin. The contribution margin represents B to provide company profits. the amount available to cover fixed expenses and thereafter Net income is computed by subtracting the fixed costs from E the contribution margin. A contribution margin style income statement cannot be used for public reporting (GAAP R used for internal reporting prohibits its use in external financial reports), but it is widely purposes. Exhibit 2.11 illustrates income statements prepared using the contribution T margin approach. LO 3 Prepare an income statement using the contribution margin approach. S , EXHIBIT 2.11 Income Statements Variable cost per unit (a) Sales revenue (10 units 3 $20) Variable cost (10 units 3 a) Contribution margin Fixed cost Net income B E Company Name N Bragg Biltmore $ 6 $200 (60) 140 (120) $ 20 $ 12 2 $200 (120) 6 80 5 (60) $ 20 7 B U USING FIXED COST TO PROVIDE A COMPETITIVE OPERATING ADVANTAGE Mary MaHall and John Strike have established tutoring companies to support themselves while they attend college. Both Ms. MaHall and Mr. Strike function as owner/ managers; they each hire other students to actually provide the tutoring services. Ms. MaHall pays her tutors salaries; her labor costs are fixed at $16,000 per year regardless of the number of hours of tutoring performed. Mr. Strike pays his employees $8 per hour; his labor is therefore a variable cost. Both businesses currently provide 2,000 hours of tutoring services at a price of $11 per hour. As shown in Exhibit 2.12, both companies currently produce the same profit. Suppose Ms. MaHall adopts a strategy to win over Mr. Strike's customers by reducing the price of tutoring services from $11 per hour to $7 per hour. If Ms. MaHall LO 2 Demonstrate the effects of operating leverage on profitability. edm10890_ch02_054-105.indd Page 62 6/18/10 5:04 PM user-f497 62 /Users/user-f497/Desktop/MHBR165 Chapter 2 EXHIBIT 2.12 Comparative Profitability at 2,000 Hours of Tutoring Number of hours of tutoring provided Service revenue ($11 per hour) Cost of tutors Net income Fixed MaHall Strike 2,000 $22,000 (16,000) $ 6,000 2,000 $22,000 (16,000) $ 6,000 Variable ($8 3 2,000) succeeds, her company's income will double as shown in Exhibit 2.13. Mr. Strike is in a vulnerable position because if he matches MaHall's price cut he will lose $1 ($7 new perhour price 2 $8 cost per hour for tutor) for each hour of tutoring service that his company provides. R O MaHall's Profitability at 4,000 Hours of Tutoring B E MaHall Number of hours R of tutoring provided 4,000 Service revenue ($7 $28,000 T per hour) Cost of tutors Fixed (16,000) S Net income (loss) $12,000 , EXHIBIT 2.13 Is Mr. Strike's business doomed? Not necessarily; Ms. MaHall's operating leverage strategy only works if volumeB increases. If Mr. Strike matches Ms. MaHall's price, thereby maintaining the existing Esales volume levels between the two companies, both companies incur losses. Exhibit 2.14 verifies this conclusion. Under these circumstances, Ms. MaHall would beN forced to raise her price or to face the same negative consequences that she is attempting to force on Mr. Strike. 2 EXHIBIT 2.14 6 5 Hours of Tutoring Comparative Profitability at 2,000 7 MaHall B Number of hours of tutoring provided 2,000 U Service revenue ($7 per hour) $14,000 Cost of tutors Net income (loss) Fixed (16,000) $ (2,000) Strike Variable ($8 3 2,000) 2,000 $14,000 (16,000) $ (2,000) MEASURING OPERATING LEVERAGE USING CONTRIBUTION MARGIN LO 4 Calculate the magnitude of operating leverage. A contribution margin income statement allows managers to easily measure operating leverage. The magnitude of operating leverage can be determined as follows: Magnitude of operating leverage 5 Contribution margin Net income edm10890_ch02_054-105.indd Page 63 6/18/10 5:04 PM user-f497 /Users/user-f497/Desktop/MHBR165 Cost Behavior, Operating Leverage, and Profitability Analysis 63 Applying this formula to the income statement data reported for Bragg Company and Biltmore Company in Exhibit 2.11 produces the following measures. Bragg Company: Magnitude of operating leverage 5 $140 57 $20 Biltmore Company: Magnitude of operating leverage 5 $80 54 $20 The computations show that Bragg is more highly leveraged than Biltmore. Bragg's change in profitability will be seven times greater than a given percentage change in revenue. In contrast, Biltmore's profits change by only four times the percentage change in revenue. For example, a 10 percent increase in revenue produces a 70 percent increase (10 percent 3 7) in profitability for Bragg Company and a 40 percent increase (10 percent 3 4) in profitability for Biltmore Company. The income statements in Exhibits 2.15 and 2.16 confirm these expectations. EXHIBIT 2.15 Comparative Income Statements for Bragg Company Units (a) Sales revenue ($20 3 a) Variable cost ($6 3 a) Contribution margin Fixed cost Net income 10 $200 (60) 140 (120) $ 20 110% 170% 11 $220 (66) 154 (120) $ 34 R O B E R T S , EXHIBIT 2.16 Comparative Income Statements for Biltmore Company Units (a) Sales revenue ($20 3 a) Variable cost ($12 3 a) Contribution margin Fixed cost Net income 10 $200 (120) 80 (60) $ 20 110% 140% 11 $220 (132) 88 (60) $ 28 B E Operating leverage itself is neither good nor bad; it represents a strategy that can N on how it is used. The next work to a company's advantage or disadvantage, depending section explains how managers can use operating leverage to create a competitive business advantage. 