the valuation of airport slots - smu

Journal of Air Law and Commerce Journal of Air Law and Commerce

Volume 74 Issue 4 Article 4

2009

The Valuation of Airport Slots The Valuation of Airport Slots

Michael Olbrich

Gerrit Brosel

Marius Hasslinger

Recommended Citation Recommended Citation Michael Olbrich et al., The Valuation of Airport Slots, 74 J. AIR L. & COM. 897 (2009) https://scholar.smu.edu/jalc/vol74/iss4/4

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THE VALUATION OF AIRPORT SLOTS

MICHAEL OLBR1CH*

GERRIT BROSEL**

MARIUS HASSLINGER***

I. INTRODUCTION

N ORDER TO SERVE coordinated airports, an airline mustown take-off and landing rights (slots).' These rights allow an

airline to use the airport's runway capacities at a specific time ona specific day.2 Take-off and landing rights are allocated by na-tional authorities free of charge, but the demand for slots farexceeds the supply.' Under certain circumstances, the airlinestherefore have a strong incentive to acquire slots by purchasingthem from other airlines. Such slot trading is allowed in theUnited States and the United Kingdom.4 In the other member

* Professor Olbrich is professor of auditing and accounting at Universitit

Trier (Germany). He obtained his Dipl.-Kfm. degree in business administrationfrom Heinrich-Heine-Universitqt Dfisseldorf in 1996, his doctor's degree fromErnst-Moritz-Arndt-Universitdit Greifswald in 1998, and his Habilitation degreefrom Fern-Universitait Hagen in 2004.

** Professor Br6sel is professor of Financial Reporting and ManagerialAccounting at Ilmenau University of Technology (Germany). He obtained hisDipl.-Kfm. degree in business administration in 1998 and his doctor's degree in2002 from Ernst Moritz Arndt University of Greifswald, and his Habilitationdegree from Ilmenau University of Technology in 2006.

*** Marius Hasslinger is a doctoral student at the chair of auditing andaccounting of Professor Olbrich at Universitat Trier (Germany). He obtained hisDipl.-Kfm. degree in business administration from Universitdt Mannheim in2007.

1 INT'L AIR TRANSP. ASS'N, WORLDWIDE SCHEDULING GUIDELINES 4 (12th ed.

2005).2 See id. at 11.

3 TRANSP. RESEARCH CTR., TRANSP. SERVS.: THE LiMITS OF (DE)REGULATION 22(2004); David Starkie, Allocating Airport Slots: a Role for the Market?, 4J. AIR TRANSP.MGMT. 111, 111 (1998).

4 Starkie, supra note 3, at 112-13.

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states of the European Union slot trading is not officially legal-ized yet, but is, on the other hand, not prosecuted anymore.5

If an airline wishes to purchase a slot, it must, first of all, de-termine its value. In this context, the aim is not to calculate anobjective value at market equilibrium, as in the case of valuationmodels in financial theory,6 but to determine the subjectivevalue in use (VIU) of the slot for the airline in question. Know-ing the VIU of a slot is of considerable importance to an airlinebecause it enables it to establish the maximum price it could payfor the slot without the transaction being disadvantageous. 7 Thegreater extent to which the price of the slot is below its VIU, themore advantageous the purchase of the take-off or landing rightfor the airline. If, on the other hand, the price of the slot ex-ceeds its VIU, the transaction is disadvantageous and should not

5 See Starkie, supra note 3, at 114. For a detailed analysis of slot trading in theUnited States, see generally Sabine J. Langner, Contractual Aspects of Transacting inSlots in the United States, 2J. AIR TRANSP. MGMT. 151 (1995); Starkie, supra note 3;David Starkie, Developments in Transport Policy-The US Market in Airport Slots, 28 J.TRANSP. ECON. & POL'Y 325, 325 (1994). On slot trading in the United Kingdomand a discussion of the buying and selling of slots in the European Union, seegenerally Communication from the Commission to the European Parliament,the Council, the European Economic and Social Committee and the Committeeof the Regions on the Application of Regulation (EEC) No 95/93 on CommonRules for the Allocation of Slots at Community Airports, as amended COM(2008) 227 final (Apr. 30, 2008); Matthias Kilian, The Development of the RegulatoryRegime of Slot Allocation in the EU, (2004) in AIRPORT SLOTS: INTERNATIONAL EXPER-

IENCES AND OPTIONS FOR REFORM 252 (Achim I. Czerny et al. Eds., 2008) [herein-after Slot Allocation]; CIVIL AVIATION AUTHORITY, THE IMPLEMENTATION OF

SECONDARY SLOT TRADING (2001); CIVIL AVIATION AUTHORITY, INTRODUCING COM-

MERCIAL ALLOCATION MECHANISMS: THE UK CIVIL AVIATION AUTHORITY'S RE-

SPONSE TO THE EUROPEAN COMMISSION'S STAFF WORKING PAPER ON SLOT REFORM

(2004); Ruwantissa I.R. Abeyratne, Management of Airport Congestion Through SlotAllocation, 6 J. AIR TRANSP. MGMT. 29 (2000); Tom C. Bass, Infrastructure Con-straints and theEC, 1J. AIR TRANSP. MGMT. 145 (1994); Matthias Kilian, Der Handelmit Slots-Die Entscheidung des High Court im Verfahren Regina vs. Airport Co-Ordina-tion Ltd., 23 TRANSPR 159 (2000) (F.R.G.).

