Businesses menagment

Continental Airlines Case Study

THE DECISION CONTEXT

In 2008, the senior management team at Continental Airlines, commanded by Lawrence Kellner, the Chairman and Chief Executive Officer, convened a special meeting to discuss the firm’s latest quarterly financial results. A bleak situation lay before them. Continental had incurred an operating loss of $71 million dollars—its second consecutive quarterly earnings decline that year. Likewise, passenger volume was significantly down, dropping by nearly 5 percent from the prior year’s quarter. Continental’s senior management needed to act swiftly to reverse this trend and return to profitability.

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

Concurrent with this revenue decline, the price of jet fuel soared to record levels during 2008.1 Thus, while revenue was decreasing, Continental was paying almost twice as much in fuel costs. Interestingly, fuel costs surpassed the firm’s salaries and wages as the highest cost in Continental’s cost structure. This obviously had a negative impact on the bottom line, squeezing even further the already strained profit margins.

The outlook for a quick recovery in the U.S. economy and, consequently, an upturn in the demand for air travel in the short term did not seem likely. Continental’s internal forecasts indicated that a further decline in passenger volume should be anticipated throughout 2009, with a recovery 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 Continental’s profits and relief was unlikely through the foreseeable future.

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 a severe recession, the prospect for growing revenues by either raising airfares or passenger volume seemed futile. Contrary to raising revenue, Continental’s managers believed that raising fares could potentially erode future revenues beyond the present level. Discounting fares did not seem a plausible solution either, because given the severity of the economic situation a fare cut could fall short in stimulating additional passenger demand and lead to lowering revenues.

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-summer of 2008.

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 in operating costs. This could most effectively be accomplished in two ways. First, through a reduction in flying capacity adjusted to match projected passenger demand. With this in mind, Continental’s management agreed to reduce flying capacity by 11 percent on domestic and international routes.2 As a result of this action, Continental would eliminate the least profitable (or unprofitable) flights and, accordingly, would ground several planes in the fleet. Management anticipated that this decision would reduce several of the firm’s operating costs.

Apart from this, Continental could achieve further reductions in costs by implementing several cost-cutting initiatives and through operational efficiencies. For example, management projected that it could achieve reductions in Passenger Services expenses by consolidating several tasks 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 discretionary spending.

In sum, to close the gap in profitability, Continental’s strategy was geared toward slashing operating costs by cutting capacity and through aggressive identification and implementation of cost-cutting initiatives.

The next step would be for management to know precisely how their decision to downsize capacity would impact the firm’s future operating costs, and also identify specific areas in which the firm could achieve additional cost reductions. Additionally, the cost analysis would help forecast the firm’s 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 categories of Continental’s costs behave is in order.

Before we begin, let us prepare with an overview of the airline industry and its competitive landscape, 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, they are exposed to tremendous risks brought by volatility inherent in their business model, as they deal with high fixed costs, labor unions, instability in fuel prices, weather and natural disasters, passenger safety, and security regulations. These aspects bring a large burden to airlines’ cost structures. 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, has hindered airlines’ pricing power and their ability to spur revenues. For these reasons, cost containment is a critically important aspect of profitability in this industry.

In order for Continental to restore profitability in this harsh environment of weak demand for air travel, it must be able to contain its operating costs, especially its massive fixed costs, which are visible in several ways. For example, salaries for pilots, flight attendants, and mechanics, as well 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 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 three major hubs in Houston, Cleveland, and Newark (Maynard 2008).

commonly referred as “capacity” costs. Since fixed costs do not self-adjust to fluctuations in passenger volume, the only way in which they can be decreased (or increased) is if management adjusts them in accordance to the level of operating capacity. In contrast, other costs, such as passenger services and reservation and distribution costs, behave as variable and would selfadjust with variations in volume or operating activity.

Hence, to assess the impact of this strategic decision to alter Continental’s cost structure, and identify the areas that could achieve the greatest reduction in costs, we must resolve how Continental’s operating costs behave and what drives them. In what follows, we learn how to apply regression analyses to examine cost behavior and forecast future costs, and then use that knowledge to assess how the reduction in flying capacity would affect Continental’s operating costs and profitability in the near term.

