Master Thesis
Can Real Options improve the results of investment valuations?
A Case study on real estate development objects in Downtown Detroit
Date:
June 2015
Author:
Tom Kircher MSc Finance and International Business
Advisor:
Stefan Hirth Department of Economics and Business
Abstract
This paper has the central objective to describe the existing concept of the real option theory, to differentiate its characteristics from the net present value and to test its applicability based on a case study. It is the goal to point out differences between the net present value and the real options analysis and to determine whether the latter of them is a superior method. The valuation is done on a chosen real estate development object in Downtown Detroit, USA. Accessable data is used together with making necessary assumptions in order to apply the real option theory. For valuation purposes, a binomial lattice model is selected. The model incorporates the option to defer, to abandon and to expand the investment and is divided into stages leading the model to contain of sequential compound options in order to capture the potential flexibility. The calculation results are compared to the before provided and estimated static net present value benchmark. The findings confirm the stated hypothesis of the real options analysis delivering better results compared to the net present value. It is found that by applying the sequential decision strategy, the payoff of the project can be increased by 12.825 percent, which is matching the existing empirical findings of previous conducted research papers.
KEY WORDS: Case study; Net present value; Real options analysis; Flexibility; Sequential compound options
I
Table of content
1.
2.
3.
Introduction.................................................................................................................. - 1 -
1.1.
Background and Motivation ................................................................................... - 1 -
1.2.
Problem Statement and Objective .......................................................................... - 3 -
1.3.
Outline .................................................................................................................... - 4 -
1.4.
Evaluation of sources .............................................................................................. - 5 -
1.5.
Delimitation ............................................................................................................ - 5 -
Methodology ................................................................................................................. - 7 -
2.1.
Research Structure .................................................................................................. - 8 -
2.2.
Research Process .................................................................................................... - 9 -
2.3.
Introducing Detroit – The Case Study .................................................................. - 12 -
Literature Review ...................................................................................................... - 15 -
3.1.
Net Present Value – A Traditional Decision Tool ................................................ - 15 -
3.1.1. 3.2.
Limitations of the Net Present Value Method ............................................... - 17 -
Real Options ......................................................................................................... - 19 -
3.2.1.
What are Options – Definition ...................................................................... - 20 -
3.2.2.
Options – Three Different States of Value .................................................... - 21 -
3.2.3.
Financial versus Real Options ....................................................................... - 24 -
3.2.4.
Types of Options ........................................................................................... - 25 -
3.2.4.1.
Option to Expand ................................................................................... - 26 -
3.2.4.2.
Option to Defer ...................................................................................... - 27 -
3.2.4.3.
Option to Contract .................................................................................. - 27 -
3.2.4.4.
Option to Abandon ................................................................................. - 27 -
3.2.4.5.
Sequential Compound Option ................................................................ - 28 -
3.2.5.
Value Drivers ................................................................................................ - 28 -
II
3.2.6. 3.3.
Real Options Valuation Methods ......................................................................... - 32 -
3.3.1.
Partial Differential Equations ........................................................................ - 32 -
3.3.2.
Simulation ..................................................................................................... - 33 -
3.3.3.
Binomial Lattice ............................................................................................ - 34 -
3.4.
Approaches to Real Options ................................................................................. - 36 -
3.4.1.
The Classic Approach ................................................................................... - 37 -
3.4.2.
The Subjective Approach .............................................................................. - 37 -
3.4.3.
The Marketed Asset Disclaimer Approach ................................................... - 37 -
3.4.4.
The Revised Classic Approach ..................................................................... - 38 -
3.4.5.
The Integrated Approach ............................................................................... - 38 -
3.5.
Real Options in Real Estate .................................................................................. - 38 -
3.5.1.
4.
Differences Net Present Value vs. Real Options Analysis............................ - 30 -
Volatility ........................................................................................................ - 40 -
3.5.1.1.
Risk versus Uncertainty ......................................................................... - 42 -
3.5.1.2.
External Risk Factors ............................................................................. - 42 -
Case Study – Reviving Downtown Detroit............................................................... - 44 -
4.1.
Project Description ............................................................................................... - 44 -
4.2.
Underlying Drivers ............................................................................................... - 46 -
4.2.1.
Income ........................................................................................................... - 46 -
4.2.1.1.
Rent ........................................................................................................ - 46 -
4.2.1.2.
Net Operating Income ............................................................................ - 47 -
4.2.1.3.
Terminal Capitalization Rate ................................................................. - 47 -
4.2.2.
Costs .............................................................................................................. - 47 -
4.2.2.1.
Construction Costs ................................................................................. - 47 -
4.2.2.2.
Operating Expenses ............................................................................... - 48 -
4.2.3.
Cost of Capital ............................................................................................... - 48 -
4.2.3.1.
Risk free rate .......................................................................................... - 48 -
III
4.3.
4.2.3.2.
Beta ........................................................................................................ - 49 -
4.2.3.3.
Market Risk premium ............................................................................ - 49 -
4.2.3.4.
Cost of Equity ........................................................................................ - 50 -
4.2.3.5.
Comparable industry ratios .................................................................... - 51 -
4.2.3.6.
Discount Rate – Development Time ...................................................... - 51 -
Base Case Valuation ............................................................................................. - 51 -
4.3.1. 4.4.
5.
6.
Expected Static Net Present Value ................................................................ - 52 -
Real Options Analysis .......................................................................................... - 53 -
4.4.1.
Volatility ........................................................................................................ - 54 -
4.4.2.
Binomial Lattice ............................................................................................ - 54 -
Discussion.................................................................................................................... - 59 -
5.1.
Results .................................................................................................................. - 59 -
5.2.
Critique and Reflection ......................................................................................... - 60 -
Conclusion .................................................................................................................. - 61 -
Bibliography ...................................................................................................................... - 63 -
Appendix ............................................................................................................................ - 66 -
IV
List of figures Figure 1 – A four-step Process ............................................................................................. - 8 Figure 2 – Research Structure .............................................................................................. - 9 Figure 3 – Comparing the S&P Case-Shiller Home Price Index ....................................... - 12 Figure 4 – Monthly Return Development of Home Price Index ........................................ - 13 Figure 5 – Payoffs Call Option .......................................................................................... - 22 Figure 6 – Payoffs Put Option ............................................................................................ - 23 Figure 7 – Mapping a Development Opportunity onto a Financial Call Option ................ - 25 Figure 8 – Displaying Advantages from Fluctuations of Options ...................................... - 26 Figure 9 – Scenarios of Real Options Value Creation ....................................................... - 31 Figure 10 – Option Value of a One-step Binomial Lattice ................................................ - 34 Figure 11 – Allocation of Expected Return ....................................................................... - 40 Figure 12 – Project Description of the Individual Stages ................................................... - 45 Figure 13 – Comparable industry ratios ............................................................................. - 51 Figure 14 – Input Variables ................................................................................................ - 52 Figure 15 – Summary Input Variables for Binomial Lattice ............................................. - 55 Figure 16 – Present Value Binomial Tree and Development of Construction Costs .......... - 56 Figure 17 – Individual Combined Equity Lattice for Phase 1, 2 and 3 ............................... - 58 -
List of tables Table 1 – Display of an Investment Opportunity ............................................................... - 17 Table 2 – Comparing Discounted Cash Flow and Real Options Analysis ......................... - 31 -
V
List of abbreviations
CAPM
-
Capital Asset Pricing Model
CF
-
Cash Flow
DCF
-
Discounted Cash Flow
ENPV
-
Expected Net Present Value
GBM
-
Geometric Brownian Motion
HPI
-
Home Price Index
MAD
-
Marketed Asset Disclaimer
MAX
-
Maximum
NPV
-
Net Present Value
PV
-
Present Value
REIT
-
Real Estate Investment Trust
ROA
-
Real Options Analysis
ROV
-
Real Options Valuation
USA
-
United States of America
VI
Acknowledgements This Thesis has been carried out from January 2015 to June 2015 at the Department of Economics and Business, Aarhus University, Denmark in order to finalize the Master of Science program in Finance and International Business. I would like to thank my supervisor, Stefan Hirth, for his guidance and energy that assisted me in understanding, structuring and writing my paper and helped me to conduct a goaloriented research. Furthermore, I would like to thank all of my classmates and the teachers, who made the years of the programme such a great experience. I am blessed to not only have learned about a new culture and education system, but also to have met several interesting and valuable people from all over the world, a lot of whom I now call friends. Finally, I am entirely appreciative for my family and especially my parents, Ellen and Frank Kircher, who always have had my back and have supported me unconditionally regardless of the direction or the difficulty of my chosen path.
-1-
1. Introduction
1.1.
Background and Motivation
Real estate investments are one of the most chosen answers if it comes to the question how best to invest money in order to gain long-term returns and secure people’s pension plan [Focus (2013)]. The endless lifespan of real estate objects hereby presents a valuable level of security together with the possibility of continuous cash flow income to the investor [Geltner et al. (2007)]. Therefore, understanding the real estate market, the relation to financial economics and its dynamics always has been in the centre of research attention for decades. Borison (2005) sees an increasing number of articles, which focus their research on how to extract the most value out of investments in real assets rather than in the more and more nonarbitrary offering financial assets. As lucrative as this might happen to be seen, as crucial it is to evaluate this investment opportunity correctly. The real estate bubble in 2008 and 2009 has shown in a spectacular way that the demand in the market and its prices can break away from one day to another and what kind of consequences and impacts wrong assessments or estimates regarding the realistic value of real estate objects can have. A lot of expertise together with an accurately working model is required, which not only is easily applicable but also includes the most important and essential variables impacting the value of the objects. Besides that, the model is required to still be able to mirror the variables in a realistic setting. Examples of those variables can include several risks and uncertainties related to demand and sale prices in the market, government risks and possible changes in regulatory or development costs. In their paper, Sun et al. (2008) identify four main categories of risks (political, social, economical and technical) influencing the real estate development process. Consequently, making the decision based on the correct and accurate valuation is essential as investments in real estate and commercial development of buildings also bind a lot of capital, which only recovers slowly and over time in form of cash flow income or the sale price. In addition to the uncertainty and the high amount of required capital, the decision to develop a real estate object often is irreversible or at least partly irreversible and is associated to a high quantity of sunk costs. One way to evaluate real estate investment opportunities is to use the net present value method. It in practice is widely adopted and supports the investor in the decision whether or
-2-
whether not to undertake the investment. Its easy application is at the same time its biggest flaw. The approach can be described as deterministic, because it misses out on taken the above mentioned variables of risk and uncertainties into account. This leads it to being a static valuation tool, which only refers to one specific moment in time. As a consequence, the investor is put into a passively spectator role, unable to react to the change of circumstances as they unfold during the development process. Once the simultaneous decision to invest is made, it is irreversible and the costs for the investment decision can be seen as fixed capital, which stands in contrast to the way a real estate development normally evolves. Real estate development is not straightforward and linear but includes different stages during the process, leaving room for changes, optimizations and adjustments. Renegotiations of terms, delaying or abandoning of further development steps or stages and the option to expand the investment are examples of the additional value an investor can receive when he takes future uncertainties and their impact on the asset into consideration before making the committing investment decision. This value of flexibility cannot be fully captured by a static model like the net present value approach, thus, making the real option theory interesting for this field of research. It has led to the literature and research to focus on retrieving an alternative approach, which is able to capture the additional value through flexible decision making and has resulted in the real options analysis. McDonald and Siegel (1986) first identify an economic value in the option to wait to invest. Williams (1991) and Quigg (1993) empirically prove that there is additional value in the option to defer a development of real estate land. And even though real options theory also has been incorporated as a decision tool in relevant books or research papers on real estate development [e.g. Geltner (2007)], the static net present value approach is still widely used in practice as the major tool for investment valuation. One reason for that is that the gap between theoretical approach and practical application of the real options valuation models are found to be too broad. In addition to that, it is often seen that it is difficult to apply the analysis or to fulfill all the industry-specific requirements due to its mathematical complexity and different assumptions needed to be made regarding specific industries [Lucius (2001)]. This paradox between theoretical and practical application of real options delivers an interesting starting point for a deeper research. In order to make a sequential development including options lucrative, the necessary criteria of high uncertainties, irreversibility of investments and the exposure to external risk factors have to be met. The real estate industry perfectly meets these criteria.
-3-
Beyond that, understanding the price dynamics and the development of the real estate market has already been a central research interest by the author since 2008, reflected also in the author’s bachelor thesis.
1.2.
Problem Statement and Objective
Although many papers and researches can be found on theoretical background that discuss and define real option models, not only the paper of Lucius (2001) shows that still only a small amount of literature actually applies the real options analysis to evaluate real estate investment objects. Though, as shown in the introduction, the real options analysis often is found to be superior over the net present value method, it is yet not as widely used in practice as the net present value method. Therefore, the goal of this thesis is to compare two approaches, the base case scenario delivered by the net present value method and a self-developed efficient model based on the theory of real option valuation [a binomial tree lattice]. Another goal is to determine the differences between the two valuation methods. Additionally, potential value drivers of the real options analysis are stated and the applicability of both models is tested and compared. This is done through a case study, conducted on investment and development objects, located in the city of Detroit, USA. The above stated goals aim to achieve a central objective of this paper, which is to contribute to a more applicable real options analysis model in the sector of real estate development. Furthermore, with the provision of the theoretical background and the appliance of the models to the case study of a real estate development project in Detroit, the following main research question shall be answered:
Can real options analysis deliver more appropriate and superior results compared to the net present value method in terms of the valuation of real estate objects through their characteristics of taking into consideration the steps of sequential development?
