Page 1 of 111

The Future for Southwest Airlines

The Unknown Story of Rising Costs

2012 FORTUNE 500 List Rank 167

Southwest has always prided itself for having the lowest cost

structures in the domestic airline industry. It consistently offers the

lowest fares and has one of the best overall customer service records.

Nonetheless, this detailed case study, analyzes the profits-revenues data

for all forty-one (41) years, from 1971-2011, using a new methodology,

based on a universal mathematical law relating profits and revenues that

has been shown to describe the financial performance of many leading

companies in the Fortune 500 list. It is shown that “costs” have been

rising continuously for Southwest, going back all the way to 1974. What

is this “costs”? Costs = (Revenues – Profits), with revenues and profits

being obtained from the annual reports. Addressing this “cost” issue, in

innovative ways, based on a greater scientific understanding of the

financial dynamics, will make Southwest Airlines even more profitable

in the coming years. There is no contradiction between “rising costs”

noted here and being the “lowest cost” domestic airliner.

Page 2 of 111

Table of Contents

§ No. Topic Page No. 1. Summary 11

2. Brief version of the story 13

3. Introduction 18

4. Profits and Revenues over time 19

5. The Profits-Revenues Linear Law 22

6. The Unknown Costs-Revenues Story of Southwest Airlines 30

7. Quarterly data and Total Operating Expenses 35

8. Maximum Point on Profits-Revenues Graph 39

9. Brief Discussion 43

10. Appendix 1: Further discussion of quarterly data 2007-2012 49

11. Appendix 2: Growth of profits and revenue in a single year 54

12. Appendix 3: Type II Behavior and Type I to Type II transition 65

13. Appendix 4: Profits and Passengers flown 71

14. Appendix 5: Profits-Revenues in Early years: Nonlinear law

The entire 41 years of profits-revenues data from 1971-2011

75

15. Now a word about Air Tran 89

16. Bibliography of related articles 105

http://upload.wikimedia.org/wikipedia/commons/5/53/Southwest_Airl

ines_Flight_1248_-1.jpg Found this interesting image of a plane landing

(doctored?) during a Google search “Southwest airlines images”.

Page 3 of 111

Let’s Make this Easy

Although this document has grown to an amazing 108 pages (it even

includes a small section on AirTran now!), there is really nothing to

it. So, here are some “tips” about how to STUDY this (assuming you

still want to study it!)

1. Ok, just go straight to page 100 of the Air Tran section! Swoosh!

2. Fun Predictions on page 10 gives the formula for revenues, R = kF.

This can be deduced from the Southwest Fact Sheet on page 9.

3. The key to the whole analysis is P = hR + c, the profits-revenues relation. It

is derived in § 5 and requires only a knowledge of the “breakeven” analysis

for profitability. (All of it in just one paragraph!) The P-R formula is then

tested and shown to hold true using actual financial data. (It has also been

tested with many other companies.) Both P and R can thus be predicted!

4. Everything else, starting with §6, is aimed at showing, through different

types of calculations, that “costs” have indeed been going up for Southwest

Airlines, actually ever since operations began.

5. Southwest today is among the major low-cost domestic airlines that has

delivered a profit consistently for 39 years in a row. Both the level of profits

and the profit margins can be increased if we understand how and why

“costs” have been increasing and, more importantly, develop INNOVATIVE

SOLUTIONS to control these “rising costs”.

6. More importantly, just look at the graphs. There is nothing mysterious about

this. Just read the captions with each graph. They tell the whole story. Study

the Southwest initial year graph, Figures 28 and 29, and the Air Tran initial

years graph in Figures 38 and 39.

With lots of LUV in the air!

Page 4 of 111

Happy Birthday

Southwest Airlines http://www.swamedia.com/channels/Our-History/pages/our-history-sort-by

Celebrating and

Living the

Southwest Way

Celebrating is an important part of the Southwest Airlines Culture. It’s

been that way from our very first flight in 1971, and it’s true today.

We’ve always subscribed to the mantra of “Work hard, play hard.”

Page 5 of 111

Quite coincidentally, this report was

completed on June 18, 2012,

the 41st anniversary of Southwest

Airlines first flight on June 18, 1971;

see History and Timeline.

Wishing even more LUV in the air!

What's LUV?

Southwest has been in LUV with our Customers from the very

beginning. Therefore, it's fitting that we began service to San Antonio

and Houston from Love Field in Dallas on June 18, 1971. As our

Company and Customers grew, our LUV grew too! With the prettiest Flight

Attendants serving "Love Bites" on our planes, and determined Employees issuing

tickets from our "Love Machines," we changed the face of the airline industry

throughout the 1970s. Then in 1977, our stock was listed on the New York Stock

Exchange under the ticker symbol "LUV." Over the ensuing years, our LUV has

spread from coast to coast and border to border thanks to our hardworking

Employees and their LUV for Customer Service.

Page 6 of 111

Our History

Select from a Category Select By Date

1966 to 1971

1967

March 15,

1967 Air Southwest Co. is incorporated.

November

27, 1967

With $500,000 in the bank, Herb files the application with the Texas

Aeronautics Commission (TAC) to serve DAL, IAH, and SAT.

Page 7 of 111

1968

January 15,

1968 Hearing before TAC begins.

February 20,

1968

TAC votes unanimously to grant Air Southwest a certificate of public

convenience and necessity.

February 21,

1968

Braniff, Trans Texas (later Texas International), and Continental Airlines obtain

a temporary restraining order from Travis County District Court prohibiting

TAC from delivering our Certificate.

August 06,

1968 Austin State District Court rules against Air Southwest.

August 06,

1968

Air Southwest files an appeal with the Third Court of Civil Appeals over the

State District Court's Aug. 6 decision.

1969

March 12,

1969

Herb files appeal with the Texas Supreme Court and offers to represent the

Company free of charge and pay all costs out of his own pocket.

March 12,

1969

State Court of Civil Appeals rules against Air Southwest, upholding the lower

court's decision.

1970

May 13, 1970 The Texas Supreme Court unanimously votes to overturn the lower courts'

findings and rules in favor of Air Southwest.

December 07,

1970

The United States Supreme Court denies appeal by Braniff and Texas

International (TI) of Texas Supreme Court decision.

1971

January 01,

1971 Lamar Muse joins Air Southwest as President.

March 10,

1971

Lamar Muse sells promissory notes for aircraft and startup costs, raising $1.25

million.

March 29,

1971 Air Southwest Co. changes its name to Southwest Airlines Co. (Southwest).

March 29,

1971

Boeing offers to sell Southwest three 737-200s with Boeing carrying 90% of the

financing.

March 29,

1971

Lamar Muse hires Dick Elliot, Jack Vidal, Donald Ogden, and Bill Franklin.

They become known as the "Over the Hill Gang."

June 08, 1971 Jun. 8, 1971 Initial Public Offering of 650,000 shares of Southwest stock at $11

Page 8 of 111

per share ($6.5 million). Thomson McKinnon Auchincloss, Inc. and Model,

Roland & Co., Inc. were the Principal Underwriters. The exchange was traded

over the counter, and we did not have a ticker symbol.

June 16, 1971

The Civil Aeronautics Board (CAB), refusing to interfere, throws out complaints

filed by Braniff and TI that Southwest's operation might violate its intrastate

exclusivity. Within hours, lawyers for the two win a restraining order from an

Austin judge barring Southwest from beginning service.

June 17, 1971

Herb pleads case to the Texas Supreme Court. Later that day, the Texas Supreme

Court overrules the State District Court's injunction preventing Southwest from

commencing service.

June 18, 1971 Dallas Provisioning base opens.

June 18, 1971

Southwest Airlines begins service to DAL, SAT, and IAH. Our flight

schedule starts with six roundtrips DAL-SAT and 12 roundtrips DAL-IAH

with $20 one-way fares.

June 18, 1971 First uniforms for hostesses and ticket agents introduced. The "love airline" is

born. Captain Emilio Salazar flies the inaugural flight.

September

29, 1971 Southwest receives fourth aircraft.

October 01,

1971

Southwest implements every-hour service DAL-IAH with 14 roundtrips and

every-other-hour service DAL-SAT with 7 roundtrips.

November

14, 1971 Begins service between HOU-SAT - closing triangle.

November

14, 1971

Southwest "revitalizes" Houston's Hobby airport (HOU) by providing air service

and transfers one-half of service from IAH to HOU.

November

21, 1971 Introduces $10 "night fare" between HOU-DAL.

November

22, 1971 Cancels Saturday service.

December 31,

1971

1971 Milestones Net Loss: $3,753,000 Revenue

passengers carried: 108,554 Trips flown: 6,051

Fleet: 4 aircrafts Employees: 195 at

year end. Cities opened: DAL, SAT, IAH,

HOU Advertising budget: $700,000

Page 9 of 111

Southwest Airlines Fact Sheet http://www.southwest.com/html/about-southwest/history/fact-sheet.html#fleet

Operates 558 Boeing 737 (as of March 30, 2012)

Fleet type Number Seats

737-300 158 137

737-500 25 122

737-700 372 137

(Beginning February 2, 2012 capacity is being increased to 143). Two 737-800s

began service April 11, 2012.

Southwest currently flies to 73 cities in 38 states.

More than 3200 flights per day.

Southwest aircrafts fly an average of six flights per day (6.18/day) or an

average of 11 hours and 12 minutes per day. (558 times 6 equals 3348.)

The average trip length is 679 miles and the average duration is 1 hour

and 58 minutes.

Southwest consumed about 1.8 billion gallons of jet fuel in 2011.

The average passenger fare is $141.72 one-way and average trip is

approx. 939 miles.

Other related studies: http://www.thomashauck.net/pdfs/1southwest.pdf

Southwest Airlines: Case Study

by Garrison & Keller, 5567 Beechmont Ave, Cinncinnati, OH 45276

http://www.dtic.mil/dtic/tr/fulltext/u2/a273125.pdf

An estimate of the MAXIMUM daily and annual revenues is readily arrived at using the

data compiled here.

Page 10 of 111

Fun Prediction Fun Formula for Revenues ( R = kF )

From Southwest Airlines Fact Sheet http://www.southwest.com/html/about-southwest/history/fact-sheet.html#fleet

Based on the information compiled in the Fact Sheet, the following formula for

total annual revenues, let’s call it R, can be easily deduced. R = kF where F is the

average fare per seat and k is a numerical constant which depends on the numbers

compiled in the Fact Sheet.

Annual Revenues ($, billions) R = kF

= 0.14683 × (Fare per seat in $)

Average fare per seat, F $ Annual Revenue R ($, billions)

$100 $14.683 B

$125 $18.358 B

$150 $22.025 B

It is assumed that 120 seats are sold per flight and that there are 3350 flights

per day, each day of the year.

The change in average seats per flight will affect the total revenues in exact

proportion.

Now, here’s the formula for predicting the profits P. It is given by P = hR + c

Here h and c are constants that can be deduced from the two line items that are

now being reported routinely in the annual and quarterly financial statements. This

can be appreciated by studying this document carefully.

HOMEWORK PROBLEM: Repeat above for Jet Blue (ok, Air Tran!) and

compare it with Southwest! Also, check out the 2011 revenues for Southwest.

Page 11 of 111

§ 1. Summary

Southwest Airlines is an amazing company which has been in service for 40 years

and has been able to report a profit year-after-year for 39 years. It is focused on

offering low fares with exemplary customer service in an industry that is extremely

competitive and notorious for its low profitability. A recent article by Seth

Stevenson, in the Slate magazine, which discusses the “keep it simple” philosophy

of this airline, prompted this analysis of the profits and revenues behavior. The

data for the twenty year period, 1992-2011 and first quarter 2012, is studied here.

The revenues have increased consistently since 1992 and revenues growth actually

seems to have accelerated since 2009. Unfortunately, the same cannot be said

about profits. Profits increased consistently from 1992 and reached a peak in 2000

after which profits have been varying wildly, showing large fluctuations. For the

period 1992-2001, a simple linear law y = hx + c = 0.123x – 0.141, where x is

revenues and y is profits, both in billions, can be shown to describe the data.

Profits increase at a fixed and steady rate with increasing revenues, once a cut-off

or “breakeven” revenue was exceeded (given by y = 0 and x = $1.15 billion).

This has been called the Type I behavior here and signifies a period of steadily

increasing profits with increasing revenues (h > 0 and c < 0). Thus, one could also

conceive of a Type II behavior (h > 0, c > 0), where profits increase at a lower rate

than in the Type I phase and also a Type III behavior (h < 0, c > 0), where profits

actually decrease with increasing revenues. Indeed, for the post-2000 period, a

careful analysis of the profits-revenues data reveals that Southwest Airlines is now

in the Type III mode: profits-revenues graph actually has a negative slope for the

period 2007-2011. Extrapolating from this recently established trend, it is also

conceivable that Southwest Airlines will soon report an annual loss, as revenues

increase further. The recently completed acquisition of Air Tran thus takes on

added significance and one would be tempted to blame this acquisition if there is

any historical first reporting of a loss.

This impending situation has been studied carefully to understand how costs have

been increasing with increasing revenues. It can be shown that costs are actually

increasing faster than revenues and this also explains the low “absolute” level of

Page 12 of 111

profits and the rather low profit margins. The total Operating Expenses, one of the

Items reported in the Consolidated Statement of Operation, and the Cost, computed

from the relation Costs = Revenues – Profits (where profits is the same as the item

called Net income), are both studied carefully to draw some conclusions that

should engage the immediate attention of Southwest Airlines management.

While the unprecedented reporting of profits, year-after-year, is unprecedented and

to be highly commended, focus must now be shifted to increasing the profit

margins and a return to the Type I behavior of the pre-2000 era. Many issues that

affect the cost structure need to be addressed in the coming years to sustain the

history of profitability. It is hoped that Southwest management will benefit from

these findings (especially those in the more detailed Appendices).

Perhaps, the most important finding here is that Southwest Airlines, like some

other companies (notably Ford Motors, Verizon Communications, Yahoo, and

Kroger) shows a maximum point on its profits-revenues (P-R) graph. Air Tran,

recently acquired by Southwest, also reveals a maximum point. The P-R graph is a

simple x-y graph of these two items, reported routinely in the consolidated

financial statements (quarterly and annual). It is truly amazing that the existence of

such a maximum point has escaped attention to date. (The present author began

these recent studies on May 18, 2012, following the disappointing Facebook IPO

launch and the general media discussion about its potential revenues growth.)

Why is there a maximum point on the profits-revenue graph?

Why would a company want to continue operations if profits actually decrease

with increasing revenues?

The appearance of a maximum point in the radiation spectrum for a blackbody

puzzled physicists in the closing years of the 19th century. Classical physics was

unable to explain the existence of such a maximum point. Now, we have, in the

humble opinion of the present author, a finding of far reaching significance that

should engage the attention of business leaders, and the finance and economics

community, both academic and day-to-day practitioners. From such an

understanding, there can be no doubt, will emerge a new, as yet unimagined, view

of how the financial world behaves. Perhaps, we can start building real “Profits

Engines”. Southwest Airlines can lead the way.

Page 13 of 111

§ 2. Brief Version of the Story

The purpose here is to make the good better and the better the best.

Southwest Airlines is already widely recognized as a highly successful low-cost

domestic airline. It has been in service for 40 years and has delivered profits, every

single year, for 39 consecutive years. Although some quarterly losses have been

reported, the company has always reported a profit for the year, taken as a whole.

A somewhat unconventional approach will therefore be taken here to show that

costs have actually been rising for Southwest Airlines, especially over the last

decade, with the emergence of what is described here as the Type III behavior.

Hence, we will first present four key findings, in the form of simple x-y graphs.

The figure captions are self-explanatory. The figure numbers used later in the text

are retained here. This is then followed by a more detailed presentation.

Figure 1: Revenues growth for Southwest Airlines for the last

twenty years (1992-2011). The rate of increase of revenues seems

to have accelerated since 2009, as seen by the increased slope.

0

2

4

6

8

10

12

14

16

18

1990 1995 2000 2005 2010 2015

Time, t [in years]

Re

ven

ues, x [

$,

billio

ns]

Page 14 of 111

Figure 2: Profits growth for Southwest airlines for the period

1992-2011. Profits increased steadily with increasing revenues

until 2000. Since then profits have been varying erratically with

the recent three years (2009-2011) yielding very low profits

compared to the historical values, with revenues having increased to record levels.

Now let us compare the profits and revenues data for the years 2000 and 2010,

obtained from the quarterly reports for each year. Specifically, we will

consider how profits “grow” during the year, with increasing revenues, when

we take a “snapshot” of the financial behavior of the company in 3 month, 6

month, 9 month, and 12 month intervals.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1990 1995 2000 2005 2010 2015

Time, t [in years]

Pro

fits

, y [

$,

billi

on

s]

Page 15 of 111

Figure 19: Composite plot comparing the evolution of profits, with

increasing revenues, during 2000 and 2010 (from the 3 months, 6

months, 9 months, and 12 month quarterly data for each year). A

linear profits-revenues equation, y = hx + c, is implied by the classical breakeven

analysis for profitability. If a is the fixed cost and b the unit variable cost, the total

cost C = a + bN where N is the number of units offered. If p is unit price, the

revenues generated from the sale of the N units is R = pN. Also, N = R/p. Hence,

the profits P = R – C = [1 – (b/p)]R – a which means the intercept c = - a and the

slope h = 1 – (b/p). The higher intercept made on the x-axis implies a higher fixed

cost. The lower slope means a lower rate of conversion of additional revenues

(beyond breakeven, or cut-off value) into profits. Since, h = 1 – (b/p), the lower

slope means a higher unit variable cost b or a lower unit price p (due to

competitive pressures). The inescapable conclusion from the above is that costs

have gone up for Southwest Airlines during the last decade although the company

is considered a major low-cost domestic airline. Is this a contradiction? NO!

-0.20

0.00

0.20

0.40

0.60

0.80

0 2 4 6 8 10 12 14

2000

2010

2000 a

nd

2010

Pro

fits

, y [

$,

billi

on

s]

Cu

mu

lati

ve

valu

es d

uri

ng

th

e y

ear

2000 and 2010 Revenues, x [$, billions] Cumulative values during the year

Page 16 of 111

Figure 26: A very clear nonlinear growth of profits with increasing

revenues for Southwest Airlines for the period 1971-1992. Costs

have been rising for a long time now, as is obvious from this graph which is

prepared using two line items from the Annual Reports (revenues and net income

or profits). There is an unmistakable deceleration in the rate of growth of profits

with increasing revenues, i.e., the slope of the mathematical curve describing the

profits-revenues relation is decreasing. Amazingly, this has escaped attention to

date. The maximum point on the profits-revenue graph (see main text, this is

OUTSIDE the range of revenues covered in this graph) is another dramatic

example of this same trend. Southwest Airlines is now operating past its maximum

point, in the region where profits decrease even as revenues increase! Some other

examples of leading Fortune 500 companies that exhibit this maximum point are

Ford Motor Company, Verizon Communications, Yahoo, and Kroger.