ESTIMATING COSTS USING REGRESSION ANALYSES

The previous discussion highlighted the importance of examining the behavior of Continental’s 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 cost behavior and predict future costs. The idea behind regression analysis is straightforward: historical data for costs, and the various activities that could potentially drive operating costs, are inserted into a mathematical calculation which yields the average amount of change in that particular cost that has occurred over time. Average values provided by regression calculations may then be applied to estimate future change that will occur in that cost given a one-unit change in one or more of the business activities which drive that cost.3 More precisely, in a regression model, cost is 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 activities drive costs, our first step in the estimation of a cost function is to identify the underlying activities or other potential factors that drive the cost in question—the cost drivers. This requires extensive knowledge of the business operation. In the case of Continental Airlines, the potential drivers of operating costs vary greatly. For instance, as previously noted, the number of passengers that Continental flies may drive the costs related to Passenger Services. Likewise, Aircraft Maintenance and Repairs costs could be driven by the number of aircraft in the fleet and by the level of flying capacity set by Continental (i.e., available seat miles).

In synthesis, to predict how Continental’s operating costs would be affected by the decision to reduce capacity, and to identify those areas in which additional room is available for cost cutting, we need to identify which costs in this firm’s cost structure behave as variable, fixed, or mixed (in which elements of both variable and fixed are observable). Equally important, we should also identify 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 this information to forecast operating costs and profitability for the upcoming year. As part of your cost analysis, you should investigate how the decision to cut flying capacity would impact the 3 For ease in exposition, cost functions and regression analyses are discussed briefly here. For further insight on cost functions and the mechanics of regression analyses, refer to the Appendix.

firm’s future operating costs and, equally important, identify those specific expense categories (or operating areas) in which this firm could attain additional cost saving by implementing costcutting initiatives. Your conclusions should be outlined in a memorandum directed to Continental’s Executive Management team.

You are provided next with a description of Continental’s operating costs and the potential drivers of costs so you can conduct regression analysis to estimate the corresponding cost functions. To help you in estimating the regressions, a comprehensive set of instructions for performing regression analysis using Microsoft Excel is provided in the Appendix. Immediately following the description of costs, a series of questions is provided that should help guide your analysis. Additionally, to help you estimate your regressions, the Excel Spreadsheet accompanying this case presents past quarterly data for all of the above expenditures for the period of April 2000 through December 2008, and also quarterly operations data over the same period.

CONTINENTAL’S OPERATING COSTS AND POTENTIAL COST DRIVERS

The spreadsheet provides ten categories of operating costs, including salaries and wages, aircraft fuel and related taxes, aircraft rentals, airport fees, aircraft maintenance and repairs, depreciation and amortization, distribution costs, passenger services, regional capacity purchases, and other expenses. Of these, some represent a single expense item. For example, the cost of aircraft rentals and airport fees together comprise a single cost item. Other costs represent cost pools comprising several cost items. Such is the case of passenger services and other expenses. The following provides a detailed description of each cost, along with the potential cost drivers.

Salaries and wages This account represents costs related to salaries and wages, as well as fringe benefits, of Continental’s workers. These include salaries for pilots and wages for flight attendants and ground crew, as well as wages for Continental’s mechanics. Additionally, a significant portion of this salary pool represents wages of reservation specialists, customer service representatives at airports, and the salaries for administrative and support personnel (e.g., flight schedulers, technology personnel, accountants, and division managers_. A possible cost driver of salaries is the available seat miles.4

Aircraft fuel and related taxes This 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 rentals These are expenses for operating leases of aircraft. The main driver is the number of leased planes in Continental’s fleet, including regional jets operated on behalf of Continental by four regional airlines under various capacity purchase agreements.

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

Airport fees Represents landing fees and passenger security fees paid to the various domestic and international airports where Continental flies. Landing fees are driven by the number of passengers.

Aircraft maintenance and repairs These are expenses associated with the service and maintenance of planes. These include expenses related to scheduled maintenance, spare parts and materials, and airframe and engine overhauls. The main drivers of these costs are the total aircraft in the fleet and the number of miles flown.

Depreciation and amortization This represents depreciation and amortization expenses of aircraft, ground equipment, buildings, and other property. It must be emphasized that the largest portion of depreciation expense relates to the depreciation of aircraft. Although depreciation expenses are driven by the acquisition cost of Continental’s capital assets, depreciation is greatly influenced by both company policy and accounting principles, such as the depreciation method, that a firm adopts.