In addition to that, the answers to the following sub-questions provide a deeper understanding of the topic and by this support the solving of the main research question:
How are real options defined and what kinds of options exist?
-4-
What assumptions have to be made or what conditions have to be matched for real options analysis to be more feasible in practice than the net present value method?
What are the variables and risk factors influencing the outcome?
What are similarities and where are differences between the two approaches?
In order to answer the above stated research questions, the structure given in section 2.1 is followed, i) determining and ii) applying the theory to a real case study, iii) describing and evaluating the data in order to achieve numerical results and iv) analyzing the findings.
1.3.
Outline
The thesis in total contains six chapters. Chapter one and two can be seen as the introduction and structural framework. Chapter three through five build the central part of the thesis concluded by the conclustion on the findings of the research.
-
Chapter one delivers the background and the motivation for this study. It states the
objective and the main research questions for this paper. It provides the outline on how the paper is structured, evaluates and reasons for the used sources and states the delimitations, which are necessary in order to accomplish an efficient and realistic scope. -
Chapter two explains how the research in this thesis is conducted in terms of strategy,
approach and methodology. It includes an overview of the different steps and the models used in the paper. It also reasons for the necessity of an accurately conducted case study and explains why the City of Detroit and its real estate situation deliver good input and the desired data for the case study. -
Chapter three contains and describes the relevant theoretical background. This
includes a review of the existing valuation models and their definitions. A comparison of the models with and to each other is made. In addition to that, all complementary models and theories are explained that are necessary in order to conduct the case study. This includes defining the term volatility and the external risk factors that can affect real options in real estate, but also the adequate approaches to incorporate these variables into a model. -
Chapter four deals with the City of Detroit and its real estate situation. It applies the
two models to the case study. This includes generating and describing the raw data
-5-
necessary to run the analysis and preparing descriptive statistics. Additionally, the data is utilized to run the numbers; and the four-step process valuation process is applied [see Methodology, Chapter 2]. -
Chapter five analyzes and discusses the findings and compares the results to previous
research findings from papers, conducted on similar topics or case studies. -
Chapter six contains the conclusion and provides the main results and findings with
references to the research questions of the paper. The results are put into perspective and suggestions for possible further research are delivered.
1.4.
Evaluation of sources
The choice of the sources is crucial for a successfully conducted research project. Therefore, the main sources used in this paper are articles from academic journals that are available online and accessable through the library of Aarhus University. This approach follows the main assumptions that published articles in highly ranked journals have to go through and pass a process of academic review and hence automatically contain quality and valuable research aspects. Additionally, prior studies on related research fields are taking into consideration and are hereby cited to provide a broader perspective and an overview of the existing and relevant research, which previously dealt with the application of real options analysis. This is done in order to deliver a better understanding of the central research question of this study.
1.5.
Delimitation
While the goal is to contribute new ideas and findings to the research regarding the applicability of real options in real estate development, the paper underlies the specific limitations. Since real options have been first introduced by Myers (1977), a lot of research on this topic has been conducted and various different models have been developed as well as more and more types of options have been defined. In order to deliver the best and most accurate results possible, the focus of this paper has been narrowed down to four different kinds of options and a comparison of one static with one dynamic model. Furthermore, research almost always aims to empirically test and prove the theoretical findings and hypotheses. The problem that often occurs is for one the limited available and accessable data. Because of the limited access, this paper uses secondary data sources such as the accessable websites census.gov and
-6-
research.stlouisfed.org, REITs published in articles and found via search engines like Business Source Complete and data directly extracted from DataStream. While the data from DataStream is considered to be unbiased, the other sources have to be read and used with a critical eye as they might be biased. Often assumptions and limitation have to be made regarding input variables used in the model which further narrows done the range and accuracy of the simulation. The author is aware of this possible error leading to incorrect or inaccurate results regarding the comparison of real options analysis and the net present value method and therefore this is taking into consideration in the final reflections and conclusions of the paper. The paper focuses on the books of Mun (2006) and Copeland and Antikarov (2003), which not only deliver a four step model to conduct the valuation, but also deliver main and important assumptions essential for applying the real options methodology to a real case study. The question of the right approach to value real option is answered, which sets out the framework of how to deal with the data. Additionally, different real options valuation methods are presented, which all fulfill two essential assumptions. For one, the concept of an efficient market with no arbitrage opportunities and the process of the geometric Brownian motion [GBM]. Both are further explained and discussed in the chapter of the literature review. The author is aware that throughout the thesis additional assumptions and limitations might be required in order to increase the accuracy or correctness of the research study.
-7-
2. Methodology In the world of research, many different real option valuation models and with it different level of complexity can be found. The goal of this paper is to find and develop a discrete-time real option valuation model, which can easily be applied to a case study and still being able to capture most of the essential variables. Therefore, the approaches described and defined by Copeland and Antikarov (2003) and Mun (2006) in their books with the titles: “ Real Options: A Practitioner’s Guide” and “Real Options Analysis – Tools and Techniques for Valuing Strategic Investments and Decisions”
build the foundation for the methodology used in this paper. The application of the model follows and includes the following four-step process approach for valuing real options [see Figure 1], where:
-
Step one contains calculating the standard and static net present value of the
investment possibility using the Discounted Cash Flow analysis. It presents the base case without flexibility, needed for further valuation and comparison. The assumption of the market asset disclaimer [MAD] holds and helps to identify the value of the underlying asset without flexibility also known as the static net present value and represents the best unbiased estimate of the market value of the investment. -
Step two has the main purpose to first identify all different possible uncertainties and
then to combine all the defined risk variables into one. This is achieved through running a Monte Carlo simulation and through the estimation of comparable market proxies, which are further defined and explained in the literature review. Examples for uncertainties can be found in sale prices, interest rates, employment rate, purchase power, rental rates, etc. and are determined in the literature review in general and then in specific regarding the case study in Chapter four. The assumption that all uncertainties are unrelated is important and therefore stated in order to simplify the analysis. This supports the ability to better evaluate and analyze the results. -
Step three uses the calculated standard deviation to build the binomial tree. The
volatility displays the up and down movements of the tree. The tree is a summary of every possible value the underlying risky asset may take through time depending on the different states, which are presented through nodes. These nodes also indicate a point of possible and potential managerial interaction as they represent real options
-8-
nodes. The viewed time in which the nodes appear are set to be regular and one year intervals, again for simplicity reasons. -
Step four describes the valuation of the different paths of the created binomial tree and it’s with coming payoffs. The risk -neutral probabilities approach is applied to assess
the different outcomes, going backwards in time and taking into consideration every node and each of the possible included different option along the path.
F i g u r e 1 - A f o u r - st e p Pr o c e ss [ S o u r c e: A d o p t ed f r o m C o p el a n d a n d A n t i k a r o v ( 2 0 0 3 ) ]
Excel and necessary extensions are used to design the modeling framework for this thesis.
2.1.
Research Structure
The research structure is divided into four main parts, which can be seen in Figure 2. Each part plays an essential role for creating a fully comprehending of the paper as it is the goal to not only display the status of the latest models and theories [Part one], but to use the in the literature existent and through previous research supplied tools and the available and generated data [Part two] to run an analysis on both the base case NPV and the developed real options valuation method [Part three] in order to come to results, a conclusion and to answer the central research questions of the paper [Part four]. All four individual steps are essential as they prepare the foundation for the thesis, gather and set up the data, run the analysis and reflect and conclude on them.
-9-
The paper only is able to contribute new findings through the application to a case study, which transforms the gathered data and identified real options into an analysis and therefore tests the hypotheses and models. Saunders, Lewis and Thornhill (2012) compare the research process to a research onion and confirm in their book the necessity of a divided structure in order to conduct and write a complete and value-adding paper. The onion refers to the different fields during the research process and is described and explained more in detail in Chapter 2.2.
F i g u r e 2 – R ese a r c h St r u c t u r e [ S o u r c e : O w n C r ea t i o n ]
2.2.
Research Process
This section deals with the research process that is utilized in this paper. That includes reasoning for the research paradigm, the research approach and the research strategy as well as the time horizon is determined. It delivers the clarification on how this thesis is conducted for example in terms of theory and data collection, which supplies the reader with a clear guideline and a better understanding throughout the paper. Positivism is a dominant chosen paradigm in how to apply research philosophy and is based on existing theoretical research and applies logical reasoning to investors, decision makers, companies and markets as well as it assumes rational and therefore utility maximizing
- 10 -
behavior. It assumes the existence of one truth, observable by the scientist and leads to science being able to predict the world. In contrast to this approach stands the post positivistic research paradigm, which can be defined as a critical realism. Ryan et al. (2002) determine the main difference in the critically dealing with the view on the truth and not only accepting the observed data as the one existing truth. Post positivistic approach followers are aware and recognize that all observations are fallible and can contain errors and that as a consequence theory is always possibly revisable. Certain objectivity cannot fully be achieved due to biases and subjectivity. A process of variation, selection and retention that theories can run through and which is a natural process of selection can lead to theories approaching the objective one truth. The author of this paper adopts the post positivistic paradigm in order to not only follow the above stated research methodology approach, but also to ensure having an invisible guideline that supports and demands the reoccurring critically questioning and challenging of the desired and intended objectivity constantly throughout the paper. The approach is reflected in the structure of the paper as the paper begins with a literature review before setting up the models, applying them to a numerical example, testing and questioning the consistence of the found empirical data and comparing it to the existent literature putting it into a perspective. The author hereby is aware that in term of the conducted case study a possible result of self made estimations and beliefs might include and lead to a certain level of subjectivity. Additionally, the post positivistic paradigm typically proposes a certain research approach to be followed by the writer, which often is the method of a deductive approach. The paper at hand embraces the deductive approach. Saunders, Lewis and Thornhill (2012) see and define five different stages in order to conduct a deductive research, where: -
The first step orders the author to deduct hypotheses from existing theoretical
literature that delivers a testable relationship between variables, factors or concepts. -
The second step is to transform the hypotheses into operation terms allowing an
indication on how the variables are to be measured. -
The third step involves the testing of prepared hypotheses involving a case study,
experiment or any different applied strategy instrument. -
The fourth step contains an examination of the results putting them into a perspective
regarding the existing theories, which leads to either confirmation or indicate a need for adjustments.
- 11 -
-
The fifth step is the follow up suggestion for modification if in step four the necessity
for that has been determined.
The research structure [see Chapter 2.1.] reflects all of those five stated stages of how to conduct and follow the deductive research approach as the starting point of the paper is the developing of hypotheses and models out of the existing literature and theories. In contrast to that, the inductive approach is seen to be appropriate when research starts with observing and generating data leading to a creation of theories and analysis. While induction emphasis the collection of quality data and allows a more flexible structure permitting the researcher to undertake changes or adjustments throughout the research progress, the deduction insist on gathering quantity data and a clear and highly structured approach to be followed. [Saunders, Lewis and Thornhill (2012)]. Reality sees no absolute black or white decision and one could argue that this paper also contains the inductive approach because the goal of the thesis at hand is to design and deliver a practical and applicable model out of generated and observed data. The author is aware of the possible combination of the two different paths in order to accomplish the goal, but for the above stated reasons the main focus is put on following and applying the deductive approach. As objective as the relationship between theory and practice might be seen, reality sees a limitation to the application of the models as they are affected by necessary assumptions made by the author resulting in a possible subjective factor of influence throughout the thesis. To achieve scientific objectivity, the above chosen deductive approach prescribes an independency from the observed results. This means that the achieved results could also be achieved by any third in a run test observation and therefore are reproducible. To support this goal, the research strategy is important. The paper at hand chooses a case study, which when simple and well-constructed enables the author to not only challenge the existing theory but also to come up with new hypotheses [Saunders, Lewis and Thornhill (2012)].
- 12 -
2.3.
Introducing Detroit – The Case Study
The importance of a well conducted and suitable case study to test the stated hypotheses, answer the research questions and apply the developed models has already been mentioned and reasoned for in this part of the paper. Robson (2002) defines a case study in general as “a strategy for doing research which involves an empirical investigation of a particular contemporary phenomenon within its real life context using multiple sources of evidence”.
This section briefly presents Detroit and determines why Detroit is feasible and chosen for the case study. Additionally, it combines the supplied model with the real life context, utilizing the above stated quote. To set up for the case study, it is important to know a few facts regarding the framework. The case study puts the investor back into the year 2010, when prices fell over proportional in Detroit as a result of a real estate bubble in 2008 and 2009 [see Figures 3 and 4].
