Cost Estimation

A Case Study on Cost Estimation andProfitability Analysis at Continental Airlines

Francisco J. Romn

ABSTRACT: This case exposes students to the application of regression analyses tobe used as a tool pursuant to understanding cost behavior and forecasting future costsusing publicly available data from Continental Airlines. Specifically, the case focuses onthe harsh financial situation faced by Continental as a result of the recent financial crisisand the challenges it faces to remain profitable. It then highlights the importance ofreducing and controlling costs as a viable strategy to restore profitability and how re-gression analysis can assist in this pursuit. Students are next presented with quarterlydata for various categories of costs and several potential cost drivers, which they mustuse to perform regressions on operating costs using a variety of cost drivers. They mustthen use their regression results to forecast operating costs and conduct a profitabilityanalysis to project quarterly profits for the upcoming fiscal year. Finally, students mustsummarize the main results of their analysis in a memorandum addressed to Continen-tals management, providing recommendations to restore profits. In particular, the con-cept of mixed cost functions is reinforced, as is the understanding of the steps requiredto perform regression analysis in Excel, interpreting the regression output, and theunderlying standard assumptions in regression analysis. The case has been tested andwell received in an intermediate cost accounting course and it is suitable for bothundergraduate and graduate students.

Keywords: cost estimation; profitability analysis; cost behavior; regression analyses;cost functions.

Data Availability: All data are from public sources and are available in hard copy insidethe case. Data are also available in electronic form by the authorupon request.

INTRODUCTION

In 2008, the senior management team at Continental Airlines, commanded by Lawrence Kell-ner, the Chairman and Chief Executive Officer, convened a special meeting to discuss thefirms latest quarterly financial results. A bleak situation lay before them. Continental hadincurred an operating loss of $71 million dollarsits second consecutive quarterly earnings de-

Francisco J. Romn is an Assistant Professor at Texas Tech University.

I thank Kent St. Pierre editor, Michael Costa, and two anonymous referees for their suggestions on previous versions ofthe case.

Editors note: Accepted by Kent St. Pierre

ISSUES IN ACCOUNTING EDUCATION American Accounting AssociationVol. 26, No. 1 DOI: 10.2308/iace.2011.26.1.1812011pp. 181200

Published Online: February 2011

181

cline that year. Likewise, passenger volume was significantly down, dropping by nearly 5 percentfrom the prior years quarter. Continentals senior management needed to act swiftly to reversethis trend and return to profitability.

Being the fourth largest airline in the U.S. and eighth largest in the world, Continental wasperceived as one of the most efficiently run companies in the airline industry. Nonetheless, 2008brought unprecedented challenges for Continental and the entire industry as the United States andmuch of the world was heading into a severe economic recession. Companies cutting deeply intotheir budgets for business travel, the highest yielding component of Continentals total revenue,together with a similar downward trend from the leisure and casual sector, combined to sharplyreduce total revenue.

Concurrent with this revenue decline, the price of jet fuel soared to record levels during2008.1 Thus, while revenue was decreasing, Continental was paying almost twice as much in fuelcosts. Interestingly, fuel costs surpassed the firms salaries and wages as the highest cost inContinentals cost structure. This obviously had a negative impact on the bottom line, squeezingeven further the already strained profit margins.

The outlook for a quick recovery in the U.S. economy and, consequently, an upturn in thedemand for air travel in the short term did not seem likely. Continentals internal forecasts indi-cated that a further decline in passenger volume should be anticipated throughout 2009, with arecovery in travel possibly occurring by the middle of 2010.

To summarize, adverse economic conditions in the U.S., coupled with the rise in fuel costs,were dragging down Continentals profits and relief was unlikely through the foreseeable future.

THE DECISION TO REDUCE FLYING CAPACITY AND THE IMPACT ONOPERATING COSTS

Given the situation described above, management needed to act swiftly to restore profitability.Several strategic options were evaluated. Since the U.S. and much of the world was facing asevere recession, the prospect for growing revenues by either raising airfares or passenger volumeseemed futile. Contrary to raising revenue, Continentals managers believed that raising farescould potentially erode future revenues beyond the present level. Discounting fares did not seema plausible solution either, because given the severity of the economic situation a fare cut couldfall short in stimulating additional passenger demand and lead to lowering revenues.

Thus, because management anticipated that revenues would remain flat for most of the year,the only viable short-term solution to restoring profits was a substantial and swift reduction inoperating costs. This could most effectively be accomplished in two ways. First, through a reduc-tion in flying capacity adjusted to match projected passenger demand. With this in mind, Conti-nentals management agreed to reduce flying capacity by 11 percent on domestic and internationalroutes.2 As a result of this action, Continental would eliminate the least profitable or unprofitableflights and, accordingly, would ground several planes in the fleet. Management anticipated that thisdecision would reduce several of the firms operating costs.

Apart from this, Continental could achieve further reductions in costs by implementing sev-eral cost-cutting initiatives and through operational efficiencies. For example, management pro-

1 To illustrate, jet fuel is tied to the price of oil and, over the past year, oil prices surged from about $70 to $135 per barrel.Consequently, the price of jet fuel increased markedly, from an average of $1.77 per gallon to $4.20 by the mid-summerof 2008.

2 Specifically, on June 13, 2008, Continental Airlines announced that it planned to reduce its flight capacity by 11 percent.By shrinking capacity, Continental expected to reduce the number of domestic and international flights from its threemajor hubs in Houston, Cleveland, and Newark Maynard 2008.

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Issues in Accounting Education Volume 26, No. 1, 2011American Accounting Association

jected that it could achieve reductions in Passenger Services expenses by consolidating severaltasks during passenger check-in and by reducing food and beverage waste served during flights.Additionally, the firm could reduce various miscellaneous expenses through targeted cuts in dis-cretionary spending.

In sum, to close the gap in profitability, Continentals strategy was geared toward slashingoperating costs by cutting capacity and through aggressive identification and implementation ofcost-cutting initiatives.

The next step would be for management to know precisely how their decision to downsizecapacity would impact the firms future operating costs, and also identify specific areas in whichthe firm could achieve additional cost reductions. Additionally, the cost analysis would helpforecast the firms operating costs and projected profits or losses for the upcoming fiscal year.However, before we can proceed with such analysis, an examination of how the various categoriesof Continentals costs behave is in order.

Before we begin, let us prepare with an overview of the airline industry and its competitivelandscape, and an understanding of why cost behavior bears particular relevance in this case.

Relative to other industries, airlines are a very difficult business to manage. In particular, theyare exposed to tremendous risks brought by volatility inherent in their business model, as they dealwith high fixed costs, labor unions, instability in fuel prices, weather and natural disasters, pas-senger safety, and security regulations. These aspects bring a large burden to airlines cost struc-tures. Moreover, competition within the industry is fierce; the proliferation of discount carriers,such as Southwest Airlines and, most recently, Jet Blue, and the end of fare regulation in 1978, hashindered airlines pricing power and their ability to spur revenues. For these reasons, cost con-tainment is a critically important aspect of profitability in this industry.