2 6 5 CHECK YOURSELF 2.3 7 Boeing Company's 2001 10K annual report filed with the Securities B and Exchange Commission refers to \"higher commercial airlines segment margins.\" Is Boeing referring to gross margins U or contribution margins? Since the data come from the company's external annual report, the reference must be to gross margins (revenue 2 cost of goods sold), a product cost measure. The contribution margin (revenue 2 variable cost) is a measure used in internal reporting. Answer COST BEHAVIOR SUMMARIZED The term fixed refers to the behavior of total fixed cost. The cost per unit of a fixed cost varies inversely with changes in the level of activity. As activity increases, fixed cost per unit decreases. As activity decreases, fixed cost per unit increases. These relationships are graphed in Exhibit 2.17. LO 1 Identify and describe fixed, variable, and mixed cost behavior. edm10890_ch02_054-105.indd Page 64 6/18/10 5:04 PM user-f497 64 /Users/user-f497/Desktop/MHBR165 Chapter 2 EXHIBIT 2.17 EXHIBIT 2.18 Graphical Presentation of Fixed Cost Behavior Graphical Presentation of Variable Cost Behavior Total Fixed Cost $ Fixed Cost per Unit $ Units Total Variable Cost $ Units Variable Cost per Unit $ Units R O Fixed and Variable Cost Behavior B When Activity Level Changes E R Fixed costs Variable costs T S , Units EXHIBIT 2.19 Total Cost Cost per Unit Remains constant Changes in direct proportion Changes inversely Remains constant The term variable refers to the behavior of total variable cost. Total variable cost increases or decreases proportionately with changes in the volume of activity. In contrast, variable cost per unit remains B fixed at all levels of activity. These relationships are graphed in Exhibit 2.18. E and variable costs are summarized in the chart in The relationships between fixed N Exhibit 2.19. Study these relationships thoroughly. Mixed Costs (Semivariable 2 Costs) Mixed costs (semivariable costs) 6 include both fixed and variable components. For example, suppose Star Productions, Inc., has to pay for janitorial services. The charge 5 fee of $1,000 plus $20 per hour required to do a for these services includes a base cleanup. The $1,000 base fee is 7 fixed. It is the same no matter how many hours it takes to accomplish the cleanup. In contrast, the $20 hourly cost is a variable cost because the B total cost increases with each additional hour it takes to complete the cleanup. Since the total janitorial cost is composed of fixed and variable components, it is frequently U called a mixed cost. It may also be called a semivariable cost. Given the $1,000 base plus $20 per hour cost components, the total janitorial cost for any cleanup can be easily computed as shown below: Total cost 5 Fixed cost 1 (Variable cost per hour 3 Number of hours) If 60 hours are required to accomplish a cleanup, the total mixed cost is: Total cost 5 $1,000 1 ($20 3 60) 5 $2,200 If 90 hours are required to accomplish a cleanup, the total mixed cost is: Total cost 5 $1,000 1 ($20 3 90) 5 $2,800 Exhibit 2.20 illustrates a variety of mixed costs businesses commonly encounter. edm10890_ch02_054-105.indd Page 65 6/18/10 5:04 PM user-f497 /Users/user-f497/Desktop/MHBR165 Cost Behavior, Operating Leverage, and Profitability Analysis 65 EXHIBIT 2.20 Examples of Mixed Costs Type of Cost Fixed Cost Component(s) Cost of sales staff Truck rental Legal fees Monthly salary Monthly rental fee Monthly retainer Outpatient service cost Salaries of doctors and nurses, depreciation of facility, utilities Phone services LP gas utility cost Cable TV services Training cost Shipping and handling Monthly connection fee Container rental fee Monthly fee Instructor salary, facility cost Salaries of employees who process packages Inventory holding cost Depreciation on inventory warehouse, salaries of employees managing inventory The Relevant Range Variable Cost Component(s) Bonus based on sales volume Cost of gas, tires, and maintenance Reimbursements to attorney for out-of-pocket costs (copying, postage, travel, filing fees) Medical supplies such as bandages, sterilization solution, and paper products Per-minute usage fee Cost of gas consumed Pay-per-view charges RTextbooks, supplies OBoxes, packing supplies, tape, and other shipping supplies, Bpostage EDelivery costs, interest on funds borrowed to finance inventory, Rcost of supplies T S , Suppose SPI, the rock concert promoter mentioned earlier, must pay $5,000 to rent a concert hall with a seating capacity of 4,000 people. Is the B cost of the concert hall fixed or variable? Since total cost remains unchanged regardless of whether one ticket, 4,000 E relative to ticket sales. Howtickets, or any number in between is sold, the cost is fixed ever, what if demand for tickets is significantly more than N4,000? In that case, SPI might rent a larger concert hall at a higher cost. In other words, the cost is fixed only for a designated range of activity (1 to 4,000). A similar circumstance affects many variable costs.2For example, a supplier may offer a volume discount to buyers who purchase more than a specified number of 6 pertain to a specified range products. The point is that descriptions of cost behavior of activity. The range of activity over which the definitions 5 of fixed and variable costs are valid is commonly called the relevant range. 