S&P Case-Shiller Home Price Index 250,00 200,00 150,00 100,00 50,00 0,00 1 0 1 0 0 0 0 2
1 0 5 0 0 0 0 2
1 0 9 0 0 0 0 2
1 0 1 0 1 0 0 2
1 0 5 0 1 0 0 2
1 0 9 0 1 0 0 2
1 0 1 0 2 0 0 2
1 0 5 0 2 0 0 2
1 0 9 0 2 0 0 2
1 0 1 0 3 0 0 2
1 0 5 0 3 0 0 2
1 0 9 0 3 0 0 2
1 0 1 0 4 0 0 2
1 0 5 0 4 0 0 2
Home Index USA
1 0 9 0 4 0 0 2
1 0 1 0 5 0 0 2
1 0 5 0 5 0 0 2
1 0 9 0 5 0 0 2
1 0 1 0 6 0 0 2
1 0 5 0 6 0 0 2
1 0 9 0 6 0 0 2
1 0 1 0 7 0 0 2
1 0 5 0 7 0 0 2
1 0 9 0 7 0 0 2
1 0 1 0 8 0 0 2
1 0 5 0 8 0 0 2
1 0 9 0 8 0 0 2
1 0 1 0 9 0 0 2
1 0 5 0 9 0 0 2
Home Index Detroit
F i g u r e 3 – C o m p a r i n g t h e S & P C a s e- S h i l l e r H o m e P r i c e I n d ex f o r D e t r o i t a n d t h e U SA [ S ou r c e: research.stlouisfed.org]
1 0 9 0 9 0 0 2
- 13 -
Monthly Development - Bubble (June 2006 - June 2009) 1,00% 0,50% 0,00% -0,50% -1,00% -1,50% -2,00% -2,50% -3,00% -3,50% -4,00% HPI USA
HPI Detroit
F i g u r e 4 – M o n t h l y R et u r n D e ve l o p m en t o f H o m e P r i c e I n d e x [ S o u r c e : r e sea r c h . s t l o u i sf e d . o r g ]
Looking at those two figures, the question that surely arises in the reader’s mind is wheth er it
is lucrative to analyze an investment opportunity under these circumstances and what exactly might create value for an investor at the beginning of the year 2010 when he thinks about investing in Detroit. Volatility and bubbles not only create downside risk that the investor has to face, but also provide upside potential of recovering markets with increasing demands and a turnaround of the devils circle in a positive nature. Detroit hereby displays a perfect example and in the opinion of the author can offer the recovery potential, which in the conducted case study shall be evaluated and revealed. Figure three shows the home price development of Detroit in the last decade. Burdened with a constantly outflow of the population, Detroit’s real estate pr ices
developed and increased under proportionally relative to the general development in the USA. Lately and regarding the figures three and four, it seems that Detroit has reached its bottom and as a consequence has shrunk to a healthy size that allows the administration to revive small parts time by time. Additionally, programs like invest Detroit1, detroitsevenpointtwo2 or the initiatives controlled and financed by Dan Gilbert’s mortgage lender company Quicken Loans 3 revive the urban area of Detroit. Investments, governmental subsidies, cheap living costs and a changing and adjusting urban Downtown attract young and skilled people and professionals. The
1
Investdetroit.org Detroitsevenpointtwo.com 3 Quickenloans.com 2
- 14 -
consequence is a gentrification process of the neighborhood, which attracts better, and more retail, and industry to settle back in. As in reality right now, this is happening in Downtown Detroit. In the case study at hand, the investor as earlier described is at the beginning of this potential process. It is not the goal of the thesis to describe and define the general process of gentrification, but to rather supply a foundation, which aims to simplify the understanding of the model and the case study itself. The starting situation is that Detroit in the year 2009 and 2010 has reached the absolute bottom in terms of unemployment, labor and living costs and value of real estates. And this is exactly where the connection to the theory exists. Real options enable the investor to fully capture on the potential upside of a recovering and revived Detroit with increasing home prices and values. Additionally, being an option; they do not bind or obligate the decision maker to make a move, which means that in case of a stagnating or even decreasing development of the situation, the investor does not have to and will not exercise the option. Testing and finding the connection between the theoretical approaches and reality is one main goal of the paper, but the author is aware of assumptions and adjustments, which always put the case study into a “reality-light” or “model” perspective.
- 15 -
3. Literature Review This chapter has the purpose to supply the necessary and relevant theoretical background in order for the reader to fully understand the numerical example and to give an overview of the relevant research that has been conducted on the topic and research tools. The literature review is divided into four main parts. First, the in reality often used net present value analysis approach is presented in order to give the reader a base case and a starting point. Limitations that this valuation method faces are pointed out leading to a presentation of the chosen alternative valuation method – the real options analysis. As real options analysis has been chosen to be compared to the net present value analysis based on the case study, it is described and defined more in detail. Options are defined in general. Different types of options are stated, explained and illustrated on the basis of an example. In addition to that, differences and similarities between financial and real options are pointed out. The definition and understanding of options are crucial to be able to correctly run the valuation process in the hereafter presented case study. A direct theoretical comparison of the two methods pointing the differences closes out the second section of this chapter. After that, a closer look is paid to the empirical evidence of real options in real estate and real estate development to introduce the reader to the external risk factors, which affect the value of real options. The term volatility is defined and specified for the up following case study. Auxiliary tools necessary for the transformation process are presented. This includes the potential approaches like the market proxy approach together with different methods used in the real option valuation procedure, like the Monte Carlo Simulation. The final part sees a presentation of the Binomial Tree approach on the basis of a simple example and additional assumptions, which need to be made in preparation for the numerical calculations in Chapter four.
3.1.
Net Present Value – A Traditional Decision Tool
This paper addresses a specific audience, which already is aware of the basic financial economics and has a certain research interest in the field of real estate. It is expected that the reader broadly is familiar with the net present value analysis and therefore this approach is hereafter only defined and presented briefly.
- 16 -
Due to its easy implication, the net present value analysis has been used and taught as a relevant investment valuation tool for a long time. It supports the firm’s decision maker whether or whether not to undertake a project opportunity and achieves this with a rather simple and easy applicable formula. Furthermore, the decision criteria can be transferred consistently to all projects and supplies the same results regardless of the investor’s risk preferences [Mun (2006)]. Koller et al. (2010) describe the solely focus on the cash flows that go in and out of the firm as one of the main reason for the method’s popularity.
in their book “ Principles of Corporate Finance” as a result of subtracting the initially required investment [ ] from the Brealey et al. (2011) define the net present value
sum of the discounted expected or anticipated future cash flows as equation 3.1 illustrates. The index of the net present value [here: t = 0; today] refers to the point in time, at which the present value of the investment opportunity shall be mirrored.
(3.1)
The sum of the discounted expected cash flows can be further divided up into an auxiliary calculation, the Discounted Cash Flow method [DCF; see equation 3.2].
The factor
(3.2)
is necessary to calculate the present value of the cash flows and hence make
them comparable. The rate of return [r ] defines the opportunity cost of capital or hurdle rate, which an investor demands in order to accept delayed payments rather to invest into financial alternatives [Brealey et al. (2011)]. It can also represent the weighted average cost of capital of the firm and therefore an intern hurdle rate that has to be overcome in order to accept and undertake the investment. Once the net present value is calculated, the method applies a rather pragmatic decision rule. While a negative net present value leads to a decrease in the shareholders’ wealth and therefore it is not recommended to undertake the project, the opposite is the case when the calculation delivers a positive result; meaning the firm should undertake the investment opportunity.
- 17 -
To clarify the above stated formula, [see equation 3.1] an example is given. The formula also is applied to the investment object of the case study. A typical and simple example for an investment opportunity is given in table 1 using the net present value method to evaluate the project. To set up the project, an initial investment of 50 US Dollar at time t = 0 [today] is required. The project is expected to generate 20 US Dollar of cash flow income over the following four years. The opportunity cost of capital is set to be five percent representing the interest rate the company could earn investing the 50 US Dollar.
Year Initial Costs Cash Flow Discounted CF
0 -50$ 0
1 0 20$ 19.05$
2 0 20$ 18.14$
3 0 20$ 17.28$
4 0 20$ 16.45$
T a b l e 1 - D i sp l a y o f a n I n v e st m e n t O p p o r t u n i t y [ S o u r c e : O w n C r e a t i o n ]
This leads to the following net present value of the project:
(3.3)
The decision rule orders the investor to undertake all projects having a positive net present value. It is simple to explain to management. A positive outcome leads to an increase in the wealth of the company, investors or shareholders and therefore is desirable [Mun (2006)]. In the example at hand, the company should undertake the project because the net present value equals 20.92 US Dollar, which means investing in this project would see the company with a net gain of 20.92 US Dollar.
3.1.1. Limitations of the Net Present Value Method
The previous section has explained and shown how simple it is to apply the net present value analysis. The straightforward decision rule might be feasible, but also entails some limitations, which in the following are determined and dealt with. Regarding the topic of the paper, the downside factors are especially looked at under the circumstances of the real estate field and its dynamics. Dixit and Pindyck (1994) state three main disadvantages that the net present value method incorporates when it is used for the purpose of an investment opportunity valuation.
- 18 -
The first problem the analysis faces is the assumption that the observed project is generating cash flows over the expected lifetime of the project, which without any contingencies can be determined. This stands in contrast to the reality. Every project in real estate underlies specific external risk factors [see Chapter 3.5.1.1] that make a certain estimation of the cash flows difficult. Cash flows usually are stochastically distributed and the net present value method misses out on assessing all of the risk factors, which impact the variation of cash flows throughout the lifetime of the project [Mun (2006)]. Additionally, the net present value method often is associated with a now or never decision rule, which states either to undertake the project today or never to invest at any point in the future. This passively treatment of the possibility to interact during the project’s lifecycle does not account for managerial flexibility. It does not reflect the reality and the field of real estate, where managers possess a certain degree of control and are able to influence the development process of the object [Mun (2006)]. As an example, the investment might be deferred until more information about uncertainties and external risk factors are available or a further stage of the development might be abandoned because it is no longer feasible. Real estate objects usually follow a sequential development incorporating different kind of valuable options [see Chapter 3.2.4] throughout the process. The net present value decision rule does not account for this created option value. Another problem that the net present value is confronted with is the assumption that all risks are completely incorporated in the discount rate that the method applies in the calculation. Mun (2006) argues that risks regarding a project or the firm can vary during the lifecycle of a project. A constant discount rate based on historical data without flexibility is inaccurate. It does not reflect the multiple possible sources of business risks a company or project can face during the development process as the underlying parameters are likely to change over time. Summing up all the above determined disadvantages, the net present value decision rule underestimates the flexibility value of a project assuming possible events are static and all decisions are carved in stone. This leads to a constantly undervaluation of possible investment opportunities. Valuing projects in the field of real estate therefore requires an adjusted assessment tool, which captures the left out possible intrinsic value of projects.
- 19 -
3.2.
Real Options
“Thales, a famous Sophist philosopher circa 600 B.C., gazed into the star-studded sky one evening and predicted an outstanding olive harvest the next season. For a small up-front fee, he bought the right from the owners of the olive presses to rent them for the usual rate during the harvest season. If the harvest turned out to be meager, there would be less need for the presses and Thales would not rent them, losing the up-front fee. But if the harvest was bountiful, he would rent the presses at the regular agreed-upon price and turn around and rent them out to the farmers at a significant margin. Sure enough, it was an outstanding harvest, and Thales rented the in-demand presses and made a fortune. He was apparently more interested in proving the wisdom of Sophists than making money, as Aristotle tells this story in Politics.” [Kodukula and Papudesu (2006)]
The above cited story is one of the earliest examples for a real option contract, giving the owner the right, but not obligating him to exercise the option on an underlying real asset. While real options evolved from financial options and similarities definitely exist, this story is a typical example for a real option because the underlying asset is a real asset and not financial nature. The theoretical framework of real options is capable of taking into consideration the flexibility that can occur in real estate development projects. The flexibility value emerges from the manager’s ability to undertake actions and react to uncertainty and changing circumstances. In order for a successful implementation, not only those uncertainties and risks have to exist and have to be successfully identified, but the decision makers also have to be aware of their existence and capable of influencing them. Mun (2006) defines the real options approach as a dynamic series of future decisions with the investors having the flexibility to adjust to changes of externalities where as the traditional method assumes a single decision pathway with fixed outcomes and regards all decision to be made in the beginning. As real options analysis has been developed on the basics of traditional discounted cash flow methods, Mun (2006) defines the real options value as a sum of the static and passive net present value and the strategic option value [see equation 3.4 and 3.5].
(3.4) (3.5)
The N (d) hereby describe the multipliers behind both benefits and costs and represent the probabilities of their occurrence achieved through a discrete simulation run in the binomial
- 20 -
lattice. In the existence of uncertainty, both N (d) are not equal to 100 percent supplying the option owner with the right to capitalize on the upside volatility while hedging the downside risk. Real options therefore deliver not only risk reduction but also add value to investment possibilities and real assets. Triantis (2005) adds that managers, who apply real options valuation, view volatility as a possibility to take advantage of rather than seeing it as a risk that is purely harmful for the venture and which should be avoided. Understandably, the increase in volatility of the outcomes leads to an increasing option value. The goal of this section is to deliver the definition of options in general, compare and find the similarities between financial and real options and define the different types of options as a preparation for the case study and following analysis. Furthermore, the value drivers of real options are stated and the differences between the net present value and the real options approach are pointed out.
3.2.1. What are Options – Definition
In contrary to the use of the net present value method, where after having made a decision the managers or decision makers are compelled to wait passively for the uncertain future outcomes to unfold, options can provide the investor with a valuable flexibility [Brealey et al. (2011)]. Although options only recently have become a major contributing part in global working markets, their history goes back centuries, for example to the Romans who already wrote option contracts on cargo ships [Smit and Trigeorgis (2004)]. The transformation of options into the modern financial world was then achieved by Black and Scholes (1973), who developed the famous and Nobel-prize winning formula that determines equity as an “option on the firm”.
Four years later, Myers (1977) first used the term of real options, defining it as a decision opportunity for a corporation or an individual. He describes real options as “a right, rather than an obligation, whose value is contingent on the uncertain price(s) of some underlying asset(s)”.
