Procurement Decisions in the Airline Industry

Table of Content

List of Figures

List of Tables

Executive Summary

Chapter 1:Introduction
1.1. Purpose/ Objective of
1.2. Structure of this

Chapter 2: Literature Review on Real
2.1. Standard Real Options
2.2. Real Options Literature on Aircraft

Chapter 3: Airline Industry
3.1. Risks in the Airline
3.2. Acquisition and Economic Evaluation of

Chapter 4: Methodology (1)
4.1. Capital
4.1.1. Net Present
4.1.2. Real Options
4.1.2.1. Different Types of
4.1.2.1. Determination of Option

Chapter 5: Case Study in the Airline
5.1. Overview of the Case
5.2. Assumptions of the Case
5.3. Factors of
5.4. Analysis of the Case
5.5. Analysis of the Purchase Option
5.6. Recommendations for “Airline Limited”
5.7. Problems and

Chapter 6: Literature Review on

Chapter 7: Methodology (2)
7.1. Procurement Decisions and Bargaining Power in Bilateral
7.2. Hold-up
7.3. Bargaining
7.3.1. Bargaining with Symmetric
7.3.2. Bargaining with Asymmetric

Chapter 8: Analysis of Strategic Power for the Airline-Aircraft
8.1. Procurement Decisions and Bargaining Power in the Airline
8.2. Hold-up Problem in the Airline
8.3. Bargaining Problem in the Airline
8.3.1. Bargaining with Symmetric
8.3.2. Bargaining with Asymmetric
8.3.3. Comparison and Limitations of the different Bargaining

Chapter 9:Conclusion

Bibliography

List of Figures

Figure 1: Revenue passenger miles from US American airliners [US Department of Transportation, 2009]

Figure 2: Upside and downside potential in the airline industry [adapted from Gibson and Morrell, 2004, p. 431]

Figure 3: Three steps of BOPM approach

Figure 4: The analysis of the purchase option case involves three steps

Figure 5: Monte Carlo Simulation: Distribution of the present values of the purchase option case (PV3)

Figure 6: Histogram depicting the relationship ln(PV3/PV0)

Figure 7: Relationship between PV3 and PV0

Figure 8: Hold-up in buyer-seller relationships

Figure 9: Hold-up problem between Airbus and “Airline Limited” when acquiring an aircraft

List of Tables

Table 1: Differences and similarities between financial and real options [adapted and modified from Cobb and Charnes, 2007, p. 177]

Table 2: Features of Airbus A320

Table 3: Boeing: Current Market Outlook (2008-2029)

Table 4: Airbus: Global Market Forecast (2006-2026)

Table 5: Cash-outflows for Airbus A320 for base year 0 (US Department of Transportation (Form 41))

Table 6: Commit now

Table 7: Option to purchase

Table 8: “Commit now” scenario

Table 9 : Sensitivity analysis of the “commit now” case

Table 10: Assumptions of purchase option for Airbus A320

Table 11: Event tree and binomial lettice for the aircraft purchase option

Table 12 : Application of Black-Scholes formula to the aircraft purchase option

Table 13: Different bargaining scenarios for the trade surplus

Executive Summary

This paper provides an insight into how the value of a European call option in the airline industry is calculated and how the surplus of the trade is divided between two companies. Airbus and the hypothetical company “Airline Limited” are used to illustrate these cases.

Two approaches, the Binomial Option Pricing Model and the Black-Scholes formula are used to determine the option value. Furthermore, bargaining power, the hold-up problem and the trade surplus are analyzed. The results suggest that it is more valuable for the hypothetical company “Airline Limited” to use the call option than to invest in the “commit-now” scenario. The application of the concept of bargaining power and the division of the trade surplus indicate that “Airline Limited” has a stronger bargaining position and will get a higher amount of the trade surplus than the aircraft manufacturer.

Most approaches in current literature focus either only on the real options approach or the bargaining problem and the hold-up problem. This paper applies both methods to the airline industry.

Chapter 1: Introduction

Over the last two decades, real options analysis (ROA) has become a fundamental part of project evaluation. Its increasing use in academia and corporations as well as its application to a wide range of industries make it a valuable tool in finance and accounting departments around the world. Classical capital budgeting approaches like net present value (NPV) techniques do not account for additional flexibility and are therefore a very static measurement.