In order for Continental to restore profitability in this harsh environment of weak demand forair travel, it must be able to contain its operating costs, especially its massive fixed costs, whichare visible in several ways. For example, salaries for pilots, flight attendants, and mechanics, aswell as aircraft leasing costs, are typically fixed, varying little with shifts in passenger volume.Because fixed costs typically embody the amount of operating capacity of a firm, they are com-monly referred as capacity costs. Since fixed costs do not self-adjust to fluctuations in passengervolume, the only way in which they can be decreased or increased is if management adjusts themin accordance to the level of operating capacity. In contrast, other costs, such as passenger servicesand reservation and distribution costs, behave as variable and would self-adjust with variations involume or operating activity.

Hence, to assess the impact of this strategic decision to alter Continentals cost structure, andidentify the areas that could achieve the greatest reduction in costs, we must resolve how Conti-nentals operating costs behave and what drives them. In what follows, we learn how to applyregression analyses to examine cost behavior and forecast future costs, and then use that knowl-edge to assess how the reduction in flying capacity would affect Continentals operating costs andprofitability in the near term.

ESTIMATING COSTS USING REGRESSION ANALYSESThe previous discussion highlighted the importance of examining the behavior of Continen-

tals operating costs to pave the way for a cost and profitability analysis using regression analysis.Regression analysis is a powerful statistical tool that is frequently used by firms to examine costbehavior and predict future costs. The idea behind regression analysis is straightforward: historicaldata for costs, and the various activities that could potentially drive operating costs, are insertedinto a mathematical calculation which yields the average amount of change in that particular costthat has occurred over time. Average values provided by regression calculations may then beapplied to estimate future change that will occur in that cost given a one-unit change in one or

A Case Study on Cost Estimation and Profitability Analysis at Continental Airlines 183


more of the business activities which drive that cost.3 More precisely, in a regression model, costis a function of one or more business activities or factors underlying a business operation.Simply put, the business activities are the drivers of operating costs. Therefore, since activitiesdrive costs, our first step in the estimation of a cost function is to identify the underlying activitiesor other potential factors that drive the cost in questionthe cost drivers. This requires extensiveknowledge of the business operation. In the case of Continental Airlines, the potential drivers ofoperating costs vary greatly. For instance, as previously noted, the number of passengers thatContinental flies may drive the costs related to Passenger Services. Likewise, Aircraft Mainte-nance and Repairs costs could be driven by the number of aircraft in the fleet and by the level offlying capacity set by Continental i.e., available seat miles.

In synthesis, to predict how Continentals operating costs would be affected by the decision toreduce capacity, and to identify those areas in which additional room is available for cost cutting,we need to identify which costs in this firms cost structure behave as variable, fixed, or mixed inwhich elements of both variable and fixed are observable. Equally important, we should alsoidentify the specific drivers if any of each cost.

Your job is to assist management in their quest to restore profitability at Continental Airlines.Specifically, you must conduct regression analyses to examine cost behavior and then use thisinformation to forecast operating costs and profitability for the upcoming year. As part of your costanalysis, you should investigate how the decision to cut flying capacity would impact the firmsfuture operating costs and, equally important, identify those specific expense categories or oper-ating areas in which this firm could attain additional costs saving by implementing cost-cuttinginitiatives. Your conclusions should be outlined in a memorandum directed to Continentals Ex-ecutive management team.

You are provided next with a description of Continentals operating costs and the potentialdrivers of costs so you can conduct regression analysis to estimate the corresponding cost func-tions. To help you in estimating the regressions, a comprehensive set of instructions for perform-ing regression analysis using Microsoft Excel is provided in the Appendix. Immediately followingthe description of costs, a series of questions is provided that should help guide your analysis.Additionally, to help you estimate your regressions, Exhibit 1 presents past quarterly data for all ofthe above expenditures for the period of January 2000 through December 2008, while Exhibit 2provides quarterly operations data for the same period of time.

CONTINENTALS OPERATING COSTS AND POTENTIAL COST DRIVERSAs shown in Exhibit 1, there are ten categories of operating costs. These include salaries and

wages, aircraft fuel and related taxes, aircraft rentals, airport fees, aircraft maintenance andrepairs, depreciation and amortization, distribution costs, passenger services, regional capacitypurchases, and other expenses. Of these, some represent a single expense item. For example, thecost of aircraft rentals and airport fees together comprise a single cost item. Other costs representcost pools comprising several cost items. Such is the case of passenger services and other ex-penses. The following provides a detailed description of each cost, along with the potential costdrivers.4

3 For ease in exposition, cost functions and regression analyses are discussed briefly here. For further insight on costfunctions and on the mechanics of regression analyses, I refer the reader to the Appendix.

4 A cost driver represents a particular business activity, which usually tends to have a cause-and-effect relationship witha given cost. For example, for airlines, a typical cost driver for landing fees is the number of daily flights carried by theairline, as well as the number of passengers flown. An increase decrease in the number of flights or passengers flownwould increase decrease landing fees.