-20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 17 of 111

http://216.139.227.101/interactive/luv2009/198/page_003.jpg

Ready for Take-off !

The Southwest Secret How the airline manages to turn a profit, year

after year after year

By Seth Stevenson Posted Tuesday, June 12, 2012, at 11:45 AM ET

e-mail: seth@sethstevenson.com

http://www.slate.com/articles/business/operations/2012/06/southwest_airlines_prof

itability_how_the_company_uses_operations_theory_to_fuel_its_success_.html

http://216.139.227.101/interactive/luv2009/ Financial Data for 2000-2009

Page 18 of 111

§ 3. Introduction

A recent article in the Slate magazine by Seth Stevenson, on the enviable profits

http://www.slate.com/articles/business/operations/2012/06/southwest_airlines_prof

itability_how_the_company_uses_operations_theory_to_fuel_its_success_.html )

record of Southwest Airlines, caught my attention and is largely responsible for the

analysis being offered here. This airline, which is mostly focused on domestic

routes, has reported a profit, year-after-year, for 39 consecutive years. This point

has also been proudly highlighted by the company in its 2011 Annual Report (see

http://southwest.investorroom.com/ ) and also in all earlier year reports (35th year,

36th year, 37

th year, and so on.) This is no small achievement, especially in the

airline industry. The reason for this success, as discussed nicely by Stevenson, is in

the company’s basic philosophy of keeping things simple. For example,

1. The airline uses only one single type of aircraft, the Boeing 737. This

introduces all kinds of cost saving s and also offers operational flexibilities

(even in aircraft maintenance, crew training, etc.).

2. No seat numbers are assigned. Passengers can sit wherever they choose.

3. The “bags fly free” policy reduces checked bags at the gate and eliminates

delays and reduces wasted time.

4. There is no hub through which flights are routed, eliminating the resulting

congestions, snags, breakdowns, and hence delayed flights. A plane can be

readied and turned around in as little as 25 minutes after landing. After all,

an airline only makes money when its planes are flying.

All of this sounded too good to be true (never had a chance to fly with them). With

my ongoing interest in analyzing the financial performance of companies in the

2012 Fortune 500 list (a report on 13 companies in the 2012 list may be found at

http://www.scribd.com/doc/95906902/Simple-Mathematical-Laws-Govern-

Corporate-Financial-Behavior-A-Brief-Compilation-of-Profits-Revenues-Data ), I

decided to take a closer look at this airline.

Happy Customers! Consistent Profits! Here was a real “Profits Engine” that I have

been fantasizing about since circa 1998, when I first started studying financial data

of companies, big and small, in all sectors of the economy, in many parts of the

Page 19 of 111

world. The results of my study, as we will see shortly, are counterintuitive and

certainly NOT what I had expected either for Southwest Airlines.

§ 4. Profits and Revenues Over time

The profits and revenues data for the past twenty years (1992-2011) have been

compiled in Table 1. This profits and revenues data can also be used arrive at the

cost, using the fundamental equation Profits = Revenues – Costs. This “computed”

cost-revenue data may be found in Table 2, see also Appendix 1 where this point is

discussed clearly with reference made to the consolidated statement of operations

for first quarter 2012. As seen in Figure 1, revenues have been increasing steadily

year-after-year. Indeed, after a small dip between 2008 and 2009, the revenue

growth seems to have accelerated since 2009.

Figure 1: Revenues growth for Southwest Airlines for the last

twenty years (1992-2011). The rate of increase of revenues seems

to have accelerated since 2009, as seen by the increased slope.

0

2

4

6

8

10

12

14

16

18

1990 1995 2000 2005 2010 2015

Time, t [in years]

Re

ven

ues, x [

$,

billio

ns]

Page 20 of 111

Unfortunately, the same cannot be said about profits growth, although the airline

has reported a profit for 39 consecutive years. Profits increased steadily with

increasing revenues, from 1992 to 2000 but profits have been varying erratically

since then, see Figure 2. Profits declined sharply after 2000 and began to increase

again between 2002 and 2007, but in a much more erratic fashion. Since 2007,

profits have been decreasing although revenues have increased significantly.

These trends and the profits-revenues relationships can be better understood further

by the various x-y graphs presented in Figures 3 to 10.

Figure 2: Profits growth for Southwest airlines for the period

1992-2011. Profits increased steadily with increasing revenues

until 2000. Since then profits have been varying erratically with

the recent three years (2009-2011) yielding very low profits

compared to the historical values, with revenues having increased to record levels.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

1990 1995 2000 2005 2010 2015

Time, t [in years]

Pro

fits

, y [

$,

billi

on

s]

Page 21 of 111

Table 1: Profits-Revenues data for Southwest Airlines

for the twenty year period (1992-2011)

Year Revenues,

x ($, bil)

Profits, y

($, bil)

Profit

Margin, y/x

% Profits

100(y/x)

Comments

2011 15.658 0.178 0.0114 1.14 Type III trend

2010 12.104 0.459 0.0379 3.79 is getting

2009 10.350 0.099 0.0096 0.96 established

2008 11.023 0.178 0.0161 1.61 Between

2007 9.861 0.645 0.0654 6.54 2007 to 2011

2006 9.086 0.499 0.0549 5.49 2005 7.584 0.548 0.0723 7.23 2004 6.530 0.313 0.0479 4.79 2003 5.937 0.442 0.0744 7.44 2002 5.522 0.241 0.0436 4.36 2001 5.555 0.511 0.0920 9.20 Highest profit

2000 5.650 0.625 0.1106 11.06 margins were

1999 4.736 0.474 0.1001 10.01 between 1998

1998 4.164 0.433 0.1040 10.40 to 2001

1997 3.817 0.318 0.0833 8.33 1996 3.406 0.207 0.0608 6.08 Type I behavior

1995 2.873 0.183 0.0637 6.37 1992-2001

1994 2.592 0.179 0.0691 6.91 All data from 1993 2.297 0.154 0.0670 6.70 Annual reports 1992 1.803 0.097 0.0538 5.38

Source: http://216.139.227.101/interactive/luv2009/ ten years 2000-2009 and

also http://southwest.investorroom.com/ 2011 Annual Report; 2007-2011

Page 22 of 111

2002 5.522 0.241

2004 6.530 0.313

2006 9.086 0.499

2007 9.861 0.645

§ 5. The Profits-Revenues Linear Law

Before we proceed with our analysis and discussion, let us consider the following

classical “breakeven” analysis for the profitability of a company making and

selling N units of a product (this could be airline seats in the case of Southwest). If

p is the unit price, the revenues generated R = pN. Let “a” denote the fixed cost

and “b” the unit variable cost. Then the total cost C = a + bN, the sum of the fixed

cost and the total variable cost. Hence, the profits P = R – C = (p – b)N – a, or

eliminating N using R = N/p, we get the relation P = [(p – b)/p] R – a . This

implies a linear law relating revenues, say x, and profits, let’s call it y. Thus,

y = hx + c …… Linear law for profits and revenues

Slope h = 1 – (b/p) .….. determined by unit price p and unit variable cost b.

Intercept c = - a .….. determined by the fixed costs of the operation.

The linear law y = hx + c, implied by this classical breakeven analysis, suggests

three different possibilities.

Type I: Positive slope, negative intercept (h > 0 and c < 0, positive intercept on

revenues-axis).

Type II: Positive slope and positive intercept (h > 0 and c > 0, positive intercept

on profits-axis).

Type III: Negative slope, positive intercept (h < 0, c > 0, positive intercepts on

both the profits and revenues axes).

Examples of companies obeying these three types of linear laws have been

discussed in another recent study (see Refs.[1,2] cited at the end of this article). We

are observing Type I behavior here with Southwest Airlines. In the first period

(before the peak profits in 2000), profits increase with increasing revenues once the

revenues exceed the “breakeven” value of $1.154 billion (intercept made on the x-

axis). Beyond this revenue level, profits increase at a fixed rate with 12.3% of the

additional revenues being converted into profits.

The profits-revenues figures for the four years listed

in the mini-table to the left again reveals a Type I

Page 23 of 111

relation (h > 0 and c > 0), y = 0.093x – 0.273 = 0.093 (x – 2.934), if we consider

the extreme (x, y) values for 2002 and 2006. The slope h has decreased slightly but

the cut-off, or “breakeven” revenue to report a profit, has increased to $2.934

billion, see the dashed line in Figure 4. This also means lower profits.

The transition from one Type I behavior to another Type I behavior, with a higher

intercept on the x-axis (which means higher “fixed costs”) and a lower slope

(which means additional revenues are converted at a lower rate into profits),

appears to have been the first noticeable effect of the fluctuations that started after

the first peak in profits in the year 2000.

Figure 3: The profits-revenues graph for the period 1992-2000.

Profits increase with increasing revenues. The equation of the

best-fit line through these points is y = hx + c = 0.123x – 0.141 =

0.123 (x – 1.154) with the linear regression coefficient having a

very high value of r2 = 0.935. Attention should also be called to the nearly

PERFECT profits-revenues graph for Apple Inc., with r2 = 0.99985, reported in

the articles cited in the references; see The Perfect Apple.

-0.2

0

0.2

0.4

0.6

0.8

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0

Revenues, x [$, billions]

Pro

fits

, y [

$,

billi

on

s]

Type I behavior y = 0.123x – 0.141 = 0.123 (x – 1.154)

r2 = 0.936

Page 24 of 111

Figure 4a: Profits-revenues graph with added data for the

period 2002-2011. This represents the profits data in Figure 2

where we see rapid fluctuations in the profits levels. A second

Type I straight line (dashed line) joining the (x, y) pairs for 2002 and 2006, with

the equation y = 0.093x – 0.273 = 0.093 (x – 2.934) captures this trend. This was

established after the first peak in profits we see in Figure 2.

All of the 20-year data is considered in Figures 4 and 5 to highlight this difference

between the two Type I behaviors and the increase in “breakeven” point, which

implies increase in the “fixed costs” for Southwest Airlines.

The fundamental significance of the intercept c in the linear law y = hx + c, or

positive intercept x = x0 = -c/h when y = 0 made on the x-axis and its relationship

to the idea of a “breakeven” revenue (x = x0 when y = 0 or revenues R = R0 when

Profits P = 0) can be appreciated if we consider the profits-revenues data for the

first few years of operation. This has been compiled from the annual reports from

1973, 1975 and 1978 and is discussed separately in Appendix 5. It is sufficient to

note here that Southwest did report a loss (on an annual basis) in 1972 before

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14 16 18 20

Revenues, x [$, billions]

Pro

fits

, y [

$,

billi

on

s]

Change in the Type I behavior

Lower slope means higher “costs” due

to higher intercept on the x-axis.

Page 25 of 111

reporting its first year of profits in 1973. The cover page of the 1973 Annual

Report says “Southwest Airlines Turned the Corner in 1973”. An extract of

this early profits-revenues data may be found in the mini-table after the graph.

Figure 4b: Profits-revenues data for the first few years of

operation, obtained from 1973, 1975, and 1978 Annual Reports

reveals even more clearly the significance of the intercept c and its relation to the

“fixed” costs of operation. A loss was reported in both 1971 (partial year of

operations) and in 1972, the first full year of operations. The solid blue line

connects the 1971 and 1973 data (y = 0.5548x – 4.934). The dashed line connects

the 1974 and 1978 data (y = 0.2245x – 1.194). The loss means revenues did not

exceed the “breakeven” level. The first “breakeven” revenue calculated from the

equation of the line connecting the 1971 and 1973 data is $8.893 million (x = x0 =

- c/h = -4.934/0.555 = 8.893). The revenue for 1973 was $9.209 million. Both

slope h and intercept c of the graph are clearly changing as the revenues increase

and profits increase.

-10

-5

0

5

10

15

20

0 20 40 60 80 100

Revenues, x [$, billions]

Pro

fits

, y [

$,

billi

on

s]

Page 26 of 111

Page 27 of 111

The slope of the straight line joining the points (x1, y1) and (x2, y2) is:

h = (y2 – y1)/(x2 – x1). Knowing h we can determine the intercept.

c = (y2 – hx2) since the line passes through (x2, y2).

It is also given by

c = (y1 – hx1) since the line passes through (x1, y1).

Conversely, if h is known, the future value y2 for a future value x2 can

be predicted. y2 = y1 + h(x2- x1).

These simple algebraic relations are very useful for our analysis.

Year Revenues, x

$, millions

Profits, y

$, millions

Costs (x –y)

$, millions

Comments

1971 2.129 -3.753 5.882 Data from

1972 5.994 -1.591 7.585 1973, 1975

1973 9.209 0.175 9.034 and 1978

1974 14.852 2.14 12.712 Annual

1975 22.828 3.40 19.428 Reports

1976 30.92 4.939 25.981

1977 49.047 7.545 41.502

1978 81.065 17.004 64.061

Operations began on June 18, 1971. The first full year of operations was 1972.

This first year data indicates a loss with a small profit in 1973.

Next, a Type III behavior is very evident when we consider the most recent data

for the years 2007-2011; see also Figure 5 and the numbers in Table 1. Profits are

decreasing with increasing revenues. Now, extrapolating along this Type III

profits-revenues (P-R) line, if the current trend continues, we can conclude that

Southwest Airlines might actually report its first ever annual loss when its

revenues exceed about $18 billion or about $2.3 to $2.5 billion over the 2011 level.

(This revenue level could be reached in 2012 or 2013.)

This “precarious” profits situation with Southwest Airlines is also highlighted by

the rather low values, less than 2%, of the profit margins (see Table 1) reported in

recent years, with the exception of 2010. This should be compared to the profit

margins in the range of 8% to 11% reported in the earlier period and with much

significantly lower revenue levels. Notice that both the absolute level of profits

Page 28 of 111

($625 million) and the profit margin (11.06%) were higher in 2000 than in 2011

($178 million and 1.14%, respectively).

Essentially the above brief review of the profits-revenues situation (using the rarely

used but simple tool of x-y graph in financial data analysis, and aided by the

classical breakeven analysis) tells us that, notwithstanding the great many cost

efficiencies arising from the “keeping it simple” philosophy, the costs for this

airline are still too high, see Table 2. Although the company has reported a profit

for 39 consecutive years, the profit levels are actually quite low, especially as a

percent of revenues, see both Tables 1 and 2. Regardless of the fact that the

company is operating in the airline industry, where just reporting a profit has been

a major issue (see discussion of Delta Airlines in Ref. [1]), this cannot be an

excuse for the low levels of profits that are being reported.

Figure 5: The profits-revenues graph for the period 2000-2011 is

lacking the remarkable Type I trend revealed for the earlier

period. As seen in Figure 2, and also in Table 1, profits have been

fluctuating wildly and decreasing (after reaching a peak in 2007)

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14 16 18 20

Revenues, x [$, billions]

Pro

fits

, y [

$,

billi

on

s]

Type III behavior

y = - 0.081x + 1.439

Joining 2007 and 2011

Page 29 of 111

even as revenues have increased. This is Type III behavior and is described by the

straight line with the negative slope. Using the (x, y) values for 2007 and 2011, the

equation of this Type III straight line is y = - 0.081x + 1.439.

Southwest management must therefore take a careful look at the reasons for the

wild fluctuations in the profits since 2000, and the cost issues implied and

address them earnestly to avoid reporting a loss in the near future.

It would be very easy, yes very, very easy, to blame such a uncharacteristic and

historically first loss on the recently completed acquisition of AirTran, if this

prediction (made on June 14, 2012) is borne out when the next annual report is

filed, or in the next couple of years at most. The profits-revenues graph for the

all forty-one years of operation, from 1971-2011, has also been prepared (see

Appendix 5) and reveals the same unmistakable trend.

Company Profile

With 40 years of service,

Southwest Airlines Co.

(Southwest), a low-fare major

domestic airline, continues to

differentiate itself from other

low-fare carriers, offering a

reliable product with

exemplary Customer Service.

Southwest was incorporated in

Texas and commenced

Customer Service on June 18,

1971 with three Boeing 737 aircraft serving three Texas cities - Dallas, Houston, and San

Antonio. Today, Southwest is the nation's largest carrier in terms of originating domestic

passengers boarded serving 73 cities in 38 states. On May 2, 2011, Southwest completed the

acquisition of AirTran Holdings, Inc., and now operates AirTran Airways as a wholly

owned subsidiary. Southwest has among the lowest cost structures in the domestic airline

industry, consistently offers the lowest and simplest fares, and has one of the best overall

Customer Service records. LUV is our stock exchange symbol, selected to represent our home at

Dallas Love Field, as well as the theme of our Employee and Customer relationships. Southwest

is one of the most honored airlines in the world known for its commitment to the triple bottom

line of Performance, People, and Planet. To read more about how Southwest is doing its part to

be a good citizen, click on the tab above to read the Southwest Airlines 2011 One Report™.

Page 30 of 111

§ 6. The Unknown Cost-Revenue Story of Southwest Airlines

The “cost” of producing the sales is highlighted in different ways in the financial

statements of a company. Here we will use the fundament equation of the financial

world, Profits = Revenues – Costs, or P = (R – C) with “profits” always being the

net income that is applied to determine the earnings per share (EPS). This also

ensures that all changes in tax laws are fully accounted for when we discuss the

profits-revenue or the costs-revenue relations. The “costs” that we will discuss now

therefore are the “overall” or the “effective” costs, after all obligations have been

met. Or, we can all it the “computed” cost to make it clear that it comes from this

simple computation.

Figure 6: The costs C = Revenues R – Profits P were deduced

from the financial data compiled in Table 1 from the annual

reports. Thus, Costs C = (x – y). The graph of costs C versus

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7 8

Revenues, x (or R), [$, billions]

Co

sts

, (x

– y

) (o

r C

), [

$,

billio

ns

]

C = 0.877 R + 0.1414 With r

2 = 0.9987

1992-2001 with 2000 excluded from

regression

Page 31 of 111

revenues R is being considered here for the two time periods, before and after the

peak in profits in 2000 that we see in Figure 2. Even with the wild fluctuations in

profit, the costs-revenues graph is remarkably linear and seemingly unaffected by

the fluctuations (this is due to low profits margins as well) and hence P as a

percent of R or C is very small).