The definition of the option being a right, rather than an obligation is important as it also leads to options never containing a negative payoff. If, for example, the option is not in-the-money meaning the value of the option is not above zero, at or before maturity date, a rational and risk-neutral investor is not going to exercise the option.
- 21 -
Consequently, in real option terms, it supports the investor with a decision rule on whether to delay, expand, abandon or reposition a project and therefore enables the owner to flexibly react and act to an uncertain and unfolding future. Additionally, Smit and Trigeorgis (2004) differentiate between call and put options. While the holder of a call option has the right, but not the obligation to acquire an asset at a prespecified price, the put option enables the owner to sell an asset at a prespecified price, both limited in terms of their specified period of time. A typical example of a call option in real option terms can be seen in a land option. It endows the owner with the right, but not the obligation to acquire land at the predetermined sales price [strike price]. Understandable, the owner of the option only is going to buy the piece of land, when his projected valuation of the land is equal or higher to the strike price and therefore the option is in-the-money. If this is not the case, the investor can just walk away, letting the option run out, facing only the price of the option as sunk costs. In general, options lower the risk of investments, because the holder can use the time until the expiration date of an option to acquire knowledge about the potential project, its risks and underlying uncertainties. The following part [see Chapter 3.2.2] sees a graphical example for the possible different money states options can possess. Furthermore, options can occur as American or European options. They differ in their possible exercise date. While an American option can be exercised at any time till the maturity date, the European option can only be exercised on its maturity date. The term maturity date hereby defines the date, where the option runs out. Finally, two different price tags have to be differentiated regarding options. First, the option price or premium represents the price paid in order to acquire the option itself. In contrast to that, the price at which the underlying asset of the option can be bought or sold is defined as the exercise or strike price [Kodukula and Papudesu (2006)].
3.2.2. Options – Three Different States of Value
After having delivered the definition of options, this part intends to explain the three different states an option can be seen in leading to the different payoff conditions. For further clarification and a better understanding, a simple numerical example is given. Figure 5 and 6 differentiate hereby between a call (right to buy) and a put (right to sell) option. A call option can take three different states in terms of money, which result from the maximization of the following formula:
- 22 -
C = Max [0, S – X], which deducts the strike or exercise price [X] from the value of the underlying asset at maturity date [S]. If the option owner has to pay more to acquire the asset than the value of the underlying asset is worth [S < X], the option is out of the money and the owner will not exercise the option. A practical example can be seen in the option to acquire a share of a company. The strike price is set to be 50 US Dollar, but at maturity date the share price actually amounts to 40 US Dollar. Exercising the option would leave the owner of the option with a negative payoff of 10 US Dollar and therefore he will not exercise the option. The second state represents the condition where the strike price and the value of the underlying asset at maturity date are equal and therefore the owner is indifferent whether or whether not to exercise the option [S = X]. The option is at the money. In terms of the earlier given example, the share price would have developed to be 50 US Dollar at maturity date. In the third state, the option owner sees a positive payoff of the option as he can acquire the asset for less than it is worth [S > X]. In this situation, the option is defined to be in the money. A share price of 60 US Dollar at maturity date is an example as the option allows us to acquire a share that is worth 60 US Dollar for the predefined strike price of 50 US Dollar. All three calculations deliver the gross profit. In order to get the final net gain or value, the option price has to be deducted from the gross profit. This has to be taken into consideration while valuating the option payoffs as a gross profit not automatically leads to a positive net value. If in case three, the price for the option is set to 11 US Dollar, the net gain is negative while the gross profit still is positive.
F i g u r e 5 – P a yo f f s C a l l O p t i o n [ S o u r c e: A d o p t ed f r o m K o d u k u l a a n d P ap u d e su ( 2 0 0 6 ) ]
- 23 -
Similar to the call option, a put option can also take on three different states. As the put option gives the owner the right to sell an underlying asset at a predetermined strike price, the maximization of the formula: P = Max [0, X – S] represents the opposite compared to the payoffs of the call option. As long as the strike price is bigger as the underlying value of the asset at maturity date, the option is therefore seen to be in the money. This is comparable to the first given example of the call option, where the strike price is set to be 50 US Dollar and the share price amounts to 40 US Dollar in the market. Being able to acquire a share through the market for 40 US Dollar and directly sell it because the option would lead to automatic gross profit of 10 US Dollar for the option owner. As the value of the underlying asset increases, the gross profit decreases, being zero when the asset value reaches the exercise price [S = X]. Further increase and exceeding of the strike price of 50 US Dollar leaves the option to be out of the money and the exercising of the option undesirable for the owner [S > X].
F i g u r e 6 – P a y of f s P u t O p t i o n [ S ou r c e: A d o p t ed f r o m K o d u k u l a a n d P a p u d esu ( 2 0 0 6 ) ]
- 24 -
3.2.3. Financial versus Real Options
As stated in section above, the central idea of real options is based on the concept of financial options provided by the paper of Black and Scholes (1973), which first have defined and explained the upside potential resulting from financial options and uncertainties. Many authors like Myers (1977) then have applied this theory to investment cases in real assets. Both financial and real options therefore show similarities in terms of variables and conceptions. While both financial and real options give the owner the right, but not the obligation to invest or to undertake a project, they differ in the underlying asset. Financial options use intangible assets traded in the market, which stands in contrary to the tangible assets used for real options such as a business unit, a factory or a real estate object, which are not being directly traded in the market. This makes one liquid [financial asset] and the other in most of the cases illiquid [real asset]. Another difference is that if the future unfolds to be favorable the owner of a financial call option can always exercise the option collecting the underlying asset directly while a real option merely presents a project or investment opportunity which still is influenced by changing and uncertain future market condition as well as possible decisions made by other investors or competitors. Adding to that is the difference in terms of the resolution of uncertainty. Kodukula and Papudesu (2006) see an automatically clarification of uncertainty along the time scale for the financial option while the holder of the real option has to further actively invest in market research or testing of a product in order to clear possible uncertainty. Financial and real options also differ in terms of how the value of the option can actively be controlled over its life period. While in the financial form, the owner has no control of the development of the value other than to observe its development, a real option leaves the owner with possibilities to achieve an increase in value through proper management actions like for example an expansion alternative or the developing of a complementary product. Figure 7 gives an example how an investment opportunity can be seen as and transformed onto a financial call option.
- 25 -
F i g u r e 7 - M a p pi p i n g a D ev el el o p m en en t O p p o r t u n i t y o n t o a F i n a n c i a l C a l l O p t i o n [ S o u r c e: e: A d o p t ed ed f r o m L u eh r m a n ( 1 9 98 98 ) ]
The present value of the underlying risky object (V) – Mirroring the value of the real
estate investment opportunity object. This is identical to the stock price when evaluating the financial call option.
Cost for investment or construction costs of the object as well The exercise price (X) – (X) – Cost as possible investment costs for the conduct of an additional phase.
The time to expiration (t) – Duration in which the option is available and the decision
whether to develop and to invest or not can be deferred.
Indicator for the value of money a firm could earn The risk-free rate of return ( ) – ) – Indicator when instead of undertaking the project; the money is invested otherwise.
The variance
– Representing
the amplitude of outcomes in terms of the
performance of a stock index and there corresponds to the riskiness of a project asset in a real option case.
3.2.4. Types of Options
After having delivered the definition of an option and how it evolved from a pure financial instrument to being also used in form of real options, this section deals with the different types of options. The earlier determined differentiation between call and put options turns up again as examples for both variations are stated.
- 26 -
Options are valuable in terms of adding flexibility in the decision making process and therefore can increase the upside potential or hedge the downside risk of an uncertain project outcome in the future [see Figure 8]. The figure illustrates in a simple but understanding way how the management can react to the spreading volatility of expected cash flows throughout the project duration. The black solid line hereby represents the predicted mean of cash flows. Both areas above and under the solid line yield considerable and additional value when the management is aware of the possibilities and possesses option to adjust to the circumstances.
F i g u r e 8 - D i s pl pl a y i n g A d v a n t a g es es f r o m F l u c t u a t i o n s o f O p t i o n s [ S o u r c e: e: A d o p t ed ed f r o m M u n ( 2 0 0 6 ) ]
While a lot of different possibilities have been created throughout the last years, the main and most relevant examples are hereafter presented in detail. In order to supply a better understanding, the definitions and clarifications are underlined by adequate and realistic examples. The chosen options also represent the options appearing in the case study. All options are set to be American options giving the option holder the right to exercise the option at any given time until the expiration date. The option to construct the object is the most basic example for a call option. It gives the owner the right to undertake the investment and due to its simplicity is hereafter not further explained in detail. 3.2.4.1.
Option to Expand
The option to expand enables the owner to increase the investment or scale if the market conditions turn out to be even more favorable than expected. A typical example for this option can be a commercial real estate object such as a factory. The firm wants to keep the
- 27 -
possibility of a later expansion open and therefore acquires the option to expand. In reality this would mean that the firm buys for example a right to build a second floor on top of the existing factory at a certain predefined price if for example production capacity needs to be increased because of increasing product demands. The choice to expand is an example for a call option. 3.2.4.2.
Option to Defer
The option to defer is another example for a call option. It provides the owner with the right to wait and to delay the investment decision to a later point in time and therefore enables the owner to acquire more information about possible outcomes and the project itself. The option to defer can often be found in real estate development, where investors acquire inexpensive or undeveloped land, but wait with the development decision until more favorable market conditions eventuate. This is especially reasonable in the field of real estate development, because once a project is started; it ties a lot of capital and the investment costs are almost irreversible and therefore fixed. 3.2.4.3.
Option to Contract
In contrary to the option to expand, the option to contract supplies the owner with the right to scale back on the project or the investment and therefore represents a put option. Usually this is achieved by disposing some of the assets. When market conditions developed into non favorable directions, the firm tries to hedge itself against the downside risk with for example a legal contract providing them with the right to sell some of not needed assets [Mun (2006)]. In terms of the earlier stated example of the factory, the firm would be able to sell some of the factory space or some of the not required productions capacity to a vendor, which would see their costs reduced. 3.2.4.4.
Option to Abandon
If the market conditions turn out to be less favorable than expected, this option gives the owner the right but not the obligation to realize the salvage or rest value of the project or object. In terms of the factory example, this means that the object or usable items and inventory can be resold for an adjusted market price or salvage value helping to recover some or all of the initial investment costs. A typical example in the field of real estate development is described by the undeveloped land that also can be resold and with it the transferred right to build or develop an object on it. This often still has an intrinsic value and can be realized. Similar to the option to contract, the abandonment option is an example for a put option. The
- 28 -
difference between the two options is that the right to abandon a project always exists resulting in the salvage value. The value of salvage can hereby in the worst case equal zero. The option to contract in contrary requires a contracting party, which acquires the assets at a predefined price. 3.2.4.5.
Sequential Compound Option
The concept of a sequential compound option describes the option on an option. It characterizes the predefined staging of development. It gives the owner the choice to flexibly adjust and react to changing conditions. This can for example be a signed contract that includes different abandoning, deferring or expanding options depending on earlier executed options. In terms of the factory, a further expanding option for example to a third floor would need a previous exercising of the option to expand the factory to a second floor. Trigeorgis (2011) defines the compound option as each stage being an option on the value of subsequence stages. In terms of the case study, the sequential compound option is represented by the possibility of exercising option two and three expanding the investment with an exercise of option one being a necessity.
3.2.5. Value Drivers
This section works under the assumption that real and financial options roughly are based on the same parts and concentrates on determining uncertainties and value drivers of the flexibility for real options. Recalling that a financial option gives its holder the right but not the obligation to buy or sell a certain amount of the underlying asset at a specific price before or at the maturity date [Copeland and Antikarov (2003)], it is the goal to point out how one can extract this generated value. Mun (2006) defines five necessary assumptions in order for real options to incorporate strategic value. First, he states the need for a finance model, which can incorporate variables. Additionally, uncertainty as an input variable is essential, because without it, real options and there flexibility value are not present. Furthermore, the uncertainty has to directly impact the project value. Consequently, decisions regarding the project are affected by the risk mapped in the financial model. Finally, the assumption of rational acting management and decision makers has to be fulfilled together with the investors possessing the options or strategic flexibility to undertake corrections. This means that the investors have to be able to react to the changing and unfolding future during the development process.
- 29 -
Having stated the necessary assumptions for real options providing value, it is the goal to define what variables impact the value of real options. Copeland and Antikarov (2003) specify six fundamental variables, which are known from financial options due to their similarities and hereafter are defined.
Present Value of the Project
In contrary to the financial options, real options are harder to estimate with absolute certainty as they are not so frequently traded on the stock markets in comparison to financial options. And even though similar housing objects and their real estate or rental prices can be used for evaluation, they only can display an approximation of the actual present value of the project. Besides that, the relationship between the underlying asset and the value of the call option is positive meaning an increase in the asset also increases the value of the option. The opposite is the case for the value of a put option.
Project Cost
This describes the investment costs to undertake a project. It corresponds to the exercise price of a financial call option and understandably stands in a negative relationship to the option value. If a company or investor has to pay for example 10.000 US Dollar instead of originally 5.000 US Dollar for a piece of land, it affects the call option value leading to a decrease and vice versa for a put option.
The risk free Interest Rate or Weighted Average Cost of Capital
The interest rate or the weighted average cost of capital stands for the opportunity costs a company faces. It represents the money a company can earn when instead of undertaking the project; it would invest the capital in financial markets earning the risk free interest. An increase in the interest rate leads to an option becoming more valuable and therefore the owner more likely to defer the investment decision. Again, put options behave reversely. In terms of the case study, the US ten year treasury spot rates are applied [see Appendix 2].