Distribution costs These expenses represent credit card discount fees, booking fees, and travel agency commissions, all of which are affected by passenger revenue. Therefore, the driver of these costs is total revenue.

Passenger services This 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 these costs is generated by Continental’s Field Services Division, the main function of which is to provide service to planes prior to take-off. Some of these expenses relate to checking in passengers, 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 of passengers.

Regional capacity purchases These 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 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, including technology expenses, security and outside services, general supplies, and advertising and promotional expenses. Further, this cost pool contains various special charges for gains and losses from the sale of retired aircraft and costs of future leases. Given the large variety of miscellaneous items, there is no clear driver of these expenses; however, a large portion of them, such as advertising and promotional expenses, are driven by total revenue.

CASE QUESTIONS

1. Using the quarterly data for operating costs and the various cost drivers of costs provided in the spreadsheet, estimate regressions for each of the ten cost categories listed above. Then, write the appropriate cost function for each category of cost and interpret your regression results.

2. Based on your regression results and your interpretation of those results, where do you see the largest reductions in costs if flying capacity is lowered by 11 percent? Also, in which areas do you see opportunities to achieve further cost reductions? Why?

3. The table below provides a quarterly forecast of revenues, jet fuel prices,5 and the projected operating activity for 2009. Using the information from your regressions and the forecast information provided, estimate Continental’s operating costs and expected profit for the upcoming fiscal year.

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

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

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

Projected Revenues and Operating Activity for 2009 Quarter Variable 1 2 3 4 Revenues $2,962,000,000 $2,767,000,000 $2,947,000,000 $2,462,000,000 Total aircraft 634 617 604 601 Leased aircraft 398 394 380 379 Flights 77,778 80,675 78,948 83,008 Passengers 14,408,000 16,348,000 16,795,000 15,258,000 Available seat miles 26,323,000,000 28,007,000,000 28,933,000,000 26,291,000,000 Available regional miles 2,971,000,000 3,044,000,000 3,130,000,000 3,002,000,000 Passenger miles flown 24,562,000,000 25,186,000,000 25,529,000,000 24,550,000,000 Employees 39,600 42,300 43,000 42,000 Fuel price $1.82 $2.07 $1.99 $1.98 Fuel consumed 403,000,000 430,000,000 369,000,000 479,000,000

Definitions of Operations Variables: Total aircraft = number of planes in the fleet, including regional routes aircraft and leased aircraft; Number of leased planes = number of leased planes; Flights = number of flights from a single point of departure to a single destination; Passengers = number of paying passengers; Available seat miles = the number of seats available multiplied by the number of miles flown; Available regional miles = available seat miles on regional routes; Passenger miles flown = number of paying passengers multiplied by the number of miles flown; Employees = number of employees, including pilots, flight attendants, and ground crew. Fuel price = average price per gallon of jet fuel in the respective quarter; and Fuel consumed = number of gallons of fuel consumed in the respective quarter.

APPENDIX

FUNDAMENTALS OF REGRESSION ANALYSIS

Regression analysis is a powerful statistical technique that is commonly used to predict a future value of a variable of interest, such as costs, revenues, etc., based on data from the past. To perform regression analysis, we must specify a regression model of the relationship between the variable of interest, the dependent variable, and one or several explanatory variables, the independent variables. One simple and frequently used way to describe the underlying relationship between the dependent variable and the independent variable is with a linear regression model. A linear model assumes that the relationship between the variables of interest is strictly linear and is described in the following way:

𝑌 = 𝑎 +𝑏𝑋 +𝑒.