In addition to this, a further core factor is the strategic aspect of the investment decision. Companies often make decisions according to strategic reasons. This raises the question of how the bargaining power is divided between a seller and a buyer. Furthermore, the influence of the hold-up problem on the two involved players is analyzed. Finally, the trade surplus of the investment is divided between the seller on the one hand and the buyer on the other hand using a game theoretic approach to model this relationship. The airline industry is examined in this paper as it offers many possibilities to apply and explain the concepts of real options and bargaining in bilateral negotiations.

1.1. Purpose/ Objective of Study

This paper sets out to analyze the value of flexibility of an investment decision and discusses, in a second step, how the strategic power between the two parties involved is allocated. In academic literature, limited research has been done to find out about the combination of a real options analysis and the distribution of the trade surplus between the different players involved.

This presents the following questions: Does an option in terms of the purchase of an aircraft have additional value in comparison to a classical and inflexible “buy now” decision for an airline? If this is the case, how much is this value worth and how is the trade surplus distributed between the two parties involved? Are there any hold-up problems? The following chapters will examine and answer these issues.

1.2. Structure of this Paper

Chapter two deals with a literature review on standard real options analysis in general and the airline sector in particular. In chapter three, background information about the airline industry is given and it is stressed why this sector is used for the capital budgeting approach. Chapter four covers the methodology that is used in chapter five. In this chapter, a case study involving the purchase decision of an aircraft is discussed using different methods to analyze the “commit-now” and purchase option scenario. Chapter six introduces the strategic aspects discussed in this paper and gives a literature review on bargaining. In chapter seven, the methodology to analyze the hold-up problem as well as the bargaining problem is explained. In a last step, chapter eight applies these concepts to the relationship between an aircraft manufacturer and an airline. Chapter nine concludes and proposes potential future research interests.

Chapter 2: Literature Review on Real Options

In corporate finance, real options are the most significant appliance for decisions under uncertainty in capital budgeting [Berk and DeMarzo, p.717]. Graham and Harvey (2001) came to the conclusion that only 27% of US firms have already employed real options to analyze investments. During the last twenty years, the concept of real options to analyze uncertain investments has been gradually adapted from practitioners as well as researchers [Grenadier, 2002].

2.1. Standard Real Options Literature

The standard literature on real options is used to differentiate this method from static valuation techniques such as net present value [Dixit and Pindyck, 1994]. Whereas NPV techniques assume passive managers with simple “now or never” investment decisions, real options methods are harder to evaluate since they include a strategic impact on the decision making process [Smit and Trigeorgis, 2007].

The concept of real options was initially focused on growth options but expanded towards deferral, learning, and shrinkage options [Kester, 1984; Trigeorgis and Mason, 1987]. Academic literature was originally concerned about options in isolation [McDonald and Siegel, 1986; Majd & Pindyck, 1987] before interactions between various options were developed [Brennan and Schwartz, 1985; Trigeorgis, 1993]. In recent years, interaction between the investment decision and strategic value for the players has been of paramount importance. Smit and Trigeorgis (2004) suggest that an option should not be considered as an isolated investment decision but in the context of a combination of a game-theoretic approach and the evaluation of the option.

Different valuation methods for financial options developed by Black and Scholes (1973) and Cox, Ross and Rubinstein (1973, 1979) have been adjusted to be applicable to real investments in order to overcome the pitfalls associated with static techniques [Myers, 1987; Trigeorgis & Mason, 1987].

Real options are now applied in various industries and corporations. For example, real options are used in oil drilling and mining companies, for research and development projects as well as in the telecommunications and airline sector [Brach, 2003].

The main advantage of real options is that this concept allows accounting for uncertainties. Long time ranges complicate the process of foreseeing unknown events. Net present value approaches tend to be static measures that do not permit changes or modifications in the future once a decision about a project has been made. Additionally, the real options model contains a learning procedure that helps managers to make sophisticated decisions when uncertainty has been resolved due to events, actions and certain points in time [Leggio, Bodde, Taylor, 2006]. This approach takes into consideration numerous paths that are a result of high uncertainty combined with the possibility of choosing the best responses once updated information is obtainable [Leggio, Bodde, Taylor, 2006]. It is highly recommended to use the net present value approach in connection with the real options approach.

Kester (1984) observed that real options have the highest value when competing projects have similar NPVs. Copeland and Antikarov (2001) add that real options analysis is most valuable when managers dispose of flexibility to reply to changes in the market environment. Bowman and Moskowitz (2001) conclude that real options analysis is beneficial as it stimulates financial managers to anticipate changes proactively and creatively. In addition to these issues, real options question the type of future investments that are about to be exerted.