Time to Expiration of an Option
The longer the company has the possibility to defer its decision, the more value lies in it as the firm can gather more and possibly essential information about the investment opportunity. In case of a real estate development, this can play a crucial rule as throughout the different, sequential stages of the development, the owner might be better able to identify and estimate
- 30 -
the underlying uncertainties of a project. Both, call and put options are positively related to the length of time to expiration date of an option.
Dividends or Opportunity Costs
In financial terms a pay of dividends automatically leads to a decrease of the call option value. It makes an earlier exercising of the call option more lucrative to allow the owner to capture the dividend and therefore dividends can be identified as opportunity costs. In the topic of real estate development, a competitor entering the market increasing the supply of houses and therefore leading to a decrease of the market price for houses or rental prices can be seen as such opportunity costs. Competition has a negative impact on the call option value and might provoke an early exercising of the call option, while a put option value increases from the investment facing additional competitors or other opportunity costs.
Volatility or Project Risks
Volatility represents the standard deviation and therefore directly mirrors the uncertainty regarding the possible performance outcomes of the underlying asset. As only positive [negative] outcomes are exercised in terms of call [put], a higher uncertainty automatically leads to an increase in the option value. The problem each real option valuation faces is that there are many different risk factors affecting the volatility of a real estate development object making it hard to fully describe and define all risks. Regarding the case study in Chapter four, a selection of risk factors are described more in detail to give the reader an overview of possible influencing factors [see Chapter 3.5.1.1]. In order to transform the selections of risk variables, which define the volatility, usually data from comparable objects regarding settings and risks are taken or the Monte Carlo simulation is applied. An overview of alternatives to estimate the volatility is given in Chapter 3.5.1 together with a further explanation of two for the case study relevant methods.
3.2.6. Differences Net Present Value vs. Real Options Analysis
Both methods have been presented and this section sums up the main differences between the two valuations approaches [see Table 2]. The discounted cash flow method is set up as a deterministic model and it neither accounts for uncertainty in a project nor is the method capable of acknowledging and incorporating the possibility of managerial adjustments to changing circumstances. The real options analysis recognizes the additional value under the
- 31 -
assumption of proper and rational managerial decision making, which means that managers undertake the value-maximizing decision at each decision node during the lifetime of the project. Discounted Cash Flow All or nothing strategy. Does not capture the value of managerial flexibility during the project life cycle. Uncertainties with future project outcomes are not considered. Undervalues the asset that currently (or in the near term) produces little or no cash flow. Expected payoff is discounted at a rate adjusted for risk. Risk is expressed as a discount premium. Investment cost is typically discounted at the same rate as the payoff, that is, at a risk-adjusted rate.
Real Options Analysis Recognizes the value in managerial flexibility to alter the course of a project. Uncertainty is a key factor that drives the option’s value. The long-term strategic value of the project is considered because of the flexibility with decision making. Payoff itself is adjusted for risk and then discounted at a risk-free rate. Risk is expressed in the probability distribution of the payoff. Investment cost is discounted at the same rate as the payoff, that is, at a risk-free rate.
T a b l e 2 - C om p a r i n g D i sc o u n t e d C ash F l o w a n d R ea l O p t i o n s A n a l y s i s [ A d o p t ed f r o m M u n ( 2 0 0 6 ) ]
Having pointed out the differences between the discounted cash flow method and the real options analysis, it is essential to determine under what circumstances the real options analysis delivers the most potential and value. Figure 9 displays a briefly division into four different categories, which depend on the level of uncertainty and managerial flexibility. Additionally, the net present value of the project plays a role in how the additional value of the real option affect the decision. A project with a very low [high] net present value might be rejected [accepted] regardless of the impact of the real options, because the additional value is negligible and the project still would be a no go. In case of the high basic net present value, the project is already lucrative enough for the company to undertake the investment.
F i g u r e 9 - S cen a r i o s o f R e a l O p t i o n s V a l u e C r e a t i o n [ S o u r c e: K o d u k u l a a n d P a p u d esu ( 2 0 0 6 ) ]
- 32 -
3.3.
Real Options Valuation Methods
Kodukula et al. (2006) state three dominant methods when valuing real options, which in the following are presented and discussed.
3.3.1. Partial Differential Equations
Mun (2006) differentiates between closed form solutions, numerical methods and analytical approximations. Generally spoken each of the partial differential equations is solved with the help of boundary conditions, which often can complicate the solving of the models. Within the partial differential equation methods, the most used version is the closed form solution, which often applies the famous Black-Scholes model (1973) and is giving by the following formula and represents the value of either European call or put options:
Where
(3.6) (3.7)
is the value of the underlying asset or stock price, X is the cost to exercise the
option or the strike price, rf is the risk free rate, T is the expiration time or the duration of the strategic option, σ is the annualized volatility of the underlying asset or stock and N stands for the cumulative probability of a normal distribution and d is given by:
(3.8) (3.9)
One big advantage of applying the closed form solutions is that all of the input parameters are known or easily calculated based on made assumptions. While delivering exact results, the models are often hard to explain due to high level of technical stochastic calculus mathematics applied. Additionally, models like the Black-Scholes Model are only exact for European options. When it comes to American options and more advanced versions of options like for example a compound option, they often deliver only an approximation. Regarding the case study, the closed form solution is not applied.
- 33 -
In order to understand the model and how it is applied, specific assumptions have to be satisfied. The main assumption states that the returns of the underlying asset follow a stochastic process, typically a geometric Brownian motion [GBM] with static drift and constant volatility parameters, which follow a Markov-Wiener stochastic process [Mun (2006)]:
Where μ is the growth variable that increases with the time steps
(3.10)
, σ defines the volatility
and represents the stochastic part, which grows at the multiplier rate of the square root of the
). This part often is called Wiener
time steps and the simulated error term variable (
process. Additionally, the error term follows a normal distribution with the mean of zero and a variance of one [N (0,1)]. Further required assumptions are that there are no transactions costs, no taxes or dividends, no riskless possibility of arbitrage, a known and constant exercise price, which can only be exercised at expiration [European Option] and therefore the existence of an efficient market.
3.3.2. Simulation
Monte Carlo simulation is an extension of but not a substitute for the Discounted Cash Flow method. Whereas the Discounted Cash Flow method takes one set of input parameters and calculates the deterministic net present value of one project, the Monte Carlo simulation makes the exact same calculation thousands of times by just changing the input parameters each time. The simulation results show a distribution of the project payoff, with the "average" case representing the net present value based on the Discounted Cash Flow method. Whereas the simple Discounted Cash Flow method is seen to be deterministic, the Monte Carlo simulation results in a probability distribution of the possible project net present values. Simulation in general has the same drawbacks as the Discounted Cash Flow method. It does not take into account the contingent decisions and their impact on the project valuation. The model beneath has been proposed by Boyle (1977) and defines the connection between present values and future predictions.
(3.11)
- 34 -
Equation 3.11 estimates the value of the underlying asset
on the basis of the value from the
, which represents the deterministic part and the multiplication of the value of the previous period with the stochastic part of the constant drift μ and the
previous period
volatility σ, multiplied with the simulated error term drawn from a standard normal
distribution with mean zero and variance of one.
3.3.3. Binomial Lattice
The third method to be presented is the binomial option pricing and was originally developed by Cox, Ross and Rubinstein (1979). Similar to the before presented simulation and BlackScholes rule, it assumes the existence of the no arbitrage rule. With the help of the binomial tree, the different possible developments of the underlying asset are displayed. The tree structure is reoccurring and creates the basic foundation for any real options model is of interest [see Figure 10]. One essential advantage of this approach is that it enables the investor to calculate exact numbers for both, the American and the European version of options. Mun (2006) describes the necessity of minimum two lattices required to mirror the option. First, there is a lattice, which replicates the value of the underlying asset and second, a lattice, which represents the intrinsic value of the option. The intrinsic value is the difference of the value of the underlying asset S and the exercise or strike price X .
F i g u r e 1 0 - O p t i o n V a l u e of a O n e - st e p B i n o m i a l L a t t i c e [ So u r c e: A d o p t e d f r o m M u n ( 2 0 0 6 ) ]
Up [u] and down [d] movement of the underlying asset can be displayed as the following:
(3.12)
- 35 -
(3.13)
Where σ stands for the volatility of the movement of the underlying asset and δt represents the predetermined time steps. Based on the calculated up and down movements, it is possible to estimate the risk neutral probabilities with the following formula:
(3.14)
The variable b hereby only comes into play in case dividends are paid or exist. The present value of the option is then calculated by discounting the individual intrinsic values of the different paths with the risk free rate rf [see equation 3.15].
(3.15)
Usually an option in the field of real estate has a maturity of more than one step. Equation 3.16 is an example for calculating the value of a two-step binomial tree of a recombining lattice.
(3.16)
It is then possible to expand the binomial tree from a one-step to a multi-step valuation tool. The following two formulas display the value of multi-step European call and put options:
(3.17) (3.18)
Where
(3.19)
- 36 -
This formula consists of the variable n for total number of steps, k for the number of up movements, (n-k) for the number of down movements and δt for the time steps. The above stated formulas represent solely the European version of options, which can only be exercised at the maturity or expiry date of the option. American options enable the owner to exercise an option early when market conditions are favorable. One important variable that makes an early exercise of the option profitable is the existence of dividends. While in the case of non-dividend paying American call options not exercising the option early protects the holder against the volatility of the value of the underlying asset and against the value to fall beneath the strike price, the holder misses out on income in the case of dividends when he does not exercise the option early. For the case study at hand two variations are important. First, the formula for maximizing the option value comparing immediate exercise with the value to abandon, which equals:
(3.20)
Where T stands for the point in time, d for the down movements within the time period, X represents the amount of costs to exercise the option at point T. The second important equation for the case study is the comparison of exercising the option immediately and the value generated through deferring the investment. Again, the following formula is maximized:
(3.21)
In order to determine the present value of the option, the comparison step of equation 3.21 is applied for every step throughout the binomial tree.
3.4.
Approaches to Real Options
Real options are based on assets that are not like financial assets widely traded, which leads to an increased importance of management assumptions in order to apply real options. Borison (2005) defines five different approaches of how to approach real options, which in the following are differentiated and discussed briefly.
- 37 -
3.4.1. The Classic Approach
Based on the assumption of no arbitrage from the classic option pricing theory, the classic approach states that with the help of a portfolio of traded investments a replicate of the returns of the real option can be created. The underlying important assumption is that the price movements follow the geometric Brownian motion [GBM]. If fulfilled, the Black-Scholes model can be used to calculate the option value. Concerning real options, this assumption often is violated. Additionally, it is difficult to identify replicating portfolios for illiquid traded real assets. On top of that, the approach does not account for market uncorrelated risk.
3.4.2. The Subjective Approach
While based on the same assumptions as the classic approach, the subjective approach uses subjective rather than objective gathered data, which leads to the approach being exposed to stating the right and accurate assumptions. Furthermore, generated data based on subjective made assumptions is hard to examine and therefore hard to verify. Ignoring potential differences between private project-related and market risk can lead to false estimation results.
3.4.3. The Marketed Asset Disclaimer Approach
In their book, Copeland and Antikarov (2003) bring up the Marketed Asset Disclaimer as approach to value real options. They reason that the best unbiased estimator of a project should be the project itself and address the market value of the underlying object as if it is traded in the market. The problem that occurs is that the approach uses subjective data and is based solely on the project itself. Possible correlations to traded similar assets are ignored, which can lead to inaccurate estimations.
More importantly, the MAD approach is not
guaranteed to follow the geometric Brownian motion because it uses subjective data. Schneider et al. (2008) address this problem and have develop an extended MAD approach, which with increasing complexity are capable of dealing with market and private risk. Borison (2005) argues that the three above stated methods should be applied with care because of the above mentioned pitfalls.
- 38 -
3.4.4. The Revised Classic Approach
The Revised Classic Approach is an answer to the problem of how to deal with market and private risk and induces that depending on the major type of risk exposure, the approach should be selected. The Black-Scholes model can be applied when the major risk type is in market form regarding the project and in contrast to that the subjective MAD approach is applied. One major disadvantage of this procedure is that by trying to handle both risk segments, it is hard to find a combined and accurate discount rate.
3.4.5. The Integrated Approach
The Integrated Approach points in the same direction as the Revised Classic Approach, trying to incorporate both risk types. This makes this approach complex to apply and suffer from similar problems, which the Revised Classic approach also faces.
3.5.
Real Options in Real Estate
As shown and stated in the introduction and background section, real options perfectly meet the necessary criteria to deliver accurate and appropriate valuation results in the field of real estate development. This section deals with the empirical evidence of real options in real estate as well as it supplies and explains the external risk factors real estate development faces. Defining external risk factors helps setting up the model in preparation for the case study, where the different risk factors are taken into account for the analysis. Various theoretical papers like Capozza and Li (1994), Titman (1985) or Lucius (2001) have dealt with the occurrence of real options in real estate. The effect on the development process is caused by the flexibility the option to defer or expand an investment, the switching or abandonment option or the time to build option can offer [Trigeorgis (1996)]. Titman (1985) identifies a relationship between the uncertainty of vacant land values and the building activity. Increased volatility leads to a decrease in building activities in order to keep the option alive. Cunningham (2006) confirms these hypotheses. He finds evidence that greater price uncertainty not only delays the decision of development, but also raises the land prices as partly the option value are implied in the rising prices. Williams (1991) adds to this work by also taking the cost of development variable into consideration and has examined the optimal density and timing for development or abandonment of an object when the value of the object is influenced by volatile outcomes.