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

In its most simple term, what the above model indicates is whether the variable Y is related to X. 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 the independent variable (number of aircraft), a and b are the estimated coefficients, the constant and the slope of the regression model, respectively, which will be explained next, and e is the residual or estimated error of the model. The “a” coefficient is a value at which the line intercepts the Y-axis. It is the value of the mean of Y when 𝑋 = 0. With respect to a cost function, it represents the fixed costs in the cost function. The “b” coefficient is called the slope because it measures the slope of the regression line. In our example, it represents the amount by which the mean of Y (aircraft maintenance 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 procedure, consider the following quarterly data for Continental Airlines for Aircraft Maintenance and Repair costs and the potential cost driver of such costs, the total number of aircraft in Continental’s fleet:

Observation Aircraft Maintenance Total Aircraft 1 $340,000 10 2 $400,000 40 3 $440,000 50 4 $480,000 80 5 $530,000 110

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

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 in the first column and the cost data in the second column. 2. Click on the “Insert” tab and select the Scatter Chart option having only markers. 3. Once the chart space has been created, select it. From the “Design” tab, click the Select Data option. 4. Click the button next to the “Chart data range” field. Select the two columns you copied into Excel, including the headers, and then hit “Enter”. The chart should populate similar to below.

As shown above, though the relationship scatter plots of Y and X will not outline a perfectly straight line, we could observe that the scatter graph shows that this relationship is indeed linear and, thus, indicates that the total 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 normal Activity) and eliminate them from the analysis. In this particular case, it can be observed that no outliers are present.

Next, we’ll proceed to estimate the regression model, where aircraft maintenance would be a function of the number of airplanes serviced. In this particular case, since we have a single predictor variable, we refer to it as a univariate regression. The regression model is expressed as follows:

$0

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

0 20 40 60 80 100 120 Total Aircraft

Aircraft Maintenance

𝐴𝑖𝑟𝑐𝑟𝑎𝑓𝑡 𝑚𝑎𝑖𝑛𝑡𝑒𝑛𝑎𝑛𝑐𝑒 = 𝑎 +𝑏 (𝑇𝑜𝑡𝑎𝑙 𝑎𝑖𝑟𝑐𝑟𝑎𝑓𝑡)+𝑒,

where aircraft maintenance substitutes for the Y variable and total aircraft for the X variable described previously; e is called the residual or error term and is defined as the difference between an actual observation of the dependent variable (cost) and its estimated or forecasted value from the regression estimation that we will run next.

The idea of regression analysis is to calculate the values of the dependent variables that minimize the sum of square of these residuals. The mechanics of regression analysis work as follows. Using the data in your sample, regression would calculate a mean and would use this mean as a benchmark to compare as a central value in the calculations. Simply put, the regression equation in this example will provide an estimate of the relationship between aircraft maintenance and the number of flights that Continental Airlines offered, on average, in the quarter. Let us now perform 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 “regression.” Note that if the “Data Analysis” command is not available, you need to install the “Analysis Toolpak add-in.” Here is how to add it: on the “Tools” menu bar, select the “Add-in” command. Then, select “Analysis Toolpak” and press “OK.”

2. Enter the cell reference for the dependent variable (i.e., aircraft maintenance); the range selected must consist of a single column of data; then proceed to select the cell reference for the independent variable (i.e., number of airplanes).

3. Select whether or not the first row or column of the input ranges contain labels (or headings). Excel generates appropriate data labels for the regression output table.

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 hand corner, and then select “Regression Analysis.” Note that if the “Data Analysis” command is 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 the “Excel Option,” then select “Add-ins” command. Then, select “Analysis Toolpak” and press “OK.”

2. Enter the cell reference for the dependent variable (i.e., aircraft maintenance); the range selected must consist of a single column of data; then proceed to select the cell reference for the independent variable (i.e., number of airplanes).

3. Select whether or not the first row or column of the input ranges contain labels (or headings). Excel generates appropriate data labels for the regression output table.