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EXHIBIT 1

REVENUES AND OPERATING COSTS DATA

Obs. Period Revenues FuelSalaries and

WagesCapacityPurchases

AircraftRentals Landing Fees

1 1Q-2000 2,277,000,000 334,000,000 672,000,000 206,000,000 129,000,0002 2Q-2000 2,571,000,000 313,000,000 719,000,000 210,000,000 138,000,0003 3Q-2000 2,622,000,000 354,000,000 748,000,000 215,000,000 133,000,0004 4Q-2000 2,429,000,000 392,000,000 736,000,000 213,000,000 132,000,0005 1Q-2001 2,451,000,000 345,000,000 758,000,000 214,000,000 141,000,0006 2Q-2001 2,556,000,000 349,000,000 800,000,000 223,000,000 153,000,0007 3Q-2001 2,223,000,000 322,000,000 779,000,000 230,000,000 139,000,0008 4Q-2001 1,739,000,000 213,000,000 684,000,000 236,000,000 148,000,0009 1Q-2002 1,993,000,000 208,000,000 732,000,000 228,000,000 161,000,00010 2Q-2002 2,192,000,000 254,000,000 746,000,000 231,000,000 160,000,00011 3Q-2002 2,178,000,000 276,000,000 743,000,000 227,000,000 163,000,00012 4Q-2002 2,039,000,000 285,000,000 738,000,000 216,000,000 149,000,00013 1Q-2003 2,042,000,000 347,000,000 778,000,000 223,000,000 152,000,00014 2Q-2003 2,216,000,000 302,000,000 762,000,000 224,000,000 152,000,00015 3Q-2003 2,365,000,000 316,000,000 778,000,000 225,000,000 165,000,00016 4Q-2003 2,247,000,000 290,000,000 738,000,000 158,000,000 224,000,000 151,000,00017 1Q-2004 2,307,000,000 333,000,000 688,000,000 317,000,000 220,000,000 160,000,00018 2Q-2004 2,553,000,000 387,000,000 711,000,000 328,000,000 222,000,000 163,000,00019 3Q-2004 2,602,000,000 414,000,000 703,000,000 347,000,000 224,000,000 171,000,00020 4Q-2004 2,437,000,000 453,000,000 717,000,000 359,000,000 225,000,000 160,000,00021 1Q-2005 2,505,000,000 470,000,000 715,000,000 353,000,000 227,000,000 171,000,00022 2Q-2005 2,857,000,000 575,000,000 649,000,000 382,000,000 229,000,000 181,000,00023 3Q-2005 3,001,000,000 684,000,000 646,000,000 406,000,000 234,000,000 182,000,00024 4Q-2005 2,845,000,000 714,000,000 639,000,000 431,000,000 238,000,000 174,000,00025 1Q-2006 2,947,000,000 672,000,000 661,000,000 415,000,000 245,000,000 185,000,00026 2Q-2006 3,507,000,000 744,000,000 791,000,000 454,000,000 248,000,000 198,000,00027 3Q-2006 3,518,000,000 858,000,000 743,000,000 475,000,000 249,000,000 195,000,00028 4Q-2006 3,156,000,000 760,000,000 680,000,000 447,000,000 248,000,000 186,000,00029 1Q-2007 3,179,000,000 684,000,000 726,000,000 430,000,000 248,000,000 193,000,00030 2Q-2007 3,710,000,000 842,000,000 821,000,000 444,000,000 248,000,000 190,000,00031 3Q-2007 3,820,000,000 895,000,000 836,000,000 446,000,000 249,000,000 209,000,00032 4Q-2007 3,523,000,000 933,000,000 744,000,000 473,000,000 249,000,000 198,000,00033 1Q-2008 3,570,000,000 1,048,000,000 729,000,000 506,000,000 247,000,000 207,000,00034 2Q-2008 4,044,000,000 1,363,000,000 704,000,000 589,000,000 246,000,000 210,000,00035 3Q-2008 4,072,000,000 1,501,000,000 765,000,000 553,000,000 244,000,000 225,000,00036 4Q-2008 3,471,000,000 993,000,000 760,000,000 425,000,000 240,000,000 210,000,000

Obs. Period Distribution CostsAircraft

Maintenance DepreciationPassengerServices Other Expenses

1 1Q-2000 248,000,000 159,000,000 95,000,000 85,000,000 286,000,0002 2Q-2000 261,000,000 171,000,000 98,000,000 91,000,000 284,000,0003 3Q-2000 255,000,000 167,000,000 102,000,000 97,000,000 288,000,0004 4Q-2000 217,000,000 149,000,000 107,000,000 89,000,000 277,000,0005 1Q-2001 243,000,000 160,000,000 105,000,000 91,000,000 318,000,0006 2Q-2001 230,000,000 162,000,000 111,000,000 96,000,000 295,000,000

(continued on next page)



Obs. Period Distribution CostsAircraft

Maintenance DepreciationPassengerServices Other Expenses

7 3Q-2001 194,000,000 142,000,000 120,000,000 89,000,000 121,000,0008 4Q-2001 142,000,000 104,000,000 131,000,000 71,000,000 166,000,0009 1Q-2002 172,000,000 114,000,000 106,000,000 77,000,000 382,000,00010 2Q-2002 158,000,000 119,000,000 112,000,000 73,000,000 454,000,00011 3Q-2002 138,000,000 119,000,000 112,000,000 78,000,000 276,000,00012 4Q-2002 124,000,000 124,000,000 114,000,000 68,000,000 277,000,00013 1Q-2003 127,000,000 133,000,000 116,000,000 70,000,000 320,000,00014 2Q-2003 138,000,000 126,000,000 110,000,000 73,000,000 91,000,00015 3Q-2003 131,000,000 135,000,000 110,000,000 81,000,000 250,000,00016 4Q-2003 135,000,000 115,000,000 108,000,000 73,000,000 455,000,00017 1Q-2004 137,000,000 112,000,000 104,000,000 69,000,000 304,000,00018 2Q-2004 140,000,000 102,000,000 105,000,000 76,000,000 279,000,00019 3Q-2004 139,000,000 107,000,000 104,000,000 84,000,000 287,000,00020 4Q-2004 136,000,000 93,000,000 102,000,000 77,000,000 278,000,00021 1Q-2005 138,000,000 112,000,000 99,000,000 77,000,000 316,000,00022 2Q-2005 154,000,000 106,000,000 98,000,000 84,000,000 280,000,00023 3Q-2005 154,000,000 116,000,000 97,000,000 91,000,000 282,000,00024 4Q-2005 142,000,000 121,000,000 95,000,000 80,000,000 305,000,00025 1Q-2006 160,000,000 127,000,000 96,000,000 82,000,000 293,000,00026 2Q-2006 178,000,000 140,000,000 97,000,000 90,000,000 323,000,00027 3Q-2006 157,000,000 140,000,000 99,000,000 97,000,000 313,000,00028 4Q-2006 155,000,000 140,000,000 99,000,000 87,000,000 333,000,00029 1Q-2007 161,000,000 144,000,000 99,000,000 90,000,000 340,000,00030 2Q-2007 176,000,000 169,000,000 101,000,000 99,000,000 357,000,00031 3Q-2007 171,000,000 166,000,000 106,000,000 105,000,000 357,000,00032 4Q-2007 174,000,000 142,000,000 107,000,000 95,000,000 328,000,00033 1Q-2008 182,000,000 159,000,000 106,000,000 96,000,000 356,000,00034 2Q-2008 194,000,000 167,000,000 108,000,000 107,000,000 427,000,00035 3Q-2008 182,000,000 152,000,000 112,000,000 113,000,000 461,000,00036 4Q-2008 159,000,000 135,000,000 111,000,000 91,000,000 372,000,000

OPERATIONS AND COST DRIVER DATA

Obs. PeriodTotal

AircraftLeasedAircraft Flights Passengers Available Seat Miles

Available SeatMiles Regional

1 1Q-2000 514 403 98,820 11,201,000 20,951,000,000 2 2Q-2000 522 410 97,871 12,084,000 21,384,000,000 3 3Q-2000 535 414 97,967 12,155,000 22,356,000,000 4 4Q-2000 522 398 98,378 11,456,000 21,409,000,000 5 1Q-2001 548 406 98,590 11,220,000 21,459,000,000 6 2Q-2001 557 416 99,018 12,256,000 22,813,000,000 7 3Q-2001 501 377 98,564 11,254,000 21,994,000,000 8 4Q-2001 522 393 81,109 9,508,000 18,219,000,000 9 1Q-2002 538 400 81,883 12,062,000 20,375,000,000 10 2Q-2002 570 404 82,815 13,099,000 22,286,000,000 11 3Q-2002 570 401 81,737 13,006,000 22,626,000,000 12 4Q-2002 554 410 78,809 12,874,000 21,054,000,000 13 1Q-2003 562 419 75,178 11,518,000 20,843,000,000 1,767,000,00014 2Q-2003 570 428 75,617 13,044,000 21,241,000,000 2,073,000,000