6 See, e.g., TOM COPELAND, TIM KOLLER &JACK MURRIN, VALUATION: MEASURING

AND MANAGING THE VALUE OF COMPANIES (3d ed. 2000); John Stonier, AirlineLong-Term Planning Under Uncertainty: The Benefits of Asset Hexibility Created ThroughProduct Commonality and Manufacturer Lead Time Reductions, in REAL OPTIONS AND

BUSINESS STRATEGY 135 (Lenos Trigeorgis ed., 1999); Fischer Black & MertonScholes, The Pricing of Options and Corporate Liabilities, 81J. POL. ECON. 637 (1973);John C. Cox, Stephen A. Ross, & Mark Rubinstein, Option Pricing: A SimplifiedApproach, 7J. FIN. ECON. 229 (1979).

7 See Thomas Hering, Michael Olbrich & Martin Steinrficke, Valuation of Star-tup Internet Companies, 33 INT'L J. TECH. MGMT. 406-19 (2006); Manfred JfirgenMatschke, Der Gesamtwert der Unternehmung als Entscheidungswert, 24 BETRIEBSWIRT-

SCHAFTLICHE FORSCHUNG UND PRAXIS 146-61 (1972).


be conducted. In light of the highly individualized market forslot trading which is characterized by extensive excess de-mand-i.e. the acquiring company is not just a price-taker-it isparticularly important to identify the subjective price limit be-cause, in some cases, airlines have to spend up to several millioneuros or U.S. dollars in order to buy a slot.' In other words, it isa substantial investment, especially for small and medium-sizedcompanies. Consequently, maximum price determination doesnot remain only an academic concern from the perspective ofvaluation theory, but is also of practical interest to the respectivecompany in the mostly bilateral negotiation process.

The importance of appropriate slot valuation, especially to anairline's capital budgeters, becomes apparent when taking alook at recent balance sheets of firms in the airline industry. In2007, for example, Continental Airlines acquired slots atLondon's Heathrow Airport for a total amount of $116 million.9Both in 2007 and 2008, the amounts invested in internationalslots represented 26% of the company's total capital expendi-ture, with the remainder consisting of the acquisition cost ofnew aircraft and related support equipment.1 0 Identifying theimpact of slot valuation on periodical cash flows from the per-spective of an airline as large as Continental Airlines indicatesthat investment in take-off and landing slots is of even greaterrelative importance to smaller airlines that intend to serve suchairports.

8 Current prices paid for slots at important international airports amount todouble-digit million euro/dollar sums. For example, it is reported that Alitaliasold several slot bundles at London's Heathrow Airport in 2007 for a total of 92million euros to competitors such as British Airways, Continental Airlines, andUS Airways. Kevin Done, Alitalia Sells Heathrow Slots, FIN. TIMES, Dec. 26, 2007,http://www.ft.com/cms/s/O/Oaea33le-b3aO-1ldc-a6df-0000779fd2ac.html. It isfurthermore reported that, among this total amount, over 30 million euros werepaid for one pair of take-off and landing rights. Id. Similarly, Continental Air-lines acquired two pairs of take-off and landing rights for $116 million ($58 mil-lion per bundle) at Heathrow Airport in 2007. Kevin Done, Continental PaysHeathrow Record, FIN. TIMES, Mar. 3, 2008, http://www.ft.com/cms/s/O/b6a47274-e955-1 1dc-8365-0000779fd2ac.html [hereinafter Continental PaysHeathrow]. For an analysis of the prices paid for slots, see Severin Borenstein, TheEvolution of U.S. Airline Competition, 6J. ECON. PERSPECTIVES 45 (1992); Slot Alloca-tion, supra note 5.

9 Continental Pays Heathrow, supra note 8.10 For further information, see Cont'l Airlines, Inc. Annual Report (Form 10-

K), at 49, 79 (Feb. 11, 2008); Cont'l Airlines, Inc. Annual Report (Form 10-K), at55, 91 (Feb. 13, 2009). Similar amounts can be found in annual reports of otherairlines. See, e.g., BRITISH AIRWAYS PLC., 2007/08 ANNUAL REPORT & ACCOUNTS 16,101 (2008). See also DEUTSCHE LUFrHANSA AG, ANNUAL REPORT 2008 155 (2009).

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Although slot trading is widely discussed in literature, there is,to date, no analysis of how to determine the subjective VIU of atake-off or landing right. The present article aims to close thisgap by examining how an airline should proceed in order tomeasure a slot's value. For this purpose, two valuation modelsare presented in Section II, which are specified by examples ofcalculations for specific valuation problems that occur in prac-tice in Section III.