7 B Context-Sensitive Definitions of Fixed and U Variable The behavior pattern of a particular cost may be either fixed or variable, depending on the context. For example, the cost of the band was fixed at $48,000 when SPI was considering hiring it to play a single concert. Regardless of how many tickets SPI sold, the total band cost was $48,000. However, the band cost becomes variable if SPI decides to hire it to perform at a series of concerts. The total cost and the cost per concert for one, two, three, four, or five concerts are shown in Exhibit 2.21. In this context, the total cost of hiring the band increases proportionately with the number of concerts while cost per concert remains constant. The band cost is therefore variable. The same cost can behave as either a fixed cost or a variable cost, depending on the activity base. When identifying a cost as fixed or variable, first ask, fixed or variable relative to what activity base? The cost of the band is fixed relative to the number of tickets sold for a specific concert; it is variable relative to the number of concerts produced. LO 5 Demonstrate how the relevant range and decision context affect cost behavior. edm10890_ch02_054-105.indd Page 66 6/18/10 5:04 PM user-f497 66 /Users/user-f497/Desktop/MHBR165 Chapter 2 EXHIBIT 2.21 Cost Behavior Relative to Number of Concerts Number of concerts (a) Cost per concert (b) Total cost (a 3 b) 1 $48,000 $48,000 2 $48,000 $96,000 3 $ 48,000 $144,000 4 $ 48,000 $192,000 5 $ 48,000 $240,000 CHECK YOURSELF 2.4 Is the compensation cost for managers of Pizza Hut Restaurants a fixed cost or a variable cost? The answer depends on the R context. For example, since a store manager's salary remains unchanged regardless of how many customers enter a particular restaurant, it can be classified as a fixed cost relativeOto the number of customers at a particular restaurant. However, the more restaurants thatBPizza Hut operates, the higher the total managers' compensation cost will be. Accordingly, managers' salary cost would be classified as a variable cost relative to the numberEof restaurants opened. Answer R T S COST AVERAGING , LO 6 Select an appropriate time period for calculating the average cost per unit. Lake Resorts, Inc. (LRI), offers water skiing lessons for guests. Since the demand for lessons is seasonal (guests buy more lessons in July than in December), LRI has chosen B to rent (rather than own) the necessary equipment (boats, skis, ropes, life jackets) only when it is needed. LRI's accountant E has collected the following data pertaining to providing ski lessons: N 1. 2. 3. 4. 5. The daily fee to rent equipment is $80. Instructors are paid $15 per2lesson hour. Fuel costs are $2 per lesson hour. 6 Lessons take one hour each. 5 LRI can provide up to 20 lessons in one day. 7 During a recent weekend, LRI provided 2 lessons on Friday, 10 on Saturday, B shows the total cost per day and average cost per and 20 on Sunday. Exhibit 2.22 lesson for each of the three days. U Since equipment rental cost is fixed relative to the number of lessons provided, the cost per lesson declines as the number of lessons increases. This explains why the cost EXHIBIT 2.22 per lesson is significantly lower on Sunday than Friday. Assume LRI uses a cost-plus pricing strategy. The cost Analysis of Total and Unit Cost per lesson figures shown in Exhibit 2.22 are not useful in determining the price to charge customers. For example, it Number of Lessons (a) 2 10 20 makes no sense to charge more for lessons on days like Cost of equipment rental $ 80 $ 80 $ 80 Friday when demand is low. Indeed, many businesses lower Cost of instruction (a 3 $15) 30 150 300 prices on days when demand is low in order to stimulate Cost of fuel (a 3 $2) 4 20 40 business. Total cost (b) $114 $250 $420 The pricing problem can be solved by averaging the costs Cost per lesson (b 4 a) $ 57 $ 25 $ 21 over a longer span of time. To illustrate, assume LRI uses the edm10890_ch02_054-105.indd Page 67 6/18/10 5:04 PM user-f497 /Users/user-f497/Desktop/MHBR165 Cost Behavior, Operating Leverage, and Profitability Analysis REALITY BYTES Alice is a business student who works part time at Costco Wholesale Corporation to help pay for her college expenses. She is currently taking a managerial accounting course and has heard her instructor refer to depreciation as a fixed cost. However, as a requirement for her first accounting course, Alice reviewed Costco's financial statements for 2006, 2007, and 2008. The depreciation expense increased about 21 percent over these three years. She is not sure why depreciation expense would be considered a fixed cost. Alice's accounting instructor reminded her that when an accountant says a cost is