Thus, the Computed Cost C = Revenues – Profits = (R – P) = (x – y) is given in

Table 2. The reason for using the twin notations C, R and P and also x and y will

become obvious in a moment.

Let us take a look at the data for 2011 and 2010. The revenues increased by the

amount ∆R = $3.554 billion but the profits decreased. Why?

Let us determine the C for each year using C = (R – P). After determining the Cs

for each year, we determine the increase in the cost ∆C = $3.835 billion. In other

words ∆C > ∆R. This surprising trend is confirmed if we consider the (C, R) pairs

for other years. Costs seem to be increasing faster than revenues and the slope of

the graph of costs versus revenues, ∆C/∆R, is therefore greater than unity (or 1).

This is the situation with Southwest Airlines for the most recent period 2001-2011,

see Figure 6. If the slope equals unity (1), then costs = revenues and there is zero

profits. If the slope is less than unity, ∆C < ∆R, then costs do not increase as fast as

revenues increase and the company will be more profitable. This was the situation

with Southwest Airlines in the earlier period, 1992-2000, see Figure 7.

The above calculations of the increase in costs ∆C and the revenues ∆R during the

post-2000 and pre-2000 periods also illustrates, perhaps, the reason for the wild

fluctuations in profits that we see in Figure 2. Although Southwest Airlines has

reported a profit, every year, for the past 39 years, the costs are actually increases

faster than revenues, especially since 2000 and this also explains the reversal in the

slope of the profits-revenues graphs – the change from Type I with a high slope to

Type I with a slightly lower slope and then to Type III.

Page 32 of 111

Table 2: Revenues-Profits-Costs data for Southwest Airlines

for the twenty year period (1992-2011)

Year Revenues,

x ($, bil)

Profits,

y

($, bil)

Costs,

C

(x –y)

∆C

Delta C

(cost)

∆R

Delta R

(revenue)

Comments

Changes are

relative 2011

2011 15.658 0.178 15.480

2010 12.104 0.459 11.645 3.835 3.554 ∆C > ∆R

2009 10.350 0.099 10.924

2008 11.023 0.178 10.172

2007 9.861 0.645 9.216 6.264 5.797 ∆C > ∆R

2006 9.086 0.499 8.587 2005 7.584 0.548 7.036 2004 6.530 0.313 6.217 9.263 9.128 ∆C > ∆R 2003 5.937 0.442 5.495 2002 5.522 0.241 4.897 10.583 10.136 ∆C > ∆R 2001 5.555 0.511 5.044 10.436 10.103 ∆C > ∆R

2000 5.650 0.625 5.025

1999 4.736 0.474 4.262 2.556 2.933 ∆C < ∆R

1998 4.164 0.433 3.731 Between 1999

1997 3.817 0.318 3.499 and 1992

1996 3.406 0.207 3.199

1995 2.873 0.183 2.69

1994 2.592 0.179 2.413 1993 2.297 0.154 2.143 1992 1.803 0.097 5.044

Since y = hx + c is the profits-revenue relation, the costs-revenue relation will

become C = (x – y) = x – hx – c = (1 – h)x – c or C = (1- h)R + a. In other words,

the slope of the C-R graph will be (1 – h) where h is the slope of the P-R graph and

the intercept of the C-R graph will be the negative of the intercept for the P-R

graph. This is exactly what we see here. The slope is 0.877 = (1 – 0.123) in

agreement with the slope of the graph (Type I behavior) in Figure 3. Now, we are

ready to consider the 2000-2011 period in the costs-revenue space.

Page 33 of 111

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14 16 18 20

-5

0

5

10

15

20

25

0 2 4 6 8 10 12 14 16 18 20 22 24

Revenues, x (or R), [$, billions]

Revenues, x (or R), [$, billions]

Pro

fits

, y (

or

P),

[$, b

illi

on

s]

Co

sts

, (x

– y

) (o

r C

), [

$,

billio

ns

]

C = 1.032 R – 0.698 r2 = 0.9977

∆C/∆R = 1.032 > 1

A

B

Page 34 of 111

Figure 7: The costs-revenues graph for the period 2000-2011. The

exact same data is considered in the upper (profits-revenues) and

lower parts (costs-revenues) of the graph. The profits graph

reveals a large “scatter”(see A) but all the points line up nicely along an upward

sloping straight line, see B, in the costs graph. (This is observed repeatedly in the

analysis of such financial data for many companies.) The red dashed line is the

costs = revenue line. Since the data fall below this line, costs are lower than

revenues and the company is reporting a profit. However, and amazingly, the slope

of the best-fit line is greater than 1. C = 1.0321R – 0.698 with r2= 0.9977. The

unmistakable conclusion is that costs are increasing at a faster than the revenues.

The discussion here about the costs of Southwest Airlines also shows why

although the company is reporting a profit each year, the level of profits is also

going down year after year. The only trend that is obvious from profits-revenues

graph is the Type III straight line for 2007-2011. The other points appear to be

“outliers” to this striking Type III behavior. However, a statistically significant P-R

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12 14 16 18 20

Revenues, x (or R), [$, billions]

Pro

fits

, y (

or

P),

[$, b

illi

on

s]

y = -0.032x + 0.698 Statistically significant

Deduced from C-R graph

y = 0.081x + 1.439

Joining 2007-2011

C

Page 35 of 111

relation can now be deduced from the extremely statistically significant C-R that

we have been able to deduce (since the linear regression coefficient is r2 = 0.9977).

From P = R – C, we get P = R – 1.0321R + 0.0698= - 0.0321R + 0.698. This

means that the statistically significant P-R graph for 2001-2011 is a straight line

with a negative slope h = - 0.0321 and a positive intercept of + 0.698. This is now

superimposed to the profits-revenues graph (see graph C in this figure).

§ 7. Quarterly Data and Total Operating Expenses

Let us now consider the quarterly data for years 2007-2011 (during which Type III

behavior seems to been established) to see if this intriguing finding of costs

increasing faster than revenues holds even if we use the quarterly time frame.

Firstly, it should be noted although Southwest Airlines has reported a profit for 39

consecutive years, the same cannot be said about the quarterly profits. Southwest

Airlines has reported a loss on several occasions, on a quarterly basis, but this was

compensated in the other quarters to yield an overall profit for the year.

In this context, we will consider both the “computed” cost C, as defined in the last

section, and also the line item referred to as Total Operating Expenses (OE) given

in the consolidated statement of operations for each quarter (and for each year). An

example of this consolidated statement of operations may be found in Appendix 1.

This illustrates the results reported for first quarter 2012. The OE is Item no. 2 and

profits (or Net Income), which was of interest thus far, is Item no. 7. The

“computed” cost (in Table 2) is the sum of Items 2, 4, 5, and 6 and accounts for

some additional expenses not included in the Total Operating Expenses (OE).

Revenues, Profits, the Total Operating Expenses and the “computed” Costs, for ten

consecutive quarters ending March 2012, are all listed in Table 3 below. Let us

first consider the overall change between the quarters ending December 2009 and

March 2012. The OE increased from $2.545 billion to $3.969 billion, an increase

of ∆(OE) = $1.424 billion. Revenues, on the other hand, increased only by $1.279

billion, from $2.7 12 billion to $3.991 billion. Hence, ∆(OE)/∆R > 1 and the rate of

increase of the total operating expenses is greater than the rate of increase of

revenues. The overall ratio ∆(OE)/∆R = 1.114 > 1 from Dec 2009 to Mar 2012.

Page 36 of 111

Table 3: Quarterly Data from Southwest Airline 10-Q SEC Filings

Quarter

ending

Revenues, x

$, billions

Profits, y

Net Income

$, billions

Total Operating

Expenses (OE)

$, billions

Computed

Costs

(x – y)

Mar 2012 3.991 0.098 3.969 3.893

Dec 2011 4.108 0.152 3.961 3.956

Sep 2011 4.311 -0.140 4.086 4.451

Jun 2011 4.136 0.161 3.929 3.975

Mar 2011 3.103 0.005 2.989 3.098

Dec 2010 3.114 0.131 2.898 2.983

Sep 2010 3.192 0.205 2.837 2.987

Jun 2010 3.168 0.112 2.805 3.056

Mar 2010 2.630 0.011 2.576 2.619

Dec 2009 2.712 0.116 2.545 2.596

An expanded version of this Table 3 is given in Appendix 1, with all of the data

from the quarters ending Sep 2006 to March 2012

We arrive at an exactly similar conclusion for ∆C/∆R. Between Dec 2009 and Mar

2012, ∆C = 1.297 and ∆R = 1.279 and ∆C/∆R = 1.297/1.279 = 1.014 > 1.

The graph of increasing Total Operating Expense (OE) with increasing revenues is

presented in Figure 8, along with the best-fit line deduced from linear regression.

The dashed red line is the y = x line, or R = OE line, when revenues equal the Total

Operating Expenses. If the data point falls below this line, the company should be

reporting a profit (some Other Expenses, Item 3, see Appendix 1, still have to be

accounted). If it falls above, it will most likely report a loss. However, the

interesting finding here is a slope greater than unity. Both the OE-revenues and

cost-revenues equations have a slope greater than unity, see Figures 8 and 9.

Total Operating Expenses (y) versus Revenues x yields, y = 1.0064x -0.209

Costs (x –y) versus Revenues x yields: C = 1.022 R – 0.162

The costs-revenue graph has a higher slope than the OE-revenues graph and both

slopes are greater t han unity if we consider the most recent period, Dec 2009 to

March 2012. This confirms the rather unpleasant trend revealed of costs rising

faster than revenues, from the analysis of the annual financial data.

Page 37 of 111

There is good news, however. If we consider the data for all quarters (Sep

2006 to Mar 2012, which span the years 2007-2011 over which Type III

behavior was established), we find a slope less than unity. This segment of the

present study is being presented in Appendix 1 for further and careful review.

Figure 8: The quarterly values of the Total Operating Expenses

(OE), our variable y, one of the line items in the consolidated

statement of operations for Southwest Airlines (and all other

companies as well) is plotted here as a function of the quarterly revenues, our

variable x. We consider the ten consecutive quarters from Dec 2009 to Mar 2012.

The best-fit line has the equation y = mx + c = 1.0064x – 0.209.The slope (m =

1.0064 > 1) is greater than unity suggesting OE rising faster than revenues. The

dashed red line is the graph of y = x with m = 1. Data points must fall below this

line for a profit. (It can be shown, in Excel computations, that the two straight lines

will indeed intersect at high x.)

-1

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

Quarterly Revenues, x [$, billions] To

tal O

pera

tin

g E

xp

en

se

s (

OE

) [$

, b

illio

ns]

Page 38 of 111

Figure 9: Since Profits = Revenues – Costs (P = R – C), we can

“compute” a cost C = R – P from the reported values of the

revenues (our variable x) and the net income or profits (variable

y in all earlier graphs). This cost C is now plotted versus the

quarterly revenues for the quarters Dec 2009 to Mar 2012. The dashed red line is

the graph of C = R. A profit is reported only when the data point falls below this

dashed line. This is a firm statement, and is always true, unlike the situation with

the Item called Total Operating Expenses where some Other Expenses still have to

be accounted for. Again, it is of interest to note that the slope of the best-fit line is

greater than unity. y = mx + c = 1.0223x – 0.162. It is actually significantly

greater than unity m = 1.0223 compared to the slope found for the graph of the

Total Operating Expenses.

-1

0

1

2

3

4

5

6

7

0 1 2 3 4 5 6 7

Quarterly Revenues, x [$, billions]

“C

om

pu

ted

” C

osts

(x –

y)

[$,

billio

ns

]

Page 39 of 111

§ 8. Maximum point on Profits-Revenue Graph

The Type I to Type III transition (with, perhaps, an intervening Type II which we

have not highlighted as being too significant) suggests that there must be a real and

continuous smooth curve relating profits and revenues, with both a negative slope

and a positive slope. In other words, the profits-revenues graph must have a

maximum point. This is illustrated in Figure 10 by the dashed curve.

Figure 10: The profits-revenues data for Southwest Airlines for

the 20-year period 1992-2011can be explained by invoking the

Type I and the Type III behaviors, as just discussed. The dashed

curve is not based on any mathematical calculations but

illustrates schematically a smooth nonlinear behavior with a maximum point.

Thus, the Type I, Type II, and Type III straight lines are short segments of this

more general curve. Indeed, one can postulate the existence of a family of such

curves, each with its own maximum point, all described by a simple mathematical

equation, y = mxn [ e

-ax/(1 + be

-ax)]+ c.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 2 4 6 8 10 12 14 16 18

Revenues, x [$, billions]

Pro

fits

, y [

$,

billi

on

s]

Page 40 of 111

A parabola, described mathematically by the general equation, y = ax2 + bx + c, or

(x – h)2 = 2p(y – k), is a familiar example of a curve with a maximum point. The

trajectory of a golf ball, or a projectile, is believed to follow this “ideal”

mathematical curve.

http://www.trajectoware.com/Screenshot.gif

Golf ball trajectories: http://www.golf-simulators.com/images/t9_1.jpg

Page 41 of 111

http://en.wikipedia.org/wiki/Laffer_curve

http://www.tennessean.com/article/20120527/BUSINESS01/305270039/Economis

t-Arthur-Laffer-enjoys-renewed-popularity Laffer curve: t* represents the rate of

taxation at which maximum revenue is generated. This is the curve as drawn by

Prof. Arthur Laffer, but in reality the curve need not be single peaked nor

symmetrical at 50%.

There is another famous curve, called the Laffer curve, which is believed to have

led to the birth of so-called supply side economics in the late 1970s. This was

embraced by President Reagan as a governing philosophy after he got elected in

November 1980. This too has a maximum point, and is traditionally represented

using a parabola, a symmetric curve, although this would, no doubt, be an extreme

“idealization” for such a complex problem as the effect of tax rates on the

government revenues.

Then, there is the famous catenary curve. It looks like a parabola but it is not a

parabola. This describes the shape taken by a heavy cable when it is suspended

between two poles. Yeah, we see them hanging over our heads, every day!

A hanging chain forms a catenary. Freely-hanging transmission lines also

form catenaries.

http://en.wikipedia.org/wiki/Catenary

Page 42 of 111

There is one more curve with a maximum point, Planck’s blackbody radiation

curve, which also describes the relics of the Big Bang radiation (see below).

http://conferences.fnal.gov/lp2003/forthepublic/cosmology/cobe_wmap.jpg

http://www.learner.org/courses/physics/visual/img_lrg/CMB_spectrum.jpg

The blackbody radiation curve, or the curve for the COBE spectrum, along with

the Maxwell-Boltzmann velocity distribution curve (from the kinetic theory of

gases, for the distribution of molecular velocities in a gas) are the only known

examples of non-symmetric theoretical curves (familiar to this author) with a

maximum point. Both the Planck curve and the Maxwell-Boltzmann distribution

curve can be derived using straightforward statistical arguments.

Obviously, such a non-symmetric curve, with a maximum point (with some

fundamental statistics based justification), should be of great interest to us now to

arrive at a quantitative picture of the profits-revenue situation with Southwest

Airlines and, more generally, with any company, see Figure 10.

Page 43 of 111

§ 9. Brief Discussion

The simplest equation for a straight line is y = mx and for a curve with a changing

slope it is y = mxn where n = 1 gives the straight line and n > 1 yielding a curve

with increasing slope (acceleration of y) and n < 1 yield a curve with decreasing

slope (deceleration of y), see Figure 11. This is called the power law and “n” is

called the power law index. Frictional, or air, resistance (or the drag), experienced

by a moving object such as a golf ball, car, truck, aircraft, or a rocket is often

expressed using the power law.

Figure 11: Simple illustration of the power-law behavior, y = mxn for the three

cases, n = 1 (linear law), n >1 yielding accelerating growth of profits with

increasing revenues and n <1 yielding decelerating growth of profits with

increasing revenues. In all three cases, there is NO limit to the maximum revenues

or profits. This situation is certainly far more desirable than the situation where a

maximum point appears on the profits-revenue curve, as with the power-

exponential equation. The Type I, Type II, and Type III behavior may all be

thought of a small linear segment of the more general power-exponential law. The

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

0.0 5.0 10.0 15.0 20.0 25.0

y = 0.1x

m = 0.1 and n = 1

y = 0.1x1.15

m = 0.1 and n = 1.15

y = 0.1x0.85

m = 0.1 and n = 0.85

Revenues, x

Pro

fits

, y

Page 44 of 111

appearance of a maximum point and the transition to Type III behavior, are

clearly not desirable.

The graph of speed versus time, in road tests routinely performed to assess the

performance of vehicles, can also be described by a power law. (I have confirmed

this with several vehicle road test data.) The acceleration a = ∆v/∆t is the slope of

the graph of speed (or more correctly velocity, hence the symbol v) versus time t.

Road tests show that the acceleration is not a constant but actually decreases with

time (or increasing speed). This is due to the air resistance (aerodynamic drag) just

mentioned and gives the nonlinear power law curve for v-t relation. Many other

examples of such nonlinear laws can be cited.

Figure 12: Illustration of the three special cases of y = mxne

-ax, which is the

simplest form of the power-exponential law: the linear law y = 0.5x (n = 1, a = 0),

the power law y = 0.6x0.67

(a = 0) and the power-exponential, y = 3x0.67

e-0.125x

. The

maximum point occurs when x = n/a = 0.67/0.125 = 5.36. For n = 0, the law

0

1

2

3

4

5

6

7

8

0 5 10 15 20 25 30 35

Pro

fits

, y

Revenues, x [$, billions]

Page 45 of 111

becomes y = me-ax

and this is “pure” exponential behavior (example, radioactive

decay).

However, the linear and nonlinear laws do not reveal a maximum point. As x

increases y increases, indefinitely, with only the rate of increase ∆y/∆x, or dy/dx

according to the calculus notation, being dictated by the exact mathematical law.

One would like profits to increase as revenues increase. Even better, if profits

would increase at an accelerating rate. However, as we see here with Southwest

Airlines, which has reported a profit for every single year for 39 years, we do not

see any acceleration in the growth of profits with increasing revenues. At best we

see a linear law. This is also true if we study the data for many other companies

(see discussion of Apple in Refs. [1] and [2]). There is no company that I am

aware of, based on many such studies of hundreds of companies since 1998, that

has consistently shown an acceleration (n > 1), for a sustained period of time, in

the profits-revenue space.

