Application of Real Option Valuation to Real Estate Investment Appraisal-- A Case Study
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Transcript of Application of Real Option Valuation to Real Estate Investment Appraisal-- A Case Study
University of Nottingham
APPLICATION OF REAL OPTION VALUATION TO
REAL ESTATE INVESTMENT APPRAISAL
— A CASE STUDY
YISHA LU
MA in Finance and Investment
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Application of Real Option Valuation to
Real Estate Investments Appraisal
—A Case Study
by
Yisha Lu
2007
A Dissertation presented in part consideration for the degree of
MA in Finance and Investment
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Abstract
This dissertation provides an insight of real option valuation application into real
estate investment appraisal. Real estates investments have the features of low liquidity,
slow payback and high sunk costs. This is especially the case appearing in emerging
economics, due to the volatile demand, house price and land costs. The application of
real options theory in real estate investment analysis considers a real estate
development as an investment opportunity that reduces the uncertainties in the real
estate development and creates economic value on real estate projects. A case study of
a Chinese real estate development project “Jiangnan New Village” is conducted to
illustrate the application of real option valuation to real estate investment appraisal in
emerging real estate market. Binomial Tree approach is employed for real option
valuation in the case study. The results lead to the conclusion that real options
embedded in the real estate projects do create significant economic values on
underlying project, and improve risk management of the project.
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Acknowledgement
I would like to take this opportunity to express my sincere thankfulness to all the
people who helped and support me in completing this dissertation.
At the very first, I would thank gratefully to my supervisor Professor David Newton,
for his invaluable guidance, comments and suggestions throughout the dissertation.
I also wish to thank all my friends Yuqi Li, Cui Wang, Hongfei Wang, Lujie Chen, Si
Zhou, Xin Ye etc. who had given me technical support for this dissertation and who
made my life brighter in last year of my scholastic life at University of Nottingham.
Finally, I would like send my deepest gratitude and love to my parents, for their
greatest encouragement and support all the way through my oversea studies.
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Contents
Abstract…………………………………………………………………...i
Acknowledgements………………………………………………………ii
Table of Contents………………………………………………………..iii
List of Tables…………………………………………………………….vi
List of Figures…………………………………………………………..vii
List of Appendices……………………………………………………....vii
Chapter 1 Introduction……………………………………………………1 1.1 Research Background……………………………………………………………...1 1.2 Research Objectives and Methodology…………………………………………....2 1.3 Research Structures………………………………………………………………..2
Chapter 2 Real Option Theory………………………………………........4 2.1 Concepts of Real Options………………………………………………………….4
2.1.1 Definitions of Real Option………………………………………………………………4
2.1.2 Types of Real Options…………………………………………………………………...8 2.2 Real Option Valuation Theory……………………………………………………14
2.2.1 Real Option Pricing fundamentals: Terminology, Intrinsic and Time Value…………..15
2.2.2 Variables Determine Real Options Value……………………………………………...16
2.2.3 Risk-neutral Valuation …………………………………………………………...........17
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2.2.4 Basic Option Pricing Models………………………………………………………….17 2.3 Summaries………………………………………………………………………..23
Chapter 3 Application of Real Options in Real Estate Investment……...24 3.1 Real Options Commonly Exist in Real Estate Investment ….…………………..24
3.2 Prior Research on Real Options Application in Real Estate …………………….26 3.3 Research in Real Option Application in Chinese Real Estate Market…………...29 3.4 Summaries………………………………………………………………………..31
Chapter 4 Case Study……………………………………………............32 4.1 Case Background………………………………………………………………...32
4.2 Case Statement—Jiangnan New Village…………………………………………34 4.3 Real option Identification………………………………………………………...35 4.4 Valuation Model Choice……………………………………………………….....37
4.4.1 Real Option Model…………………………………………………………………….37
4.4.2 Expanded NPV Framework…………………………………………………………...38
Chapter 5 Real Options valuation and Analysis………………………...39 5.1 Time-to-build Option…………………………………………………………….39
5.1.1 Parameters Estimation………………………………………………………………...39
5.1.2 Time-to-build Option Valuation……………………………………………………….42
5.2 Option to Abandon...……………………………………………………………..47
5.2.1 Parameters Estimation…………………………………………………………...........47
5.2.2 Abandon Option Valuation…………………………………………………………….48
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5.3 Result Analysis and Further Discussion………………………………………….50 5.4 Sensitivity Analysis………………………………………………………………52