fixed, he or she means the cost is fixed in relation to one particular factor. A cost that is fixed in relation to one factor can be variable when compared to some other factor. For example, the depreciation for a retailer may be fixed R relative to the number of customers who visit a particular store, O but variable relative to the number of stores the company opens. In fact, Costco's depreciation increased from 2006 to 2008 mainly B because the company built and opened additional stores. E Alice's instructor suggested that Costco's depreciation expense would be more stable if analyzed on a per store basis, rather than in total. Being curious, Alice prepared the following table, where costs are in thousands. Over the three years, she R noted that total depreciation expense increased 21.1 percent, while depreciation per store increased only 11.8 percent. Although Tdepreciation costs, they still were not fixed, so she asked her the costs on a per store basis were more stable than the total instructor for further explanation. S , Fiscal year Total Depreciation Expense 2006 2007 2008 Average Depreciation Expense per Store $515,285B 566,385E 653,082 N $1,125.1 1,160.6 1,275.6 The instructor suggested Costco's average per store depreciation costs were increasing because the equipment and build2 ings purchased for the new stores (opened from 2006 to 2008) probably cost more than those purchased for the older stores and Costco's new stores are often bigger than its older stores. This would raise the average depreciation expense per store. The 6 instructor also reminded her that in the real world very few costs are perfectly fixed or perfectly variable. 5 7 B that the costs for the week weekly average instead of a daily average. Further, assume include the following: U Equipment rental (7 days 3 $80 per day) Cost of instruction ($15 3 50 lessons) Cost of fuel ($2 3 50 lessons) Total Average cost per lesson $ 560 750 100 $1,410 $1,410/50 lessons 5 $28.20 If LRI desires to earn a profit of $10 per lesson, the company will set the price at $38.20 ($28.20 weekly average cost per lesson 1 $10.00 profit) per lesson regardless of the day of the week that a lesson is administered. On slow days the daily profit margin 67 edm10890_ch02_054-105.indd Page 68 6/18/10 5:04 PM user-f497 68 /Users/user-f497/Desktop/MHBR165 Chapter 2 is less than $10 per lesson. Indeed, on Friday, when only two lessons are provided, LRI incurs a loss of $18.80 per lesson ($38.20 price per lesson 2 $57 daily average cost per lesson). This loss is offset on busy days when the daily profit margin exceeds the $10 weekly average. For example, on Sunday, when 20 lessons are administered, the profit margin is $17.20 per lesson ($38.20 price per lesson 2 $21 daily average cost per lesson). The differences in the daily profit margins average out over the course of the week. As a result, LRI is able to charge the same price per lesson regardless of the daily demand and still attain an average profit margin of $10 per lesson for the week. The need for a weekly average occurs because the number of lessons per day fluctuates radically, thereby causing significant differences in the cost per lesson when calculated on a daily basis. A similar problem occurs if the number of lessons per week fluctuates radically from week to week. For example, the demand for skiing lessons may increase significantly during the week of July 4th or other holidays. Similarly, the demand for lessons may taper off toward the end of the summer. In this case, it will be necessary to expand the time frame for which the average is calculated, perhaps over the summer months or even several seasons. Distortions can occur when the time period is too long as well as too short. For example, the price of fuel and R equipment rental changes over time. If older costs are mixed with newer costs, the average O does not represent current conditions. Choosing the best time frame for calculating the average cost of a product or service requires B thoughtful analysis and judgment. E USE OF ESTIMATESRIN REAL-WORLD PROBLEMS T Imagine trying to classify as fixed or variable all the different costs incurred by a large company such as Delta Airlines.SRecord keeping would be horrendous. Further complications would arise because some , costs are mixed costs. Consider the cost Delta incurs LO 7 Use the high-low method, scattergraphs, and regression analysis to estimate fixed and variable costs. to use airport facilities. An airport may charge Delta a flat annual rental fee for terminal space plus a charge each time a plane takes off or lands. The flat rental fee is a fixed cost while the charge per flight B is variable. The total facilities cost is mixed. To minimize the record-keeping difficulties involved in identifying actual fixed and E variable costs, many companies make decisions using estimated rather than actual costs. Several techniques exist to divideNtotal cost into estimated fixed and variable components. High-Low Method of Estimating Fixed and Variable Costs 2 EXHIBIT 2.23 Cost Data Month January February March April May June July August September October November December Units Sold 30,000 