- 39 -
Quigg (1993) has been among the first to test the empirical evidence of the value to wait to develop land using a sample of market prices. She confirms a mean premium of six percent as well as 18 to 28 percent implied volatility for the prices. Geltner et al. (2007) endorse the volatility findings and set the typical volatility of individual properties in a range from 10 to 25 percent. Additionally, Geltner et al. (2007) see the real option theory as a central element of investment decision regarding land development due to their ability to capture the value and flexibility of sequential development. This stands in contrast to the paper of Lucius (2001), which sees the still rare practical applications of real options theory in the real estate development process being a result of mathematical complexity. Though, a number of papers have applied and tested the real options analysis using market data from real estate. Sing and Patel (2001) investigate transactions of properties in the United Kingdom estimating a premium for the option to delay investment and development in the sectors of office, retail and industry. Bulan et al. (2002) find an empirical connection between uncertainty and investment in development of objects. Their results based on evidence in Vancouver confirm the hypothesis that an increase in return uncertainty drives down the amount of investment. Furthermore, a direct comparison of the two at valuation methods, the net present value and the real options analysis, and their performance in the field of real estate has been examined by Rocha et al. (2007). Their findings point out that the real options methodology is superior compared to the net present value. The applied methodology follows a sequential decision making process, which enables the investor to identify the right strategy along the path. Because of this strategy, the applied real options model not only increases the value of the project by ten percent, but also reduces risk the project is confronted with by more than 50 percent in comparison to the static and traditional discounted cash flow analysis. Baldi (2013) applies the real option theory to a real estate development project and compares the inherent flexibility of that process with the static net present value. His results support the findings of Rocha et al. (2007) that applying the real option valuations allow the investor to capitalize on the volatility in either directions because of the strategic nature of call and put options. Because the discounted cash flow method misses out on the managerial flexibility, following this approach would lead to a constantly underestimation of the assets in real estate. In the following, the above mentioned term volatility is presented and determined more in detail.
- 40 -
3.5.1. Volatility
Pomykacz (2013) defines volatility as the amplitude of how a future price or value of a stock can vary. Transformed to the field of real estate, volatility represents the standard deviation and therefore directly mirrors the risk regarding the possible performance outcomes of the underlying asset. Because it has a relevant impact on the value of the option, it is an important variable for the real options analysis process. Volatility in the field of real estate is difficult to calculate or estimate, which often leads to the usage of historical volatility indices. The problem that arises out of this method is that making predictions about future development of the volatility based on historical data can be inaccurate or flawed, because historical developments cannot guarantee a prediction for future development. Part of this sections supplies tools that offer a way on how to deal with data in order to estimate volatility. Figure 11 shows two examples for normal distributed curves of expected returns r and their distribution for the underlying asset and explain in a simple way how different levels of volatility can create value. The dashed line hereby contains a higher standard variation in comparison to the solid line illustrated through the wider range of returns. This is of interest regarding the case study as the two valuation approaches treat risk and therefore the standard deviation, which impacts the object, differently. The static approach of the net present value reacts to the increase of volatility by adjusting the discount rate. This is a result of perceiving the higher volatility purely as higher risk affecting the project, which leads to a lower estimated outcome. In contrast to that, the real options analysis incorporates the flexibility of managerial interactions and therefore enables the investor to adjust to both possible directions movement of the volatility.
F i g u r e 1 1 - A l l o c a t i o n o f E x p ec t ed R et u r n [ S o u r c e : O w n C r ea t i o n ]
- 41 -
The problem that arises when the volatility is calculated is that even though the factor in the options models is represented by one combined variable [Kodukula and Papudesu (2006)], multiple risk factors exist and influence the uncertainty of the cash flows of the underlying asset. Examples can be found in directly attributable factors like the sale price or the building costs or indirectly through external risk factors emerging from social, political or economical nature. In order to deal with the different sources of uncertainty and to make them applicable, Kodukula and Papudesu (2006) see two different possibilities of dealing with the volatility. For one, it is possible to retain all the variance separately when it is assumed that the variables are uncorrelated, develop differently in the viewed timeframe and influence the value of the object in opposite directions. The second method suggests combining all individual risk factors into a merged and representative variable. The transformation process irrelevant of the chosen approach can be conducted using five different methods, which in the following are presented and described briefly. Based on Kodukula et al. [2006] and Mun [2006] a short overview of different methods to estimate volatility is given.
Logarithmic Cash Flow Returns or Logarithmic Stock Price Returns Method – is
mainly applied when the volatility is calculated on the basis of liquid and tradable assets, for example the price of oil or electricity. It benefits from its easy implementation, high transparency and that it uses the same cash flow estimates as in the calculation of the underlying asset value. Main disadvantages of this approach are that it cannot be used for negative cash flows and in the case of only a few quantities of cash flows, the volatility generally is overstated.
Logarithmic Present Value Returns Approach – is applied when the volatility of assets
with cash flows are calculated. While it does account for negative cash flows and through more rigorous analysis delivers more accurate estimation of the volatility, it requires simulation to obtain a single volatility.
Generalized Autoregressive Conditional Heteroskedasticity [GARCH] – similar to the
first method is used for liquid assets and is capable of delivering different estimates over time, but its econometric complexity and high data demand require advanced expertise.
Management Assumptions or Guesses – can be used for both financial and real options
and is easy applicable. Subjective guesses though do not deliver very reliable estimates.
- 42 -
Market Proxy Using Comparables or Indices – is mainly used in order to compare
liquid and non-liquid assets. The need for comparable market-, sector-, or industryspecific data can be the downside of the method, as it can be hard to identify a public traded company or project with a similar risk profile. 3.5.1.1.
Risk versus Uncertainty
Mun (2006) states an important differentiation between risk and uncertainty as they are often treated and defined to be the same. The uncertainty that a project has can throughout the duration of the option, interactions or events and the lifecycle of the project be resolved while the risk of a project is carried along the project. Risk is an outcome of uncertainty and while it stays constant, the uncertainty increases over the project time duration. 3.5.1.2.
External Risk Factors
This section deals with the factors of risk and uncertainty influencing the process of real estate development. Sun et al. (2008) identify four main groups of risks affecting the industry of real estate of which three (Political, Social and Economical) hereafter are presented more in detail. They are found to be the most significant for the case study. The goal of this section is to give an overview of what each category includes and stands for as well as give a preview of how the risk factors are applied to case study. Political Risk
Real Estate development underlies regulation which can include industrial policy in terms of commercial real estate development as well as development of factories or producing real estate. In addition to that, Sun et al (2008) name housing regulation and land regulation reforms as possible influencing factors. This can appear in regulations regarding on directly housing attributes such as how high or densely an object can be built as well as land regulations, whether or not the owner is allowed to build the desirable type of real estate. Social Risk
Social risk can include very external and broad aspects like the changing city planning, which can have a direct influence on the development of the housing prices. Imagine for example the city decides to construct a new city highway which passes directly the real estate object of the investor. Resulting noise and smug might directly lead to decrease in value. A further risk might be seen in zone development, which can have both a positive and negative effect on the investment opportunity. Shopping centers, bars, restaurants, cultural objects or parks can upgrade the investor’s land value while for example the developing of an industrial area
- 43 -
would see the prices directly decrease. In addition to that, the process of gentrification can influence the value of the real estate positively as well as the building of ghettos, including increased crime rates or unemployment rate, can have a negative impact on the firm’s
investment. Economical Risk
Not since the real estate bubble in 2008 and 2009, the financing is a topic in the real estate industry. While through credit financing and hypothecs, the demand for housing and therefore the value and sale prices of objects can be increased, it has its limits. The financial situation of the city or the population of the city therefore always has a direct influence on the price and represents a risk factor. Breaking away of big industrial companies can be essential for the going-concern of a city and its financial situation as it is directly mirrored in terms of employment, purchasing power and paid taxes. The example of Detroit illustrates perfectly this potential devil circle.
- 44 -
4. Case Study – Reviving Downtown Detroit Using the real options approach to value real estate development projects is crucial to capture the flexibility value. Recalling the earlier mentioned equations describing the difference between the static net present value and the expanded version that incorporates the intrinsic option value [Trigeorgis (2005)]:
(4.1) (4.2)
This chapter aims to apply the delivered theoretical framework of real options analysis to a real estate development project in Downtown Detroit. Running the numbers, this section additionally aims to answer the posted theoretical hypotheses. An interesting area with two suitable investment projects has been identified and chosen for this case study. Where exact specifics and characteristics of the objects have been hard to obtain, assumptions are made in order to comply with the requirements. The two chosen buildings [The Broderick Tower and The David Whitney Building]4 are located side by side in Central Downtown Detroit, USA. Both are separately financed through Detroit investment funds and belong to different clients.
4.1.
Project Description
In the case study at hand, several important adjustments are made in order apply the real options analysis to the development objects. First, the investment case puts the decision maker back into the beginning of the year 2010. The decisions whether to renovate the investment objects have not been made. Furthermore, the objects are seen as one combined project, divided into different sequential stages that can be developed by the option holder [investor]. The different stages underlie a specific order of construction. In reality, both real estate objects possess a share of retail, which in the case study is combined to one. The third stage can only be developed if option one and two are exercised and constructed.
4
investdetroit.com/representative-projects/
- 45 -
Additionally, it is assumed that in the base case scenario only one phase can be constructed at the same time, which means that the earliest construction of phase two is year three of the option, even if an earlier exercise of the option would be profitable because of favorable market developments. In the real options analysis, the construction of the up following phase can start as soon as the option of the prior option has been exercised. The construction or renovation time for the options one and two are two years and one year for option three. The project is assumed to be completely equity financed. Therefore the Capital Asset Price Model is applied in order to calculate the essential inputs for the cost of capital rates. Figure 12 shows a summary of the basic facts regarding the different stages. The numbers are based on real figures, retrievable on the website investdetroit.com, but edited in order to make each option valuable and dividable. The total building area is the result of numbers of apartments multiplied with the average square foot per apartment. For simplifying reasons, the two apartments possess the same size. One major assumption has been made in order of efficiency, which describes the percental share of the total building area that is available for leasing. The maturity of the options has been set to two and five years for option one and two and ten years for option three. The longer maturity of option three realistically reflects the adaption time of the multihousting apartments. The option therefore should enable the owner throughout the lifecycle to identify whether a retail investment expansion is profitable.
F i g u r e 1 2 - P r o j e ct D e sc r i p t i o n o f t h e I n d i v i d u a l S t a ge s
- 46 -
In contrast to the staging of the different phases in the used real option approach, the static valuation applies an inflexible development, which means that the up following phase is constructed immediately after the previous one is finished. In order to be able to successfully estimate the underlying drivers of the assets it is important to select a suitable approach, which is applied to the case study. It sets out the direction of how the data of the case study is treated and which assumptions are necessary to be made and followed. Recalling the different approaches to apply real options, presented in Chapter 3.4, it is hard to select one specific approach. The case study at hand utilizes a mixture of different approaches, because it is for one hard to believe that the assumption of an efficient market is satisfied, but on the other hand essential to rely on market comparable data in order to be able to calculate the underlying drivers. The consequence of a possible violation of assumptions is therefore critically questioned in the results.
4.2.
Underlying Drivers
Different variables that impact the value of the project have to be estimated before the valuation can be applied. This is done on the foundation of assumptions and historical data.
4.2.1. Income
The potential income from the different phases of the project is divided into the income generated from rent [multi-housing and commercial] and the terminal capitalization, which in the following are described and estimated. 4.2.1.1.
Rent
Historical data of the rent index in Detroit is used in order to estimate the average percental changes throughout the years from 1982 to 2010 [See Appendix 3]. The mean growth rate of the rent for the mentioned period has been estimated to 4.10 percent. The growth rate is hereafter assumed to be constant throughout the time of the project. Therefore, rents in the static discounted cash flow valuation therefore are set to grow constantly with 4.10 percent per year. The detroitsevenpointtwo5 report delivers an exact figure in terms of the rent per square foot for the Broderick Tower in the year 2014. The 1.88 US Dollar per square foot rent, which represent the monthly per square foot figure, is discounted back and forward with the
5
7.2SQ – Final report – detroitsevenpointtwo.com
- 47 -
calculated average rent growth rate [4.10 percent] for the years of the project. For the year 2010, this means a rent of estimated 1.60 US Dollar per square foot. Additionally, the rent is an essential variable of the income parameters and underlies fluctuation. The volatility of the rent income is assumed to follow the geometric Brownian motion stochastic process. A simulation with 50.000 iterations has been run in order to confirm the average fluctuation of the rent growth [see Appendix 4 and Excel sheet “GBM Simulation]. 4.2.1.2.
Net Operating Income
The net operating income is crucial in the valuation process because it impacts all income variables resulting from the received rent and it defines the terminal value the object generates for the owner. The net operating income results from subtracting the vacancy costs and the operating expenses from the potential gross income. The terminal capitalization is hereafter defined. 4.2.1.3.
Terminal Capitalization Rate
The rate determines the resale value of the real estate object at the end of the leasing lifecycle. It is estimated by dividing the anticipated expected net operating income of the following year by the exit cap rate. The cap rate survey estimates the exit cap rate within a range from 7.5 – 8.5 percent for the area of Detroit and to stay constant in the forecast [see Appendix 8]. The rate for the case study has been fixed to 7.8 percent, which lies within the normal estimated range.