It has to be kept in mind that the real options concept also has pitfalls. Investments are usually affected by more than one source of uncertainty [Cobb and Charnes, 2004] which complicates the application of the evaluation methods. Furthermore, there is a potential deficiency of structure. Real options are difficult to quantify as every setup is different and involves various assumptions concerning the parameters. A further problem becomes apparent in a market with a small number of competitors because different options may interact [Brealey, Myers, Allen, 2008].

2.2. Real Options Literature on Aircraft Evaluation

Most research on real options and aircraft evaluation has been done from the perspective of the aircraft manufacturer.

Stonier (1998) wrote an article on aircraft delivery and switch options and depicted the option value as a function of option time to maturity and mean reversion. He concluded that the longer the maturity and the higher the volatility, the bigger is the value of the option.

Clarke and Miller (2004) applied real options to evaluate the production and development of new aircraft models using a system dynamics model. They concluded that for this particular case, the option premium exceeded the strike price and the value of the defer option was small.

In 2007, Mathews and Johnson used real options for “The Boeing Approach”. They discussed an example using an unmanned aerial vehicle (UAV) to value a growth option from Boeings` point of view.

Brealey, Myers and Allen (2008) compared an aircraft purchase option with the “wait and decide later” scenario. They found out that the purchase option case always yields higher returns than the waiting strategy since there is always the possibility to let the option expire and renegotiate the contract.

Chapter 3: Airline Industry Background

In the last twenty years, airlines in Europe (Lufthansa, British Airways, Iberia), Latin America (LAN Chile), and recently in Asia (China Southern, Thai International) have been privatized. In the United States, the airline market was deregulated in 1979, which resulted in increasing competition and decreasing air fares [Gowrisankaran, 2002, p.1]. This tendency away from government funding and ownership towards privatization has led to the necessity for financially sound and transparent investments to maintain and improve profitability and growth in the airline industry [Gibson and Morrell, 2004, p.428].

The airline sector is immensely dependent on the status of the economy. This market can be described as highly competitive and demand for air travel is elastic. Increasing pressure on prices is due to the rising numbers of low-cost carriers which make life complicated for incumbent airlines [Grimm, Lee, Smith, 2006, pp.52-57].

The worldwide airline industry comprises more than 2,000 airlines operating roughly 23,000 commercial aircrafts connecting to over 3,750 airports. In 2007, more than 2.2 billion passengers were transferred and 29,000 flights were executed [Air Transport Action Group, 2008, p.4]. The market of aircraft producers is of duopolistic structure and dominated by Airbus and Boeing [Grant, 2008, p.106]. During the last thirty years, air travel increased by approximately 5% annually, with high fluctuations because of varying economic trends and different growth rates in various countries [Belobaba, 2009, p.2].

Demand for air travel is usually measured by revenue passenger miles (RPM) and figure 1 shows the development of RPM of US American airliners from 1998-2008.

Figure 1: Revenue passenger miles from US American airliners [US Department of Transportation, 2009]

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3.1. Risks in the Airline Sector

The aerospace sector exhibits large specific risks. High capital intensity in terms of expensive production goods (e.g. aircrafts), strong fluctuations in demand and homogeneity of the product make investments in this sector risky and volatile. Furthermore, unstable fuel prices complicate the planning process and lead to additional uncertainty [Joppien, 2002, pp.113-115]. The following figure depicts the upside chances and the downside risks of an investment decision in the airline sector.

Figure 2: Upside and downside potential in the airline industry [adapted from Gibson and Morrell, 2004, p.431]

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3.2. Acquisition and Economic Evaluation of Aircrafts

Generally, there are two ways for an airline to acquire an aircraft: operating lease or purchase. Operating leases make up for about 25% of new aircrafts whereas purchases represent the remaining 75%. Leases have the advantage of low-initial cash outflows and risk reduction in terms of residual value. Purchases save the buyer the leasing fee and enable him to decide upon the selling date [Gibson and Morrell, 2004, p.428]. The case study in chapter five takes into account the purchase decision of an aircraft.

The decision to buy an aircraft involves large capital expenses. The list prices for Airbus aircrafts start at 59.1 million United States Dollars (USD) for an A318 and go up to 327.4 million USD for the largest commercial aircraft, the A380 [Airbus, 2008, p.1]. Due to the high inherent risks in this sector, it is therefore strongly important to properly evaluate such an investment decision.

Belobaba (2009, p.153) claims that airline fleet decisions are among the most vital long-term strategic decisions for an airline. The decision to purchase an aircraft has a direct influence on an airlines’ overall financial position and its operating costs. In addition, large capital investments are committed which affect the long-term economic horizon of an airline.