14,000 12,000 25,000 10,000 11,000 20,000 18,000 17,000 16,000 27,000 34,000 The management of Rainy Day 6 Books (RDB) wants to expand operations. To help evaluate the risks involved in opening an additional store, the company president wants 5 to know the amount of fixed cost a new store will likely incur. Suppose RDB's accountant decides to use the high-low method to supply 7 the president with the requested information. The estimated amount B the new store would be developed in the following of fixed cost for four steps. U Total Cost $450,000 300,000 150,000 440,000 180,000 240,000 350,000 400,000 360,000 320,000 490,000 540,000 Step 1 Assemble sales volume and cost history for an existing store. Assuming the new store would operate with roughly the same cost structure, the accountant can use the historical data to estimate the fixed cost likely to be incurred by the new store. To illustrate, assume the accounting data set for the existing store is displayed in Exhibit 2.23. Step 2 Select the high and low points in the data set. In this example, the month with the lowest number of units sold does not correspond to the month with the lowest total cost. The lowest point in units sold occurred in May; the lowest total cost occurred in March. Because the total cost depends on the number of units sold, May should be edm10890_ch02_054-105.indd Page 69 6/18/10 5:04 PM user-f497 /Users/user-f497/Desktop/MHBR165 Cost Behavior, Operating Leverage, and Profitability Analysis classified as the low point. The high point in sales volume occurred in December. The units sold and cost data for the December and May high and low points follow: High (December) Low (May) Step 3 Units Sold Total Cost 34,000 10,000 $540,000 $180,000 Determine the estimated variable cost per unit. The variable cost per unit is determined by dividing the difference in the total cost by the difference in the number of units sold. In this case, the variable cost per unit is as follows: Variable 5 Difference in total cost 5 ($540,000 2 $180,000) 5 $360,000 5 $15 Difference in volume (34,000 2 10,000) 24,000 cost per unit Step 4 Determine the estimated total fixed cost. The total fixed cost can now be R the total cost using either determined by subtracting the variable cost from the high point or the low point. Either point O yields the same result. Computations using the high point follow: B E Fixed cost 5 Total cost 2 Variable cost R Fixed cost 5 $540,000T2 ($15 3 34,000 units) Fixed cost 5 $30,000 S Once determined, the total fixed cost and variable , cost per unit estimates can Fixed cost 1 Variable cost 5 Total cost be used to predict expected total cost at any volume of activity as follows: Total cost 5 Fixed cost 1 (Variable cost per unit 3 Number of units) B E Total cost 5 $30,000 1 ($15 3 22,000) 5 $360,000 N If 22,000 books are sold, the total estimated cost is: If 32,000 books are sold, the total estimated cost is: Total cost 5 $30,000 1 ($15 3 32,000) 5 $510,000 2 Although 12 data points are available, the high-low method uses only 2 of them to esti6 mate the amounts of fixed and variable costs. If either or both of these points is not 5 variable costs, the estimates representative of the true relationship between fixed and produced by the high-low method will be inaccurate. The chief advantage of the high-low 7 method is its simplicity; the chief disadvantage is its vulnerability to inaccuracy. RDB's B accountant decides to test the accuracy of the high-low method results. U Scattergraph Method of Estimating Fixed and Variable Costs Scattergraphs are sometimes used as an estimation technique for dividing total cost into fixed and variable cost components. To assess the accuracy of the high-low estimate of fixed cost, RDB's accountant constructs a scattergraph. The horizontal axis is labeled with the number of books sold and the vertical axis with total costs. The 12 data points are plotted on the graph, and a line is drawn through the high and low points in the data set. The result is shown in Exhibit 2.24. After studying the scattergraph in Exhibit 2.24, the accountant is certain that the high and low points are not representative of the data set. Most of the data points are above the high-low line. As shown in the second scattergraph in Exhibit 2.25, the line should be shifted upward to reflect the influence of the other data points. 69 edm10890_ch02_054-105.indd Page 70 6/18/10 5:04 PM user-f497 Chapter 2 EXHIBIT 2.24 Scattergraph Depicting High-Low Estimate 550 High point 500 Total cost (in thousands) 450 400 350 300 250 Low point 200 150 100 R O 0 5 10 15 20 0 25 B Units (in thousands) E R EXHIBIT 2.25 T Scattergraph Depicting Line S Drawn by Visual Inspection , 550 50 Fixed cost as per high/low estimate is $30,000 30 35 500 B E N 450 Total cost (in thousands) 70 /Users/user-f497/Desktop/MHBR165 400 350 300 250 200 150 100 50 0 0 2 6 5 Fixed cost as per visual inspection = 7 $100,000 B 5 10 U 15 20 25 30 35 Units (in thousands) The graph in Exhibit 2.25 is identical to the graph in Exhibit 2.24 except the straight line is plotted through the center of the entire data set rather than just the high and low points. The new