Should we expect to see a maximum point on the profits-revenue graph? While it

is easy to speculate about this point, why would one expect to see a maximum

point? This is so counter-intuitive to whole idea of always trying to “maximize”

profits, which is just another way of saying (never mind the semantics) that we

want to see profits increasing indefinitely as revenues increase – all the way to

INFINITY!. An infinity of revenues with an infinity of profits! Wow!

Alas, over this past month (since the Facebook IPO), I find that many real world

companies do show a maximum point on their profits-revenues graph. Southwest

Airlines is the latest example of such a company that I have found. The others are

Ford Motor Company, Verizon, Yahoo, and Kroger. Each one of these companies

is seemingly profitable but each one is “struggling”.

Perhaps, there is some as yet undiscovered natural law (of behavioral

economics and finance) that is responsible for the maximum point. Also, think

about the indefinite increase in profits with increasing revenues. In mathematics,

we can say, and we often do, as x → ∞, y → ∞. This might be true as long as we

are dealing with purely conceptual mathematical entities. Now, apply it to finance

or money and we are dealing with an untenable “double” infinity of sorts, isn’t it?

How can infinite revenues yield infinite profits? Unless, of course, costs go to

Page 46 of 111

zero! May be now we have stumbled upon a simple (mathematical?) explanation

for the maximum point in the profits-revenues graph.

So, now, going a step further, the simplest equation for a curve with a maximum

point is y = mxne

-ax. This is called the power-exponential law. If a = 0, the

maximum point disappears and we get the power law. If a = 0 and n = 1, we get the

simple linear law or straight line. But, alas, straight lines are nice but they do not

always pass through the origin. Hence, we must add the nonzero constant c to our

equations. As seen here, the nonzero “c” in the profits-revenues graph is due to the

“fixed” costs. The general equation for a straight line is y = hx + c.

However, instead of the simpler y = mxne

-ax, it is more appealing (at least

intellectually speaking) to consider the slightly modified power-exponential

equation y = mxn [e

-ax /(1 + be

-ax) ] since this is nothing more than the generalized

statement of the famous equation from blackbody radiation, first derived by Max

Planck in December 1900. Planck’s original equation can be written as

u = (8πν2/c

3) U

where, U = ε [ e-ε/kT

/(1 – e-ε/kT

) ]

and, ε = hν

giving, u = (8πh/c3) ν

3 [ e

-ε/kT /(1 – e

-ε/kT) ] …………(1)

We do not have to understand everything about equation 1 (especially all the

subtleties of the physics that led to the discovery of this law) except to note that the

frequency ν is our variable x and the radiation energy density u is our variable y.

The frequency is raised to the power 3 which is to be replaced by the general

power law index n. The exponential factor within the square brackets is easily

recognized. In the original Planck equation a = h/kT (where T is the temperature

and k is a constant, called the Boltzmann constant). The constant m which precedes

all is given by (8πh/c3). In Planck’s theory c is the speed of light and “h” is now

called the Planck constant.

This modified form of the power-exponential equation is preferred since we can

readily derive Planck’s equation using the same statistical arguments that Planck

Page 47 of 111

used in 1900 and apply it instead to the problem of “profits” or “revenues” get

distributed among many different products that a company produces and sells.

Thus, the power-exponential equation y = mxn [e

-ax/(1 + be

-ax)] + c is the simplest

mathematical law relating x and y which also reveals a maximum point. The

significance of this law may be understood quite simply, as follows, by considering

various special cases.

Linear law: For n = 1, and a = b = 0, the power-exponential law reduces to the

linear law y = mx + c.

Power law: For a = 0 we get the simple power law, y = Mxn, where M = m/(1+b)

is a new constant that replaces m and absorbs the nonzero b in the denominator. In

this case, there is NO maximum point. The derivative dy/dx = n(y/x) is nonzero for

all values of x. Hence, the profits y will increase indefinitely without limit, with

increasing revenues x either at an accelerating rate (for n > 1) or at a decelerating

rate (for n < 1) with increasing revenues (see Figure 9, also Figures 26 and 27 in

Appendix 5). For n = 0, we get “pure” exponential behavior (e.g. radioactive

decay, charging of batteries, etc.)

Power-exponential law: A maximum point appears only when a > 0, however,

small. This can be appreciated by considering the simpler case of b = 0 and c = 0,

for which y = mxne

-ax. The derivative dy/dx = (n- ax)(y/x). Hence, there is a

maximum point on the graph at x = n/a. For x < n/a the derivative dy/dx > 0 and y

increases with increasing x. For x > n/a, the derivative dy/dx is negative and y

decreases with increasing x. This is the type of behavior that we are witnessing

with Southwest Airlines (see schematic graphs in Figures 10 and 12).

This simple nonlinear Planck equation, with a maximum point, may be used to

explain the appearance of the maximum point on the profits-revenues graph for

Southwest Airlines. Or, one might think in terms of the Maxwell-Boltzmann type

of distribution in the financial and economic world. Exactly, similar observations,

regarding the maximum point, have also been made (since I began this recent study

after the disappointing Facebook IPO on Friday May 18, 2012) with several

companies, most notably Ford Motor Company. The Ford data reveals a maximum

point, like we see here, again with a lot of scatter.

Page 48 of 111

In many ways, both Ford and Southwest Airlines are similar. They are both

currently profitable and appear to be doing quite well. However, they are not able

to report consistently high level of profits. There are too many wild fluctuations.

The reason, as we see here, lies in the fact that, for both companies, costs seem to

be increasing at a higher rate than revenues. In other words, the ratio ∆C/∆R > 1.

This trend must be reversed. As we see from the Southwest data, for the earlier

period (1992-2001), when ∆C/∆R < 1, profits were increasing with increasing

revenues and the profit margins were also higher.

Also, the negative (Type III) relation established since 2007 between profits and

revenues is a cause for some concern. This point has been discussed in more detail

in Ref. [1]. Many other companies, notably Ford, Verizon, Yahoo, and Kroger,

also reveal this “toxic” Type III behavior. This seems to be a precursor to company

reporting a continued losses even as revenues increase or, as with GM, the filing of

bankruptcy after a long period spent in the Type III mode, or, as with Air Tran,

becoming a target for merger/acquisition, see §15, page 89. (A discussion of the

“old GM” financial data, from 1991 to 2008, before the bankruptcy filing in June

2009 will be presented separately.)

This is what both Ford and Southwest can learn from the “old GM”. Type III

behavior is the recipe for eventual failure and should be reversed at the earliest.

http://1.bp.blogspot.com/_R2yHiPgsajA/SsFIHuETLaI/AAAAAAAAB5k/iaFISjQ

9pK8/s400/southwest+airlines+1981.bmp

Page 49 of 111

§ 10. Appendix 1: Southwest Airlines Consolidated Statement of Operations First Quarter 2012

Item

No.

Description

Three months

ending

March 2012

Three months

ending

March 2011

1 Total Operating Revenues 3,991 3103

2 OPERATING EXPENSES

2.1 Salary, Wages, and Benefits 1,141 954

2.2 Fuel and Oil 1.510 1038

2.3 Maintenance materials and repairs 272 199

2.4 Aircraft rentals 88 46

2.5 Landing fees and other rentals 254 201

2.6 Depreciation and amortization 201 155

2.7 Acquisition and integration 13 17

2.8 Other operating expenses 490 379

TOTAL Operating Expenses 3,969 2,989

3 Operating Income 22 114

4 OTHER EXPENSES (INCOME)

4.1 Interest Expense 40 43

4.2 Capitalized interest (5) (3)

4.3 Interest income (2) (3)

4.4 Other (gains) losses, net (170) 59

TOTAL Other (income) Expenses (137) 96

5 Income Before Income Taxes 159 18

6 Provision for Income Taxes 61 13

7 Net Income (Profits in this study) 98 5

All numerical values here are in millions of dollars.

This is an example of the consolidated statement of operations from the 10Q SEC

filings. Our interest in this study has been on Revenues, x, reported as Item no. 1

and the Net income reported as Item no. 7. It is this Net Income that has been

called the Profits, y. The Total Operating Expenses (Item no. 2) plus the items 4, 5

and 6 taken together would thus represent what has been referred to as Cost (or the

Page 50 of 111

“computed” Cost for clarity). Of these, Item no. 2, the Total Operating Expenses is

the major portion of the Cost.

Hence, let us now take a look at how Item 2, which will simply be referred to as

the Operating Expense (Op. Exp or OE) has varied over the last ten consecutive

quarters as revenues have either increased or decreased. The data that will be

analyzed is given below as Table 3.

Table 3: Quarterly Data from Southwest Airline 10-Q SEC Filings

Quarter

ending

Revenues, x

$, billions

Profits, y

Net Income

$, billions

Total Operating

Expenses (OE)

$, billions

Computed

Costs

(x – y)

Mar 2012 3.991 0.098 3.969 3.893

Dec 2011 4.108 0.152 3.961 3.956

Sep 2011 4.311 -0.140 4.086 4.451

Jun 2011 4.136 0.161 3.929 3.975

Mar 2011 3.103 0.005 2.989 3.098

Dec 2010 3.114 0.131 2.898 2.983

Sep 2010 3.192 0.205 2.837 2.987

Jun 2010 3.168 0.112 2.805 3.056

Mar 2010 2.630 0.011 2.576 2.619

Dec 2009 2.712 0.116 2.545 2.596

Sep 2009 2.666 -0.016 2.644 2.682

Jun 2009 2.616 0.054 2.493 2.562

Mar 2009 2.357 -0.091 2.407 2.448

Dec 2008 2.734 -0.056 2.664 2.790

Sep 2008 2.891 -0.120 2.805 3.011

Jun 2008 2.869 0.321 2.664 2.548

Mar 2008 2.530 0.034 2.442 2.496

Dec 2007 2.492 0.111 2.366 2.381

Sep 2007 2.588 0.162 2.337 2.426

Jun 2007 2.583 0.278 2.255 2.305

Mar 2007 2.198 0.093 2.114 2.105

Dec 2006 2.276 0.057 2.102 2.219

Sep 2006 2.342 0.048 2.081 2.294

Notice that quarterly losses (highlighted) have been reported by Southwest

Airlines but this was compensated by increased profits in the other quarters for

the same year. The “computed” cost C = (R – P) = (x – y) in the last column is

Page 51 of 111

always greater than The Total Operating Expenses (hereafter just OE Item no. 2

in the consolidated statements) since there are still some Other Expenses, Item

no. 4, which are not accounted for in the OE.

For the most recent quarters, from Dec 2009 to Mar 2012, the quarterly Operating

Expenses (OE) reveal the same trend that we saw with the annualized costs. The

OE is increasing faster than revenues since the linear regression reveals a slope

greater than unity, see Figure 8. Also, if we compute the cost again from Cost =

Revenues – Profits = (x – y), we again find that the slope of the cost-revenue graph

is also greater than unity. The quarterly costs are also increasing faster than the

quarterly revenues, see Figure 9.

However, if we consider all of the data in Table 3, from Sep 2006 to Mar 2012

(the period over which we saw the establishment of the Type III trend in the

annualized profits-revenues graph, Figures 3 to 7) we can derive some solace from

the fact that the best-fit lines for both these graphs have a slope of less than unity.

The best-fit equations are given below and the graphs have been included for

completeness as Figures 13 and 14.

Total Operating Expenses (OE) versus Revenues:

Mar 2012 and Dec 2009: y = mx + c = 1.1134x – 0.474 slope m > 1 for recent

quarters, which should be cause for concern and serious study by management.

Mar 2007 and Sep 2011 (highest and lowest revenues): y = 0.933x + 62.67

Best-fit equation for all quarters: y = 0.972x - 0.75 with r2 = 0.97

In all the above equations x is revenues and y is the Total Operating Expenses

(OE), Item No. 2 from the consolidated statements. For recent quarters the slope is

greater than unity, although when Type III has been established (with annualized

data), the quarterly data seems to reveal that OE is rising at a fixed rate and is

lower than the revenues (which means potential for profits, providing Other

Expenses, Item 4 and Taxes do not overwhelm and lead to a loss).

Page 52 of 111

Figure 13: Total Operating Expenses (hereafter just OE), Item no.

2 in the consolidated statements given earlier, increases at a

remarkably fixed rate as revenues (quarterly) increase. Data for

all quarters ending Sep 2006 to Mar 2012 has been plotted here.

This covers the period 2007-2011 during which the Type III behavior was

established in the annualize profits-revenues graph. The best-fit equation y = mx +

c = 0.972x – 0.075. The slope m = 0.972 < 1 which means that OE is increased at

a fixed rate with increasing revenues. It also means that less 3% of revenues is

available to cover “Other Expenses”, Item 4, taxes, Items 5 and 6, and still report

a profit, item no. 7. This trend also explains the very low profit margins that we

see being reported, although Southwest has consistently reported profits on an

annualized basis.

“Computed” Costs versus Revenues

Next, we consider the quarterly results and “compute” the costs C from the basic

equation Profits = Revenues – Costs, or P = R – C which means C = R – P. These

values are to be found in the last column of Table 3. The graph again reveals a

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

Quarterly revenues, x [$, billions]

Tota

l Op

era

tin

g Ex

pe

nse

s (O

E) [

$, b

illio

ns]

y = 0.972x – 0.075, with r2 = 0.97

Quarters Sep 2006 to Mar 2012 Covers period for Type III pattern in annualized data

Page 53 of 111

remarkably consistent increase in costs (just as for the OE) with increasing

revenues. The best-fit line has the equation C = 0.996R – 0.64 with a very high

value for the correlation coefficient r2 = 0.9665 (perfect correlation r

2 = +1.0).

Figure 14: Since Profits = Revenues – Costs, P = R – C, we can

deduce costs C from the revenues (Item no. 1) and the profits, or

net income (Item no. 7) reported in the consolidated statement of

operations. The data for all the quarters from the quarters ending Sep 2006 to Mar

2012 is plotted here. This reveals a remarkably nice and consistent upward trend.

The best-fit line through the data has the equation C = 0.996R – 0.64 which means

the statistically significant relation for for quarterly profits is P = 0.004 R + 0.64.

The slope here is like the marginal tax rate. If revenues increase by $1 million,

profits only increase by $4000, or about 0.4% conversion rate for additional

revenues into profits. Hence, in addition to sustaining profitability, Southwest must

also focus into efforts on improving its profit margins.

-1

0

1

2

3

4

5

6

0 1 2 3 4 5 6 7

Quarterly revenues, x [$, billions]

“Co

mp

ute

d”

Co

sts

C =

(x

– y)

[$

, bill

ion

s]

Sep 2006 to Mar 2012 C = 0.996 R – 0.64

which means P = 0.004R + 0.64

Page 54 of 111

Since P = R – C, we can use the C-R equation to deduce the P-R equation and it is

therefore given by P = R – 0.996E + 0.64 = 0.004R + 0.64. This means that only a

very small amount of the additional revenues (beyond breakeven revenues) is

being converted into profits. The exact numerical value is 0.4%, less than one-half

percent.

This should be cause for concern for a company that is proud of its profits record,

of delivering profits consistently year-after-year for 39 years. Now, let the focus be

on improving this profit margin. As discussed in Refs. [1-3] there are many

companies with a slope h in the profits-revenues equation in excess of 0.20. The

goal should be to convert at least one-third of the additional revenues into profits.

In summary, the analysis here suggests that Southwest Airlines must take steps to

avoid what appears to be the inevitable reporting of an annualized loss for the first

time in its history. The maximum point revealed on the profit-revenues graph

should be taken very, very, seriously and the underlying reasons for this maximum

must be studied and understood.

§ 11. Appendix 2 Profits-Revenues-Costs-OE growth in a single year

Consolidated Statement of Operations First Quarter 2012

We usually look at financial data on a quarterly, or annual, basis. These are found

in what is known as the 10-K and 10-Q SEC filings of all companies. There are

many good reasons for doing this, one of them being the seasonal nature of

revenues due to what we all do (as consumers) during any given year. And,

depending on the nature of the business, there is a definitely a very marked

seasonality attached to both revenues and profits.

This also gives us a nice way to understand how exactly profits, revenues, costs

and the Total Operating Expenses (OE) “grow”, literally “grow” each year. We

will consider three-month, six-month, nine-month and the annual data for a single

year and study how profits and revenues evolve. We will use two approaches.

Page 55 of 111

1. Consider the data for each quarter (ending March, June, September and

December). We see significant variations between the four quarters in a

single year. For example, in 2009, Southwest Airlines reported losses for the

quarters ending March and September and profits for the quarters ending

June and December, yielding overall profit for the whole year. For 2011, the

loss in the third quarter was overcome by profits in the other three.

2. Consider the data for period ending three-months, six-months, nine-months,

and twelve-months. This second approach tells us about how “evolution” of

revenues and profits occur during a year, until the cycle is then repeated for

the next year.

The following min-table gives the data for 2011. Although the profits-revenues

graph yields a lot of scatter (as would be expected from a look at the numbers), the

costs-revenues graph reveals a nice upward sloping trend with hardly any scatter.

Revenues, x TOE Profits, y Costs ( x- y)

millions millions millions millions Mar 2011 3,103 2,989 5 3,098 Jun 2011 4,136 3,929 161 3,975 Sep 2011 4,311 4,086 -140 4,451 Dec 2011 4,108 3,961 152 3,956

The above table has data for three-months (one quarter) ending as indicated.

Cumulative Revenues, x TOE Profits, y Costs ( x- y)

values millions millions millions millions Mar 2011 3,103 2,989 5 3,098 Jun 2011 7,239 6,918 166 7,073 Sep 2011 11,550 11,004 26 11,524 Dec 2011 15,658 14,965 178 15,480

The above table has data for cumulative values for 3, 6, 9, and 12 months. The

profits at the end of June 2011 were $166 million, the sum of the two quarters.

The cumulative profits dropped to $26 million because of the loss in third

quarter, and so on.

The costs-revenues equation is C = 0.986R + 37.757. The OE-revenues graph also

has a similar pattern with the equation y = mx + c = 0.954x +29.101 where x is

revenues and y is the OE. All values are in millions. These equations were

Page 56 of 111

obtained by simply joining the first and fourth quarter (x, y) pairs, after confirming

the linearity of the graphs.

Both slopes are less than unity. Converting the cost equation to the profits

equation, we get P = R – C = hR + c = 0.014R – 37.757. The negative intercept c =

-37.757 means that once revenues exceed the breakeven value (R0 = - c/h) $2740

million, about 1.4% of the additional revenues are converted into profits.