II. VALUATION MODELS

A. PRESENT VALUE TECHNIQUE

In Section I, reference was made constantly to the value of "a"slot. However, a closer look at the situation reveals that one sin-gle slot is generally useless to an airline because, in addition to atake-off right at Airport A, it needs a landing right at Airport B.Also, to enable the aircraft to fly back home, a take-off right atAirport B and a landing right at Airport A are needed (or evenmore slots, if the airline does not fly back directly from B to Abut, for example, from B via C back to A). That is, in order tovalue slots, even for the most simple case, it is generally neces-sary to consider a bundle of at least four slots (Airport A: take-off and landing, Airport B: landing and take-off), and to mea-sure the VIU, not of one single slot, but of this bundle of slots. 1

In this context, the earnings (net cash flows) CF, that the airlinewill gain through the bundle of slots in future periods t are dis-counted to the present day. 2 These net cash flows derive fromthe periodical turnover T earned from passenger and freighttransport, the expenses associated with the use of the aircraft EP,(for example, fuel and personnel costs) and airport-related ex-penses EA, (such as airport charges and gate leases):

(1) CF, = Tt- EPr- EAt.

Characteristic of the valuation of slots is the fact that the life-time of this asset is generally unlimited. As long as the airlineuses the take-off and landing capacity of a slot at least to an ex-tent of 80% during a flight period, the take-off and landingright does not expire ("use it or lose it rule"). Therefore, in the

11 See Hans-Jfirgen Ewers et al., M6glichkeiten der besseren Nutzung von ZeitnischenaufFlughdfen (Slots), in DEUTSCHLAND UND DER EU 15 (2001) (unpublished work-ing paper, on file with Technische Universitdt Berlin).

12 See GUNTER JAENSCH, WERT UND PREIS DER GANZEN UNTERNEHMUNG 23-33(1966).

900


event that the airline does not plan to sell the slot in the future,the valuation time horizon is indefinite and hence differs fromthose of other capital expenditures. However, if the airline doesnot plan to use the take-off and landing rights itself, but to leasethem to another company for certain periods (which is possiblein the United States), the periodic net cash flows are the earn-ings gained from the leasing contract L,:

(2) CFt = Lt.If the airline aims to sell the bundle of slots at the end of itsperiods of usage to another company, the surplus of the last pe-riod t = n is obtained from the earnings according to Equation(1) plus the net turnover NT that will be realized by selling theslots at the end of period n:

(3) CFn = T, - EPn - EA, + NT,.

With discount rate i, periods of usage t E {1, . , n} and exclu-sive use by the airline itself (that is, no lease), the VIU of the slotbundle is calculated by:

(), T, - EP, - EA, NT.(4) VRU=Z +-t=, (1+ i)' (l+ i)'

With the use of equations (1) and (3), this can be formulatedmore simply as:

(5) VlU Y CF,t=U (1 + i)t

The discount rate i that is used in this context for calculatingthe present value is the internal rate of return (IRR) of the bestalternative investment that the airline could make with themoney needed to purchase the slot bundle, for example thepurchase of another aircraft or the redemption of a credit.'3

Consequently, not only the forecast of future cash flows gener-ated by the slot bundle, but also the determination of the rele-vant discount rate has to be carried out from a strict subjectiveperspective. This constitutes the central characteristic of themodels presented in this article. Unlike this approach, valua-tion models in financial theory are typically based on the marketequilibrium assumption in order to determine investment alter-natives, capital structure, risk disposition, and, hence, the dis-count rate. When applying these models, the actual investmentand financing alternatives of the specific airline are not taken

13 See THOMAS HERING, INVESTIT1ONSTHEORIE (2d ed. 2003).

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into account. In consequence, values that are calculated basedon financial theory typically do not represent subjective maxi-mum prices.

When the VIU of the slot bundle has been determined in themanner shown above, the airline gains information about themaximum price it can pay for the four slots together, withoutthe transaction being disadvantageous. That is, the sum of theprices Ps that the airline pays for the four slots (S E {1, 2, 3, 4})must not exceed the VIU of the slot bundle: 4

4

(6) ZP < V1u.S=I

The calculation of the maximum price can be demonstratedby means of the following simple example:

An airline considers the acquisition of a take-off and landingright at Airport A and a take-off and landing right at Airport B.The company forecasts that flying between A and B will lead toperiodic net cash flows of three million euros that remain con-stant over the future periods one to three. For the sake of sim-plicity, we assume just three future periods of slot usage. Thecompany knows that the return on its best alternative invest-ment is 4%. The VIU of the slot bundle at Airports A and B isthen calculated as:

' 3 million euros

t=1 (1.04) t

= 8.33 million euros.

The sum of the prices P, of the slot bundle at Airports A and Bmust not exceed 8.33 million euros.

If the airline knows the IRR of the best alternative investment,the present value method is preferred to linear programming(presented in Section II. B.) because no further assumptions re-lating to the application of linear programming need to be spec-ified. Thus, valuation complexity is reduced if the present value

14 Once the VIU is determined using the present value technique, it can alsoeasily be applied to the decision to sell a bundle of slots. For this purpose, theVIU characterizes the minimum price for which the airline should sell the slotbundle in order to prevent a disadvantageous situation. Therefore, the followingcondition holds:

4

sil

902


method can be applied. However, in reality, an airline fre-quently does not know the best alternative investment comparedto the purchase of slots because, due to its size or group struc-ture, it has a complex program of financing and investment op-tions. If the airline lacks information on the best alternativeinvestment, it also does not know the IRR of this investment.This is when linear programming can be applied.