line, a visual fit line, is drawn to visually minimize the total distance between the data points and the line. Usually, half of the data points are above and half below a visual fit line. The estimated variable cost per unit is measured by the slope (steepness) of the visual fit line. The fixed cost is the point (the intercept) where the visual fit line intersects the vertical axis (the total cost line). The intercept in Exhibit 2.25 provides a fixed cost estimate of $100,000. Although RDB's president had only asked for the amount of fixed cost, the variable cost can be easily determined by subtracting the fixed cost from the total cost at any point along edm10890_ch02_054-105.indd Page 71 7/9/10 4:27 PM user-f497 /Volumes/105/PHS00142/work/indd Cost Behavior, Operating Leverage, and Profitability Analysis 71 FOCUS ON INTERNATIONAL ISSUES ANOTHER REASON FIXED COSTS AREN'T ALWAYS FIXED Suppose that a company is renting a facility at an annual rental rate that does not change for the next five years no matter what. Is this a fixed cost? By now, you are aware that the proper response is to ask fixed in relation to what? Is the rental cost of this facility fixed in relation to the activity at this facility? The answer seems to be yes, but it might be \"not necessarily.\" Consider the Exxon Mobil Corporation. If Exxon Mobil rents facilities in a country in the eastern hemisphere, Malaysia for example, the annual rental fee may be stated and paid in the local currency. In Malaysia, this is the ringgit. Even though Exxon Mobil may be paying the same number of ringgit in rent each year, Exxon Mobil's rental cost in U.S. dollars could vary greatly over time. Such potential foreign currency exchange fluctuations cause companiesR to enter very complex hedging arrangements to add stability to transactions that must be paid in O foreign currencies. Exxon Mobil was founded and has its headquarters in B the United States. It does much business in the United States. Furthermore,E it is listed on the New York Stock Exchange and prepares its financial statements in U.S. dolR more assets in lars. However, it does much more business and has many countries outside the United States. Consider the following T table from Exxon Mobil's 2008 financial statements. Before a multinational company can determine whether a cost is fixed, it must determine the applicable currency. Geographical Area United States Non-United States Totals S ,Percentage Earnings* $ 8,616 37,894 $46,510 *Amounts in millions. B E N of Total Total Assets* Percentage of Total 19% 81 100% $ 46,240 139,094 $185,334 25% 75 100% 2 the visual fit line. For example, at 15,000 units, total cost 6 is $300,000. Variable cost is determined as follows: 5 7 Variable cost 5 Total cost 2 Fixed cost B Variable cost 5 $300,000 2 $100,000 U Fixed cost 1 Variable cost 5 Total cost Variable cost 5 $200,000 Variable cost per unit is $13.3333, calculated by dividing the total variable cost by the number of units ($200,000 4 15,000 units 5 $13.3333 per unit). As with the high-low method these total fixed cost and variable cost per unit estimates can be used to predict expected total cost at any volume of activity as follows: Total cost 5 Fixed cost 1 (Variable cost per unit 3 Number of units) If 22,000 books are sold, the total estimated cost is: Total cost 5 $100,000 1 ($13.3333 3 22,000) 5 $393,333 If 32,000 books are sold, the total estimated cost is: Total cost 5 $100,000 1 ($13.3333 3 32,000) 5 $526,666 edm10890_ch02_054-105.indd Page 72 72 7/9/10 4:27 PM user-f497 /Volumes/105/PHS00142/work/indd Chapter 2 Clearly, the visual fit scattergraph approach produces different estimates of total cost than the high-low method provides. Remember, both approaches produce estimates about anticipated future costs. Accuracy cannot be determined until actual costs are incurred. Accountants must exercise judgment in deciding which method is the best approach for the particular circumstances under consideration. Regression Method of Cost Estimation Since the scattergraph is drawn by simple visual inspection, it is subject to human error. A better fit can be obtained using a statistical procedure known as least-squares regression.2 Many of today's spreadsheet programs include a regression procedure. For example, the regression estimates shown in Exhibit 2.26 were generated in an Excel spreadsheet by performing the following functions. EXHIBIT 2.26 R O B E R T S , Excel Spreadsheet Showing the Results of Least-Squares Regression B E N 2 6 5 7 B U 2 Although the least-squares regression is a more accurate method than the high-low method and the visual scattergraph method, the three methods follow the same logical reasoning. Basically, the procedure locates a straight line on a coordinate with the Y axis representing the cost in dollars and the X axis representing the cost driver. In the examples shown in this chapter, the measurement of production in units is used as the cost driver and appears on the X axis. The basic regression model can be explained in the following equation: Y 5 a + bX Where a 5 total fixed cost, or the Y intercept of the regression line b 5 variable cost per unit of X, or the slope of the regression line X 5 independent variable Y 5 dependent variable edm10890_ch02_054-105.indd Page 73 6/18/10 5:04 PM user-f497 /Users/user-f497/Desktop/MHBR165 Cost Behavior, Operating Leverage, and Profitability Analysis 1. Enter the data in spreadsheet columns3 (see columns B and C, rows 3 through 14 in Exhibit 2.26). 