Figure 15: The evolution of profits and revenues during a single

year (2010). The straight line joining the two extreme points

reveals the overall trend nicely. One could determine the best-fit

equation but such a computational accuracy is not really

0

0.1

0.2

0.3

0.4

0.5

0.6

0 2 4 6 8 10 12 14 16

2010 Revenues, x [$, billions] Cumulative values during the year

2010 P

rofi

ts,

y [

$, b

illio

ns]

Cu

mu

lati

ve

valu

es d

uri

ng

ye

ar

Page 57 of 111

necessary to understand these basics. The profits-revenues equation, y = hx + c or

P = 0.0473 R – 0.113. The cut-off or breakeven revenue is obtained by setting P =

0 = -c/h = 0.113/0.0473 = $2.397 billion (see intercept where profits go to zero).

The data for 2010 can also be viewed in the same fashion. Only the “cumulative”

values are given below. The costs-revenues equation is C = 0.953R +113.37 or P =

0.0473 R – 113.37, see Figure 15. The “break even” revenue R0 = 113.37/0.0127 =

$2397 million is slightly lower than for 2011 but the slope h = 0.0473 is much

higher than for 2011.

In other words, costs increased between 2010 and 2011, C = 0.986R + 37.757 for

2011 versus C = 0.953R +113.37 for 2010. Both the slope and the intercept

increased in 2011 compared to 2010. What is the reason for these variations from

year-to-year?

Cumulative Revenues, x TOE Profits, y Costs ( x- y)

values billions billions billions billions

Mar 2010 2.630 2.576 0.011 2.619 Jun 2010 5.798 5.381 0.123 5.686 Sep 2010 8.990 8.218 0.328 8.785 Dec 2010 12.104 11.116 0.459 11.973

The above table has cumulative data through the month ending as indicated.

Finally, let us consider now the data for the year 2000, the year of peak profits

before the wild fluctuations started, see Table below and Figure 16.

Cumulative Revenues, x Profits, y Costs ( x- y)

values billions billions billions Mar 2000 1.428 0.121 1.307 Jun 2000 2.982 0.297 2.685 Sep 2000 4.461 0.481 3.980 Dec 2000 5.928 0.636 5.292

The above table has cumulative data through the month ending as indicated

The profits-revenues equation y = hx + c = 0.114x – 0.0424, determined by

joining the start and end values. The slope h = (0.636 – 0.121)/(5.928 – 1.428) =

0.114 and the intercept c is then fixed from the (x, y) values at either the start

or the end (since h is known, and x and y are known, c is calculated easily).

Page 58 of 111

Figure 16: The evolution of profits and revenues during a single

year (2000). The straight line joining the two extreme points again reveals the

overall trend nicely. Comparing this with Figure 15 for 2010, the most noticeable

difference is the healthy profit for the first quarter and the smaller intercept made

on the x-axis. Perhaps, this explains why the first quarter profits were higher in

2000 compared to 2010. The higher “fixed costs” seem to be a factor in this

difference. Obviously, the finding being reported here needs more careful study,

with data for many other companies and perhaps also for Southwest Airlines.

With modern computers one could analyze large volumes of data in a matter of

days, or hours, if not minutes. The present author took only a week (while engaged

in other important personal activities) to perform all these calculations, prepare

all the graphs and finish writing this entire report.

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 1 2 3 4 5 6 7

2000 Revenues, x [$, billions] Cumulative values during the year

20

00 P

rofi

ts,

y [

$, b

illio

ns]

Cu

mu

lati

ve

valu

es d

uri

ng

ye

ar

Page 59 of 111

Figure 17: The red dashed line P = 0.0851 R – 0.042, connecting the data for Mar

and Sep has a higher slope compared to the blue solid line, P = 0.0695R – 0.042,

connecting the Mar and Dec data. The intercepts made on the revenues-axis are

thus different. The data for Jun lies practically on the line joining the Mar-Dec

data. Why did the slope (or the intercept) change during the year, between the

various quarters? The best-fit line has an intermediate slope.

The quarterly data for 2007 (when Type III seems to be initiated) also reveal the

similar pattern, see table below. The slope is lower and intercept higher than 2000.

Cumulative Revenues, x Profits, y Costs ( x- y)

values billions billions billions Mar 2007 2.198 0.111 2.087 Jun 2007 4.781 0.273 4.508 Sep 2007 7.369 0.551 6.818 Dec 2007 9.861 0.644 9.217

-0.2

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10 12

2007 Revenues, x [$, billions] Cumulative values during the year

20

07

Pro

fits

, y [

$, b

illio

ns]

Cu

mu

lati

ve

valu

es d

uri

ng

ye

ar

Page 60 of 111

The profits-revenue graph reveals a nice linear behavior. The straight line

connecting the Mar and Dec (R, P) data yields P = 0.0695 R – 0.042 while the

Mar and Sep (R, P) data yields a higher slope, P = 0.0851R – 0.076. The best-

fit line through these four points has an intermediate slope, P = 0.0735R – 0.05

= 0.0735 (R – 0.68). The slope is lower than for 2000 and the cut-off or

breakeven revenue has also increased.

Figure 18: Best-fit line through the 2007 “intrayear” data has the

slope that falls between the high and low values of the slope

indicated in Figure 17. These detailed calculations are presented

to illustrate that “costs” are increasing although Southwest prides

itself as a low-cost airline. Now we have to understand what operational factors

contribute to these subtleties in “cost” increases.

These simple calculations based on “intrayear” data show that there is significant

change in both the slope of profits-revenue graph over the past decade and also the

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 12

2007 Revenues, x [$, billions] Cumulative values during the year

20

07

Pro

fits

, y [

$, b

illio

ns]

Cu

mu

lati

ve

valu

es d

uri

ng

ye

ar

Page 61 of 111

intercept, suggesting changes in both the “fixed” costs and the “variable” costs.

Recall that, according to the classical breakeven analysis for profitability, the slope

of the profits-revenues equation y = hx + c, is given by h = 1 – (b/p) is related to

the unit price p and the unit variable cost b. The intercept c = - a related to the

fixed cost. The results are summarized below for convenience.

P = 0.014R – 37.757 = 0.014 (R – 2.740) for 2011

P = 0.0473 R – 113.37 = 0.0473 (R – 2.397) for 2010

P = 0.0734R – 0.05 = 0.0734 (R – 0.68) for 2007

P = 0.114R – 0.0424 = 0.114 (R – 0.371) for 2000

The decreasing value of the slope h and the increasing values of R = R0 the

minimum revenue to report a profit are unmistakable and quite obvious here.

The visual appearance of the first data point in the 2010 graph (just above the cut

off revenue level) versus the 2000 graph, the considerably lower scatter in the

graph for 2000 versus 2010, and, above all, the scale of the two graphs - revenues

have more than doubled between 2000 and 2010 - should all engage our attention,

see also the composite plot that follows.

Yet, profits in 2010 were lower than the profits in 2000, significantly lower - $459

million in 2010 and $636 million in 2000!

In summary, the simple calculations presented in this Appendix reveal the

“dynamic” nature of the changes in the operations of a company (especially the

cost structure which is of interest to us), occurring from quarter-to-quarter and also

year-to-year. Such intra-year variations, and inter-year variations, must be

carefully studied to more fully understand the basic “laws” governing financial

performance of various companies.

Page 62 of 111

Figure 19: Composite plot comparing the evolution of profits during 2000 and

2010 (from the 3 months, 6 months, 9 months, and 12 month quarterly data for

each year). A linear profits-revenues equation is implied by the classical

breakeven analysis for profitability. If a is the fixed cost and b the unit variable

cost, the total cost C = a + bN where N is the number of units offered. If p is unit

price, the revenues generated from the sale of the N units is R = pN. Also, N = R/p.

Hence, the profits P = R – C = [1 – (b/p)]R – a which means the intercept c = - a

and the slope h = 1 – (b/p). The higher intercept made on the x-axis implies a

higher fixed cost. The lower slope means a lower rate of conversion of additional

revenues (beyond breakeven) into profits. Since, h = 1 – (b/p), the lower slope

means a higher unit variable cost b or a lower unit price p (due to competitive

pressures). The inescapable conclusion from the above is that costs have gone up

for Southwest Airlines during the last decade although the company prides itself on

being a major low-cost domestic airline. Is this a contradiction? NO, if one

understands the meanings of “costs” being discussed here. The good can still

become better and the better can become the best!

-0.20

0.00

0.20

0.40

0.60

0.80

0 2 4 6 8 10 12 14

2000

2010

2000 a

nd

2010

Pro

fits

, y [

$,

billi

on

s]

Cu

mu

lati

ve

va

lue

s d

uri

ng

th

e y

ea

r

2000 and 2010 Revenues, x [$, billions] Cumulative values during the year

Page 63 of 111

Summary listing of Profits-Revenues Equations

The following table summarizes the profits-revenues equations deduced, as

discussed here, from the quarterly data for a single year, by considering the growth

in 3 month, 6 month, 9 month, and 12 month intervals.

Year Profits-revenues equation

Units of x and y are indicated

Slope h Breakeven

R0 = - c/h

$, millions

Comment

1974 y = 0.133x +157.6 in 000s 0.133 Type II

1975 y = 0.151x -39.52 in 000s 0.151 0.26 M Type I

1978 y = 0.22x – 826.73 in 000s 0.22 3.76 M Type I

1979 y = 0.121x + 230.12 in 000s 0.121 Type II

1980 y = 0.139x – 1302.5 in 000s 0.139 9.33 M Type I

1981 y = 0.130x - 1.088 millions 0.130 8.35 M Type I

1982 y = 0.115x - 4.222 millions 0.115 36.58 M Type I

1983 y = 0.101x - 4.477 millions 0.101 44.26 M Type I

1984 y = 0.096x – 1.80 millions 0.096 18.74 M Type I

1985 y = 0.077x – 5.14 millions 0.077 66.65 M Type I

1986 y = 0.079x -11.036 millions 0.079 138.93 M Type I

1987 y = 0.049x – 18.75 millions 0.049 375.12 M Type I

1988 y = 0.085x -14.965 millions 0.085 176.59 M Type I

1989 y = 0.066x + 4.487 millions 0.066 Type II

1990 y = 0.0453x -6.72 millions 0.045 148.22 Gulf War!

Made a Profit

1991 y = 0.034x – 17.85 millions 0.034 523.83 Type I

1992 y = 0.059x – 8.62 millions 0.059 145.84 M Type I

1992

y = 0.058x -6.86 millions

0.058

118.6 M

1993 & 1992

reports have

diff. values

1993 y = 0.019x – 17.97 millions 0.019 919.3 M Type I

1994 y = 0.0713x + 0.0046 billions 0.0713 Intercept c ≈ 0

1995 y = 0.075x + 0.071 billions 0.075 Type II

2000 y = 0.114x – 0.0424 billions 0.114 371 M Type I

2007 y = 0.0734 x – 0.05 billions 0.073 680 M Type I

2010 y = 0.0473 x – 113.37 billions 0.047 239.7 M Type I

2011 y = 0.014 x – 37.57 billions 0.014 274 M Type I

Page 64 of 111

First quarter 1987, first quarterly loss since first quarter of 1973.

http://www.chron.com/CDA/archives/archive.mpl/1987_459421/southwest-in-the-

red-for-first-time-since-73.html

There are frequent back-and-forth transitions from Type I to Type II

behavior between years. (This is like an engine running erratically and

misfiring.) We also see a general trend of decreasing slope h (less of the

revenues are converted into profits) and a rising value of the “breakeven”

revenues, i.e., intercept c, along implying higher costs and lower profits.

Southwest Airlines route network maps from key focus cities.

Goegraphy Lesson: Don’t be misled by this map and try to find the Pacific Ocean

near Tucson, Arizona. San Diego is southernmost city here in the continental USA,

on the Pacific coast. California’s southern border with Mexico (the nearly

horizontal stretch, east of San Diego) then begins. The Baja peninsula, part of

Mexico, sticks out of southern California into the Pacific Ocean. All the other states

to the east, all the way to Texas, share a border with Mexico.

Hahaha for fooling me today!

Page 65 of 111

§ 12. Appendix 3 Type II behavior and Type I to Type II transition

The following data, obtained from the Southwest Annual Report for 1995 is of

interest since it reveals an interesting example of Type II behavior when we

consider the “intrayear” data for 1995, i.e., the growth of revenues and profits

during the year, reported in quarterly reports and summarized in the annual report.

The annual report for 1995 also provides the data for the years 1991-1995 which

also, reveals, as we will see a Type II behavior.

Revenues, x Profits, y Costs ( x- y)

Billions billions billions Mar 1995 0.621 0.118 0.503 Jun 1995 0.738 0.060 0.678 Sep 1995 0.765 0.067 0.698 Dec 1995 0.749 0.043 0.706

The above table has data for three-months (one quarter) ending as indicated.

Cumulative Revenues, x Profits, y Costs ( x- y)

Values Billions billions billions Mar 1995 0.621 0.118 0.503 Jun 1995 1.359 0.178 1.181 Sep 1995 2.124 0.245 1.879 Dec 1995 2.873 0.288 2.585

The above table has data for cumulative values for 3, 6, 9, and 12 months. The

profits at the end of June 1995 were $0.118 + $0.060 = $0.178 billion, the sum

of the individual values for the two quarters, and so on.

Revenues, x Profits, y Costs ( x- y)

Billions billions billions 1995 2.873 0.183 2.690 1994 2.592 0.179 2.413 1993 2.297 0.169 2.128 1992 1.803 0.110 1.693 1991 1.379 0.033 1.346

The above table has annualized data for each year as indicated.

Page 66 of 111

Figure 20: The cumulative profits and costs (see table) are increasing during the

year. In 1995 every quarter was profitable. The profits and revenues vary from one

quarter to the next. Nonetheless, the profits-revenues graph, as we see above, and

also the costs-revenues reveal a nice linear behavior. The straight line, y = hx + c

= 0.0756x + 0.071, or equivalently, P = 0.0756R + 0.071, joining the Mar and

Dec data points makes a small positive intercept on the profits axis. This describes

the data quite well. This is Type II behavior (h > 0, c > 0), as discussed in §5 of

main text before analysis of the profits-revenues data was presented. (The best-fit

line will have a slightly higher slope and slightly smaller intercept, since one data

point, the nine-months ending data, is above this Type II line.) The “intrayear”

1994 data seems to reveal the “verge” of Type I to Type II transition. On a similar

profits-revenues graph, the best-fit line through the four data points makes a very

small positive intercept (h = 0.071 and c = 0.00458 > 0).

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

1995 Revenues, x [$, billions] Cumulative values during the year

19

95

Pro

fits

, y [

$, b

illio

ns]

Cu

mu

lati

ve

valu

es d

uri

ng

ye

ar

Page 67 of 111

Figure 21: The intrayear profits-revenues data for 1994 and 1995. The

“diamonds” are the values for 1995 and the “squares” the values for 1994. Profits

were higher in 1995 compared to 1994 for similar revenue levels. For 1994, we

get y = hx + c = 0.0713x + 0.00458 and for 1995 y = 0.0756x + 0.071. The nearly

zero value of the constant c implies that the company is going through the Type I to

Type II transition with c < 0 (Type I), c = 0, and c > 0 (Type II).

The data for the yeas 1991-1995 also shows and interesting pattern. As we see

from the table, between 1991 and 1992 there is a significant increase in profits but

this rate seems to have slowed down in subsequent years. One could describe this

with a Type I behavior going into a Type II behavior. However, it is preferable to

consider the alternative and more conservative viewpoint of an overall Type I

behavior with a smaller slope. As we know (after data is already in place, with the

benefit of hindsight, as they say) from the analysis of the entire 1991-2000 period,

the conclusion of a Type I behavior is a much better conclusion.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5

1994 and 1995 Revenues, x [$, billions] Cumulative values during the year

1994 a

nd

1995

Pro

fits

, y [

$,

billi

on

s]

Cu

mu

lati

ve

valu

es d

uri

ng

th

e y

ear

1994

1995

Page 68 of 111

Figure 22: The profits-revenues data for the period 1991-1995,

obtained from the 1995 Annual Report. Profits increased rapidly,

as we see here, between 1991 and 1992. This was followed by a

period with a slower rate of increase of profits. This can be described

mathematically as a Type I to Type II transition (or by using a smooth nonlinear

curve, such as the power law y = mxn + c, with the index n < 1). However, one

should seek nonlinearity (or postulate linear transitions such suggested above)

only after careful consideration of the alternative viewpoint of a single linear trend

to describe the same data, see Figure 23.

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Annual Revenues, x [$, billions]

An

nu

al

Pro

fits

, y [

$, b

illi

on

s]

Page 69 of 111

Figure 23: The alternative viewpoint of a single Type I linear

trend is to be preferred and must be considered before accepting

the transition from Type I to Type II, in other words, a permanent

transition to a lower profitability mode.

Nonetheless, one must look for “clues” about such a transition and take appropriate

actions to avoid a “permanent” lapse into a less desirable mode.

The Type I to Type III transition, that seems to have occurred between 2007-2011,

and discussed more fully in this article, is a case in point. Southwest management

must address this issue immediately to avoid reporting a historical first annual loss

in the near future and also carefully consider and review the historical patterns

pointed out here. It should be noted that the 1995 Southwest Annual Report seems

to be unique in providing data for all the four quarters for year 1995 (and also for

1994). This is usually not readily available in annual reports, as seen below.