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 should appear as in Exhibit A1, below. Let us now proceed to analyze each main statistic of the regression output. The intercept, with a value of $328,707.48, is commonly referred to as the alpha coefficient and is a constant value in the regression function. In the specific case of cost estimation, this value represents the amount of fixed costs present in the cost function. In our example, this value indicates that $328,707 of maintenance costs is fixed and would not change at all given any change in the number of planes in Continental’s fleet. Further, the second statistic of interest is the coefficient estimate for the total number of Aircraft, which has a value of 1,884.35. This is the slope of the regression function and it is referred as the beta coefficient. In cost estimation, this value represents the portion of variable costs in the cost function; that is, the portion of maintenance costs that would vary given any changes in the number of planes. In our example, the slope coefficient is interpreted as follows: for each plane in which Continental provides scheduled maintenance, the amount of maintenance costs 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 the slope is ever examined in isolation. Each coefficient must be analyzed in combination with its corresponding t-statistic, or the respective p-value. The t-statistic is the ratio of the value of the coefficient to its standard error. The standard error of the coefficient represents the amount of variation in costs that is unexplained by the cost driver; in our example, total aircaft. The lower (higher) the standard error, the better (worse) each coefficient is. Going back to the t-statistic, this value indicates whether each of the two coefficients is different from zero. A rule of thumb is that if the t-statistic is at least 1.96 or greater, then we are 95 percent confident that the value of the coefficient is significantly greater than zero. This implies that the coefficient is a valid estimate and, therefore, could be used in the cost function as a way to predict future costs. If the t-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 the Regression Output Table, the t-statistics for the intercept and the slope coefficients are 32.34 and 12.49, respectively. Therefore, we can conclude that both coefficients are not zero and, thereby, the estimates 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 value, or the p-value. Each t-statistic has a corresponding p-value. The p-value is the reciprocal of the tstatistic in that it tells us the probability that the coefficient estimate is significantly different from zero. If the p-value is less than or at least equal to 0.05, we are 95 percent confident that the coefficient estimate for the intercept or the slope coefficient is statistically significantly different from zero. A smaller p-value indicates a larger t-statistic. For example, the p-value for the tstatistic in the intercept coefficient equals 0.0000649, and 0.0011 for the slope coefficient.

Exhibit A1 SUMMARY OUTPUT

Regression Statistics Multiple R 0.990524645 R Square 0.981139072 Adjusted R Square 0.974852096 Standard Error 11566.62648 Observations 5

ANOVA

df SS MS F

Significance F Regression 1 20878639456 20878639456 156.0589831 0.001105628 Residual 3 401360544.2 133786848.1 Total 4 21280000000

Coefficients

Standard Error t Stat P-value Lower 95% Upper 95%

Lower 95.0%

Upper 95.0% Intercept 328707.483 10163.56279 32.3417575 6.49662E-05 296362.4901 361052.4758 296362.4901 361052.4758 No. of Aircraft 1884.353741 150.8405294 12.49235699 0.001105628 1404.311856 2364.395627 1404.311856 2364.395627

This means that both coefficients are not zero. More formally, this means that fixed costs have a probability of being zero about six in 100,000 times, and the variable cost about one in 1,000 times.

The last statistic of interest in our analysis is the R2, or the Adjusted R2. The R2 represents the goodness 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 variable (aircraft maintenance) that is explained by the independent variable (total aircraft). This value ranges between 0 and 1, with the larger value representing a higher explained variation in costs. In our example, the R2 equals 0.98, which indicates that approximately 98 percent of the variation in aircraft maintenance costs is explained by the total number of planes which were serviced. A follow-up question is “which cutoff value is acceptable?” This is subjective and will definitely depend on the underlying analysis. In the case of cost estimation, perhaps we may want to have at least 30 percent of the variation in costs explained by the cost driver.

Multivariate regression analyses

Thus 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, two cost drivers) as predictors of the dependent variable (Aircraft Maintenance and Repair costs). For example, it is feasible that besides the number of planes in Continental’s fleet, aircraft maintenance and repair costs may also be driven by other factors, such as the average utilization of each plane 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 +⋯+𝑏𝑛𝑋𝑛 +𝑒,

where Y represents the dependent variable (Aircraft Maintenance and Repair costs), 𝑋1 is independent variable one (number of aircraft in the fleet), and 𝑋2 is independent variable two (average daily miles flown on each aircraft). Just as in the case of a univariate regression, a and b are the estimated coefficients of the constants and the slopes of the regression model; that is, the fixed costs and the slopes of the cost function, 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 each of the potential cost drivers discussed above:

Observation

Aircraft Maintenance Total Aircraft Daily Miles Flown 1 $340,000 10 1,166 2 $400,000 40 1,270 3 $440,000 50 1,457 4 $480,000 80 1,450

5 $530,000 110 1,433

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

1. Enter the cell reference for the dependent variable (i.e., aircraft maintenance); the range selected must consist of a single column of data.

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

3. Select if the first row or column of the input ranges contain labels (or headings); clear if your input has no labels; Excel generates appropriate data labels for the regression output table.