For the economic evaluation of an aircraft, airlines are well-advised to use cash-based methods such as net present value techniques and real options analysis. Gibson and Morrell (2005, p.19) found out that traditional approaches such as NPV are still more extensively used than real options techniques in the airline sector. Managers have an apparent tendency to counterbalance the uncertainty and volatility in the airline industry with artificial additions to the discount rate. A better approach involves a moderate and average discount rate and adjusting for volatility utilizing Monte Carlo Simulation. Afterwards, the expected net present value is computed and real options used to account for flexibility in the investment decision [Gibson and Morrel, 2004, p.428].

The main problem that airline managers face is long lead times. Lead times refer to the time between ordering and delivering an aircraft. These time spans can increase to several years, even though it might be the case that airlines have no need for the planes in the future [Brealey, Myers, Allen, 2008, p.67]. This aspect highlights the importance of purchase options for the airline industry.

A purchase option can further be regarded as a call option. The airline has the right, but not the obligation to make use of the option [Brealey and Myers, 2003, p.631]. For example, Airbus uses real option analysis in order to value purchase options for airlines [Miller and Bertus, 2005, p.226]. Triantis and Borison (2001, p.14) refer to the purchase option as a “typical application of the binomial model” because it includes a single underlying uncertain variable (the NPV of the project) which consists of additional uncertain factors.

Chapter 4: Methodology (1)

Chapter four gives an overview about the methodology that is used for capital budgeting in the case study in chapter five.

4.1. Capital Budgeting

In finance literature, capital budgeting is defined as “the process of planning and managing a firm`s long-term investments” [Ross, Westerfield, Jordan, 2006, p.2]. The basic idea behind this concept is to generate value for a company. This goal is accomplished when investments are undertaken that are more valuable than the costs of obtaining them. In terms of cash-flows, which are mostly applied to investment decisions, it means that the value of the cash-inflows of a project surpasses the value of the cash-outflows [Brealey, Myers, 2003, p.5].

Financial managers may use several evaluation methods to quantify and analyze investment decisions. Different traditional investment criteria such as discounted cash-flow (net present value, internal rate of return), payback approaches (payback period) and accounting rules (average accounting return) are utilized to decide upon the value of projects and help rank them [Ross, Westerfield, Jordan, 2006, p.286].

A survey of 4,400 firms in the United States undertaken by Graham and Harvey (2001, p.198) revealed that discounted cash flow techniques are used by 75% of the Chief Financial Officers interviewed, whereas other methods such as payback period and average accounting return are employed by only 56% and 20%, respectively. Thus, NPV techniques are used by most financial managers in the corporate environment and will also be used and explained in this dissertation.

4.1.1. Net Present Value

The net present value (NPV) of an investment is defined as “a project’s net contribution to wealth” and is therefore represented by the present value of future cash flows minus the initial outlay [Brealey and Myers, 2003, p.1046].

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Where:

Ct = cash inflows

C0 = cash outflow

r = cost of capital

T = number of periods

If this number is positive, the project adds value to a company. The advantage of the NPV is that it takes into account the time value of money, considers cash-flows rather than accounting income and adjusts the risk of future cash-flows by applying the cost of capital [Brealey and Meyers, 2003, pp.92-94].

The disadvantages of using NPV include the problem of estimating the accurate cost of capital as well as a possible change in it as projects become more or less risky over their lifespan. NPV techniques disregard the value of flexibility (static measure) which is intrinsic to many investment decisions [Kester, 1984, pp.153-154]. This traditional approach cannot account for uncertainty in investment decisions. Furthermore, according to Copeland and Antikarov (2001, p.5), NPV calculations underestimate the value of every project by not valuing flexibility.

In general, future events may make it attractive for decision makers to alter initial projects by expanding them or launching new technologies at a later point in time [Kester, 1984, p.155]. Another important pitfall of traditional approaches is that the value of strategic assets is not embedded in these methods [Boer, 2002, p.54]. Therefore, different approaches are needed to explain these issues in order to quantify investments adequately.

4.1.2. Real Options Analysis

The concept of real options has been adapted from financial options. Copeland and Antikarov (2001, p.5) define real options as

“the right, but not the obligation, to take an action (e.g. deferring, expanding, contracting, or abandoning) at a predetermined cost called the exercise price, for a predetermined period of time – the life of the option”.

The main differences and similarities between financial options and real options are listed in table 1.