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OPERATIONS AND COST DRIVER DATA

Obs. PeriodTotal

AircraftLeasedAircraft Flights Passengers Available Seat Miles

Available SeatMiles Regional

15 3Q-2003 570 428 76,297 13,727,000 22,819,000,000 1,605,000,00016 4Q-2003 579 434 75,650 13,769,000 21,907,000,000 2,980,000,00017 1Q-2004 586 437 74,859 12,810,000 22,670,000,000 2,400,000,00018 2Q-2004 587 440 75,816 14,558,000 24,150,000,000 2,603,000,00019 3Q-2004 592 445 74,211 14,862,000 24,674,000,000 1,999,000,00020 4Q-2004 594 448 74,443 14,252,000 23,588,000,000 3,408,000,00021 1Q-2005 598 453 71,494 14,122,000 23,585,000,000 2,740,000,00022 2Q-2005 604 459 74,651 15,540,000 25,482,000,000 3,026,000,00023 3Q-2005 611 466 74,630 15,905,000 26,833,000,000 3,112,000,00024 4Q-2005 622 477 75,886 15,448,000 25,720,000,000 3,095,000,00025 1Q-2006 630 483 74,962 15,594,000 26,117,000,000 3,082,000,00026 2Q-2006 634 484 77,729 17,596,000 28,259,000,000 3,374,000,00027 3Q-2006 648 482 77,468 17,328,000 29,262,000,000 3,503,000,00028 4Q-2006 648 480 79,030 16,601,000 27,280,000,000 3,292,000,00029 1Q-2007 630 446 78,601 16,176,000 27,250,000,000 3,126,000,00030 2Q-2007 625 418 82,582 18,120,000 29,592,000,000 3,177,000,00031 3Q-2007 631 415 81,118 17,901,000 30,346,000,000 3,193,000,00032 4Q-2007 628 415 80,850 16,733,000 28,550,000,000 3,104,000,00033 1Q-2008 641 414 76,719 16,440,000 28,376,000,000 3,098,000,00034 2Q-2008 630 390 76,096 17,108,000 30,304,000,000 3,450,000,00035 3Q-2008 653 412 78,599 17,962,000 30,383,000,000 3,390,000,00036 4Q-2008 632 397 76,000 15,183,000 26,448,000,000 3,046,000,000

Obs. PeriodPassenger Miles

Flown Employees Fuel Price Fuel Consumed

1 1Q-2000 15,005,000,000 45,000 $0.829 377,000,0002 2Q-2000 16,491,000,000 45,500 $0.797 386,000,0003 3Q-2000 17,325,000,000 46,000 $0.865 398,000,0004 4Q-2000 15,340,000,000 45,944 $0.885 372,000,0005 1Q-2001 15,114,000,000 38,396 $0.856 369,000,0006 2Q-2001 17,053,000,000 39,000 $0.815 391,000,0007 3Q-2001 16,206,000,000 39,500 $0.824 373,000,0008 4Q-2001 12,767,000,000 39,461 $0.826 369,000,0009 1Q-2002 14,867,000,000 40,229 $0.644 308,000,00010 2Q-2002 16,489,000,000 41,011 $0.723 332,000,00011 3Q-2002 16,960,000,000 41,809 $0.760 340,000,00012 4Q-2002 17,252,000,000 40,244 $0.740 316,000,00013 1Q-2003 14,352,000,000 38,960 $1.029 305,000,00014 2Q-2003 16,129,000,000 39,000 $0.881 308,000,00015 3Q-2003 18,041,000,000 39,500 $0.857 330,000,00016 4Q-2003 16,412,000,000 39,000 $0.872 314,000,00017 1Q-2004 16,255,000,000 38,240 $1.041 320,000,00018 2Q-2004 18,735,000,000 37,496 $1.787 347,000,00019 3Q-2004 19,922,000,000 36,766 $1.199 345,000,00020 4Q-2004 18,239,000,000 38,255 $1.190 321,000,00021 1Q-2005 18,112,000,000 41,831 $1.453 324,000,00022 2Q-2005 20,292,000,000 45,742 $1.670 344,000,000




Salaries and WagesThis account represents costs related to salaries and wages, as well as fringe benefits, of

Continentals workers. These include salaries for pilots and wages for flight attendants and groundcrew, as well as wages for Continentals mechanics. Additionally, a significant portion of thissalary pool represents wages of reservation specialists, customer service representatives at air-ports, and the salaries for administrative and support personnel e.g., flight schedulers, technology

Obs. PeriodPassenger Miles

Flown Employees Fuel Price Fuel Consumed

23 3Q-2005 21,762,000,000 50,018 $1.880 364,000,00024 4Q-2005 20,033,000,000 42,200 $1.776 344,000,00025 1Q-2006 20,336,000,000 42,600 $1.904 347,000,00026 2Q-2006 23,367,000,000 43,450 $2.110 375,000,00027 3Q-2006 24,042,000,000 41,500 $2.215 387,000,00028 4Q-2006 21,772,000,000 38,033 $2.064 362,000,00029 1Q-2007 21,450,000,000 41,800 $1.895 361,000,00030 2Q-2007 24,623,000,000 43,300 $2.079 395,000,00031 3Q-2007 25,422,000,000 41,400 $2.206 406,000,00032 4Q-2007 22,670,000,000 39,640 $2.499 380,000,00033 1Q-2008 22,280,000,000 43,000 $2.797 375,000,00034 2Q-2008 24,836,000,000 40,100 $3.856 389,000,00035 3Q-2008 24,746,000,000 43,500 $3.450 395,000,00036 4Q-2008 20,825,000,000 42,490 $2.925 339,000,000

EXHIBIT 2

PROJECTIONS OF REVENUES AND OPERATING ACTIVITY FOR YEAR 2009

Variable Quarter 1 Quarter 2 Quarter 3 Quarter 4

Revenues $2,962,000,000 $2,767,000,000 $2,947,000,000 $2,462,000,000Available seat miles 26,323,000,000 28,007,000,000 28,933,000,000 26,291,000,000Available regional seat miles 2,971,000,000 3,044,000,000 3,130,000,000 3,002,000,000Number of passengers 14,408,000 16,348,000 16,795,000 15,258,000Number of planes 634 617 604 601Number leased planes 398 394 380 379Price of fuel per gallon $1.82 $2.07 $1.99 $1.98Gallons of fuel consumed 403,000,000 430,000,000 369,000,000 479,000,000

All financial and operational data represent quarterly data for the quarter beginning January 2000 Observation 1 throughDecember 2008. Data have been compiled from Continentals 8-K and10-K reports, submitted to the Securities andExchange Commission.