2. Click the Data tab. 3. Click Data Analysis.4 4. Click Regression and then OK. 5. Define data ranges and click Line Fit Plot. 6. Click OK. Cost Estimates The regression function returns a fixed cost estimate of $72,848 and a variable cost estimate of $14.30 per unit. These estimates are highlighted in blue in the spreadsheet shown in Exhibit 2.26. As with the high-low and visual fit scattergraph methods, the total fixed cost and variable cost per unit estimates computed using regression can be used to predict expected total cost at any volume of activity as follows: Total cost 5 Fixed cost 1 (Variable cost per unit 3 Number of units) R O Total cost 5 $72,848 1 ($14.30 3 22,000) 5 $387,448 B If 32,000 books are sold, the total estimated cost is: E Total cost 5 $72,848 1 ($14.30 3 32,000) 5 $530,448 R As with the high-low method, regression analysis can be skewed by data points that T are not representative of the complete data set. Here also, such outliers can be identified S using visual fit scattergraphs. Again, management accountants must use common sense when interpreting the cost estimates. Choosing among the high-low method, visual fit , If 22,000 books are sold, the total estimated cost is: scattergraphs, or regression analysis requires judgment. All three methods may be used to evaluate the consistency of the results. B Regression Statistics E An advantage of the regression method is that it provides statistics that give insight N (R2), highlighted in red in as to the reliability of the cost estimates. The R Square Exhibit 2.26, is the most commonly used measure of reliability. The R2 statistic represents the percentage of change in the dependent variable (total cost) that is explained by a change in the independent variable (units sold). In the2case of Rainy Day Books, the cost of operating a new store is R2 suggests that 86% of the change in the total monthly 6 caused by a change in the number of books sold. In other words, some factors other 5 than the number of books sold also affect total costs. For example, the weight and size 7 costs. of the books, as well as the number sold, may affect shipping The R2 values vary between zero and 100 percent. Higher R2 values suggest that the B independent variable more strongly influences the dependent variable. For Rainy Day 2 U of books sold will sigBooks, the relatively high R of 86% suggests that the number nificantly affect the total cost of operating a new store. Multiple Regression Analysis As discussed above, Rainy Day Books' dependent variable (total cost) is influenced by more factors than the single independent variable (units sold). Multiple regression analysis is a statistical tool that permits analysis of how a number of independent variables 3 Statistical reliability requires an information set that includes more than 30 data points. The illustration shown here has been limited in size to simplify the demonstration. 4 If the data tab does not contain a data analysis option, it is likely that the statistical functions have not been activated in your program. You will need to consult the Excel user manual or help routine for instructions to activate the statistical functions. 73 edm10890_ch02_054-105.indd Page 74 6/18/10 10:53 PM user-f497 74 /Users/user-f497/Desktop/MHBR165 Chapter 2 simultaneously affect a dependent variable. Multiple regression analysis can improve the accuracy of fixed and variable cost estimates. A trial and error process using multiple regression analysis is frequently used to assess the relative importance of a variety of independent variables. The regression analysis is performed repeatedly, dropping and adding independent variables, until an acceptable level of accuracy is achieved. > A Look Forward The next chapter will show you how changes in cost, volume, and pricing affect profitability. You will learn to determine the number of units of product that must be produced and sold in order to break even (the number of units that will produce an amount of revenue that is exactly equal to total cost). You will learn to establish the price of a product using a cost-plus pricing approach and to establish the cost of a product using edm10890_ch02_054-105.indd Page 75 6/18/10 5:04 PM user-f497 /Users/user-f497/Desktop/MHBR165 Cost Behavior, Operating Leverage, and Profitability Analysis Mensa Mountaineering Company (MMC) provides guided mountain climbing expeditions in the Rocky Mountains. Its only major expense is guide salaries; it pays each guide $4,800 per climbing expedition. MMC charges its customers $1,500 per expedition and expects to take five climbers on each expedition. R Base your answers on the preceding information. O Required B a. Determine the total cost of guide salaries and the cost of guide E salaries per climber assuming that four, five, or six climbers are included