4.2.2. Costs
The outcome is reduced to two variables. First, the construction costs of the different phases when the option is exercised and second, the operating expenses, which arise when the apartments or the commercial area is leased out. 4.2.2.1.
Construction Costs
The development of the construction costs has an essential impact on the timing of the development, because over proportional increasing costs for construction raise the opportunity costs a firm faces and might lead to an early exercise of the option. Data from the years 19922010 have been collected and the average increase during this time has been estimated. The result accounts for a mean increase of 3.406 percent per year, which is considered to be constant for the lifetime of the valuation.
- 48 -
Appendix 1 additionally shows the development of the American Consumer Price Index as a benchmark putting the development of the construction costs into perspective. It is assumed that the growth rate of the construction costs is independent and outweighing the discounting risk free rate and therefore displays an additional opportunity cost in order to cause a possible early exercising of the option. 4.2.2.2.
Operating Expenses
Operating expenses are all costs, arising from running the object. This includes costs for property management, wages for stuff and employees, costs of vacancies or maintaining costs. Usually, the operating expenses ratio varies depending on the type of building and range between 40 and 50 percent of the rent per square foot.6 To simplify the application of the case study, one constant operating expense ratio is predetermined, which is then directly related and connected to the rent income. For both types of buildings [multi-housing and commercial retail], the ratio is fixed to 35 percent of the effective gross income. The lower than average ratio rate results from the fact that the costs of vacancies already have been accounted for.
4.2.3. Cost of Capital
In order to simplify the application of the case study, it is assumed that the investment is purely equity financed. The case at hand is based on adjustments and assumptions made by the author, which differ from the reality, because no direct data regarding the investment company and its cost of capital or beta exists. Instead, it is assumed that the financial estimates of the investing firm are conform to the figures of the S&P Case-Shiller Detroit Home Price Index on which basis the beta is calculated [see Appendix 2 and Excel sheet “S&P Beta Calculation”].
4.2.3.1.
Risk free rate
The risk free rate is estimated based on the average interest rate of US 10-Treasury bonds. The average of the years 2001-2009 accounts to 4.28 percent [see Appendix 2]. 100 bps are deducted from the computed average risk free rate in order to account for an inflation premium [Geltner et al. (2007)]. This results in a final risk free rate of 3.28 percent, which displays a realistic figure for the estimated period. The ten years of the treasury bonds reflect the maturity time of the longest option regarding the project and therefore are a realistic
6
Income and Expenses Survey 2014 – naahq.org
- 49 -
estimate. The calculated risk free rate is assumed to stay the same throughout the life cycle of the project. 4.2.3.2.
Beta
The beta represents the sensitivity of an underlying asset to the volatility of the market. Mun (2006) defines it as a measurement of risk, which is not hedgeable and systematic relatively seen to the market. The calculation of the beta supports the investor to find the appropriate discount rate in order to compensate for the undiversifiable and systematic risk. It is
calculated as the covariance cov of the returns from the underlying asset and the market
[see Equation 4.3.].
and then divided by the variance var of the market returns
(4.3)
To compute the beta for the case study, it is assumed that the imaginary investing company possesses a return structure identical to the S&P / Case Shiller Michigan Detroit Home Price Index [see Excel sheet “S&P Beta Calculation”]. Then, the index is compared to the S&P / Case-Shiller 20-City Composite Home Price Index in order to calculate the beta based on formula 4.3. The average beta for the years 2002 to 2010 amounts to 0.813. Although this figure lies within the region of the industry comparable ratios [see Chapter 4.2.3.5.], the estimate seems smaller than expected, especially if a closer look is paid to the previous and more essential [crisis] years regarding the future development. To calculate a comparable figure, the whole range of years is taken into account and delivers a beta of 1.083. This is found to be more appropriate and is selected to be the beta for the case study. The beta is assumed to be constant throughout the project valuation time.
4.2.3.3.
Market Risk premium
To calculate the risk premium, the Capital Asset Pricing Model is applied:
(4.4) (4.5)
- 50 -
The average expected return of the market is estimated on the basis of the Morgan Stanley Capital Index for the whole world7, which amounts to an average of 7.28 percent annual return in the time range from 1970 to 2010. The risk premium is calculated by deducting the computed risk free rate from the market return rate. The result is 7.28 percent – 3.28 percent = 4.00 percent. 4.2.3.4.
Cost of Equity
The Capital Asset Pricing Model is applied in order to estimate the cost of equity. The chosen method is suitable regarding the integrated approach and the underlying assumption of an efficient market with no arbitrage opportunities. The CAPM is a risk-adjusted discount rate model [Trigeorgis (2000)]. It captures two types of risk, diversifiable and non-diversifiable risk. The first type results from industry specific factors and therefore can easily be hedged as they are not related to potential changes of market conditions. The second risk results from economic conditions that affect the price but cannot be diversified nor influenced. Because of that, it is often called systematic risk. As the CAPM compensates for the risk of the project, it is important to find a security that correlates perfectly with the investment. In the field of real estate development, this is rather difficult. Potential proxies mirror the best possible approximation. Additionally, the CAPM assumes interest rates to be held constant over the duration of the project, which is not very realistic. To simplify the case study, the interest rates are assumed to be constant though. This leads to required return on equity, derived from the CAPM and stated as the following:
In the case at hand, the required return on equity equals
(4.6)
= 3.28 percent + 1.083 x (7.28
percent – 3.28 percent) = 7.612 percent.
7
www.msci.com/end-of-day-data-search [see Excel sheet “MSCI World ’70 – ‘10”]
- 51 -
4.2.3.5.
Comparable industry ratios
Figure 13 confirms the previous calculations. The estimated beta and the cost of equity lay within the range of comparable ratios of similar industries and therefore display realistic figures for the valuation process.
Name of Industry
Number of firms
Beta
Return on Equity
R.E.I.T.
213
0.79
6.69%
Real Estate Development
18
1.02
8.04%
Real Estate Operation & Services
52
1.30
9.66%
Average
-
1.037
8.13%
F i g u r e 1 3 - C om p a r a b l e i n d u s t r y r a t i o s [ S o u r c e: A d o p t ed f r o m h t t p : / / p a g es. st e r n . n y u . e d u / ~ a d a m o d a r / N e w _H o m e _ Pa g e/ d a t a f i l e/ B e t a s. h t m l ]
4.2.3.6.
Discount Rate – Development Time
In order to account for the higher risk an investment company faces during the development [here: renovation] of the object, a higher discount rate has been set to ten percent and is kept till the individual phase reaches an absorption level of 90 percent. After that, the normal cost of equity rate of 7.612 percent per year is applied.
4.3.
Base Case Valuation
In order to commence with the calculation of the net present value, it is important to recall some of the mentioned assumptions the approach underlies. The approach assumes no flexibility in the decision making together with deciding at t = 0, whether or not to undertake the whole project. It is assumed that each stage is then constructed immediately after the previous phase has been completed in order to avoid an unnecessary increase of the construction costs. In the model at hand, three discount rates are applied. The first one is the risk free rate, which is used to discount the construction costs to the present value. In contrast to that, the cost of capital [hereby the cost of equity due to purely equity financed firm] is applied to all income in order to meet the different and higher systematic risk after the object reaches a 90 percent absorption level. Before that, the higher perceived risk level is accounted for in the higher so called development discount rate. Achieved rent and the exit cap rate payment at the end of the project’s lifetime are therefore discounted depending on the absorption level of each individual option.
- 52 -
To compute the project’s total net present value all three projects are added up after their
individual net present value has been calculated.
(4.7)
Summary Input Variables
Exit Cap Rate Detroit 2010 Long-Term Building Vacancy Inflation - Average CPI
0.0780 0.1011 0.0243
10 Year US Treasury Risk Free Rate MSCI Average Return Risk Premium (rm-rf)
0.0428 0.0328 0.0728 0.0400
Construction Cost Growth
0,0341
Operating Expenses Operating Expenses Growth
0.035*E(Rent) Attached to Rent Growth
Rent Growth Beta Return on Equity (Stab. Discount Rate)
0.0410 1.0828 0.0762
F i g u r e 1 4 - I n p u t V a r i a b l es [ So u r c e: O w n C o n st r u c t i o n ]
Figure 14 sums up the main input variables, which previously have been calculated [see Chapter 4.2. and ExcelSheet “Masterthesis Calculations”]. The project is assumed to have a
total lifecycle of 18 years, in which income is generated before the owner alienates the property. The time interval between decision nodes has been set to one year.
4.3.1. Expected Static Net Present Value
The net present value of the whole project is estimated by adding up the individual, expected net present values of the different phases [see Equation 4.7.]. The calculation of the figures in detail can be viewed in Appendix 5 or in the Excel sheet “Static NPV Chart”.
- 53 -
While phase one has a positive net present value, the stages two and three are expected to result in a negative outcome with a total return of -10.109 mio US Dollar. The static valuation approaches assumes the project to be seen as one whole combined investment and not in sequential stages. A decision has to be made whether to undertake the whole investment or not at the beginning of the project. Under these circumstances, the recommendation would be to decline the project, because of the negative payoff. This view on the valuation can be seen as deterministic and not stochastic, because the expected payoffs and net present value does not incorporate the uncertainty of the development of the rent. Instead, it is assumed that the rent growths with a constant and in advance known rate.
4.4.
Real Options Analysis
In order to be able to start valuing the strategic value of the options regarding the project and its different phases, the existing real options have to be stated and identified. In the literature review, the main types of options are determined and are applied also within the project. In the case at hand, the option to defer and abandon the investment is present. On top of that, the three options themselves appear as a sequential compound option. This is the case, because exercising option two and after that on option three only is possible when option one has been exercised. Also, option two and three can be seen as the option to expand the investment, because phase one can be completed without the necessity to further invest and develop stage two and three. The option to defer is existent in any of the three options due to the fact that the option is assumed to give the holder a building or in this case the renovation permit for the maturity of the option. Option one hereby has a maturity of two years, option two and three possess a maturity of five and ten years. At the end of the lifecycle of each option, the owner has the right to not exercise the option, but instead to abandon the investment if the development of the market conditions is unfavorable for the owner. Furthermore, it is assumed that the cost of not undertaking the renovation is negligible. The flexibility of the applied sequential strategy for the three options at hand is illustrated and further explained in Appendix 7. The exercise of option one hereby depends on the development of the market. This is similar for the option two and three, but additionally the
- 54 -
second and third phases require an exercise of the previous option. The in Appendix 7 shown structure of the compound option has to be taken into consideration regarding the valuation model in order to test the stated hypotheses of additional flexibility value offered by real options.
4.4.1. Volatility
To calculate the volatility of the underlying asset [here: the uncertainty regarding the development of the rent price], the development of the Detroit Rent Index has been chosen as a comparable and suitable proxy. The result sees an average annual volatility of 5.43 percent. This is lower than expected and relatively far away of what other studies and textbooks have found out. Geltner et al. (2007) determines the volatility of individual built properties typically within the range of 10 to 25 percent. Mun (2006) argues that a mean volatility rate of 20 percent is adequate. One reason for the underestimation of the volatility can be found in the way the index handles the changes within the time period until the next number is published. It takes the average figure for the time period [here: quarter of a year] and therefore evens out potential up and down movements. Because of the above mentioned studies, this thesis assumes an annually volatility of 15 percent, which is held constant over the estimation period. This is found to be a reasonable estimate for Detroit, because the real estate market in Detroit is assumed to have more volatile outcomes than the market averages, especially in the observed time frame and in relation to the applied indices. Additionally, the result of the performed Monte Carlo Simulation using the rent as input variable points in the same direction resulting in an averaged annually standard deviation of 16.02 percent for the years of the project [see Excel sheet “GBM Simulation”].
4.4.2. Binomial Lattice
Figure 15 sums up the main input variables needed for the binomial lattice that in the following is valued. The annual risk free rate has been determined in the previous section and the time steps per year have been set to one for simplifying reasons. The up and down movements have been calculated for the lattice for both, with and without dividends, using the following equations:
(3.12)
- 55 -
With the time steps
(3.13)
=1 and σ= 0.15 the up movement results in 1.1618 and the down
movement in 0.8607. This is identical in the case of including dividends. Regarding the risk neutral probabilities, the result differs when applying the following formula:
(3.14)
The input variable b hereby represents the dividend yield. The dividend yield is held constant for the valuation time frame as discussed in Chapter 3.2.5. For the case without dividends, the formula leads to risk neutral probabilities of 0.5735 for the up and 0.4265 for the down movement. The probabilities for up and down including dividends amount to 0.5224 and 0.4776.
Input Parameters
Annual Risk free Rate
0.0328
Annual Standard Deviation of PV
0.1500
Periods per Year
1.0000
Calculated Parameters
Up Movement per Step
1.1618
Down Movement per Step
0.8607
Annual Risk free Rate + 1
1.0328
Risk neutral probability (up)
0.5735
Risk neutral probability (down)
0.4265
Calculated Parameters with Dividend
Up Movement
1.1618
Down Movement
0.8607
Annual Risk free Rate
1.0328
Dividend
0.0150
Risk neutral probability up
0.5224
Risk neutral probability down
0.4776
o r Binomial Lattice [Source: Excel Sheet “Binomial Lattice”] F i g u r e 1 5 – Su m m a r y I n p u t V a r i a b l e s f
- 56 -
Figure 16 displays the development of the whole project for the upcoming ten years, which equals the length of the longest maturity, the maturity time of option three. The starting point for the binomial lattice is formed by the present value of the project as if it has been constructed. The result of 129.89 mio US Dollar is therefore the result of the cash inflows and the terminalization value of the constructed property. In order to give an example of how each of the individual figures is calculated, the value of year 0,6 is selected. The calculation results in:
.