Definitions of Operations Variables:Available seat miles the number of seats available multiplied by the number of miles flown;

Available regional seat miles available seat miles on regional routes;Number of passengers number of paying passengers flown;

Number of planes number of planes in the fleet, including regional routes aircraft;Number of leased planes number of leased planes;

Price of jet fuel average price per gallon of jet fuel in the respective quarter; andGallons of fuel consumed number of gallons of fuel consumed in the respective quarter.

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personnel, accountants, and division managers. A possible cost driver of salaries is the availableseat miles.5

Aircraft Fuel and Related TaxesThis represents the cost of jet fuel and related fuel taxes. Jet fuel cost tends to be driven by the

current price of jet fuel and gallons of jet fuel consumed.

Aircraft RentalsThese are expenses for capital leases of aircraft. The main driver is the number of leased

planes in Continentals fleet, including regional jets operated on behalf of Continental by fourregional airlines under various capacity purchase agreements.

Airport FeesRepresents landing fees and passenger security fees paid to the various domestic and inter-

national airports where Continental flies. Landing fees are driven by the number of passengers.

Aircraft Maintenance and RepairsThese are expenses associated with the service and maintenance of planes. These include

expenses related to scheduled maintenance, spare parts and materials, and airframe and engineoverhauls. The main drivers of these costs are the number of planes in the fleet and the number ofmiles flown.

Depreciation and AmortizationThis represents depreciation and amortization expenses of aircraft, ground equipment, build-

ings, and other property. It must be emphasized that the largest portion of depreciation expenserelates to the depreciation of aircraft. Although depreciation expenses are driven by the acquisitioncost of Continentals capital assets, depreciation is greatly influenced by both company policy andaccounting principles, such as the depreciation method, that a firm adopts.

Distribution CostsThese expenses represent credit card discount fees, booking fees, and travel agency commis-

sions, all of which are affected by passenger revenue. Therefore, the driver of these costs is totalrevenue.

Passenger ServicesThis is also a cost pool that includes expenses related to processing and servicing passengers

prior to take-off, during flight, and after arrival at their destination. A significant portion of thesecosts is generated by Continentals Field Services Division, the main function of which is toprovide service to planes prior to take-off. Some of these expenses relate to checking in passen-gers, handling luggage on and off planes, cleaning planes, stocking planes with beverage and food,and refueling the aircraft prior to take-off. The potential cost driver of these costs is the number ofpassengers.

Regional Capacity PurchasesThese are costs related to the purchase of regional routes served by several regional airlines

on behalf of Continental ExpressJet, Chautauqua, CommutAir, and Cogan. These costs are

5 Available seat miles is calculated as the number of seats available for passengers multiplied by the number of scheduledmiles those seats are flown.



driven by the combined flying capacity of the four airlines: available regional seat miles.

Other Expenses

This is a cost pool that comprises many ancillary and discretionary expenditures, includingtechnology expenses, security and outside services, general supplies, and advertising and promo-tional expenses. Further, this cost pool contains various special charges for gains and losses fromthe sale of retired aircraft and costs of future leases. Given the large variety of miscellaneousitems, there is no clear driver of these expenses; however, a large portion of them, such asadvertising and promotional expenses, are driven by total revenue.

DISCUSSION QUESTIONS

1. Using the quarterly data for operating costs and the various cost drivers of costs providedby Exhibits 1 and 2, estimate regression for cost category of costs. Then, write theappropriate cost function for each category of cost and then interpret your regressionresults.

2. Based on your regression results, where do you see the largest reductions in costs if flyingcapacity is lowered by 11 percent? Also, in which areas do you see opportunities toachieve further cost reductions and why?

3. Exhibit 2 provides a quarterly forecast of revenues, jet fuel prices,6 and the projectedoperating activity for 2009. Using the information from your regressions and the forecastinformation provided in Exhibit 2, estimate Continentals operating costs and expectedprofit for the upcoming fiscal year.

4. Based on the results of your profitability analysis, what can you say about the firmsfinancial outlook? Would Continental be earning an operating profit in 2009? If not, whatshould Continentals management do to restore profitability in 2009?

5. Summarize your conclusions in a memorandum addressed to Continentals CEO. In thememo, you must clearly communicate your main findings, emphasizing specific areas inwhich you see the greatest potential to achieve further reductions in costs and, based onyour profitability analysis, sum up the financial outlook for 2009.

6 You should note that Continental has entered into several future contracts to hedge the exposed risks of rising fuelprices. The projected costs for jet fuel on exhibit reflects the value of the various future contracts which guaranteeContinental a fixed price for jet fuel at various maturity dates in 2009, as well the estimated gallons of fuel thatContinental plans to use during the year.

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CASE LEARNING OBJECTIVES AND IMPLEMENTATION GUIDANCECost estimation is a fundamental aspect of managerial/cost accounting Datar et al. 2008;

Eldenburg and Wolcott 2005. For example, cost estimation is critical for developing budgets,setting up cost standards, inventory valuation, product costing, and many other applications. Ul-timately, firms ability to accurately predict production and operating costs has a profound impacton decision-making. Additionally, given the frequency with which firms downsize or expand theiroperations in response to economic or market-wide conditions, knowing how this strategic deci-sion of scaling output impacts firms future operating costs, and which tools can facilitate this task,has become increasingly relevant for firms.

Nonetheless, despite its importance, cost estimation is a topic that merits further discussion inaccounting textbooks. Although several managerial/cost accounting textbooks provide rich theo-retical discussions of cost estimation, including cost behavior, cost functions, and, to some extent,regression analyses, the examples that are typically used to illustrate such an important conceptoften lack a sense of realism. Either fictitious data are commonly used in cost estimation, or theexamples covered fail to capture realistic situations faced by firms in a real world context.Accordingly, this case aims to close this gap.

The objective is to support students in learning how to apply regression analyses to under-stand cost behavior and forecast future costs using real data from firms. The case focuses on theharsh financial situation faced by Continental Airlines as a result of the recent financial crisis andthe challenges it faces to remain profitable. It then highlights the importance of reducing andcontrolling costs as a viable strategy to restore profitability, and how regression analysis can assistin this pursuit. Students are next presented with quarterly data for various categories of costs andseveral potential cost drivers, which they must analyze and then perform regressions on operatingcosts using a variety of cost drivers. Based on these results, students have to examine how costsbehave and then use the regression output to forecast the firms operating costs for year 2009. Aspart of the cost analysis, students must also identify specific areas in which Continental couldachieve the largest cost savings as a result of cutting capacity and implementing other cost-cuttingmeasures. Apart from this, they must conduct a profitability analysis to project quarterly profits forthe upcoming fiscal year.

The learning objectives of the case are as follows:

1. Students learn to conduct regression analysis in Excel and use this technique to study costbehavior and forecast future costs.