Table 1: Differences and similarities between financial and real options [adapted and modified from Cobb and Charnes, 2007, p.177]

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Charnes (2007, pp.188-189) divides three applications of real options into three different types: Investment or growth options involve the possibility to increase investments when favorable circumstances occur. Deferral or learning options describe opportunities to postpone investments until more information is received. Disinvestment and shrinkage options take into consideration that new information might decrease expected payoffs of a project and make it possible to close down or decrease investments before completion. Deferral options are one of the focus points in this dissertation.

4.1.2.1. Different Types of Options

Two types of options are distinguished in practice and academic literature, namely put and call options. Put (call) options give the owner the right but not the obligation to sell (buy) an asset at a specified price at a specified point in time [Hull, 2006, p.6]. Call options are exercised when the price of the underlying exceeds the price of the strike [max (S-K, 0)]. Put options are exercised when the price of the underlying decreases below the strike level [max (K-S, 0)]. American options can be exercised at any time during the life of the option whereas European options can only be exercised at the expiry date. Options limit downside losses as they do not have to be exercised, but they still incorporate the advantage for upside gains.

4.1.2.2. Determination of Option Value

There are different possibilities to determine the value of an option:

In a first method, options can be valued by the Binomial Option Pricing Model (BOPM). This approach goes back to Cox, Ross and Rubinstein^[1], and assumes that stock prices can only have two possible values at the end of the following period (discrete time approach). Therefore, the payoff of an option can be calculated by constructing a replicating portfolio consisting of a risk-free bond and an underlying asset [Berk and DeMarzo, 2006, p.686]. The smaller the subperiods are, the more accurate the value of the option becomes [Brealey, Myers, 2003, p.601]. Large numbers of periods and little movements in the price of the underlying will therefore lead to a realistic value of the option [Berk and DeMarzo, 2006, p.693]. In the following, three steps are explained to determine the value of an option using the BOPM approach:

Figure 3: Three steps of BOPM approach

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The first step involves the creation of the binomial tree which is built by working forward from time zero to the expiration date. At each step, the underlying can either move up or down by a particular factor (u or d, where u ≥ 1 and 0 < d ≤ 1). If S is equal to the underlying (current stock price), then the stock price in the following period will be either: Su = S*u or Sd = S*d.

The up and down factors depend on the volatility (σ), the duration of the option (T) and the number of steps (n):

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The BOPM approach assumes that an up and down move yields the same result as a down and up move. This characteristic decreases the number of tree nodes. The value at T is equal to:

Abbildung in dieser Leseprobe nicht enthalten

Where:

n = number of up moves

S0 = asset value at the start

The second step involves the determination of each closing node using [max (S-K, 0)] for call and [max (K-S, 0)] for put options.

In the third step, risk-neutral probabilities are calculated to determine the value at each node. In the Binomial model the option price can be computed without knowing the probability of each potential subsequent stock price. Risk-neutral probabilities assume that the probabilities of the outcomes are known. Therefore, the expected payoff of an option can be computed with net present value techniques.

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Where:

Pu = risk-neutral probability of an up move

Pd = risk-neutral probability of a down move

rf = risk-free rate of interest

The following equation is then applied for the valuation of assets using risk neutral probabilities:

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Where:

C0 = market value in period 0

Cu = value of asset after an up move

Cd = value of asset after a down move

The advantage of the BOPM approach is that decisions can be conducted at discrete points in time when new information has become available. The disadvantage is the estimate of the appropriate cost of capital.

A second method to determine the value of an option is the Black-Scholes Model^[2]. This approach has had a vast influence on option pricing since its invention in 1973 by Fischer Black and Myron Scholes. The Black-Scholes Model can be inferred from the Binomial Option Pricing Model. The number of time periods of the option needs to increase infinitely, while the period’s length eventually expires [Hull, 2006, p.281]. The result is that the “distribution of possible stock price changes approaches a lognormal distribution” [Brealey, Myers, 2003, p.602]. A lognormal distribution considers that the price of the underlying can never decrease by more than 100%, but there is a possibility that it increases by much more than 100% [Brealey, Myers, 2003, p.603].