5.4.1 Volatility Sensitivity Analysis………………………………………………………….53
5.4.2 Risk-free Rate Sensitivity Analysis…………………………………………………....54
5.5 Limitations…………………………………………………………..56
5.5.1 Oversimplified Model Assumptions…………………………………………………...56
5.5.2 Limitations of the Real Options Approach…………………………………………….57
Chapter 6 Conclusion…………………………………………………...59
References……………………………………………………………….61
Appendices………………………………………………………………70
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List of Tables
Table 5.1 Volatility Estimation……………………………………………………..41
Table 5.2 Inputs…………………………………………………………………….42
Table 5.3 Estimation of underlying asset value…………………………………….43
Table 5.4 Phase III option value Tree……………………………………………....45
Table 5.5 Phase II Option Value Tree……………………………………………....46
Table 5.6 Compound Option value Tree……………………………………………47
Table 5.7 Abandonment Option Value Tree………………………………………...49
Table 5.8 Volatility Sensitive Analysis……………………………………………..53
Table 5.9 Risk-free Interest Rate Sensitive Analysis……………………………….54
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List of Figures Figure 5.1 Relationship between Volatility and Real Option Value………………….53 Figure 5.2 Relationship between Risk-free Rate and Real Option Value……………55
List of Appendices Appendix 1 Analogy between Real Options and Financial Options………………71
Appendix 2 Jiangnan New Village Investment Cash Flows, NPV and Construction
Costs…………………………………………………………………...72 Appendix 3 Sales Plan for Jiangnan New Village…………………………………73
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Chapter 1 Introduction
1.1 Research Background
Real estate investments are characterized by low liquidity, slow payback and high
sunk costs, involving high uncertainties about demand, house price and land costs
(Rocha et al., 2007). These characteristics are particularly notable in emerging
markets such as Chinese real estate market. Traditional NPV (Net Present Value)
approach for real estate investment appraisal ignores changing dynamics of real estate
markets and the inherent flexibilities in decision-making process. For example, the
actual cash flows may differ from the streams what real estate developers originally
expected, and developers may have flexibility to alter its original strategy by deferring,
expanding, contracting, abandoning or redeveloping real estate projects to capitalize
opportunities or to mitigate potential losses (Rocha et al., 2007). Such investment
flexibilities can represent a substantial part of the real estate projects values.
Neglecting them can grossly undervalue the real estate investments and lead to
misallocations of resources in the economy (Schwartz and Trigeorgis, 2001).
Real option theory, on the other hand, provides a better valuation methodology for
investment projects in the presence of these managerial flexibilities involved in the
process of real estate investment decision-making. The use of real options analysis
realizes management flexibilities and the economic values they create, by which
enhancing real estate project expected net present value and facilitate decision-making
effectiveness. By identifying and managing these flexibilities, real estate developers
could obtain a more accurate estimation of the project value, and a better analysis of
investment opportunities. Competitive advantages thereby can be sustained by
developers.
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Nevertheless, there is a considerable gap between theory and practical applications of
real option, and this is especially the case in emerging market. One application
example in emerging market is Rocha et al. (2007), who study a two-phase residential
housing in the west zone of Rio de Janeiro in Brazil, showed that real option
application in emerging real estate market improves the risk management of project
by identifying the optimal strategy and timing for the construction phases. Interactions
among multiple real options embedded in one single underlying project barriers the
effective application of real option models in real world context.
1.2 Research Objectives and Methodology
The dissertation is motivated by the gap between the real option theory and its
practical application, as well as the limit examples in emerging market application.
The objective of this dissertation is to give a practical example of application of real
option valuation into real estate investment appraisal in an emerging market,
providing an insight of how real options can add economic values on real estate
projects, and offer managerial implications for real estate developers’ investment
decision-makings. Methodology of case study will be used in this dissertation, where
a real option valuation on real estate investment project in Guangzhou China
representing an emerging market example will be employed. Binomial tree approach
will be chosen as the valuation model for the real options embedded in the case.