2. Students also learn how to use actual firm-level data from public sources for estimatingcosts, and apply cost estimation in a real world context that involves a widespreaddecision among firms: downsizing capacity. Moreover, learning to use public financialinformation in cost estimation could have implications that reach beyond accounting;learning to access public financial information exposes students to the possibilities ofapplying regression analysis for business analysis in general, including cost and profit-ability analyses.

3. The case requires students to synthesize their findings in a memorandum addressed toContinentals CEO; thus, students are also exposed to refining their writing skills in abusiness setting.

Implementation GuidanceThis case is primarily designed for use in an intermediate managerial/cost accounting under-

graduate class; however, it could also work well in a graduate-level managerial accounting course,at either the masters level or M.B.A.



The realistic nature of the setting everyone can easily identify with the business model ofairlines makes a particularly appealing environment for students to learn how regression analysescan be applied in cost estimation in a real-world context. The questions presented in the caseinclude both practical and theoretical questions. As an augmentation of the principles contained inthe application of this case, instructors could enhance the student experience by devoting time toreviewing the concepts of cost functions and cost estimation, as well as discussing the fundamen-tals of regression analyses, so students can be exposed to these concepts prior to receiving thecase. Alternatively, students can review these concepts on their own. The Appendix provides adetailed explanation of cost functions and regression analysis and describes the steps to performregression analysis in Excel. Additionally, it provides students with broad guidelines to write aneffective memorandum.

Student FeedbackThe case was administered to two sections of an upper-level intermediate undergraduate cost

accounting class at a major U.S. university. Seventy-seven students responded to an evaluationsurvey to assess whether they improved their understanding of the concepts illustrated in the case,as well as to whether the case illustrated a real world application in predicting operating costs.As shown in Table 1, students agreed that the case enhanced their understanding of the use ofregression analyses in predicting future costs mean of 4.17, based on a five-point scale, the caseencouraged them to think critically about the behavior of operating costs in a real world contextmean of 4.03, based on a five-point scale; plus, they found the case interesting and recommendedit for use in teaching cost estimation via regression analyses mean of 4.07, based on a five-pointscale; see also Table 2. Similar positive responses are shown in Table 2. For example, Table 2reports students knowledge on the use of regression analysis before and after working on the case.As shown, students significantly enhanced their knowledge on cost estimation after reading thecase mean 2.80 before and a mean of 4.47 after on a five-point scale.

TABLE 1

Students Assessment of Case Learning Objectives

Survey QuestionsMean

(n 58)Median(n 58)

The case helped me improve myunderstanding of how regression analysiscan be used in predicting future costs.

4.17 4.00

The context of the assignment represents arealistic real world scenario.

4.29 4.00

The case taught me the necessary skills toperform regression analysis in Excel andto use such techniques to estimate futurecosts.

4.34 4.00

The case encouraged me to think criticallyabout the behavior of operating costs ina real world context.

4.03 4.00

I found the case interesting and recommendits use for teaching cost estimation.

4.07 4.00

Scale: 1 strongly disagree to 5 strongly agree.

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Additionally, students were asked to write specific comments about their experience workingon this case. Some of these comments are as follows:

Useful assignment, especially for students who are unskilled at statistics This case improved my understanding of regression analysis and how to use it for pre-

dicting costs

APPENDIXFundamentals of Regression Analyses

Regression analysis is a powerful statistical technique that is commonly used to predict afuture value of a variable of interest, such as costs, revenues, etc., based on data from the past. Toperform regression analysis, we must specify a regression model of the relationship between thevariable of interest, the dependent variable, and one or several explanatory variables, the indepen-dent variables. One simple and frequently used way to describe the underlying relationship be-tween the dependent variable and the independent variable is with a linear regression model. Alinear model assumes that the relationship between the variables of interest is strictly linear and isdescribed in the following way:

Y = a + bX + e.

To better illustrate, suppose that you want to estimate Aircraft Maintenance and Repair costs atContinental Airlines. In this case, the dependent variable is the underlying cost that we are tryingto predict and the independent variable is whatever factor causes that cost to rise or drop. Forexample, a common factor that tends to affect Aircraft Maintenance and Repair costs for airlinesis the number of aircraft in their fleet. Therefore, this would be the independent or predictorvariable of Aircraft Maintenance and Repair costs.

In its most simple term, what the above model indicates is whether the variable Y is related toX. More formally, the regression model represents the mean of Y for a given change in X. That is,whether the mean of Y is linearly related to X plus some error term.

Where Y represents the dependent variable Aircraft Maintenance and Repair costs, X is theindependent variable number of aircraft, a and b are the estimated coefficients, the constant andthe slope of the regression model, respectively, which will be explained next, and e is the residual

TABLE 2

Students Perception of Skills Proficiency Before and After the Case

Survey QuestionsMean Before

(n 58)Mean After

(n 58)

Understanding of how regression analysesare conducted

2.81 4.47

Interpreting the regression output andapplying it in cost estimation

2.60 4.34

Understanding the main statistics inregression

2.79 4.50

Understanding the difference betweenunivariate and multivariate regression

2.43 4.24

Understanding the advantage/limitations ofregression analysis for cost estimation

2.38 4.12

Scale: 1 least knowledgeable to 5 knowledgeable.



or estimated error of the model. The a coefficient is a value at which the line intercepts theY-axis. It is the value of the mean of Y when X0. With respect to a cost function, it representsthe fixed costs in the cost function. The b coefficient is called the slope because it measures theslope of the regression line. In our example, it represents the amount by which the mean of Ymaintenance costs changes if X number of the aircraft changes by one unit.

The next question is how do we perform regression analysis in Excel? To explain the proce-dure, consider the following quarterly data for Continental Airlines for Aircraft Maintenance andRepair costs and the potential cost driver of such costs, the number of aircraft in Continentalsfleet:

Observation Maintenance Costs No. of Aircraft

1 $340,000 102 $400,000 403 $440,000 504 $480,000 805 $530,000 110

The first step in regression analysis is to see whether a linear relationship exists between thedependent variable and the independent predictor variable. This may be accomplished by plottingthe data on a graph. Data for maintenance costs, the dependent variable, is plotted on the Yvertical axis, and data for the number of aircraft, the independent variable, on the X horizontalaxis.

To create this graph in Excel, follow these steps:

1. Copy the data into an Excel spreadsheet, copying the data pertaining to the cost driver inthe first column and the cost data in the second column.

2. Click on the Insert menu bar and select the Chart option; alternatively, you may alsoselect the Chart Wizard toolbar.

3. Select the XY Scatter graph option.4. Select the cells that contain the data you want to use for your chart.5. Press Next to add a title and to label the Y and X axis.6. Press Finish to display the chart. Using the above data, the Scatter plot chart looks as

follows:

Maintenance Costs vs. No. of Aircraft

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

0 20 40 60 80 100 120

No. of Planes

As shown above, though the relationship scatter plots of Y and X will not outline a perfectlystraight line, we could observe that the scatter graph shows that this relationship is indeed linearand, thus, indicates that the number of planes is a good predictor of Maintenance costs. Moreover,by plotting the data, we could identify potential outliers data points that do not represent normalactivity and eliminate them from the analysis. In this particular case, it can be observed that nooutliers are present.