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

An

nu

al

Pro

fits

, y [

$, b

illi

on

s]

Annual Revenues, x [$, billions]

Page 70 of 111

1995 ANNUAL REPORT

ITEM 6. SELECTED FINANCIAL DATA (Pages 9 and 10)

YEARS ENDED DECEMBER 31,

-----------------------------------------------------------------------------

1995 1994 1993 1992 1991

---- ---- ---- ---- ----

FINANCIAL DATA:

(in thousands except per share amounts)

Operating revenues

$2,872,751 $2,591,933 $2,296,673 $1,802,979 $1,379,286

Operating expenses

2,559,220 2,275,224 2,004,700 1,609,175 1,306,675

------- ---------- ---------- ---------- ----------

Operating income . . . . . . . . . . . . . . 313,531

316,709 291,973 193,804 72,611

------ ---------- ---------- ---------- ----------

Net income (1)

$182,626 $179,331 $ 169,543 $ 109,923 $ 33,148

========== ========== ========== ========== ==========

ITEM 8 : FINANCIAL STATEMENTS AND SUPPLEMENTARY DATA (Page 11)

QUARTERLY FINANCIAL DATA (UNAUDITED)

(IN THOUSANDS EXCEPT PER SHARE AMOUNTS)

----------------------------------------------------

1995 MARCH 31 JUNE 30 SEPT. 30 DEC. 31

-------- ------- -------- -------

Operating revenues $620,999 $738,205 $764,975 $748,572

Operating income 23,409 103,425 114,098 72,599

Income before income taxes 20,034 100,801 114,215 70,090

Net income 11,826 59,724 67,717 43,359

Net income per common and .08 .41 .45 .29

common equivalent share

Page 71 of 111

§ 13. Appendix 4

Profits and Passengers Flown

One would expect to find a steady increase in profits as the number of passengers

flown by an airline increases. Surprisingly, the data in this regard, for Southwest

Airlines, shows a good bit of scatter, see http://www.swamedia.com/channels/By-

Category/pages/yearend-summary . This is summarized in Table 4.

Table 4: Profits and Passengers flown for Southwest Airlines

Year

Revenue

Passengers

(millions)

Net Income

($, millions)

Year

Revenue

Passengers

(in 000s)

Net Income

($, millions)

1971 108.554 -3.753

2010 88.191 459 1972 308.999 -1.591

2009 86.301 99 1973 543.407 0.175

2008 88.529 178 1974 759.721 2.141

2007 88.713 645 1975 1,136.32 3.4

2006 96.3 499 1976 1,539.11 4.939

2005 77.694 548 1977 2,339.52 7.545

2004 70.9 313 1978 3,528.11 17.004

2003 65.674 240.969 1979 5,000.09 16.652

2002 63.046 240.969 1980 5,976.62 28.447

2001 64.447 511.147 1981 6,792.93 34.165

2000 63.678 625.224 1982 7,965.55 34.004

1983 9,511.00 40.867

1984 10,697.54 49.724

1985 12,651.24 47.278

1986 13,637.52 50.035

While the number of (revenue producing) passengers did not vary significantly in

recent years (from 2007 to 2010, a low of 86.3 million to a high of 88.7 million),

notice the erratic variation in profits (net income), with a low of $99 million in

2009 and a high of $645 million in 2007. Compare also the profits for 2010 with

Page 72 of 111

the profits for 2008 with nearly the same number of passengers. Not surprisingly

the x-y graph in Figure 24 thus reveals a lot of scatter.

Figure 24: Net income versus number of passengers flown for the

period 2000-2010. Although there is a lot of scatter, a linear

trend, in agreement with data for earlier period (see 1971-1986 in Figure 25) is

suggested if we consider the data selectively. The straight line connecting the data

for 2002 and 2006 is shown here and has the equation y = 7.759 (x – 31.99). In

other words, a certain minimum number of revenue producing passengers, about

32 million, must be flown before a profit can be reported. After this “breakeven”

level, profits increase at a fixed rate of about $7.76 per passenger. This can now

be compared to the earlier period.

Nonetheless, a nice linear trend is revealed, if we overlook the scatter and consider

the data selectively. The same linear trend is also suggested by the data for the

early years (1971-1986) which can also be obtained at the same website.

0

100

200

300

400

500

600

700

800

0 20 40 60 80 100 120 140

Number of passengers, x [millions]

Ne

t In

co

me

(P

rofi

ts),

y [

$,

mil

lio

ns]

Recent years (2000-2010) y = 7.759x – 248.23 = 7.759 (x – 31.99)

Page 73 of 111

An estimate of the (additional) profits produced per (additional) passenger can be

obtained from the slope of such a graph. As we see from the Table 4, in 1971 and

1972, Southwest reported a loss. It reported its first profitable year in 1973. The

number of passengers increased steadily during this period. Thus, it is clear that a

certain minimum number of passengers is required (to cover the fixed costs, or the

breakeven revenue discussed earlier) to report a profit. Once this minimum is

exceeded, profits increase at a fixed rate per passenger.

For 2000-2010 period, y = 7.756x – 248.23 = 7.756 (x – 31.99) where x and y are

both in millions. Thus, profits increase at a fixed rate of about $7.76 per passenger

once the “breakeven” level, about 32 million passengers is reached. This can be

compared to the earlier period, 1971-1986, see Figure 25.

Figure 25: Net income versus number of passengers flown for the

first full sixteen years of operation (1971-1986), with 1971 being

only a partial year of operation.

-10

0

10

20

30

40

50

60

70

0 4,000 8,000 12,000 16,000

Number of passengers, x [thousands]

Early years 1971-1986

y = 0.00415 x – 0.475

= 0.00415 (x – 114.54)

Net

Inco

me (

Pro

fits

), y

[$,

milli

on

s]

Page 74 of 111

A nice upward trend is observed for this earlier period. The best-fit line through

the data points yields a slope of $4.15 per passenger, or about one-half the

current value of nearly $8 per passenger.

A number of line segments, with varying slopes and intercepts, can also be

conceived for this earlier period. For these “local” segments, an estimate as high as

$9.80 per passenger (example for the 1979 and 1981 data points, dashed line) is

possible. The results here thus yield a somewhat conflicting picture and should be

investigated more completely. While the per-passenger profit seems to have

improved in recent years, the absolute level of profits and also the profit margins

have also greatly decreased.

Improved statistical models must be developed to predict profitability per

passenger and also profits per unit of revenue. The latter now seems to be the more

predictable of the two.

******************************************************************

New Fashion Police: Southwest Airlines

A woman was booted off a Southwest

Airlines flight in Reno for wearing a

T-shirt with the pictures of President

Bush and Vice President Dick Cheney

and the F-word. Don't they have

anything better to do, like look for

potential hijackers? This was poor

judgment and the airline should apologize

for sticking their nose where it doesn't

belong. Have you ever seen the

ridiculous uniforms worn by most pilots and flight attendants? They are the last

people on earth who should be telling people what to wear.

Above found at http://www.waynebesen.com/blog/2005_10_02_archive.html

Page 75 of 111

The slope of the straight line joining the points (x1, y1) and (x2, y2) is:

h = (y2 – y1)/(x2 – x1). Knowing h we can determine the intercept.

c = (y2 – hx2) since the line passes through (x2, y2).

It is also given by

c = (y1 – hx1) since the line passes through (x1, y1).

Conversely, if h is known, the future value y2 for a future value x2 can

be predicted. y2 = y1 + h(x2- x1).

These simple algebraic relations are very useful for our analysis.

The straight line connecting 1971 and 1973 data therefore has the

equation y = 0.5548x – 0.00493 = 0.555(x – 0.008894) where x and y

are in billions. The “breakeven revenue was x0 = -c/h = $8.89 million

when Southwest only had 3 aircrafts and operated between 3 cities

in Texas: Dallas, San Antonio, and Houston. The first slope h = 0.555

is very high and 55.5% of additional revenues, beyond breakeven,

were being converted into profits.

§ 14. Appendix 5

Profits-Revenues for Early years The nonlinear Power law model

Year Revenues, x

$, millions

Profits, y

$, millions

Costs (x –y)

$, millions

Comments

1971 2.129 -3.753 5.882 Data from

1972 5.994 -1.591 7.585 1973, 1975

1973 9.209 0.175 9.034 and 1978

1974 14.852 2.14 12.712 Annual

1975 22.828 3.40 19.428 Reports

1976 30.92 4.939 25.981

1977 49.047 7.545 41.502

1978 81.065 17.004 64.061

Operations began on June 18, 1971. The first full year of operations was 1972.

This first year data indicates a loss with a small profit in 1973.

Page 76 of 111

Pictorial depiction of the distribution of expenses for Southwest

Airlines from their 1982 Annual Report. Fuel & Oil (36.3%) and

Employee Salaries and Benefits (27.7%) are the top two items.

Insurance and Taxes (the focus of much political debate) only

accounts for 2.1% of total expenses.

In this section we will first summarize certain operational features and

how Southwest Airlines has grown in the early years and then consider

the profits-revenues data.

For 1973, the first full year of operations with a small profits, the

following data was obtained from the Annual Report. There were 10,619

flights. Still there are a number of interesting issues that affect the

number of flights as noted in the 197s report. The company operated

three aircrafts in its first quarter of operation (in 1971) and four aircrafts

in its second quarter (in 1971). The fourth aircraft was disposed off in

May 1972. Saturday operations were discontinued until November 1972.

According to the 1980 annual report, the fleet size (made up of Boeing

737-200’s) increased from 6 in 1976, to 10 in 1977, to 13 in 1978 to 18

Page 77 of 111

in 1979 and to 23 in 1980 and aircraft utilization increased from 9 hours

and 22 mins per day in 1976 to a maximum on 11 hours 37 mins in

1979. According to the 1984 annual report, the Southwest route system

covered 24 cities and 25 airports in 11 states. The trips operated in 1984

was 200,124. Aircraft utilization varied from 11 hours and 16 mins per

day to 11 hours and 11 hours and 46 mins between 1980 and 1984. They

had 48 owned aircraft at year end, with three new and one used aircraft

being added to the fleet during the year. According to the 1986 Annual

Report, the airline was operating a fleet of 46 Boeing 737-200’s and 17

Boeing 737-300’s. Nine more Boeing 737-300’s were to be delivered in

1987. The trips operated were 262,082 in 1982 and 230,227 in 1981.

This means about 4000 trips per aircraft per year or about 10 to 11 trips

per aircraft per day – an amazingly high number of trips for one aircraft

in a single day!

From the 1984 Annual Report

Now you have to believe they offer Exemplary Customer Service!

Page 78 of 111

A careful examination of the overall growth in both profits and revenues, since

Southwest airlines began its operations 41 years ago, almost to the date, on June

18, 1971, reveals a clear non1inear trend, especially if we consider the data for the

period 1971-1992. This is indicated by the graph prepared in Figure 26 below.

Figure 26: A very clear nonlinear growth of profits with increasing

revenues for Southwest Airlines for the period 1971-1992.

Profits increase with increasing revenues but at a decreasing rate as revenues

increase. In other words, the slope of the profits-revenues graph is decreasing

continuously. If revenues increase by an amount ∆x (say by $10 million), profits

increase by an amount ∆y. What is the relation between ∆x and ∆y? Can we

predict the increase in profits? This is the whole point of discovering the

fundamental mathematical laws governing the profits-revenues growth. If the ratio

∆y/∆x = h, a constant, profits will always grow by exactly the same fixed amount if

revenues increase by a fixed amount. The law relating profits and revenues is y =

hx + c and the slope h = dy/dx = ∆y/∆x is a constant. However, this linear behavior

is clearly not being observed when we consider the data for the entire 1971-1992

-20

0

20

40

60

80

100

120

0 200 400 600 800 1000 1200 1400 1600 1800 2000

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 79 of 111

period. Hence, we must consider the possibility of fitting the data with a nonlinear

upward rising curve.

Figure 27: The profits-revenues data for the period 1971-1992

can be described using the power-law model y = mxn + c. First

we fix the power law index n = 0.66 ≈ 2/3. With this choice of n, it is easily shown

that the curves for m = 0.7 (lower curve, blue) and m = 0.87 (upper curve, red)

bracket the entire data set. The nonzero value of c = - 5 provides the best match

for the reported loss in 1971 and 1972. The value of n ≈ 2/3 is picked here since

such a value of n is commonly observed in many, well understood, physical process

where we observe deviations from the linear law; see text. The four year with low

profits are obviously exceptional cases.

The simplest such law is the power law, y = mxn + c, which was discussed earlier.

The nonzero constant c is included here since at very low revenue levels,

Southwest did report a loss, for both the partial year of operation in 1971 and the

first full year of operation in 1972. A profit was reported only in 1973 (even first

-20

0

20

40

60

80

100

120

140

0 500 1000 1500 2000

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 80 of 111

quarter of 1973 was a loss). Choosing n = 0.66 ≈ 2/3 as the power law index, it is

readily shown that the entire data set is bracketed between the curves with m = 0.7

and 0.87. The nonzero constant c = - 5 and this value is the best choice to match

with the reported loss in 1972.

Why n ≈ 2/3? This value of n is commonly observed in many physical processes

where we see deviations from a linear law. The most common example of a liner

law is Ohm’s law for an electrical conductor, V = RI, or Newton’s law of viscosity.

If the voltage V applied to a conductor increases, the current I flowing through the

circuit increases proportionally. The constant of proportionality is the electrical

resistance R. This is mathematically the same as y = hx + c with c = 0. However,

not all electrical circuits are linear. Some also show nonlinear, or non-Ohmic,

behavior. The power law (or even the power exponential law) is a simple model for

such nonlinear electrical circuit.

When we stir a fluid like motor oil, or water, the viscous resistance we feel does

not increase as the stirring rate increases. Such a fluid is called a Newtonian fluid

and its behavior is described by the law y = μx where x is the shearing (stirring)

rate and y the shear stress (proportional to viscous resistance). The constant of

proportionality is called the viscosity μ. It is this law that is used to fix the

viscosity values of most common liquids like motor oil, machine oil, etc.

But there are more complex fluids, like paint, honey, molasses, etc. which show a

varying viscous resistance as the rate of shearing is increased. Fluids with small

dispersed particles (what is called two-phase mixtures, or dough or pancake mix

with added ingredients) are other examples. Fluids whose viscosity varies with the

shearing rate lead to what is known as shear thinning or shear thickening behavior.

Stirring a paint makes it seem less viscous and this actually allows us to paint a

wall. If we stop the brushing (i.e., shearing of the paint), the paint stops flowing

and stays on the wall! Some other fluids show the opposite behavior and become

very stiff if we stir them. The more vigorously it is stirred, the stiffer it gets.

Other examples are processes such as “coarsening” of particles in materials

science. If a system is made of very small microscopic particles, it also has a lot of

“energy” associated with the surface of the particles. Hence, given the opportunity,

the system will try to become “coarse” (to minimize its total energy and thus

Page 81 of 111

become more stable), with the bigger particles actually trying to absorb the smaller

particles. Coarsening rates often follows a fractional nonlinear law, with n ≈ 1/3.

A company like Southwest and its operations may be thought of in a similar way.

Although the company has a “keep it simple” philosophy, as fleet sizes grow, as

the number of routes increase, and as the number of cities covered increase, the

operations become more complex. For example, fuel costs (one of the two top cost

items) vary nonlinearly depending on the distances flown by the aircraft. Short

haul flights are different from longer hauls. Other processes similar to those just

described interact in complex ways. Various subunits of the organization (like the

many microscopically small particles in a physical system) interact with each other

in unpredictable ways. This increases the operational “resistance”, similar to that

seen in a shear thickening or shear thinning fluid, or as in the coarsening model.

These analogies from the physical and engineering sciences can be quite useful and

it is obvious that the choice of n ≈ 2/3 is eminently justified. Social systems, with a

complex organizational structure and hierarchy can be thought of in a similar way

– like many “particles” that interact with each other. How this interaction occurs

determines the value of the index n. Simple fractions such as ½, ⅓, ⅔, 3/2, or

whole numbers like 2 (quadratic or parabolic law) are often encountered.

Of course, one could also use n = 0.5, or 0.8 or 0.85 and try “to fit” the data. It will

soon become obvious that not all values of “n” are appropriate to describe the

overall trend. If we consider the data for a very different company (say Apple,

Google, or Facebook, see Refs. [1-3] cited in bibliography), a different value of “n

“might apply, because of its unique “culture” and “management philosophy”.

Costs have been going up for a long time now, ever since operations began in 1971

and this is reason for the changing slopes [mostly decreasing implying increasing

variable costs, mathematically, h = 1 – (b/p) where b is unit variable cost and p the

unit price in the simple breakeven analysis] and increasing values of the intercept

made on the revenues-axis (implying higher fixed costs). The nonlinearity we saw

for the period 1971-1992 is further evidence of the “rising costs”. Composite plots

for the entire 40+ years of operation are presented next to call attention to this

same message.

Page 82 of 111

Figure 28: The profits-revenues graph for Southwest Airlines for

all 41 years, 1971-2011, for which data is available. 1971 was a

partial year of operation. Every straight line on this graph, with a decreased slope,

implies lower rate of conversion of revenues into profits. The dashed red line with

the steepest slope highlights the initial rate of conversion of revenues to profits (y

= hx + c = 0.555x – 0.00493, i.e., 55% of revenues beyond breakeven was

converted into profits in this period). This portion of the graph is being presented

using an expanded scale, separately as Figure 29. The airline’s operations then

“settled” to a lower rate of profits generation (y = 0.142x – 0.16), indicated by the

reduced slope of the blue line (only about 14% of the revenues beyond breakeven

are now being converted into profits). The dashed blue line, joining the 2007 (x, y)

pair to the origin, has an even lower slope h = 0.065 and only about 6.5% of the

revenues appeared as profits. The current trend was then established (negative

slope h < 0, c > 0) with profits decreasing even as revenues have increased, i.e., a

Type III behavior, with the attendant appearance of a maximum point. Southwest

Airlines is now actually operating past this maximum point. (A smooth curve, with

a maximum point, can be envisioned on this graph, see Figure 10).

-0.2

0.0

0.2

0.4

0.6

0.8

0 2 4 6 8 10 12 14 16 18 20

Revenues, x [$, billions]

Pro

fits

, y [

$,

billi

on

s]

Page 83 of 111

Figure 29: The profits-revenues graph for the first four years,

1971, 1972, 1973, and 1974 using a “zoomed in” scale. Notice

how the first three data points line almost perfectly on the straight

line y = 0.555x – 4.934 = 0.555 (x – 8.894). As revenues increase profits increase

(or what is the same, losses decrease). Hence, a profit is reported only when the

revenues exceeded the minimum of $8.894 million. Hence, no profits were reported

in 1972 when revenue was only $6 million. The revenues for 1973 increased to

$9.2 million and hence Southwest was able to report a small profit. The slope h =

0.555 means that 55.5% of the additional revenues (beyond breakeven) were being

converted into profits. However, this high rate of conversion of revenues to profits

could not be sustained, even in 1974. Although both revenues and profits increased

in 1974, the profits for 1974 were lower than the prediction based upon the

extrapolation of the 1971-1973 P-R line.

-5.0

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

0 2 4 6 8 10 12 14 16 18 20

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 84 of 111

Figure 30: The data plotted here for 1971-1978 were obtained

from the 1975 and 1978 Annual Reports. The solid blue line has

the equation y = 0.555x – 4.934 = 0.555 (x – 8.893) and joins the

1971 and 1973 data. The profit y = 0 when revenues x = x0 = -c/h = 4.934/0.555 =

$8.893 million. The slope h = 0.555 indicates that 55% of the revenues (beyond

this breakeven level) were being converted into profits between 1971 and 1973.