1.3 Research Structures
The rest of the dissertation is organized as follow. Chapter 2 is going to present a
literature review on general real option theories. First, definition and origins of real
options will be introduced, where concepts of real option will be explained. Different
types of real option and literatures on them will be interpreted. Further, real option
valuation theory will be review, in which fundamentals of real option valuation will
be explained; real option valuation models include binomial tree model,
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Black-Scholes model and compound option model will then be introduced.
Chapter 3 provides review on literatures specifically in the application of real option
in real estate market. It starts from introduction of typical real options exist in real
estate market, followed by the review of previous research contributions. As the
example is from Chinese real estate market, literatures of real option application in
Chinese real estate market will also be reviewed.
Chapter 4 introduces the case of Jiangnan New Village, an investment project carried
out by Guangzhou City Construction & Development Property Holdings Co., Ltd.
(GCCDP) in Haizhu District, Guangzhou, one of the most boom areas of real estate
development in China. Case statement will be presented, followed by the
identification of real options embedded and the preference of real option valuation
methodology.
Real option valuation and analysis is then conducted in Chapter 5. Results will be
discussed based on its implications for improving economic analysis of real estate
investments and decision-making support. Limitations of model assumptions and real
options approach will be discussed at the end of the chapter.
Finally, chapter 6 will summarize the whole paper, and discuss the further
implications.
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Chapter 2 Real Option Theory
This chapter aims to give review of existing literature of general real options, its
concepts and pricing theories and applications. As the real option analysis provides a
framework analyzing and quantifying the flexibilities to react to uncertainties in real
estate investment projects, this chapter presents as a background for real options
application in real estate development projects.
2.1 Concepts of Real Options
2.1.1 Definition of Real Options
“A real option is the right, but not the obligation, to take an action (e.g., deferring,
expanding, contracting, or abandoning) at a predetermined cost called the exercise
price, for a predetermined period of time—the life of the option”. (Copeland and
Antikarov, 2003, p5) A simple example of real options could be a vacant land that
gives its holder the right but not obligation to develop it (Titman, 1985).
The real options revolution for investment valuation arose partly because of the
dissatisfaction of traditional NPV approaches by corporate practitioners, and some
academics with traditional capital budgeting techniques (Schwartz and Trigeorgis,
2001). The traditional approach that most widely used for valuation of real estate and
other investment projects is based on net present value (NPV), which essentially
involves discounting the expected net cash flows from a project at a discount rate that
reflects the risk of those cash flows (i.e. the “risk-adjusted” discount rate) (Schwartz
and Trigeorgis, 2001). It makes implicit assumptions of passive investment
management, implies that a) the cash flows in each year must be estimated precisely,
so does the corresponding risk-adjusted discount rate; b) once the project has started,
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it has to follow the expected scenario of cash flows until end of the expected project
life, which has no management flexibilities. However, in the actual market place, the
realized cash flows may differ from what management have expected due to
uncertainties and changes involved in the market. Management may have valuable
flexibility to alter its operating strategy (e.g. defer, expand, contract, abandon a
planned or in processing project) to capitalize on favorable future opportunities or
mitigate losses, since arrival of new information may resolve the uncertainties about
market conditions and future cash flows (Trigeorgis, 2001). Corporate managers and
strategists were grappling intuitively elements of managerial operating flexibility and
strategic interactions (Schwartz and Trigeorgis, 2001), but traditional NPV valuation
approach cannot capture such management flexibilities and trends to underinvestment
investment projects.
Early critics on traditional NPV approach are Dean (1951), Hayes and Abernathy
(1980), Hayes and Garvin (1982). They recognize that traditional discounted cash
flow method often undervalued investment opportunities by either ignore or disvalue
important strategic considerations, thereby induce myopic decisions, underinvestment
and loss competitive positions eventually (Schwartz and Trigeorgis, 2001). Followers
like Hodder and Riggs (1985) argued that the problem of underinvestment arises from
the misapplications of traditional DCF techniques. On the other hand, Hertz (1964),
Magee (1964) suggested that simulation and decision tree analysis may capture the
value of operating management flexibility instead of traditional NPV methods.
Myers (1977) further points out that the inherent limitations of traditional discount
cash flow method are its ignorance of significant operating or strategic options in
investment. He suggests that option pricing provide the best means to value such
investments. For example, sequential interdependence among investment over time
may be neglected by traditional DCF method, while option pricing model may capture
such interdependences. Myers (1977) is the one who first proposed the analogy of
management flexibilities to options, who recognizes that companies’ discretionary
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investment opportunities can be seen as call options on the future growth which offers
companies the rights but not the obligations to buy financial assets.