B. LINEAR PROGRAMMING

In a situation in which the present value technique cannot beused because the airline does not know the IRR of the best alter-native investment, valuation must be based on a model that isnot dependent on this information. The ZGPM (Zustands-Grenzpreismodell, state marginal price model) is just such amodel. 15 It determines the VIU of a bundle of slots with the aidof linear programming. 16 Linear programming enables the air-line to determine the maximum price of the slot bundle basedon the company's actual investment and financing alternativeswithout the need to discount future cash flows. Rather, themodel computes the maximum amount that can be investedwith the airline reaching the identical wealth level that isachieved if the acquisition is not conducted.

For the airline, the following assumptions are made. Its plan-ning period extends over n possible future states. In the base-line situation (present state t = 0), there are m investment orfinancing objects which the airline may choose individually orcombine. Each object j is characterized by the state-contingentcash stream g- = (go, g1,, . •., g, . . ., g,) with gj being the cashflow of object j in state t. The decision variable xj indicates howoften the object (investment/financing alternative) j is under-taken. For the variables x, there may be upper bounds xj"(which can also be o). Moreover, for every state t, there is anautonomous cash flow b1, that can be negative, zero, or positive,

15 See Thomas Hering, Das allgemeine Zustands-Grenzpreismodell zur Bewertung vonUnternehmen und anderen unsicheren Zahlungsstr6men, 60 DIE BETRIEBSWIRTSCHArL-

362 (2000).16 See id.; see also JAENSCH, supra note 12, at 664-65; Hans M. Weingartner,

Mathematical Programming and the Analysis of Capital Budgeting Problems (1963);Herbert Hax, Investitions-und Finanzplanung mit Hilfe der Linearen Program-mierung, 16 SCHMALENBACHS ZEITSCHRIFT FOR BETRIEBSWIRTSCHAFTrLICHE FOR-

SCHUNG 430 (1964); Helmut Laux & Gfinter Franke, Zum Problem der Bewertungvon Unternehmungen und anderen Investitionsgutern, 13 UNTERNEHMENSFORSCHUNG

205 (1969); Matschke, supra note 7.

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and that is in no way dependent on the objects to be assessed.'If the airline pursues the goal of maximizing its wealth, it willstrive for the greatest possible sum asset value (AV) of weightedwithdrawals, where the cash flow G, in state t enters into the ob-jective function with weight w. The n+1 liquidity constraints en-sure that in each state t, the sum of all cash flows remainspositive or zero. The variables G, and xj are also limited to posi-tive values or zero. All in all, the "baseline program" (the com-bination of financing and investment options that maximizesthe airline's success without the purchase of the slot bundle inquestion) is derived from the following linear optimizationapproach:

n

max. AV; AV: = w t Gtt-0

m-E--git. xi+G t <bt VtE={f0,1,..n}

j=1

x X max VjE{1,2,...,m}

Gt~xi 0 Vt and j

The simplex algorithm allows an easy calculation of the baselineprogram resulting in an optimal AV*. Then, buying the bundleof slots at a price p is only economically viable if it at least yieldsthe optimal AV* of the baseline program.

If the airline buys the bundle of slots, it thus receives its state-contingent cash stream gK = (0, gKl, gK2, .. ., gK, . ., gK) and pays(in t = 0) the price p. The VIU must then be found, that is, themaximum price p that the airline can just afford to pay, withoutthe slot acquisition putting the company in a worse positionthan if, instead, it had implemented the available baseline pro-gram. In this manner, p must consequently be maximized, tak-ing into account the restrictions of the original decisionenvironment, extended by the cash stream from using the ac-quired bundle of slots and subject to the additional condition ofnot violating AV*. The "valuation program" (the combinationof financing and investment options that includes the acquiredslot bundle in question) is calculated by the following linear op-timization approach:

17 The cash flow b, is thus obtained from established and regular paymentssuch as salaries, ongoing revenues, or debt servicing.

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2009] THE VALUATION OF AIRPORT SLOTS 905

max. VIU; VIU:= pm

-g 0 "xi+G 0 +p <bj=1

m-I-ggj " xi + Gt <t b+gKt Vte{1,2,...,n}j=l

n

wtG < -AV*t=O

x maxx VjE{1,2,...,m}

Gt,p,xi >0 Vt and j

Again, the simplex algorithm generates the optimal solutionand thus provides not only the maximum price p* (that is, theVIU), but also the airline's optimal investment and financingprogram, restructured through including earnings from the slotbundle in exchange for the acquisition price p*.

The manner in which the VIU of a bundle of slots can becalculated by the ZGPM is demonstrated below by means of anexample, in which we consider four future states that are inter-preted as annual points in time. In order to reduce the com-plexity of the example we assume, in addition to this shortplanning horizon of four years, that the airline has only a fewinvestment and finance options. First, the airline can invest in atangible asset T (for example, an acquisition of another aircraft)which is associated with the payment stream (-80, 40, 40, 40) (inmillion euros). Second, the airline is able to invest money infinancial assets F that promise a return of 5% per annum. Fur-thermore, the airline can borrow money Mat an interest rate of10% per annum. The airline's business generates annual auton-omous cash flows b, amounting to thirty million euros. The ob-jective is to compute the VIU, which is the maximum price p*the airline could pay for the bundle of four slots. Table 1 givesan overview of the data relating to this example.