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 appears as shown in Exhibit A2.

The statistics of interest are the same from the case of the univariate regression. The only difference is that now we have two slope coefficients. Let us summarize the main statistics of interest. The Intercept represents the alpha coefficient or the constant value in the regression function and, thus, indicates that there is $181,834.40 of fixed costs. The coefficient estimate for the Number of Aircraft has a value of $1,552.18 and indicates that for every aircraft in Continental’s fleet, Maintenance and Repair costs rise by this amount. And, the coefficient estimate for Daily Miles Flown indicates that for every mile that each aircraft in the fleet is flown daily, maintenance costs increase, on average, by $122.59. Note that the t-statistic for each coefficient is greater than 2 and, thus, indicates that both coefficients are different from zero. The Adjusted R2 indicates that 99% of the variation in aircraft maintenance is explained by both cost drivers. An additional statistic of interest in multivariate regression is the F-statistic, which indicates the fitness of the model; that is, how well all predictors as a whole explain changes in the dependent variable. An F-statistic of two or greater indicates that the independent variables as a whole make a good prediction of changes in aircraft maintenance costs.

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

Exhibit A2 SUMMARY OUTPUT

Regression Statistics Multiple R 0.999500305 R Square 0.999000859 Adjusted R Square 0.998001718 Standard Error 3260.500131 Observations 5

ANOVA

df SS MS F

Significance F Regression 2 21258738278 10629369139 999.8596569 0.000999141 Residual 2 21261722.21 10630861.11 Total 4 21280000000

Coefficients

Standard Error t Stat P-value Lower 95% Upper 95%

Lower 95.0%

Upper 95.0% Intercept 181834.4026 24729.33755 7.352983161 0.01799797 75432.65089 288236.1544 75432.65089 288236.1544 No. of Aircraft 1552.183215 69.95682026 22.18773251 0.002025132 1251.183311 1853.183119 1251.183311 1853.183119 Daily Miles Flown 122.5936916 20.50237078 5.979488566 0.026847454 34.37911005 210.8082732 34.37911005 210.8082732

Development of a cost function to estimate future costs

A 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 how Aircraft Maintenance and Repair costs would change given a one-unit change in the number of aircraft. Using our prior results from the univariate regression, the cost function is written as follows:

𝑌 = $328,707.48+$1,324.94(𝑋).

The above cost function indicates that $328,707.48 of Aircraft Maintenance and Repair costs is fixed and would not change irrespective of changes in the number of aircraft in the fleet, and Maintenance and Repair costs would increase by $ 1,884.35 for every aircraft in Continental’s fleet.

After setting up the cost function, we can now proceed to estimate Maintenance and Repair costs. 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+$1,324.94(142) = $516,848.96.

Therefore, given the projection with respect to the number of airplanes, we can conclude that Continental Airlines would incur approximately $516,848.96 in Aircraft Maintenance and Repair Costs for next year.

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

𝑌 = $181,834.40+$1,552.18(𝑋1)+$122.59(𝑋2).

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

𝑌 = $181,834.40+$1,552.18(142)+$122.59(1,550) = $592,258.50.

Hence, given the projection of the number of airplanes and the average utilization of miles that Continental plans to fly each plane, we can conclude that Continental Airlines would incur approximately $592,259 in Aircraft Maintenance and Repair costs for next year.

Guidelines to Writing a Memorandum

1. Begin your memorandum with a general statement about the core issue you are discussing.

2. The second paragraph should include a short explanation as to how you arrive at your conclusion. Specifically, it must describe how the analysis was conducted (i.e., regression analysis) and the assumptions taken.

3. The memorandum should then incorporate a more detailed discussion of the findings supporting your conclusion. Specifically, indicate which areas would experience the largest reduction in costs and how that can be achieved. Also discuss the profit outlook for 2009 and provide a list of recommendations to further reduce operating costs to reverse losses and return the company to profitability.

4. Pay special attention to grammar, including spelling, fragmented, and convoluted sentences. Focus on parsimony over length, as long as clarity and understanding are not jeopardized. The memo should not exceed 1-2 pages double-spaced. (Note: memos are typically one page, single-spaced, but double-spaced between paragraphs.)

References

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