Kester (1984)’s study is consistent with Myers’s (1977) argument, indicating that the
value of growth options contribute to over half of companies’ equity market value. He
further emphasizes the importance of capital allocation, which could help companies
develop growth opportunity and thus to achieve competitive advantages.
Consequently, an insight of growth options can assist companies integrate capital
budgeting with long-term strategic planning.
Trigeorgis and Mason (1987) further introduced option valuation as an
economically-corrected version of decision tree analysis, which is thought to be better
suited for valuing various strategic management flexibilities. They argued that
traditional NPV analysis is inadequate to capture the operating flexibilities (e.g.
option to defer, expand or abandon a project) and the strategic option values (i.e. the
option value on a project from its interdependence with future investments) embedded
in an investment project. While reorganization of these operating flexibilities and
strategic option values can improve the risk management of projects and take
advantage of the upside potential gains at the mean time, thereby enhance the
expected project net present value. Option premiums thus should be paid for the
additional economic values that the flexibilities and strategic options enhanced, to
recognize and exercise these real options.
Besides Myers (1977) and Kester (1984), Dixit and Pindyck (1995) present an
alternative conceptual real option framework for capital investment, evaluating the
effects of real option approach on the investment decision-making process. They
emphasis the importance of the option to wait, referring to the feature of irreversibility
(due to specialized assets and huge sunk costs) in most investment projects. They state
that option to wait is analogous to a call option that offers investment decision-maker
the right but not the obligation to exploit an investment opportunity. Decision-maker
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can either wait for more information gathered if the uncertainties are high or exercise
this call option immediately by carrying out the investment. In the latter case, the
option to wait is an opportunity cost that should be taken into capital investment
decision.
Kogut and Kulatilaka (1994) suggest that corporations should focus on long-term
growth opportunities from the viewpoint of real option approach. Current investment
can be viewed as the options for future further investments, by which companies can
bide their time for full investment. They figure out that options pricing theory can be
used for quantify such investment opportunities. And later, Amram and Kulatilaka
(1999) argued that, for investment appraisal of a multi-phased project (especially
sequential multi-phased project) with high uncertain expected cash flow returns, real
option approach is highly recommended, which can capture the value of operating
flexibilities in multi-phasing decision-making.
Based on above, an “expanded NPV” rule represented by Trigeorgis (2001) arises in
response to the needs of management flexibilities adaptation and enhancing
investment opportunities’ value. The rule reflects both traditional NPV of direct cash
flows (with passive management) and the value of operating and strategic flexibilities.
“This does not mean that traditional NPV should be scrapped, but rather should be
seen as a crucial and necessary input to an options-based, expanded NPV analysis, i.e.,
Expanded (strategic) NPV= Static (passive) NPV of expected cash flows + Value of
options from active management” (Trigeorgis, 1996, p124).
Real option approach thus allows both conception and quantification of strategic
values created from active management. This value is presented as a collection of real
options embedded in capital investment opportunities, with gross project value of
expected operating cash flow as the underlying asset (Trigeorgis, 2001).
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2.1.2 Types of Real Options
Real options’ classification are primarily based on the type of flexibility they offer
(Copeland and Antikarov, 2003). For example, Trigeogis (1996) classified common
real options into seven categories: option to defer, time-to-build option, option to alter
operating scale, option to abandon, option to switch, option to growth and multiple
interacting options; in which option to alter operating scale includes option to expand,
option to contract and option to shut down and restart. One of the most boosting real
options literature areas is on valuing these various types of real options quantitatively
by deriving analytic, closed-form solutions.
Option to defer
Option to defer is important in industries with long-term operating horizons and
highly uncertain investment environments, like natural resource extraction industries,
real estate development, farming and paper products (Trigeorgis, 1988). It is an
American call option where one has the right to delay the start of a project (Copeland
and Antikarov, 2003). When uncertainty is high, the opportunity to wait allow
investment decision maker to gather more information and to protect the investment
returns from the high uncertainty.
Literatures contributed to real options to defer includes Tourinho (1979), Titman
(1985), McDonald & Siegel (1986), Paddock, Siegel & Smith (1988), Ingersoll &
Ross (1992).