906 JOURNAL OF AIR LAW AND COMMERCE

Table 1. Data used in the example

Year t T M0 M, M2 F0 F, F2 b,(Tangible (Finance (") (") (Financial (") (") (Autonomous

asset in cash asset) cash flow inmillion flows) millioneuros) euros)

0 -80 1 -1 30

1 40 -1.1 1 1.05 -1 30

2 40 -1.1 1 1.05 -1 30

3 40 -1.1 1.05 30

Limit 1 0 . ... .

In the baseline program, the airline proceeds with the tangi-ble asset investment (acquisition of another aircraft), which is,in the first year, financed partly by means of a loan. The sur-pluses gained in the succeeding years are-after repaying theloan-invested in financial assets. At the end of the third year,the airline achieves an asset value of 160.0375 million euros. InTable 2, the described baseline program is shown with all cashstreams that occur during the four years.

Table 2. Baseline program

Year t= 0 t= 1 t=2 t= 3

Tangible asset T -80 40 40 40

Autonomous cash flow b, 30 30 30 30

Loan L 50 -55

Financial asset F, -15 15.75

Financial asset F2 -85.75 90.0375

Asset value 160.0375

With regard to the valuation program, this means that the air-line must also be able to gain an asset value at the end of thethird year of at least 160.0375 million euros after the acquisitionof the slot bundle. The maximum price p* that can be paidunder these conditions is calculated by the following linear op-timization approach. In this context, the airline forecasts cashinflows by using the slot bundle with an amount of 4 millioneuros in t = 1, 3 million euros in t = 2, and 2 million euros in t =


max. VIU; VIU: = p80 T + FO- LO + p < 30-40 T - 1.05 F0 + 1.1 L0 + F1 - L 30+4-40 T - 1.05 F, + 1.1 L1 + F 2 - L 2 30+ 3G3 - 40 T - 1.05 F 2 + 1.1 L 2 < 30+ 2

T < 1G3 > 160.0375

G3, T, F0, F1, F 2 , L0, L1, L2, p > 0

The maximum price that can be paid for the bundle of fourslots is p* = 7.8829 million euros. The valuation program in-cludes the tangible asset investment, bundle of four slots, loanin the first and second years, and financial asset investment inthe third year. In Table 3, the described valuation program isshown with all cash streams that occur during the four years.

Table 3. Valuation program

Year t=0 t= 1 t=2 t= 3

Tangible asset T -80 40 40 40Autonomous cash flow b, + 30 34 33 32slot cash flow gK,Price p* -7.8829Loan L0 57.8829 -63.6712Financial asset F, -10.3288 10.8453Financial asset F2 -83.8453 88.0375

Asset value 160.0375

As shown in the example, the simplex algorithm not only deter-mines the maximum price the airline can pay for the slot bun-dle, which is necessary in order to prevent a disadvantageousinvestment, but additionally provides the airline's optimal in-vestment and financing program, including cash flows from theslot bundle and the acquisition price p*.

Consequently, in cases when the airline does not know theIRR of the best alternative investment, linear programming candeliver the relevant maximum price. Applying linear program-ming requires first determining the maximum success repre-sented by the maximum asset value of the airlines' combinationof financing and investment options without considering thepurchase of the slot bundle. Therefore, the airline has to iden-tify current investment and finance options, and by solving asimplex algorithm, calculate the attainable value at the end ofthe investment period. Second, the airline must determine themaximum price payable in state t = 0 by solving the second sim-

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908 JOURNAL OF AIR LAW AND COMMERCE [74

plex algorithm, taking into account the additional cash flowstream generated by the slot bundle.

Although linear programming was only shown for thepurchase decision, it can likewise be applied to the decision tosell the slot bundle. For this purpose, the airline has to deter-mine the optimum value AV* of its baseline program as the firststep, including the cash flow stream generated by the slot bun-dle.'1 Second, the valuation program must be slightly modified:since the airline now considers selling the slot bundle, the valua-tion model has to derive the minimum price V that allows theairline to retain the optimum AV*, taking into account that thecash flow stream generated by the slot bundle is no longer con-sidered. Consequently, the valuation program can be calculatedby the following linear optimization program: 9

min. V; V:= pm1n--9jo " xi + Go -p< boj=lii

m-Egjt "Xj--G t b bt -gKt V t G 11,2,...,n}I

j=1

n-ywt.G t <-AV*

t=0

x xax Vj {1,2,...,m}

Gp x __ 0 Vt and j

III. VALUATION IN PRACTICE

A. SUBJECTIVE DECISION FIELDS

As the core concern of this article, the determination of theVIU is based on the subjective investment and financing alterna-tives the individual has at the moment of valuation. Unlike thissubjective perspective, discounted cash flow models 20 in finan-cial theory are based on approaches such as the Capital Asset

18 Applying the same numerical example to the disposal situation with the in-vestment in asset , the autonomous cash flow b, + the slot cash flow gK, reveals anoptimum AV* = 169.5975 million euros.

19 The continuation of the numerical example for the sale of the slots deliversthe minimum price p* = 7.8829 million euros.