The Black-Scholes method presumes that the value of a project follows a geometric Brownian Motion stochastic process [Charnes, 2007, p.190]. By this process the return of the stock in a small period of time is normally distributed and the returns in two overlapping periods are unrelated [Hull, 2006, p.276]. The calculation of the Black-Scholes price of a call option on a non-dividend paying stock is illustrated in the following formula:

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Where:

S = current price of the stock

T = number of years left to expiration

rf = risk-free interest rate

K = exercise price

σ = annual volatility (standard deviation) of the stock`s return

N(d) = cumulative normal distribution

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And:

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The advantage of the Black-Scholes method is that only five parameters are needed to obtain a price for an option. However, for real options, there is no single volatility factor as risk usually consists of more than just one variable and interrelated decisions are not considered. In order to determine the standard deviation of a project with more than one uncertain variable, a Monte Carlo Analysis can be used.

A Monte Carlo Simulation is a valuable tool to carry out risk analysis for discounted cash flow models. Random values of at least two uncertain variables will be created frequently to simulate different payoffs which are built on predefined probability distributions [Mun, 2006, p.61]. The advantage of Monte Carlo Analysis is that it can calculate values for different scenarios at the same time [Brealey, Myers, 2006, p.263].

There are similar underlying assumptions in both the Binomial Model and the Black-Scholes formula. They may assume, for example, that a perfect capital market exists and interest rate and volatility remain constant over the life of the option [Hull, 2006, pp.381-283]. Copeland and Antikarov (2001, p.205) refer to the Binomial Option Pricing Model as the limit of the Black-Scholes formula. If the BOPM is extended to a continuous time form by accounting for an increasing frequency of time intervals and no dividends are paid, the value of a European call option will approach the value calculated by using the Black-Scholes formula.

Chapter 5: Case Study in the Airline Industry

Chapter five illustrates a case study on capital budgeting in the airline industry. Different approaches and techniques are applied, quantified and finally analyzed. At the end, recommendations of actions and limitations are discussed.

5.1. Overview of the Case Study

This case study deals with a NPV and real options analysis (ROA) in the airline industry. It shows the “commit now” scenario using the traditional discounted cash flow method and the implementation and evaluation of the “option to purchase” case considering the perspective of an airline.

In this case study, the hypothetical company “Airline Limited” is used to explain different capital budgeting techniques in the airline industry. It should be mentioned that its basic characteristics concerning routes and passengers resemble those of US Airways or Southwest and other incumbent and low-cost airlines in the United States. The data for flight operating expenses for the aircrafts were adapted from the US Department of Transportation (Form 41)^[3]. They are average values for different aircraft types of all airlines operating in the United States. The cost of capital applied is an average for the worldwide airline industry. The lifespan of the aircraft has been set to nine years since maintenance costs tend to increase exponentially afterwards. Furthermore, a salvage value has been assigned to the aircraft after nine operating years (see lifespan).

“Airline Limited” hypothetically decides to acquire a new Airbus A320 passenger jet. The Airbus A300 family is considered to be the most efficient aircraft fleet. Typical routes include New York (United States) – Paris (France) or Boston (United States) - New York (United States). The Airbus A320 family fleet as well as the Boeing 737 fleet operate in the single-aisle segment which is the most important niche for airlines and manufacturers. It represents 70% of all aircraft deliveries [Airbus: Global Market Forecast 2006-2026].

The features of the Airbus machine are presented in table 2:

Table 2: Features of Airbus A320

Abbildung in dieser Leseprobe nicht enthalten^[4]

5.2. Assumptions of the Case Study

“Airline Limited” can choose between (1) acquiring an Airbus A320 aircraft now or (2) buying an option to purchase the plane in the future.

There are several assumptions that are valid for the aircraft in both cases: the discount rate known as the weighted average cost of capital (WACC) equals 7.5%^[5] and the airplane is presumed to have a lifespan of nine years. Further assumptions contain a yearly rise in maintenance costs of 10%.

For demand growth, the number of passengers in the airline industry forecasted by Airbus and Boeing is used (see tables 3 and 4).

Table 3: Boeing: Current Market Outlook (2008-2029)

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[...]

^[1] For further information about the Binomial Option Pricing Model see Cox, J., Ross, S. and Rubinstein, M. , “Option Pricing, A Simplified Approach, “Journal of Financial Economics 7(3) (1979): 229-263.

^[2] J. Hull (2006) deviates and explains the Black-Scholes formula in his book “Options, Futures and Other Derivatives“, pp. 281-340.

^[3] The US Department of Transportation publishes annual airline data and other statistics for the US transportation sector on its website. For example, the annual average flight operating expenses for each aircraft type of all US American airlines can be found in this database.

^[4] Numbers as of June 2009.

^[5] Morrell (2007, p. 8) indicates a cost of capital of 7.5% in the airline industry as a whole.