Titman (1985), by using a simple binomial model illustrated that to leave a valuable
land vacant rather than develop them immediately can contribute significantly to the
value of land. And the value of the option adding to the land is positively related to
the uncertainty towards construction costs and risk free interest.
McDonald and Sigel (1986) built a model for the value of option to wait and applied
to a commodity producing project. They find that the consideration of investment
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timing is quantitatively important and the optimal timing to invest is when the net
present value of cash flow returns is double the investment cost. McDonald and Sigel
again, address the practical importance of the value of option to wait.
Paddock, Siegel and Smith (1988) conduct valuation of offshore petroleum leases
taking into consideration of the option to defer, by which they confirm that the real
option approach offer a more accurate estimation of the lease value than traditional
NPV approach does and grant a guide for the optimal develop timing.
In addition, Tourinho (1979) have done further research in valuation of the option to
reserves of natural resources. Ingersoll and Ross (1992) examine the impact of
risk-free interest rate variation on the uncertain cash flow returns, finding that
variation of risk-free interest rate creates the value of option to wait, where increase in
volatility of risk-free interest rate declines the immediate investment value.
Time-to-Build Option
Many capital projects (e.g. real estate development and R&D project investments)
involve staging investments where the investment decisions and outlays are often
made sequentially throughout the project’s life, rather than a single decision and
expenditure only at the beginning of the project. Such a series of outlays creates the
option to default given stage if market situation is acceptable, or to abandon the
investment in midstream if new information is unfavorable to the project.
Construction of previous stage created the right but not the obligation to default
subsequent stage. Hence, each stage can be viewed as an option on the value of
subsequent stages, and valued as a compound option (Trigeorgis, 2001).
Such real options are most observable in R&D intensive industries, especially
pharmaceuticals and long-development capital-intensive projects, such as large-scale
construction or energy-generating plants, as well as start-up ventures (Trigeorgis,
2001).
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Majd and Pindyck (1987) try to derive optimal decision rules for each investment
stage and to value a time to build option by determining the effects of time to build,
opportunity cost and uncertainty on the investment decision. Their research shows
that investment decisions can be extremely sensitive to the level of risk, and the
simple NPV rule can mislead investment decisions due to the ignorance of the stage
sequential investment flexibilities embedded in the project. Carr (1988) also provided
valuation of sequential exchange options, with further stage expenditures into
consideration.
Option to alter operating scale
Option to alter operating scales allows investment decision makers adapt various
management flexibilities according to different market conditions. If the market
conditions are more favorable than expected, there is an option to expand capacity or
accelerate resource utilization; if the market conditions become less favorable,
decision makers can shrink the scale of operations, cut cost and protect business from
further loss. In the extreme case of unfavorable market conditions, investment
decision makers can even temporarily shut down the projects, which can be reopen
until the market conditions getting better (Trigeorgis, 2001). Hence, option to alter
operating scale including three types of real options: option to expand, option to
contract or scale down and option to shut down and restart. Such management
flexibilities provide opportunities to pick up the upside profit potential while limiting
downside losses, which should be taken into investment decision considerations
(Trigeorgis and Mason, 1987).
These kind of real options are especially important in natural resource industries (e.g.
mine operations), commercial real estate developments, and high-tech incentive
industries. They are also common in cyclical industries (e.g. in facilities planning and
construction), fashion apparel and consumer goods industries. (Trigeorgis, 2001)
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Pindyck (1988)’s research is an example analysis for option to expand, who develops
a model to quantify the option to expand, by which the optimal capacity of a firm can
then be decided. The research result shows that a firm’s optimal capacity will be
achieve under the condition that the expected cash flow from a marginal unit of
capacity equals to the total cost of that marginal unit (composed by purchase and
installation costs, and opportunity cost of exercising the option to buy the unit).
Companies are recommended to hold less capacity if they face highly uncertain or
unknown demands. Pindyck highlights the importance of including the opportunity
cost for exercising the expand option when making expand decision, ignoring which
would lead to overinvestment on expansion.
An example of temporarily abandon option valuation is illustrated by Brennan and
Schwartz (1985) using an example of mine operation. They recognize that operating
flexibilities embedded in natural resource projects allows operator to close or reopen
the mines according to the natural resource prices. Real option approach is confirmed
to be a better valuation method in capture the temporarily abandon options, which
contributes a substantial fraction to the overall mine value.