20 With respect to discounted cash flow models, see generally COPELAND et al.,supra note 6, at 62-67.


Pricing Model (CAPM),21 which relies on certain premises thatare necessary for determining objective market values in marketequilibrium. As an example, Deutsche Lufthansa AG appliesthe cash value-added concept as its companywide value-basedmanagement measure. 22 In this model, a certain capital expen-diture generates additional value if cash flows exceed the cost ofcapital applied. Cost of capital applied represents the return oninvestment expected by investors and is determined using theweighted average cost of capital (WACC) which is calculatedbased on the assumptions of the CAPM. Critical assumptions ofthe CAPM include, for example, identical information of mar-ket participants and, accordingly, homogeneous expectations.Consequently, all investors hold identical portfolios of risky as-sets (that is, the market portfolio). Additionally, derived marketprices are based on the presumed possibility of borrowing andinvesting money at a constant interest rate that is available toany investor in the market.

In contrast, it is necessary to take into account the real alter-native investment and financing decisions of the subject con-ducting the valuation (that is, the subjective portfolio), so as toderive values that are relevant to decisions. This is why, in short,the VIU can also be referred to as the decision value. Thus, inprinciple, there are no limitations with respect to the number ofpossible realizations since they are specific to the respective indi-vidual. Hence, for the purpose of valuing take-off and landingrights, the airline's alternatives-the subjective decision field-could be represented by, for example, the redemption of acredit, the investment in slots at another airport, and the leaseof aircrafts to competitors, but also any other investment or fi-nancing project the airline is able to undertake. These alterna-tives have an effect on both the cash flows generated by theusage of the slots (for example, tangible asset investment T inthe linear programming example shown above) and on the rele-vant discount rate that is applied in the present value technique.

21 For specifications regarding the CAPM, see John Lintner, The Valuation of

Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,47 REv. OF ECON. & STATS. 13 (1965); Harry Markowitz, Portfolio Selection, 7J. FIN.

77 (1952);Jan Mossin, Equilibrium in a Capital Asset Market, 34 ECONOMETRiCA 768(1966); William F. Sharpe, Capital Asset Prices: A Theory of Market Equilibrium UnderConditions of Risk, 19J. FIN. 425, 427, 433-34 (1964).

22 See DEUTSCHE LUFTHANSA AG, supra note 10, at 39.

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B. BUNDLE PROBLEM

As mentioned in Section II. A., the VIU must generally be cal-culated not for a single slot, but for a bundle of at least fourslots. This may constitute a problem because the valuation com-putes the price limit for the four slots together. Yet, it is fre-quently the case that four slots cannot be purchased in onetransaction. In other words, the airline has the challenging situ-ation of negotiating more than one slot transaction. For exam-ple, the airline may be engaged in two negotiations (first, buyinga take-off and a landing right at Airport A, and second, buying alanding and a take-off right at Airport B), for which the sum ofthe two individual price negotiations must not exceed the VIUof the bundle of four slots. In many cases, it will not be possiblefor the airline to conduct parallel negotiations, such that succes-sive acquisitions of the four slots are often the only practical so-lution. In these situations, the airline bears the risk of beingable to buy part of the slot bundle in the first negotiation butnot the entire bundle because the price limit for the bundle isexceeded in the second negotiation. However, in such a case,there are two ways out of the dilemma, either by buying otherslots as a substitute (for example, landing and take-off rights atAirport C) or reselling those parts of the slot bundle that havealready been purchased.

Apart from the situation in which at least four slots are valuedaltogether, constellations may also be found where a VIU mustbe calculated for less than four slots. This can occur, for exam-ple, if an airline in the European Union receives take-off andlanding rights in Stockholm and landing and take-off rights inFrankfurt from the national authorities, but wishes to buy take-off and landing rights at London Heathrow for flying Heathrow-Frankfurt instead of Stockholm-Frankfurt. In order to deter-mine the VIU of the two Heathrow slots that the airline plans tobuy, only the cash flow changes that occur through the slot ac-quisition, in comparison to the initial constellation, must thenbe taken into account. Section III. D. 1. presents an exemplaryspecification of this practical valuation task.

C. PROBLEM OF UNCERTAINTY

In addition to considering the subjective alternatives at agiven point in time for the determination of decision-relevantvalues, the airline undertakes the difficult task of estimating theelements needed to calculate the slot value. These include, for

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example, the turnover earned from passenger and freight trans-port, expenses associated with aircraft and airports, and the dis-count rate. All of these quantities will occur in the future, thatis, they are uncertain and must therefore be forecasted. Thisuncertainty cannot be eliminated, but it is useful to integratethe likely effects visibly into the slot value. A risk analysis basedon a Monte Carlo simulation 2

1 is a particularly suitable instru-ment for this purpose. It computes the statistical distribution ofthe VIU, based on the assumed distributions of the elementsused for the valuation. In order to conduct the risk analysis, theairline must perform three steps. First, it must estimate the pos-sible range of magnitudes of each element entering into the val-uation (turnover, expenses, discount rate) and the probabilityof each magnitude occurring. Second, for each uncertain ele-ment, a particular amount is selected at random from the distri-butions assumed in step one, and the value of the slot bundle iscalculated using these selected amounts. This selection of mag-nitudes is repeated several times with the aid of a computer, andthe value calculated on the basis of each selection is saved. Ifthis process is repeated often enough, the frequency distribu-tion of the VIU evolves from these calculations. After this fre-quency distribution has been determined, the interpretation ofthe results follows as step three. In addition to the calculation ofmeans and medians, it is particularly useful to transform the re-sults into diagrams, for example into a histogram or a risk pro-file. The results of the risk analysis are of considerablesignificance to the airline because they show the complete rangeof possible outcomes of the VIU of the slot bundle and theirrespective probabilities. It is the airline's individual decision asto how to apply these results to identify a certain VIU, that is, toset a specific price limit for the slot bundle. For example, a risk-neutral airline will choose the mean VIU as the price limit, butan airline that prefers to take certain risks will choose a pricelimit that exceeds the mean. The application of a Monte Carlosimulation in practice will be shown in Section III.D.2.