F i g u r e 1 6 – P r e sen t V a l u e B i n o m i a l T r e e a n d D e v el o p m e n t o f C o n s t r u c t i o n C o s t s [ S o u r c e : E x c el
She et “Bi nom ia l Latt ice ”]
The second part of Figure 16 sums up the development of the construction costs during the life period of the options. The annual growth is assumed to be constant and has been implemented in order to trigger a possible early exercise of the individual underlying
- 57 -
American options. Without facing opportunity costs, the investor would always postpone the decision to the latest point in time in order to gather more information about the uncertainties. Year zero hereby represents the year 2010 for all three options. The application of the binomial lattice model is pretty straightforward. The in theory provided steps to estimate the value of simple single options is similar to valuing compound options in the case at hand. It is important though to solve the options backwards meaning to start with the option three. The valuation process follows the principles of the theory in Chapter 3.3.3 and applies the calculated risk neutral probabilities and the up and down factors from section 4.4.2. Figure 17 displays the already combined Equity Lattice including the dividends as opportunity costs of option three. The different colors regarding the numbers set out the instruction whether to construct [green], defer [yellow] or abandon [red] the option. The full valuation process of all three options can be viewed in Appendix 6 and in the Excel sheet “Binomial Lattice”.
Starting with the option three, the terminal nodes are calculated by applying equation 3.20 resulting in the following:
This then is repeated for the rest of the row of option three. The intermediate nodes are determined using the equation 3.20 with the following result as an example:
The procedure is then repeated for the whole lattice of option three and also for option two, where the combined equity lattice with dividends [see Figure 17] is the underlying foundation for calculating the values of option two. The final option lattice one uses the lattice of option two as the underlying asset. Option one not only represents the final lattice, but also contains the expanded net present value at point 0,0 regarding the project.
- 58 -
F i g u r e 1 7 – In div id ual Co m bi ned Eq uit y La tt ic e fo r Ph ase 1, 2 and 3 [S our ce: Ex cel Sheet “Bi nom ia l
La tti ce ”]
- 59 -
5. Discussion
5.1.
Results
Comparing both results, the difference is evident. The lattice includes the optimal decision making throughout the path considering the possibility of deferring or abandoning the project together with the opportunity of the right timing for the construction of each phase. In the case study at hand, the optimal decision sees a delay of option one at time = 0 rather than an immediate exercise of the option. At time t = 1, the decision to further defer or instead abandon the project depends on whether the value of the project develops positively [up] or negatively [down]. In year two, the decision then has to be made between exercising and abandoning the option, because the option runs out. Figure 17 shows that only in the case of a subsequent positive development of the value of the project in the first two years, option one is exercised and the project is undertaken. Summarized, by delaying the investment at t = 0, the dynamic expected net present value of the project can be increased by 16.66 million US Dollar compared to the figures of the static net present value:
. This confirms that the static approach underestimates the net present value of the project, because the additional value offered by flexibility and active management is ignored. The payoff indicates that under given circumstances the binomial valuation method increases the payoff result of the project by 12.825 percent resulting in additional value of 16.66 million US Dollar. More importantly, the decision whether to undertake the project or not differs depending on the chosen valuation approach. While the static DCF method would instruct the investor to not undertake the project, the binomial lattice method comes up with a positive outcome. Figure 17 indicates that the compound option model can lead to options instructing the owner to exercise the phase [for example: green path of option three] while the option is not yet “alive”. Alive means that the previous underlying options have to be exercised as a
requirement for the option of interest being exercisable. In the case study, the optimal decision at t = 0 for option three would be to construct, while for option two and one it is to delay the decision. Therefore, the construction of option three is deferred even though the optimal decision would be to immediately construct the phase.
- 60 -
5.2.
Critique and Reflection
The case study at hand has faced main critique points proposed in real estate literature, theoretically reflected on them and after having run the figures and calculations, it can be said that the application of real option valuation approaches indeed can be a difficult task and some of the critique points can be confirmed. Not only the timing of when to exercise the option has to be correct and managed ex ante, but also often the analysis fails to fulfill essential assumptions like for example the mentioned necessity of efficient working markets. Additionally, the real estate sector is impacted by asymmetric information, infrequently traded objects and therefore missing comparables which mirror the high individual risk profiles regarding projects. This leads to an inability to fully diversify risk and incorporates that applying the risk free rate to value the options is at least questionable. Furthermore, limited available data has lead to both the beta and the volatility to differ from the expected range. The author has made adjustments regarding the applied beta and volatility in order for them to fit the proposed model, which might have violated assumptions resulting in an incorrect valuation. Another assumptions, that can be critically reflected, is that the author states all rates regarding the growth of the construction costs, the volatility, the beta, the risk free rate and therefore also the cost of equity stay constant throughout the process of the valuation. Although it helps to simplify and apply the model, it can lead to an inappropriate and unrealistic display of the case study and the investment objects. The case study at hand does not apply the method of closed form solutions. This is due to the choice of American rather than European Options, where the closed form approach only delivers approximations or requires a lot of additional assumptions in order to work properly. Because the paper already works under utilization of assumptions, it has been found that applying the closed form solution would have been too theoretical in its implementation requirements.
- 61 -
6. Conclusion Investment bubbles and financial crisis are becoming more and more a part of the everyday life impacting nearly every sector and leaving people, firms and objects exposed to risk. As mentioned in the introduction, investments in real estate objects fall into that category due to their high intensity of capital outflows together with uncertainty in demand and the volatility in cash flow income. Therefore, making the right investment decision is not only crucial for the going concern of companies, today more than ever, but also has lead to the literature to focus its research on how to better and more accurately evaluate investment possibilities in order to maximize value and minimize the risk. Throughout the time, different approaches have been developed and compared to each other together with the gained insight that staging decisions adds flexibility value. Because the real options analysis incorporates this, it is often found that it represent a better valuation tool in theory. This has lead to the central research question of this paper:
Can real options analysis deliver more appropriate and superior results compared to the net present value method in terms of the valuation of real estate objects through their characteristics of taking into consideration the steps of sequential development?
The provoking question whether real options can offer additional value has been clearly confirmed by the underlying case study. The result of the dynamic valuation improved the results by almost 13 percent compared to the basic net present value. On top of that, the application of the real options valuation model changed the recommendation of whether to undertake the investment or not. While the result of the net present value saw the project with a negative outcome, the calculation of the real options analysis attached results in a net gain of 6.55 million US Dollar for the project.
Furthermore, the case study has identified different types of option and has showed that they all can offer additional value to the investor. Postponing Decisions and dividing the development process into stages enables the investor to capitalize on the volatility of outcomes. This also stops the decision from being simultaneous and leads to viewing the
- 62 -
decision making and the development process as a sequential one with different interaction possibilities and individual decisions possible at each different time node. Additionally, the thesis has compared and has shown the differences between the two approaches. Further, it has described options in general and shown how they are applied to a specific case study. Though the main hypothesis has been confirmed, the author also has critically reflected on potential difficulties the application of real options analysis in reality faces. In order to extract the maximum value of future outcomes, not only the flexibility to react has to exist in the first place, also the timing of the decisions has to be right. The lattice has shown the optimal paths, but is applied backwards. In reality, the decisions are made ex ante leaving the decision maker with facing the problems of irrational human behavior and inefficient markets.
All in all, the thesis has shown that the value of flexibility cannot and should not be ignored when investment possibilities are valued. Real options can further improve the correctness of the result. Nonetheless, in order to make the real option the dominant decision tool, improved processes have to be found to secure reliable and accurate figures of important variables, such as the volatility or adequate rates regarding the cost of capital.
- 63 -
Bibliography Baldi, F. 2013, “Valuing a Greenfield Real Estate Property Development Project: A Real Options Approach”, Journal of European Real Estate Research, Vol. 6 (2), pp. 186-217. Black, F. & Scholes, M. 1973, “The Pricing of Options and Corporate Liabilities”, Journal of Political Economy, Vol. 81 (3), pp. 637-654. Boyle, P.P. 1977, “Options: A Monte Carlo Approach”, Journal of Financial Economics, Vol. 4 (3), pp. 323-338.
Borison, A. 2005, “Real Options Analysis: Where Are the Emperor’s Clothes?” Journal of Applied Corporate Finance, Vol. 17 (2), pp. 17-32. Brealey, R.A., Myers, S.C & Allen, F. 2011, Principles of Corporate Finance, Tenth Edition, New York, NY. Brennan, M.J. & Trigeorgis, L. 2000, “Real Options: Development and New Contributions”, Project Flexibility, Agency, and Competition: New Developments in the Theory and Application of Real Options, Oxford University Press, USA, pp. 1-9. Bulan, L., Mayer, C. & Somerville, T. 2002, “Irreversible Investment, Real Options, and Competition: Evidence from the Real Estate Development”, Working Paper, UBC Commerce Center for Urban Economics and Real Estate. Capozza, D. & Li, Y. 1994, “The Intensity and Timing of Investment: The Case of Land”, The American Economic Review, Vol. 84 (4), pp. 889-904. Copeland, T.E. & Antikarov, V. 2003, Real Options: A Practitioner’s Guide, New York, NY. Cox, J., Ross, S. & Rubinstein, M. 1979, “ Option Pricing: A Simplified Approach”, Journal of Financial Economics, Vol. 7 (3), pp. 229-263. Cunningham, C.R. 2006, “House Price Uncertainty, Timing of Development, and Vacant Land Prices: Evidence for Real Options in Seattle”, Journal of Urban Economics, Vol. 59, pp. 1-31. Cunningham, C.R. 2007, “Growth Controls, Real Options, and Land Development”, The Review of Economics and Statistics, Vol. 89 (2), pp. 343-358. Dixit, A.K. & Pindyck, R.S. 1994, Investment under Uncertainty , Princeton University Press, Princeton, NJ. Geltner, D. 2007, Commercial Real Estate Analysis and Investments , Thompson SouthWestern, Mason, OH. Kodukula, P. & Papudesu, C. 2006, Project Valuation Using Real Options: A Practitioner’s Guide, J. Ross Publishing Inc., Fort Lauderdale, FL. Koller, T., Goedhart, M. & Wessels, D. 2010, Valuation – Measuring and Managing the Value of Companies, Fifth Edition, John Wiley & Sons, Hoboken, NJ.
- 64 -
Lucius, D.I. 2001, “Real Options in Real Estate Development”, Journal of Property Investment and Finance, Vol. 19 (1), pp. 73-78. Luehrman, T.A. 1998, “Investment Opportunities as Real Options: Getting Started on the Numbers”, Harvard Business Review, pp. 51-66. McDonald, R. & Siegel, D. 1986, “The Value of Waiting to Invest”, The Quarterly Journal of Economics, Vol. 101 (4), pp. 707-728. Mun, J. 2006, Real Options Analysis: Tools and Techniques for Valuing Strategic Investments and Decisions, John Wiley & Sons, New York, NY. Myers, S.C. 1977, “Determinants of Corporate Borrowing”, Journal of Financial Economics, Vol. 5, pp. 147-175. Pomykacz, M. 2013, “Options in Real Estate Valuation”, The Appraisal Journal, Vol. 81 (3), pp. 227-238. Quigg, L. 1993, “Empirical Testing of Real Option-pricing Models”, Journal of Finance, Vol. 48 (2), pp. 621-640. Robson, C. 2002, Real World Research, Blackwell, Oxford, UK. Rocha, K., Salles, L., Garcia, F.A.A., Sardinha, J.A., Teixeira, J.P. 2007, “Real Estate and Real Options – A case study”, Emerging Markets Review, Vol. 8 (1), pp. 67-79. Ryan, B., Scapens, R.W. & Theobold, M. 2002, Research Method and Methodology in Finance and Accounting, Thomson Learning, London, UK. Saunders, M., Lewis, P. & Thornhill, A. 2012, Research Methods for Business Students, Sixth Edition, Pearson. Schneider, M., Tejeda, M. Dondi, G., Herzog, F., Keel, S. & Geering, H. 2008, “Making Real Options Work for Practitioners: A Generic Model for Valuing R&D projects”, R&D Management, Vol 38 (1), pp. 85-106.
Sing, T.F. & Patel, K. 2001, “Empirical Evaluation of the Value of Waiting to Invest”, Journal of Property Investment and Finance, Vol. 19, pp. 535-553. Smit, H.T.J. & Trigeorgis, L. 2004, Strategic Investment – Real Options and Games , Princeton University Press, Princeton, NJ. Sun, Y., Huang, R., Chen, D. & Li, H. 2008, “Fuzzy Set-Base Risk Evaluation Model for Real Estate Projects”, Tsinghua Science and Technology , Vol. 13 (1), pp. 158-164. Titman, S. 1985, “Urban Land Prices under Uncertainty”, The American Economic Review, Vol. 75, pp. 505-514. Triantis, A. 2005, “Realizing the Potential of Real Options: Does Theory Meet Practice? ” Journal of Applied Corporate Finance, Vol. 17 (2), pp. 8-16. Trigeorgis, L. 1996, Real Options: Managerial Flexibility and Strategy in Resource Allocation, The MIT Press, Cambridge, MA.