Option to abandon
If the market conditions decline severely, the option to abandon provides the
flexibility to abandon current project for the realized resale value of rest capital assets,
which protect against failure of the project and the further losses. It is analogous to an
American-style put option on the current project value, with the salvage value or the
best alternative use as the exercise price (Myers and Majd, 1990). In this case the
salvage value is the main determinant for abandonment option value, where general
capital asset has higher salvage value than specific capital asset.
Option to abandon is vital in capital intensive industries, such as airlines and railroads,
financial services industries and new product introductions in uncertain markets
(Trigeorgis, 2001).
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Myers and Majd (1990) presented numerical estimates for abandonment value of a
capital investment project. They set up a portfolio that can replicating abandonment
option’s payoff, and valued the option to abandon as an American put option. The
computation starts with the value at the terminal boundary, and working back to the
abandonment values at the start of the project. At each point of time, the expected
value of option to abandon is compared with the immediate exercise payoff, if
immediate exercise payoff is relatively high, the project will be abandoned.
Option to switch (e.g. outputs or inputs)
In the case of the demand sensitive operating system, management has the option to
change the output mix of the facility (i.e. “product” flexibility), or in the case of
volatile supply, the same outputs can be produced using different types of inputs (i.e.
“process” flexibility) (Trigeorgis, 2001).
Example operation systems that have potential to apply such management flexibilities
are consumer electronics, toys, machine parts, autos productions for output shifts; and
all feedstock-dependent facilities for input shifts, like oil, electric power, chemicals,
crop switching and sourcing (Trigeorgis, 2001).
The typical literature that analyzed the option to switch is Kulatilaka and Trigeorgis
(1994). Kulatilaka and Trigeorgis present a simple analysis of the generic flexibility to
switch between alternative operating modes, by which they found that the value of the
project with switch flexibilities can be seen as the value of the project without such
flexibilities plus the sum of the future switch option values. Nevertheless, they realize
that there are compoundness effect by exercising the switch options, and the effect
consist with the problem of that immediate exercise of switching although seems
attractive in short term, it may be long-term optimal to wait.
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Growth options
Growth options are compound options, i.e. one option is on another. An early
investment, such as R&D, lease on undeveloped land or oil reserves, strategic
acquisition or information network/infrastructure, is a prerequisite or link in a chain of
interrelated projects, opening up future growth opportunities, like new generation
product or process, oil reserves, access to new market, strengthening of core
capabilities (Trigeorgis, 2001). Companies also often cite “strategic” value when
taking on negative NPV projects, which however reveals call options on follow-on
projects in addition to the immediate projects’ cash flows.
Growth options are commonly embedded in infrastructure-based or strategic
industries, especially high-tech, R&D industries, or multiple product generations or
applications (e.g., computer, pharmaceuticals industries) and multinational operations,
also common in strategic acquisition (Trigeorgis, 2001).
Such real options are analyzed by Myers (1977), Brealey and Myers (2000), Kester
(1984), Trigeorgis (1988), Pindyck (1988), Chung and Charoenwong (1991). For
instance, Kester (1984) conducted a comparison among 15 listed companies’ expected
cash inflows and their market value, reveal that the value of growth options contribute
to over half of companies’ equity market value.
Multiple interacting options
Often in real life applications, there is a “collection” of various options embedded in a
single project, both upward-potential enhancing calls and downward-protection put
options present in combination (Trigeorgis, 2001). Such combination of options does
not mean their effect on the project value is simply sum of each option value. They
interact and may also interact with financial flexibility options (Trigeorgis, 2001).
Hence literatures for valuing these interactions are presented, such as Brennan and
Schwartz (1985), Trigeorgis (1993) and Kulatilaka (1994).
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Brennan and Schwartz (1985), besides their contribution on research of temporarily
abandon option in natural resource industries, is an early study on interaction with
single real options. They realized the inertia effect of exercising switch mine
operating state, which causes partial irreversibility from the costs of switch. This
makes it optimal in long-term to remain the original operating state regardless the
switching option is attractive in short-term cash flow consideration. But the
interactions effect among individual option values are not explicitly addressed in this
paper (Trigeorgis, 2001). Similar findings of such interaction effect are shown in the
study of Kulatilaka and Trigeorgis (1995).