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Next, well proceed to estimate the regression model, where maintenance costs would be afunction of the number of airplanes serviced. In this particular case, since we have a singlepredictor variable, we refer to it as a univariate regression. The regression model is expressed asfollows:

Maintenance costs = a + bnumber of planes + e

where maintenance costs substitutes for the Y variable and the number of planes for the X variabledescribed previously; e is called the residual or error term and is defined as the difference betweenan actual observation of the dependent variable cost and its estimated or forecasted value fromthe regression estimation that we will run next.

The idea of regression analysis is to calculate the values of the dependent variables thatminimize the sum of square of these residuals. The mechanics of regression analysis work asfollows: Using the data in your sample, regression would calculate a mean and would use thismean as a benchmark to compare as a central value in the calculations. Simply put, the regressionequation in this example will provide an estimate of the relationship between maintenance costsand the number of flights that Continental Airlines offered, on average, in the quarter. Let us nowperform the regression in Excel.

To estimate a regression in Excel MS Office 97 thru 2005 versions, follow these steps:

1. On the Tools menu bar, select the Data Analysis command, and then select regres-sion. Note that if the Data Analysis command is not available, you need to install theAnalysis Toolpak add-in. Here is how to add it: on the Tools menu bar, select theAdd-in command. Then, select Analysis Toolpak and press OK.

2. Enter the cell reference for the dependent variable i.e., maintenance costs; the rangeselected must consist of a single column of data; then proceed to select the cell referencefor the independent variable i.e., number of airplanes.

3. Select if the first row or column of the input ranges contain labels or headings; clear ifyour input has no labels; Excel generates appropriate data labels for the regression outputtable.

4. Click to create a new worksheet containing the regression output.5. Press OK to generate the Regression Output Table.

To estimate a regression in Excel MS Office 2007 version, follow these steps:

1. On the Data menu bar, select the Data Analysis command located on the right handcorner, and then select Regression Analysis. Note that if the Data Analysis commandis not available, you need to install the Analysis Toolpak add-in. Here is how to add it:press the Office icon located on the left-hand side of the Excel menu bar, select theExcel Option, then select Add-ins command. Then, select Analysis Toolpak andpress OK.

2. Enter the cell reference for the dependent variable i.e., maintenance costs; the rangeselected must consist of a single column of data; then proceed to select the cell referencefor the independent variable i.e., number of airplanes.


4. Click to create a new worksheet containing the regression output.



5. Press OK to generate the Regression Output Table.Using the above data, the Regression Output Table looks as follows:

Regression Statistics

Multiple R 0.990524645R2 0.981139072Adjusted R2 0.974852096Std Error 11566.62648Observations 5

ANOVA

df SS MS F Significance F

Regression 1 20878639456 20878639456 156.0589831 0.001105628Residual 3 401360544.2 133786848.1

Total 4 21280000000

CoefficientsStandard

Error t-stat p-value Lower 95% Upper 95%

Intercept 328707.483 10163.56279 32.3417575 6.49662E05 296362.4902 361052.4758No. of Aircraft 1884.353741 150.8405294 12.49235699 0.001105628 1404.311856 2364.395627

Let us now proceed to analyze each main statistic of the regression output. The intercept, with avalue of 328,707.48, is commonly referred to as the alpha coefficient and is a constant value in theregression function. In the specific case of cost estimation, this value represents the amount of fixedcosts present in the cost function. In our example, this value indicates that $328,707 ofMaintenance costs is fixed and would not change at all given any change in the number of planesin Continentals fleet. Further, the second statistic of interest is the coefficient estimate for theNumber of Aircraft, which has a value of 1,884.35. This is the slope of the regression function andit is referred as the beta coefficient. In cost estimation, this value represents the portion of variablecosts in the cost function; that is, the portion of Maintenance costs that would vary given anychanges in the number of planes. In our example, the slope coefficient is interpreted as follows: foreach plane in which Continental provides scheduled maintenance, the amount of Maintenancecosts is expected to increase, on average, by $1,884.35 dollars.

An important issue in the examination of both coefficients is that neither the intercept nor theslope is ever examined in isolation. Each coefficient must be analyzed in combination with itscorresponding t-statistic, or the respective p-value. The t-statistic is the ratio of the value of thecoefficient to its standard error. The standard error of the coefficient represents the amount ofvariation in costs that is unexplained by the cost driver; in our example, the number of planes. Thelower higher the standard error, the better worse each coefficient is. Going back to thet-statistic, this value indicates whether each of the two coefficients is different from zero. A rule ofthumb is that if the t-statistic is at least 1.96 or greater, then we are 95 percent confident that thevalue of the coefficient is significantly greater than zero. This implies that the coefficient is a validestimate and, therefore, could be used in the cost function as a way to predict future costs. If thet-value is less than 1.96, then we cannot rule out the possibility that the coefficient is zero and,therefore, the coefficient should not be used in the prediction of costs. If we take a look at theRegression Output Table, the t-statistics for the intercept and the slope coefficients are 32.34 and12.49, respectively. Therefore, we can conclude that both coefficients are not zero and, thereby, theestimates of fixed costs and variable costs per unit are valid estimates.

The second statistic of importance in the examination of each coefficient is the probability

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value, or the p-value. Each t-statistic has a corresponding p-value. The p-value is the reciprocal ofthe t-statistic in that it tells us the probability that the coefficient estimate is significantly differentfrom zero. If the p-value is less than or at least equal to 0.05, we are 95 percent confident that thecoefficient estimate for the intercept or the slope coefficient is statistically significant differentfrom zero. The smaller the p-value, the larger the t-statistic. For example, the p-value for thet-statistic in the intercept coefficient equals 0.0000649, and 0.0011 for the slope coefficient. Thismeans that both coefficients are not zero. More formally, this means that fixed costs have aprobability of being zero about six in 100,000 times, and the variable cost about one in 1,000times.

The last statistic of interest in our analysis is the R2, or the Adjusted R2. The R2 represents thegoodness of fit of the model, or the explanatory power of the model. In the case of the Adjusted R2,it measures the same thing, but after adjusting for degrees of freedom in the regression model.Simply put, the R2 Adjusted R2 represents the percentage of variation in the dependent variablemaintenance costs that is explained by the independent variable number of planes. This valueranges between 0 and 1, with the larger value representing a higher explained variation in costs. Inour example, the R2 equals 0.98, which indicates that approximately 98 percent of the variation inmaintenance costs is explained by the number of planes which were serviced. A follow-up ques-tion is which cutoff value is acceptable? This is subjective and will definitely depend on theunderlying analysis. In the case of cost estimation, perhaps we may want to have at least 30percent of the variation in costs explained by the cost driver.