in a trip. Relative to the number of climbers in a single expedition, is the cost of guides a fixed or a variableR cost? b. Relative to the number of expeditions, is the cost of guidesTa fixed or a variable cost? c. Determine the profit of an expedition assuming that five climbers are included in the trip. S d. Determine the profit assuming a 20 percent increase (six climbers total) in expedition revenue. , What is the percentage change in profitability? Part 1 e. Determine the profit assuming a 20 percent decrease (four climbers total) in expedition revenue. What is the percentage change in profitability? B f. Explain why a 20 percent shift in revenue produces more than a 20 percent shift in profitability. E What term describes this phenomenon? N Part 2 Assume that the guides offer to make the climbs for a percentage of expedition fees. Specifically, MMC will pay guides $960 per climber on the expedition. Assume also that the expedition fee 2 charged to climbers remains at $1,500 per climber. 6 5 salaries per climber assuming Determine the total cost of guide salaries and the cost of guide that four, five, or six climbers are included in a trip. Relative 7 to the number of climbers in a single expedition, is the cost of guides a fixed or a variable cost? Relative to the number of expeditions, is the cost of guidesBa fixed or a variable cost? Determine the profit of an expedition assuming that five climbers are included in the trip. U Required g. h. i. j. Determine the profit assuming a 20 percent increase (six climbers total) in expedition revenue. What is the percentage change in profitability? k. Determine the profit assuming a 20 percent decrease (four climbers total) in expedition revenue. What is the percentage change in profitability? l. Explain why a 20 percent shift in revenue does not produce more than a 20 percent shift in profitability. Solution to Part 1, Requirement a Number of climbers (a) Total cost of guide salaries (b) Cost per climber (b 4 a) 4 $4,800 1,200 5 $4,800 960 6 $4,800 800 nds2011 SELF-STUDY REVIEW PROBLEM .com/ed hhe mo A step-by-step audio-narrated series of slides is provided on the text website at www.mhhe.com/edmonds2011. www .m a target-pricing approach. Finally, the chapter will show you how to use a break-even chart to examine potential profitability over a range of operating activity and how to use a technique known as sensitivity analysis to examine how simultaneous changes in sales price, volume, fixed costs, and variable costs affect profitability. 75 edm10890_ch02_054-105.indd Page 76 6/18/10 10:53 PM user-f497 76 /Users/user-f497/Desktop/MHBR165 Chapter 2 Since the total cost remains constant (fixed) regardless of the number of climbers on a particular expedition, the cost is classified as fixed. Note that the cost per climber decreases as the number of climbers increases. This is the per-unit behavior pattern of a fixed cost. Solution to Part 1, Requirement b Since the total cost of guide salaries changes proportionately each time the number of expeditions increases or decreases, the cost of salaries is variable relative to the number of expeditions. Solution to Part 1, Requirements c, d, and e Number of Climbers Revenue ($1,500 per climber) Cost of guide salaries (fixed) Net income Percentage Change 4 $6,000 4,800 $ 1,200 (20%) (55.6%) Percentage Change 5 $7,500 4,800 $ 2,700 120% 155.6% 6 $9,000 4,800 $ 4,200 Percentage change in revenue: 6$1,500 4 $7,500 5 620% Percentage change in profit: 6$1,500 4 $2,700 5 655.6% R Solution to Part 1, RequirementO f B fixed while volume (number of climbers) changes, the change Since the cost of guide salaries remains in net income, measured in absoluteEdollars, exactly matches the change in revenue. More specifically, each time MMC increases the number of climbers by one, revenue and net income increase by R income ($2,700) is lower than the base figure for revenue $1,500. Since the base figure for net ($7,500), the percentage change in net T income ($1,500 4 $2,700 5 55.6%) is higher than percentage change in revenue ($1,500 $7,500). This phenomenon is called operating leverage. S Solution for Part 2, Requirement g , Number of climbers (a) Per climber cost of guide B salaries (b) Cost per climber (b 3 a) 4 $ 960 3,840 5 $ 960 4,800 6 $ 960 5,760 E N Since the total cost changes in proportion to changes in the number of climbers, the cost is classified as variable. Note that the cost per climber remains constant (stays the same) as the number of climbers increases or decreases. This is the per-unit behavior pattern of a variable cost. 2 6 Since the total cost of guide salaries changes proportionately with changes in the number of 5 variable relative to the number of expeditions. expeditions, the cost of salaries is also 7 i, j, and k Solution for Part 2, Requirements B Percentage Percentage U4 Number of Climbers Change 5 Change 6 Solution for Part 2, Requirement h Revenue ($1,500 per climber) Cost of guide salaries (variable) Net income $6,000 3,840 $2,160 (20%) (20%) $7,500 4,800 $2,700 120% 120% $9,000 5,760 $3,240 Percentage change in revenue: 6$1,500 4 $7,500 5 620% Percentage change in profit: 6$540 4 $2,700 5 62