23 See generally David B. Hertz, Risk Analysis in Capital Investment, 42 HARV. Bus.REV. 95 (1964); William Gibson & Peter Morrell, Theory and Practice in AircraftFinancial Evaluation, 10 J. AIR TRANSP. MGMT. 427 (2004).

2009]


D. EXEMPLARY SLOT VALUE DETERMINATION

1. The Consideration of Real Alternatives

For the purpose of presenting some of the valuation situationsthat arise in practice, it is appropriate to refer again to the ex-ample introduced in Section II.A. as our base case: we consideran airline that owns a take-off and a landing right at Airport Aand a landing and a take-off right at Airport B. The companyforecasts that flying between A and B will lead to periodic netcash flows of three million euros that remain constant over thefuture periods one to three (for the sake of simplicity, we as-sume just three future periods of slot usage). As shown in Sec-tion II.A., the maximum price the airline should be willing topay, considering the IRR of its best alternative investment of 4%,amounts to 8.33 million euros.

As a variation of the airline's realizable investment portfolio ata given moment, let us now assume that immediately (that is,one logical second) after the acquisition of the slot bundle forserving the route A to B (in the analysis below, it is assumed thatthe airline had to pay its maximum subjective acquisition priceof 8.33 million euros at locations A and B, so that the transac-tion is neither advantageous nor disadvantageous, but is, never-theless, conducted), the airline has the chance to acquire a take-off and landing right at Airport C. The airline now considerswhether it is financially advantageous to include destination Cin its route network.

In a situation like this, the airline can-in addition to main-taining the status quo (that is, serving the route A to B)-chooseamong the following two investment strategies. First, the airlinecould consider whether it is advantageous to include Airport Cas an additional destination in its flight plan with the conse-quence that Airport C could be approached from either AirportA or B (Alternative (a)). Second, the airline could considerwhether it could also be beneficial to acquire the slots at AirportC, while at the same time selling the already acquired take-offand landing rights at, for example, Airport B (Alternative (b)).Hence, slots at Airport C would represent a substitute for therights at Airport B. The appraisal of the two investment alterna-tives are carried out separately below:

Regarding Alternative (a)--the assessment of the strategy to in-clude Airport C as an additional location in the flight plan-theairline forecasts constant periodic net cash flows of 5 million eu-ros over the periods one to three. That is, adding Airport C to

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the route network leads to a rise in the cash flow per periodACFt of two million euros. Because the airline knows that theIRR of its best alternative investment is 4%, the VIU of the bun-dle of landing and take-off rights at Airport C is calculated as:

(7) VU =- ACF.t=1 (1I+ i)t

Entering the data from the example, it follows:3 2 million euros

t= (1.04)t

= 5.55 million euros.

That is, for the two slots at Airport C, the airline can afford topay a maximum price of 5.55 million euros. If it paid more, theacquisition of the slots at Airport C as an additional destinationwould be disadvantageous, and the transaction should not beexecuted.

In order to illustrate the decision process, it is furthermoreassumed that the airline can acquire the take-off and landingright at Airport C for four million euros. Consequently, sincethe actual acquisition price is lower than the subjective maxi-mum price of 5.55 million euros, the acquisition and additionaloperation to Airport C is beneficial to the airline (it is assumedthat the airline has four million euros available in liquid fundswhich would be invested and yield 4% if the acquisition does nottake place). Thus, after the airline has also acquired the slots atAirport C, its flight operations between A, B, and C generateperiodic net cash flows of 5.0 million euros with a VIU of 13.88million euros, while the total acquisition price amounts to 12.33million euros. Hence, Alternative (a) yields an IRR of 10.50%. Anoverview of the investment characteristics with respect to Alterna-live (a) is shown in Table 4.

Table 4. Investment overview Alternative (a)

Year t=0 t=I t=2 t=3

IRR of best alternative investment 4.00%Acquisition of slots at Airports A and B -8.33Acquisition of slots at Airport C -4.00Slot cash flows 5.00 5.00 5.00Value in use (discount rate 4.00%) 13.88Total acquisition price 12.33IRR Alternative (a) 10.50%

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With respect to Alternative (b)-the valuation of the acquisi-tion of the slots at Airport C while selling the slots at Airport B-it is assumed that the switch of Airports from B to C leads to arise in the net cash flow per period of 0.5 million euros over theperiods one to three. Additionally, because the airline can fi-nance the acquisition of the slots at Destination C from its liquidfunds, it can reinvest the money that is received from the dispo-sal of the slots at Airport B in a financial asset yielding the origi-nal best rate of 4%. For quantification reasons it is thenassumed that, besides the acquisition of the slots at DestinationC amounting to four million euros, the slots at Airport B can besold for 2.5 million euros. Consequently, the reinvestment of2.5 million euros yields periodic interest payments of 0.1 millioneuros and the redemption of 2.5 million euros in t = 3.