However, this period of high revenues to profits conversion did not last very long

and the slope of the profits-revenues graph has been decreasing ever since. The

highest (x, y) data here is for 1978. The dashed blue line joining the (x, y) pairs for

1974 and 1978 has the equation y = 0.224x – 1.194 = 0.224 (x – 5.32). This means

that only 22.4% of the revenues were being converted into profits in this period.

The slope h deduced here is greater than the slope of h = 0.142 (solid blue line) in

Figure 28 which indicates further decrease in the rate of revenues-profits

conversion. Since then a Type III behavior has been established as discussed in

detail. Costs have thus been increasing but have largely escaped attention because

financial data are seldom analyzed using methods such as those being described

here – very common in the physical and engineering sciences.

-10

-5

0

5

10

15

20

0 20 40 60 80 100

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 85 of 111

Figure 31: The data re-plotted here is for the period 1971-1984

and was obtained from the various Annual Reports. The red

dashed line with the highest slope is for the initial period 1971-1973. The solid

blue line connecting 1974 and 1980 data has the equation y = 0.133x + 0.00017

and essentially passes through the origin. Thus, the period 1974 to 1980 represents

a much lower rate of conversion of revenues to profits. The slope h = 0.133

deduced here is consistent with h = 0.123 deduced earlier for 1992-2001[see

Figure 3, best-fit equation y = 0.123x – 0.141 = 0.123 (x – 1.154)]. However, the

data for 1980 to 1984 begins to deviate from the line with slope h = 0.133, as

indicated by the blue dotted line connecting the 1980 and 1984 data. (Hence, a

continuous power law curve, with n < 1, can also be used to describe the data

instead of these line segments of various slopes. However, care must be exercised

when making predictions using nonlinear laws, which can lead to either overly

“bearish” or “bullish” predictions. The linear law is more reliable when making

short term extrapolations when a “fixed” rate seems to be observed. Nonlinear law

should be used only after a thorough understanding of the system’s behavior.)

-0.01

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.00 0.10 0.20 0.30 0.40 0.50 0.60

Revenues, x [$, billions]

Pro

fits

, y [

$,

billi

on

s]

1971-1973 1974-1980

1980-1984

Page 86 of 111

The forty-one year profits-revenue

history for Southwest Airlines

The first twenty years (1971-1990)

Year Revenues, x

$, billions

Profits, y

$, billions

Comments

1971 0.0021 -0.0037

1972 0.006 -0.0016

1973 0.0092 0.0002 First profit

1974 0.0149 0.0021

1975 0.0228 0.0034

1976 0.0309 0.0049

1977 0.0490 0.0075

1978 0.0811 0.0170

1979 0.1361 0.0167

1980 0.2130 0.0284

1981 0.2704 0.0342

1982 0.3312 0.0340

1983 0.4482 0.0409

1984 0.5359 0.0497

1985 0.6797 0.0473

1986 0.7688 0.0500

1987 0.7783 0.0202

1988 0.8604 0.0580

1989 0.9736 0.0745

1990 1.1868 0.0471 $1 billion Revenues

1991 1.3793 0.0370

1991 1.3136 0.0269

The data for 1992-2011 (and first quarter 2012) have been presented in Table

1 of the main text. Most of the data was obtained from the annual reports.

Sometimes discrepancies were noticed, especially with revenues between

various reports. Both values are included in such instances.

The following values were obtained from the ten-year summary in the 1993

Annual Report and show slight discrepancies with earlier reports.

Page 87 of 111

From 1993 Annual Report: Ten-year Summary

Year

Revenues, x

$, millions

Profits, y

$, millions

Comments

1984 519.106 49.724

1985 656.689 47.278

1986 742.287 50.035

1987 751.649 20.155

1988 828.343 57.952

1989 973.568 74.505

1990 1144.421 50.605 $1 billion Revenues

1991 1267.897 33.148

1991 519.106 49.724

From the 1974 Annual Report

SWA began its operations between just three Texas cities.

Service to Rio Grande Valley was added on February 11, 1975.

Now Southwest flies to 73 cities in 38 states.

Page 88 of 111

What a difference a decade makes (see page 77)

From the 1974 Annual Report Those were the days!!!

Somewhere in the skies over Texas With lots of LUV in the air!

Page 89 of 111

§ 15. Now, a word about AirTran!

Since the AirTran acquisition will play a major role in the future of Southwest

Airlines, let’s take a quick look at the AirTran 10-year profits-revenues data. The

results are presented here without much discussion, with the x-y graphs telling the

story for us. First, consider the following data from the 2010 Annual Report.

Year Revenues, x

$, millions

Profits, y

$, millions

Costs (x – y)

$, millions

2010 2619.712 38.543 2581.169

2009 2341.442 134.662 2206.78

2008 2552.478 -266.334 2818.812

2007 2309.983 52.683 2257.3

Figure 32: AirTran profits-revenues graph for 2007-2010 showing an interesting

criss-crossing Type III behavior (or a back and forth Air Tran “swooshing”). The

-300

-250

-200

-150

-100

-50

0

50

100

150

200

2250 2300 2350 2400 2450 2500 2550 2600 2650

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 90 of 111

horizontal red line is the x-axis. One expects profits to increase with increasing

revenues. This is the normal Type I behavior (positive intercept on revenues-axis)

or Type II behavior (positive intercept on the profits-axis) But, we also see the

opposite behavior with several companies, at least in some situations. If profits

decrease with increasing revenues, or increase with decreasing revenues (yes, it is

possible!), we have Type III behavior. This is what we see here with Air Tran.

We see a very interesting pattern in the time-evolution of profits and revenues.

This can be described by three straight line segments all with a negative slope.

For 2007 and 2008: y = -1.315x + 3092

For 2008 and 2009: y = -1.315x + 3092

For 2009 and 2010: y = -0.345x + 943.43

The revenues increased between 2007 and 2008 but the profits decreased – so

much that AirTran actually reported a huge loss! This is what was classified as

Type III behavior and is indicated by the line with the negative slope (h < 0, c > 0).

Using the formulas given earlier, for the equation of a straight line connecting any

two points, we get y = -1.315x + 3092. The arrow shows the direction of time.

Next, revenues decreased between 2008 and 2009 but now AirTran reported a nice

profit. The dashed line, with the negative slope, indicates this and takes us to the

point above the red line. This is an interesting variant of the Type III behavior,

with profits increasing with decreasing revenues. (This is observed with other

companies as well, see Yahoo discussed in Refs. [1-3].) The equation for the new

Type III line is y = -1.315x + 3092.

Next, revenues increased between 2009 and 2010 but profits decreased once again

but a loss was avoided. This too is Type III behavior, similar to that observed

between 2007 and 2008. The equation of this line is y = -0.345x + 943.43.

If we consider the data for prior years, the ten-year period 2001-2010, and prepare

a x-y graph, no real pattern is detected. The data is given in the table below.

A successful company must report a profit. AirTran has reported a profit for 8 out

of 10 years, with a small loss in 2001 and a much bigger loss in 2008. But look at

the profits-revenues graph. It is totally chaotic. The behavior is like that of an

Page 91 of 111

engine that works erratically each time you turn it on. It does not run smoothly and

misfires and so the ride is jerky! This seems to be the way some companies are

behaving today. In other words, the “Profits Engine” is not running smoothly.

Year Revenues, x

$, millions

Profits, y

$, millions

Costs (x – y)

$, millions

2006 1892.083 14.714 1877.369

2005 1450.544 1.722 1448.822

2004 1041.422 12.255 1029.167

2004 918.04 100.517 817.523

2002 733.37 10.745 722.625

2001 665.164 -2.757 667.921

Figure 33: Erratic profits-revenue graph for AirTran for the period 2001-2010.

The situation is like that of the old steam engines before James Watt started

studying the reasons for their erratic behavior. During his investigations, on the old

Newcomen engine (which was made available to the young James Watt for study,

-300

-250

-200

-150

-100

-50

0

50

100

150

200

0 500 1000 1500 2000 2500 3000

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 92 of 111

by the University of Glasgow; Watt had just finished his education and was looking

things to do to launch his professional career and earn a living), Watt learned

about a remarkable property of steam called its latent heat (Professor Black, from

what we would now call their physics department, had also been studying the

properties of steam). Armed with this knowledge, Watt built a steam condenser

and essentially started recycling the exhaust steam back which dramatically

reduced the consumption of coal. He also reduced heat losses by improving the

insulation used. These “scientific” studies on the steam engine led to dramatic

improvements in efficiency (it was more than doubled) and led to what we now

call the Industrial Revolution.

Alas, many companies today seem to be behaving like the old Newcomen engine

before Watt. The AirTran profits-revenues graph seems like a perfect example.

Figure 34: The costs-revenues graph for AirTran prepared using the profits and

revenues data from the Annual Reports. The straight line connecting the 2003 and

2010 data has the equation C = 1.0364 R – 133.952. The descriptive symbols are

-500

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500

Revenues, x [$, millions]

Co

sts

, (x

– y

), [

$, m

illio

ns]

Page 93 of 111

used here for clarity instead of x and C = (x – y). But, they are retained in the axis

labels to show the relationship with the profits-revenues graph.

Figure 35: The AirTran costs-revenues graph with the best-fit

equation C = 1.10292 – 57.98. The linear regression coefficient r2 = 0.9834 is very

high, indicating a high degree of confidence in the important conclusion here that

the slope of the graph dC/dR > 1. In other words, costs are increasing faster than

revenues and so the company’s profits vary erratically.

The situation, however, changes dramatically if we consider the “costs” in the last

column, determined using the simple equation which is universally applicable to

all companies: Profits = Revenues - Costs or C = (x – y). We will also use the

descriptive notation R, P and C in this context to minimize confusion. The C-R

graph shows a remarkably linear relationship. As revenues increase, costs also

increase, even if we find that profits are varying erratically and there is no pattern.

(A nice linear P-R relation, as we saw in the early years with Southwest, Figure 3,

-500

0

500

1000

1500

2000

2500

3000

3500

0 500 1000 1500 2000 2500 3000 3500

Revenues, x [$, millions]

Co

sts

, (x

– y

), [

$, m

illio

ns]

Page 94 of 111

is the ideal situation; see also P-R graphs

for Apple discussed in the articles cited.

Even if P-R graph is a scatter, the C-R

relation is often linear, as we see here.)

Notice that the slope of the straight line

joining the (C, R) data for 2003 and 2010

is greater than 1. The revenues increased

by ∆R = (2619.712 – 918.04) = 1701.672

but ∆C = 1763.646. Thus, ∆C > ∆R, as

we also saw earlier with the Southwest

data in the post 2007 period. This means

that for AirTran, costs have been

increasing faster than revenues.

To test if this is a “fluke”, arising from

the specific choice of the data points, a

linear regression analysis was performed

to determine the equation of the best-fit

line through these 10 points. This is given

below and is now included in the new

graph prepared in Figure 35.

C = 1.0292 – 57.98 with r2 = 0.9834

With the high value for the linear

regression coefficient, it is clear that the

statistically significant value of the slope

of the graph is also greater than 1. The

best-fit line does not go exactly through

the points we picked but is very close to

them. The slope dC/dR = 1.0292 > 1, as

we learned in our elementary calculus.

The following alternative view is

possible if we ignore the loss in 2008.

To use a sports analogy, this

is like keeping golf scores.

A player is allowed a certain

number of strokes, say y, to play

a hole. This is called par for the

hole. A good player may take

fewer strokes (a birdie, - 1, or

eagle - 2, or rarely a double

eagle -3). Or, the player can

take extra strokes (bogey, +1,

double bogey +2, triple bogey

+3, quadrupule bogey, +4).

Birdies and bogeys arrive

erratically and the scores kept

in this way go from positive

(too many bogeys) to negative

(lots of birdies).

But, the total cumulative

strokes y will always increases

as the total holes played x

increases. This law cannot be

violated. The law is y = hx + c.

We can test this law with

several world class golfers and

arrive at the values of h and c

for them. (Or use “hypothetical”

scores.) We are doing the same

here. Profits and losses are like

keeping scores above and below

par. But, costs will always go up

as revenues increase, regardless

of profits or losses. This too is

an inviolable law.

Page 95 of 111

Figure 36: An alternative view of the AirTran profits-revenues

graph, if we completely ignore the 2008 data.

Now the profits data can be described by two straight lines. The red line, with the

equation y = hx + c = 0.024x + 78.5 simply joins the 2003 and 2009 data. This is

Type II behavior (h > 0, c > 0). Profits increase with increasing revenues but

usually at a lower rate than a Type I behavior (h > 0, c < 0).

The blue line is the best-fit line through the remaining data points, with the

equation y = 0.0214x – 14.48 = 0.0214 (x – 676.2). This is clearly a Type I

behavior. The line makes a positive intercept of x = x0 = -c/h = 14.48/0.0214 =

$676.2 million on the revenues-axis. The data for 2001 confirms this cut off since

AirTran had a small loss with revenues of $665.164 million. Beyond this cut-off,

or breakeven, revenues, AirTran was able to report a small profits (much less than

with the Type II situation, the difference being the large positive intercept).

The situation we see here with AirTran is thus unusual. There is clear evidence of

costs increasing faster than revenues, if we include all the profits and losses data. If

-40

-20

0

20

40

60

80

100

120

140

160

180

0 500 1000 1500 2000 2500 3000 3500

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 96 of 111

we analyze it more selectively, AirTran seems to exhibit both Type I and Type II

behavior in overlapping periods. The slope h is roughly the same for both --- the

Type I and Type II lines seem to be roughly parallel in our graph. But, the situation

including the huge loss, with dC/dR > 1, suggests a Type III behavior (see below).

Figure 37: The profits-revenues graph for AirTran for the sixteen year (16) period

1995-2010. Air Tran reported a profit for only 2 out of the 6 additional years (in

2000 and 1995). All data are taken from the Annual Reports. The graph of costs

versus revenues, where Costs = Revenues – Profits = (x – y), again shows a nice

linearity with very little scatter. However, the slope of the best-fit line is now

slightly less than one. The C-R equation is C = 0.997R+ 7.53 = kR + A, with a

linear regression coefficient r2 = 0.9885. A very small positive intercept (A = 7.53)

is made on the cost-axis (when R = 0, C = 7.53) and so the best-fit C-R line

essentially passes through the origin. Costs increase with increasing revenues.

Since the linear regression coefficient is so high, this is a statistically significant

result. Using the C-R equation, we can deduce the profits-revenues equation from

P = R – C which yields P = 0.003R – 7.53 = hR + c, with a very small positive

-300

-250

-200

-150

-100

-50

0

50

100

150

200

0 500 1000 1500 2000 2500 3000

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 97 of 111

slope h = 0.003. In other words, only 0.3% of the revenues can be converted into

profits. Or, 99.7% of revenues are being absorbed as “costs” and very little

appears as profits. The analogy with Einstein’s work function from the

photoelectric law (discussed in the references cited) is very telling in this case.

Also, intriguing is the possibility of a maximum point, as suggested by the dashed

curves (NOT derived from any mathematical calculations). The four points along

the curve past the maximum are for 2007-2010 which led to the criss-crossing

Type III behavior discussed earlier.

Figure 38: Possible appearance of a maximum point on the profits-revenues graph

for AirTran. Perhaps, this was precursor to the “acquisition” of Air Tran. A

company cannot continue to operate for long in the Type III mode with profits

decreasing as revenues increase, or vice versa. (In the case of General Motors,

where a similar Type III mode was observed over several years, it eventually led to

its historic bankruptcy filing in June 2009.) Notice how different conclusions are

permitted by the 10-year data and the 16-year data. The falling part of the curve

can be envisioned with the 10-year data but the rising part is only revealed if we

-300

-250

-200

-150

-100

-50

0

50

100

150

200

0 500 1000 1500 2000 2500 3000

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Page 98 of 111

consider the 16-year data. Type III behavior is always preceded by Type I and/or

Type II. A rise precedes every fall. Hence, the Type III behavior usually suggests

the existence of a maximum point on the profits-revenues graph.

In summary, the profits-revenues and costs-revenues pattern for AirTran, in the

ten-year period immediately preceding its acquisition by Southwest, reveals

interesting challenges ahead for the new company.

The following is from the 2011 Southwest Annual Report. The issuance of the

SOC means there is only ONE company now, legally speaking, even if the rest of

the integration is not complete.

Since the AirTran acquisition on May 2, 2011, we have made tremendous progress on integrating it into Southwest Airlines. Our efforts to begin optimizing the combined network have resulted in significant changes to AirTran’s route network. In 2012, AirTran is closing 15 cities that proved unsustainable with today’s dramatically higher fuel prices. We will serve 97 cities total between our separate networks based on our joint schedules currently published through November. On March 1, 2012, we received approval from the Federal Aviation Administration (FAA) for a Single Operating Certificate (SOC), marking a key milestone in the integration of the two airlines. AirTran can now begin transferring aircraft to be converted to the Southwest livery, and we can begin transitioning AirTran airport facilities to Southwest, beginning with Seattle in August 2012.

http://www.airtran.com/common/pdf/SpreadingLowFares_FactSheet.pdf

Page 99 of 111

http://www.getfilings.com/o0000931763-98-000779.html

Airline Southwest Air Tran

Stock Symbol LUV AAI

Founded June 18,1971 Oct 26, 1993

Headquarters Dallas, Texas Orlando, Florida

Employees 34,636 8,083

Fleet (Active, as of Sep 27, 2010) 547 138

For completeness, the following is a summary of the profits-revenues data for

AirTran since its operations began in 1993.