Multivariate Regression AnalysesThus far, we have explored regression analyses with one independent variable. Then, the

question becomes what happens if we have two or more independent variables in our case, twocost drivers as predictors of the dependent variable Aircraft Maintenance and Repair costs. Forexample, it is feasible that besides the number of planes in Continentals fleet, Aircraft Mainte-nance and Repair costs may also be driven by other factors, such as the average utilization of eachplane in miles or hours.

In this case, the regression model varies subtly from the case of a single predictor variable.The mathematical notation for a multivariate regression model is expressed as follows:

Y = a + b1X1 + b2X2 + b2X2 + bkXk . . . + e

where Y represents the dependent variable Aircraft Maintenance and Repair costs, X1 is inde-pendent variable one number of aircraft in the fleet, and X2 average daily miles flown on eachaircraft. Just as in the case of a univariate regression, a and b are the estimated coefficients of theconstants and the slopes of the regression model; that is, the fixed costs and the slopes of the costfunction, respectively, and e is the residual or estimated error of the regression model.

Assume the following quarterly data for Aircraft Maintenance and Repair costs and for eachof the potential cost drivers discussed above:

Observation Maintenance Costs No. of Aircraft Daily Miles Flown

1 $340,000 10 1,1662 $400,000 40 1,2703 $440,000 50 1,4574 $480,000 80 1,4505 $530,000 110 1,433

To estimate a multivariate regression in Excel, we must follow Step 1, described previously, plusthe following additional steps:



1. Enter the cell reference for the dependent variable i.e., maintenance costs; the rangeselected must consist of a single column of data.

2. Then, proceed to select the cell reference for all the independent variables number ofairplanes, average age, and the average number of hours flown daily; the range selectedmust consist of two or more columns. Note that all independent variables must be listedin sequential order; that is, next to each other.


4. Click to create a new worksheet containing the regression output.5. Press OK to generate the Regression Output Table.

Using the above data, the Regression Output Table for the multivariate regression looks as fol-lows:

Regression Statistics

Multiple R 0.999719472R2 0.999439023Adjusted R2 0.998878045Standard Error 2443.112692Observations 5

ANOVA

df SS MS F Significance F

Regression 2 21268062401 10634031200 1781.60298 0.000560977Residual 2 11937599.25 5968799.625

Total 4 21280000000

CoefficientsStandard

Error t-stat p-value Lower 95% Upper 95%

Intercept 147096.4284 22586.32684 6.512631708 0.022774575 49915.30752 244277.5492No. of Aircraft 1324.949381 76.23333561 17.38018375 0.003294134 996.943811 1652.95495Daily Miles Flown 155.6548193 19.27060294 8.077319625 0.014983671 72.74010699 238.5695317

The statistics of interest are the same from the case of the univariate regression. The onlydifference is that now we have two slope coefficients. Let us summarize the main statistics ofinterest. The Intercept represents the alpha coefficient or the constant value in the regressionfunction and, thus, indicates that there is $147,096 of fixed costs. The coefficient estimate for theNumber of Aircraft has a value of $1,324.94 and indicates that for every aircraft in Continentalsfleet, Maintenance and Repair costs rise by this amount. And, the coefficient estimate for DailyMiles Flown indicates that for every mile that each aircraft in the fleet is flown daily, Maintenancecosts increase, on average, by $155. Note that the t-statistic for each coefficient is greater than 2and, thus, indicates that both coefficients are different from zero. The Adjusted R2 indicates that 99percent of the variation in Maintenance costs is explained by both cost drivers. An additionalstatistic of interest in multivariate regression is the F-statistic, which indicates the fitness of themodel; that is, how well all predictors as a whole explain changes in the dependent variable. AnF-statistic of two or greater indicates that the independent variables as a whole make a goodprediction of changes in Maintenance costs.

Let us now proceed to discuss how we can develop the cost functions as a way to estimateAircraft Maintenance and Repair costs.

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Development of the Cost Function to Estimate Future CostsA cost function is simply an algebraic representation of how a given cost would change given

a change in the cost driver. For example, in our example, the cost function would represent howAircraft Maintenance and Repair costs would change given a one-unit change in the number ofaircraft. Using our prior results from the univariate regression, the cost function is written asfollows:

Y = $328,707.48 + $1,324.94X

The above cost function indicates that $328,707.48 of Aircraft Maintenance and Repair costs isfixed and would not change irrespective of changes in the number of aircraft in the fleet, andMaintenance and Repair costs would rise by $ 1,884.35 for every aircraft in Continentals fleet.

After setting up the cost function, we can now proceed to estimate Maintenance and Repaircosts. Let us assume that Continental Airlines plans to have 142 planes in its fleet next year.Plugging this figure into the cost function, we obtain the following result:

Y = $328,707.48 + $1,884.35142

Y = $596,285.18

Therefore, given the projection with respect to the number of airplanes, we can conclude thatContinental Airlines would incur approximately $596,285.18 in Aircraft Maintenance and RepairCosts for next year.

The same procedure is applied to the case in which there are multiple cost drivers. Referringto our prior results from the multivariate regression, the cost function is written as follows:

Y = $147,096.42 + $1,324.94X1 + $155.65X2

Using the same projection as before of 142 planes for next year, plus assuming that the averageutilization of miles for each plane is 1,550 miles, then total Aircraft Maintenance costs for nextyear is calculated as follows:

Y = $147,096.42 + $1,324.94142 + $155.651,550

Y = $576,495.40

Hence, given the projection of the number of airplanes and the average utilization of miles thatContinental plans to fly each plane, we can conclude that Continental Airlines would incur ap-proximately $576,495 in Aircraft Maintenance and Repair costs for next year.

TEACHING NOTESTeaching Notes are available only to full-member subscribers to Issues in Accounting Edu-

cation through the American Accounting Associations electronic publications system at http://aaapubs.org/. Full-member subscribers should use their usernames and passwords for entry intothe system where the Teaching Notes can be reviewed and printed. Please do not make theTeaching Notes available to students or post them on websites.

If you are a full member of AAA with a subscription to Issues in Accounting Education andhave any trouble accessing this material, then please contact the AAA headquarters office [email protected] or 941 921-7747.



http://aaapubs.org/http://aaapubs.org/[email protected]

REFERENCES

Datar, S., C. Horngren, G. Foster, and C. Ittner. 2008. Cost Accounting: A Managerial Emphasis. 13thedition. Englewood Cliffs, NJ: Prentice Hall.

Eldenburg, L., and S. Wolcott. 2005. Cost Management: Measuring, Monitoring, and Motivating Perfor-mance. 1st edition. New York, NY: John Wiley and Sons.

Maynard, M. 2008. Big airlines in a rush go small. The New York Times June 6.

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