Since the IRR of Alternative (a) of 10.50% exceeds the IRR ofthe best alternative investment of 4% at the starting point of theexample, it is the new benchmark for assessing whether Alterna-tive (b) is preferred to Alternative (a). Applying the rate of10.50% in order to determine the subjective VIU of Alternative(b) reveals a value of 10.73 million euros. Given that the acquisi-tion of the slots at Airport C requires the investment of 4.0 mil-lion euros and the initial investment in the slots at Airports Aand B of 8.33 million euros,2 4 Alternative (b) is not beneficialcompared to the realization of Alternative (a) since the investedamount exceeds the airline's VIU. Table 5 summarizes the re-sults of the appraisal of Alternative (b):

Table 5. Investment overview Alternative (b)

Year t = 0 t = 1 t - 2 t = 3

IRR of best alternative investment 10.50%Acquisition of slots at Airports A and B -8.33Acquisition of slots at Airport C -4.0Disposal of slots at Airport B 2.5Slot cash flows 3.5 3.5 3.5Cash flows from reinvestment -2.5 0.1 0.1 2.6Value in use (discount rate 10.50%) 10.73Total amount invested 12.33IRR Alternative (b) 3.54%

The example presented above underlines the critical impor-tance of considering the valuation subject's individual invest-

24 Because the proceeds from the disposal of the slots at Airport B are rein-vested, the total amount invested remains at a constant level of 12.33 millioneuros.

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ment and financing options at a given point in time. If it is theintention to determine subjective maximum (purchase deci-sion) or minimum (disposal decision) prices that prevent disad-vantageous situations, any change in the range of an individual'spossible investment and financing realizations affecting bothcash-flow streams and the discount rate must be taken intoaccount.

2. The Consideration of Uncertainty

In the following analysis, the valuation of slots using risk anal-ysis is shown for the example already presented in SectionIII.D.I., which has been modified slightly for this purpose:

We still assume that an airline knows the IRR of its best alter-native investment, which is 4%. It is further assumed that thisrate is constant over time and is also certain. With respect to thefuture cash flows that can be earned from the slot bundle, theairline forecasts, based on market research and existing freighttransport contracts, a certain surplus of three million euros in t= 1. Due to the difficulty of predicting future market develop-ments, the earnings in the following periods are uncertain, sothat the airline forecasts earnings for the periods t = 2, t = 3, andt = 4 to -, are subject to a normal distribution with the expectedvalues (3.25, 3.50, 3.75) (in million euros) and the standard de-viations (0.25, 0.50, 0.75). From ten thousand calculationprocesses, the following histogram of the slot bundle's VIU isobtained.

240

0,02 -...........................................

180

1200 ,0 1 --- -- --- -- --- -- --- -- ----- ---.I-- --- -- --- -- --- -- --- -- --

60

60.00 80.00 100.00 120.00 40

in million euros

Table 6: Histogram of VIUThe mean VIU amounts to 92.3 million euros. A presentationof the risk-analysis results equivalent to the histogram yields the

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risk profile shown in the following table. It demonstrates thelikelihood of the VIU exceeding a certain level on the abscissa.For example, the likelihood is 56.06% that the value of the slotswill exceed ninety million euros.

1,00 9.950

0,75 ---

0,50 --

0,25

60.00 80.00 100.00 120.00

in million euros

Table 7: Risk profile of VIU

As explained above, it depends on the airline's individual riskpreference whether it chooses a maximum price in the acquisi-tion process below the mean value of 92.3 million euros (riskaverse), a maximum price that is equal to the mean value (riskneutral), or an amount exceeding the mean value (riskfriendly).

IV. SUMMARY

Airlines that intend to buy take-off or landing rights, as is pos-sible in the United States and United Kingdom, must, first of all,determine a value for these slots. The aim is not to calculate anobjective market value, but to identify the subjective VIU thatthe slots have for the airline in question. The VIU indicates themaximum price the airline can spend on the slots without thetransaction being disadvantageous. In order to compute thisprice limit, a simple present value technique can be used if theairline knows both its best alternative investment compared tothe slot acquisition and the IRR of this investment. The latter isused as the discount rate in the present value technique. If theairline does not know the best alternative investment because ofits very complex investment and financing portfolio, the slot val-uation can be based on linear programming, that is, the ZGPM.Two problems occur within the context of the valuation. First,the bundle problem results from the fact that the value can gen-

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2009] THE VALUATION OF AIRPORT SLOTS 917

erally be calculated only for a bundle of at least four slots, butpurchasing these slots is often possible only in several individualtransactions. The sum of the prices negotiated in these individ-ual transactions must not exceed the VIU, which takes into ac-count the airline's alternative investment and financingprojects. Furthermore, there is the problem of uncertainty, be-cause the valuation must always be based on magnitudes that areobtained in the future. This uncertainty cannot be eliminated,but its effects on the slot value can be identified with the help ofa Monte Carlo simulation.

ILAS. I

the valuation of airport slots - smu

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