Year Revenues, x

$, millions

Profits, y

$, millions

Costs (x – y)

$, millions

2000 624.094 47.436 576.658

1999 523.468 -99.394 622.862

1998 439.307 -40.738 480.045

1997 211.456 -96.663 308.119

1996 219.636 -41.469 261.105

1995 367.757 67.763 299.994

1994 133.901 20.732 113.169

1993 5.811 -0.894 6.705

The data for 2001-2010 has been presented earlier. The merger with

Southwest was approved overwhelmingly by shareholders on March 23, 2011.

http://travel.usatoday.com/flights/post/2011/03/airtran-shareholders-ok-southwest-

merger/148989/1

On May 11, 1996, the (predecessor) company (ValuJet Airlines) tragically lost

Flight 592, from Miami to Atlanta. The plane crashed shortly after take-off after a

cabin fire. http://en.wikipedia.org/wiki/ValuJet_Flight_592 . There were no

survivors. The ensuing adverse media coverage (about low cost airlines), and the

intense FAA scrutiny that followed, led to a total shutdown of all operations on

June 17, 1996. FAA returned the company’s operating certificate on Aug 29. The

DOT issued a “show cause” order about the fitness to be an air carrier and gave its

Page 100 of 111

It can be shown that the sum of all the deviations from the profits predicted by the initial

Type I line equals $3.624 billion (see tables given here for 1993-2010). The sum of all the

revenues equals $19.05 billion. Multiply $19 B by 20%, for a quick calculation. We get

$3.8 B. Or, use the exact slope and convert 18.9% of $19.05 B. We get $3.61 B. Add that

small intercept. We get $3.624 billion – the sum of all the profits NOT made. Case

CLOSED for this type of an analysis!

final approval on Sep 26, 1996. Operations then resumed on Sep 30 with flights

between Atlanta and four other cities. These tragic events explain the “sudden”

loss of revenues in 1996 and also the losses. But, this seems to have lingered

(through 1999???). Profitability was finally achieved only in 2000.

Figure 39: Air Tran data reveals a Type I behavior between 1993 and 1995, as

indicated by the solid blue line. The profits-revenue equation y = 0.1897x – 1.996

= 0.1897 (x – 10.52). The reader (assuming we have one!!!) is strongly urged to

deduce this equation using the data presented in the tables here. Only then will its

impact be truly felt! Ideally, every point we see here should fall on this Type I line.

-400

-300

-200

-100

0

100

200

300

400

500

600

0 500 1000 1500 2000 2500 3000

Revenues, x [$, millions]

Pro

fits

, y [

$,

mil

lio

ns

]

Type I behavior 1993-1995

y = 0.189x – 1.996 = 0.1897 (x – 10.52)

Page 101 of 111

Nonetheless, the availability of this historical

data, since Air Tran began its operations in

1993, permits us to draw an interesting, but

cautionary, conclusion about the growth and

evolution of companies. As with Southwest

Airlines, between 1971 and 1974, we see

revenues increasing between 1993 and 1995.

Unlike Southwest, which reported a loss in

1972, its first full year of operation (it only

“turned the corner” in 1973 and reported a full

year of profits), Air Tran “turned the corner”

in its first full year of operations in 1994 and

reported a profit. Both profits and revenues

increased in 1995. This was followed by four

continuous years of losses with profits

returning only in 2000. But the profits were

lower: only $47.44 million versus $116.4

million obtained by extrapolation!

If Air Tran had continued to follow this initial profits-revenues line, in 2003, when

it reported a profit, it would have reported $172 million instead of $100 million.

This shows that something went seriously wrong (was it the accident in May

1996?) with the initial very successful plans and “costs” started increasing after

1995 and went totally out of control.

And, instead of reporting a historically high profit of about $436 million in 2007,

Air Tran reported a profit of only $52.7 million. And, instead of a profit of $482

million in 2008, it reported its highest loss of about $266 million.

The potential for high profits, even in the airlines business, stares us in the

face here! This can also be appreciated if we consider how profits evolve with

increasing revenues during a single year. The following tables summarize the data

(from the various annual reports) for 3 month, 6 month, 9 month, and 12 month

periods for1995, 2003, 2009 and 2010. Comparing the cumulative profits and

revenues for 1995 and 2003 and also 1995 and 2010 it is quite obvious that

From 1993-2010

Sum Total of

Revenues

$19,049.67 million

$19.05 billion

Profits

($6.477) millions

Page 102 of 111

1. The fixed costs have been rising from 1995 to 2003 to 2010, as indicated by

the increasingly more positive values of the “breakeven” revenue, given by

the intercept made on the revenues-axis.

2. The rate at which additional revenues (beyond the breakeven) are being

converted into profits has also decreased. This is indicated by the decreasing

values of the slope h of the graphs. It was 19% in 1995 (h = 0.1911),

decreased to 13.8% in 2003 (h = 0.1387) and had reduced to just 2.5% in

2010 (h = 0.0251).

Now all of this is water down the bridge!

Yes, the potential for high profits, even in the airlines business, stares us in the

right in the face here! Just imagine converting about 18% or

20%, okay let’s do just 10%, of additional revenues

beyond breakeven into profits! Air Tran did it in 1994 and 1995. It can be done

again in 2014 and 2015. Wow! Let’s do it with a Swoosh!

Air Tran Quarterly data: Profits-revenues growth during a single year

Quarter Revenues,

quarterly

$, millions

Profits,

quarterly

$, millions

Cum. Rev,

x

$, millions

Cum Profit,

y

$, millions

P-R equation

For growth

in the year

1Q2010 605.141 -12.025 605.141 -12.025 h = 0.0251

2Q2010 700.557 12.380 1305.698 0.355 c = -27.22

3Q2010 667.934 36.263 1973.632 36.618 y = hx + c

4Q2010 645.540 1.925 2619.172 38.543 x0 = - c/h

= 1084.1 All slopes h obtained from the lowest and highest (x, y) pairs.

1Q2009 541.955 28.707 541.955 28.707 h = 0.0589

2Q2009 603.653 78.438 1145.608 107.145 c = -3.204

3Q2009 597.402 10.426 1743.01 117.571 y = hx + c

4Q2009 598.432 17.091 2341.442 134.662 x0 = - c/h

= 54.41 Graphs were prepared in all cases, even if not included here.

1Q2003 208.002 2.036 208.002 2.036 h = 0.1387

2Q2003 233.901 57.191 441.903 59.227 c = -26.81

3Q2003 237.311 19.613 679.214 78.84 y = hx + c

4Q2003 238.826 21.677 918.04 100.517 x0 = - c/h

= 193.32

Page 103 of 111

Air Tran Quarterly data: Profits-revenues growth during a single year

Quarter Revenues,

quarterly

$, millions

Profits,

quarterly

$, millions

Cum. Rev,

x

$, millions

Cum Profit,

y

$, millions

P-R equation

For growth

in the year

1Q1995 60.747 9.071 60.747 9.071 h = 0.1912

2Q1995 86.913 16.860 147.66 25.931 c = -2.542

3Q1995 109.296 22.661 256.956 48.592 y = hx + c

4Q1995 110.801 19.171 367.757 67.763 x0 = - c/h

= 13.298 Slope h from the lowest and highest (x, y) pairs

Figure 40: Comparison of the evolution of profits and revenues in a single year at

three-month, six-month, nine-month, and 12-month intervals, using the quarterly

data. The revenues for just the first quarter of 2010 was almost double the revenue

for the entire year in 1995. Yet, profits were lower in 2010. Firstly, notice the large

intercept made on the revenues axis in 2010 compared to 1995. This means (using

-100

0

100

200

300

400

500

600

700

0 500 1000 1500 2000 2500 3000 3500

Cumulative Revenues, x [$, millions]

Growth during a single year

Cu

mu

lati

ve

Pro

fits

, y [

$, m

illi

on

s]

Gro

wth

du

rin

g a

sin

gle

ye

ar y = 0.1912x – 2.54 = 0.1912 (x – 13.3)

x0 = 13.3 in 1995 and h = 0.19

y = 0.025x – 27.2 = 0.025 (x – 1084) x0 = 1084 in 2010 (higher fixed cost) and h = 0.025 (lower slope means

higher unit variable cost)

Page 104 of 111

the breakeven analysis for profitability of a company making and selling N units of

a single product) that the fixed costs have gone up between 1995 and 2010.

Secondly, the high slope for 1995 is higher. Nearly 20% of the revenues (beyond

breakeven value) were being converted into profits in 1995 but only about 2.5%

was being converted into profits in 2010. According to the breakeven model the

slope h = 1 – (b/p), see §5 in main text (page 22). Hence, the unit variable cost b

has increased between 1995 and 2010, or more correctly, the ratio b/p, where p is

the unit price, has increased. It is to be hoped that Air Tran and Southwest can still

benefit from these findings! 1995 extrapolation equals $498 M profits in 2010.

Figure 41: A very unique Air Tran Type III profits-revenues graph, which lies

entirely in the fourth quadrant, with losses reported for every single quarter during

the year, in 2008. The cumulative quarterly loss was -$273.83 million (slight

discrepancy with the annual value given, -$266.33 million). The solid line joins the

-350

-300

-250

-200

-150

-100

-50

0

50

0 500 1000 1500 2000 2500 3000

Cumulative Revenues, x [$, millions]

Growth during a single year

Cu

mu

lati

ve

Pro

fits

, y [

$, m

illi

on

s]

Gro

wth

du

rin

g a

sin

gle

year

y =-0.122x + 38.07 Solid line y = -0.178x + 182.01 Dashed line

2008 Evolution of revenues-losses

Page 105 of 111

cumulative values for first and fourth quarters but the Type III dashed line begs

attention. This joins the second quarter to the fourth quarter. The general trend is

what is important here, not the exact numerical values. Type III behavior we see

here seems to be the precursor for either a merger (if someone is interested) or a

bankruptcy filing (when no suitors are available, as with General Motors. When

GM publicly announced its willingness to sell off some of its money losing

foundries, back in 1990s, which produce many critical automotive castings there

were no buyers! The latter is based on recollection of published reports during that

time.)This should be compared to the graph for 1995 when Air Tran was able to

report profits with very small revenues. The annual revenue for 1995 was only

$367.757 million, between 50% to 60% of the revenue for any one quarter in 2008.

Still, Air Tran could not report a profit in 2008.

Figure 42: The profitable year 1995, with Type I behavior revealed by the solid

upward sloping line, is compared with the Type III behavior observed in 1996,

-400

-300

-200

-100

0

100

200

0 500 1000 1500 2000 2500 3000

1995

2008

1997

1996

Cu

mu

lati

ve

Pro

fits

, y [

$, m

illi

on

s]

Gro

wth

du

rin

g a

sin

gle

year

Cumulative Revenues, x [$, millions]

Growth during a single year

Page 106 of 111

1997, and 2008 with annual losses. Even with greatly increased revenues, as

revealed by the fact that the data for 1995-1997 are crowded together near the

origin, Air Tran was unable to report a profit in 2008. (The Type III line for 1997

is an interesting “financial example” of a line with a negative slope which makes a

negative intercept on BOTH the profits and the revenues axes. Most Type III lines

make a positive intercept on both the axes. ) Instead of profits indicated by the

extrapolation of the Type I line for 1995, it reported its highest losses, revealed by

the two Type III lines for 2008. In other words, the quadrant four graph is to be

wholly avoided when we consider the cumulative data (from quarterly reports) in a

single year. It may be the precursor to either bankruptcy filing (if no one want to

take over the company) or a merger with a willing suitor.

Air Tran Quarterly data: Profits-revenues growth during a single year

Quarter Revenues,

quarterly

$, millions

Profits,

quarterly

$, millions

Cum. Rev,

x

$, millions

Cum Profit,

y

$, millions

P-R equation

For growth

in the year

1Q2008 589.115 -34.813 596.391 -34.813 h = -0.122

2Q2008 589.115 -13.538 1289.771 -48.351 c = 38.97

3Q2008 589.115 -107.087 1963.063 -155.438 y = hx + c

4Q2008 589.115 -118.391 2552.178 -273.829 x0 = - c/h

= 311.5 Slope h from the lowest and highest (x, y) pairs

In this case the 2Q and 4Q data beg attention, h = -0.179

How could I say all this without that a x-y graph?

If anyone is reading this, please go back now and enjoy the story

told by each of these graphs!

Page 107 of 111

If anyone is reading this, please go back now and enjoy the story

told by each of these graphs!

Illustration of DC-9 ValuJet, Flight 592. The plane was observed crashing.

It crashed on a lovely Saturday afternoon, the day before Mother’s day.

The improper placement and loading of canisters with chemicals (that are used to produce Oxygen

for the Emergency System), in the cargo compartment below the passenger cabin,

http://en.wikipedia.org/wiki/ValuJet_Flight_592

seems to have contributed to the spark that led to the fire and the crash.

Sadly, this is, perhaps, the clearest example of incompetent and/or ignorant employees,

working without proper training or supervision, doing what they think is best! They just

did not know how stupid it was to do what they did! The loss of the space shuttle

Challenger, on January 28 1986, seconds after launch, is another example of a similar

tragedy that could have been avoided.

It is really the story of what we all do each day, as employees, to

make the company we work for profitable, to enrich our own lives,

and to enrich the communities we live in.

Lurking behind each of our actions is that demon called the “costs”.

And before we know it h > 0 turns into h < 0

And the day of reckoning arrives!

It happened between 1993 and 2011!

http://psiresearcher.files.wordpress.com/2011/09/flighteverglades-plane-crash-

2_05320299.jpg?w=640

http://www.theatlantic.com/magazine/archive/1998/03/the-lessons-of-valujet-

592/6534/ Time to get over that fateful 1996 crash!

Page 108 of 111

§ 16. Bibliography

Related Internet articles posted at this website

Since the Facebook IPO on May 18, 2012

1. http://www.scribd.com/doc/95906902/Simple-Mathematical-Laws-Govern-

Corporate-Financial-Behavior-A-Brief-Compilation-of-Profits-Revenues-

Data Current article with all others above cited for completeness, Published

June 4, 2012 with several revisions incorporating more examples.

2. http://www.scribd.com/doc/94647467/Three-Types-of-Companies-From-

Quantum-Physics-to-Economics Basic discussion of three types of

companies, Published May 24, 2012. Examples of Google, Facebook,

ExxonMobil, Best Buy, Ford, Universal Insurance Holdings

3. http://www.scribd.com/doc/96228131/The-Perfect-Apple-How-it-can-be-

destroyed Detailed discussion of Apple Inc. data. Published June 7, 2012.

4. http://www.scribd.com/doc/95140101/Ford-Motor-Company-Data-Reveals-

Mount-Profit Ford Motor Company graph illustrating pronounced

maximum point, Published May 29, 2012.

5. http://www.scribd.com/doc/95329905/Planck-s-Blackbody-Radiation-Law-

Rederived-for-more-General-Case Generalization of Planck’s law, Published

May 30, 2012.

6. http://www.scribd.com/doc/94325593/The-Future-of-Facebook-I Facebook

and Google data are compared here. Published May 21, 2012.

7. http://www.scribd.com/doc/94103265/The-FaceBook-Future Published

May 19, 2012 (the day after IPO launch on Friday May 18, 2012).

8. http://www.scribd.com/doc/95728457/What-is-Entropy Discussion of the

meaning of entropy (using example given by Boltzmann in 1877, later also

used by Planck to develop quantum physics in 1900). The example here

shows the concepts of entropy S and energy U (and the derivative T =

dU/dS) can be extended beyond physics with energy = money, or any

property of interest. Published June 3, 2012.

9. The Future of Southwest Airlines, Completed June 14, 2012 (to be

published).

Page 109 of 111

About the author

V. Laxmanan, Sc. D.

The author obtained his Bachelor’s degree (B. E.) in Mechanical Engineering from

the University of Poona and his Master’s degree (M. E.), also in Mechanical

Engineering, from the Indian Institute of Science, Bangalore, followed by a

Master’s (S. M.) and Doctoral (Sc. D.) degrees in Materials Engineering from the

Massachusetts Institute of Technology, Cambridge, MA, USA. He then spent his

entire professional career at leading US research institutions (MIT, Allied

Chemical Corporate R & D, now part of Honeywell, NASA, Case Western Reserve

University (CWRU), and General Motors Research and Development Center in

Warren, MI). He holds four patents in materials processing, has co-authored two

books and published several scientific papers in leading peer-reviewed

international journals. His expertise includes developing simple mathematical

models to explain the behavior of complex systems.

While at NASA and CWRU, he was responsible for developing material processing

experiments to be performed aboard the space shuttle and developed a simple

mathematical model to explain the growth Christmas-tree, or snowflake, like

structures (called dendrites) widely observed in many types of liquid-to-solid phase

transformations (e.g., freezing of all commercial metals and alloys, freezing of

water, and, yes, production of snowflakes!). This led to a simple model to explain

the growth of dendritic structures in both the ground-based experiments and in the

space shuttle experiments.

More recently, he has been interested in the analysis of the large volumes of data

from financial and economic systems and has developed what may be called the

Quantum Business Model (QBM). This extends (to financial and economic

systems) the mathematical arguments used by Max Planck to develop quantum

physics using the analogy Energy = Money, i.e., energy in physics is like money in

economics. Einstein applied Planck’s ideas to describe the photoelectric effect (by

treating light as being composed of particles called photons, each with the fixed

quantum of energy conceived by Planck). The mathematical law deduced by

Planck, referred to here as the generalized power-exponential law, might actually

Page 110 of 111

have many applications far beyond blackbody radiation studies where it was first

conceived.

Einstein’s photoelectric law is a simple linear law, as we see here, and was

deduced from Planck’s non-linear law for describing blackbody radiation. It

appears that financial and economic systems can be modeled using a similar

approach. Finance, business, economics and management sciences now essentially

seem to operate like astronomy and physics before the advent of Kepler and

Newton.

Cover page of AirTran 2000 Annual Report

Acknowledgements

With sincere thanks to the many Internet sources that have been

used to compile this document – as evident by all the corporate logos

and various photographs used here to make the presentation more

interesting. All of them have cited and are liberally and profusely

acknowledged.

Page 111 of 111

What are the Odds?

“Southwest Airlines is America’s largest domestic airline, as measured by

originating domestic passengers boarded (based on third quarter 2011 data from

the U.S. Department of Transportation (DOT)). We remain one of the lowest cost

producers among major airlines with one of the world’s largest mainline fleets.”

From the 2011 Annual Report

Gary C Kelly

Chairman of the Board, President

Chief Executive Officer

In Annual Report after annual report, Southwest Airlines has

proudly emphasized its status as the low-cost leader in the industry.

What then are the chances of any of these

ideas and the discussion here about rising

costs getting accepted?

Only time will tell.

If the predictions here have any validity, we can expect Southwest

Airlines to go through a period of reporting losses - with its acquisition

of AirTran and rapidly changing nature of its complex

operations being held at fault. But there is a different reason

and it lies buried in the story here. Costs have been rising

for a long long time, as evident from the nonlinear curve

for 1971-1992. Even if losses are avoided, Southwest can greatly

improve its profitability by studying some of the ideas outlined here.

With lots of LUV in the air!