Subsequently, Trigeorgis (1993) studies the nature of the real options interaction,
shows the non-additivity principle of individual option values. He find that the
presence of subsequent options increase the value of the earlier options, whereas
exercise of earlier real options (e.g. expand or contract option), may change the
underlying asset value, and hence the value of subsequent options on it. Trigeorgis
finally concluded that the combined value of a collection of real options may differ
from the sum of single option values.
Kulatilaka (1995) further examines the interactions effects among multiple real
options on their optimal exercise schedules. By realizing the interdependences
between real options, the gap between a theoretical real option research and practical
application will be bridged.
2.2 Real Option Valuation Theory
For the valuation of the real options, due to the relationship between real options and
financial options1, may numerical methods derived from financial options valuation
can be applied in the valuation of real options. 1 See appendix 1 Analogy between Real Options and Financial Options
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2.2.1 Real Option Pricing Fundamentals: Terminology, Intrinsic and Time Value
Real options use the same terminologies as financial options even though there are
remarkable differences between them in terms of underlying asset2 and time to
maturity.
Ø A call option is the right but not the obligation to acquire a given asset at some
future time for a predetermined cost.
Ø A put option is the right but not the obligation to sell a given asset in future for a
predetermined price.
Ø An American option can be exercised on or at any time before the maturity date.
Ø A European option can only be exercised on the maturity date.
Ø A compound option is an option whose value is based on another option.
Ø A rainbow option is any options with the uncertainties from more than one
source.
Ø A call option is in the money when the underlying asset value is above the
exercise price.
Ø A call option is out of money if the underlying asset value is lower than the
exercise price. In this case, the call will not be exercised immediately. But one
could not lose money on the option other than what have paid for obtaining the
option (i.e. option premium).
The value of a real option, same as the financial option, is composed by its intrinsic
value and its time value. The intrinsic value is the value if the option is exercised
immediately (i.e. S0-X). The time value refers to volatility value, reflecting the value
of uncertainties that leads to the fluctuation of underlying asset value (Bodie, Kane
and Marcus, 2005). Therefore, option value is dependent not just on the current
underlying asset value and its exercise price, but also the volatility of underlying asset,
2 The main difference between real option and financial options is that exercise of real options can change value of underlying asset (e.g. an expand option will enhance the underlying asset value).
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the time to maturity, the payout of underlying asset, and the risk-free interest rate. The
effects of these factors influencing real option values are analyzed in next section.
2.2.2 Variables Determine Real Options Value
Also similar to financial options, value of real options depends on five basic variables
(Copeland and Antikarov, 2003), which are the inputs for applying option valuation
model for real option valuation:
1. The value of underlying risky asset, for example, a project, investment, or
acquisition, or even an option in the case of compound options;
2. The exercise price, which is the money invested to exercise the option if buying
the asset or money received if selling the asset;
3. The time to expiration of the option;
4. The standard deviation of the value of the underlying risky asset;
5. Risk-free rate of interest over the life of the option.
If there are dividends that may be paid out by the underlying assets, the sixth variable
is required, which is the cash outflows or inflows over its life.
According to Copeland and Antikarove (2003), each of the six variables will have an
effect on the real options analysis value. An increase in the present value of the
project will increase the NPV and therefore the real option value. It has to be pointed
out that one of the important differences between real and financial option is that the
option holder can affect the value of the underlying asset. The value of the underlying
asset could be increased by the operating management, so is the option value.
Exercise price has a negative effect on the real option value; higher investment cost
gives a lower real option value. A longer time to expiration allow more knowledge of
uncertainty, thus leads to higher real option value. Volatility (i.e. uncertainty about the
present value of the underlying assets) is positively related to the value of real option
value. An increase in risk-free interest rate will increase the time value of money thus
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increase real option value. And dividends (e.g. cash outflows) will decrease the real
option value.
2.2.3 Risk-neutral Valuation
Risk-neutral valuation is the basic idea behind options and real options valuations.
Cox and Ross’s (1976) recognize that an option can be replicated (or a “synthetic
option” created) by an equivalent portfolio of traded securities assuming no arbitrage
opportunities. Rubinstein (1976) extend Cox and Ross’s idea to risk aversion situation,
where standard option pricing formulas can be alternatively derived, thus the risk-less
hedging assumption is not necessary. It implies that the risk attitudes are not relevant
to option valuations. Such risk-neutral valuation enables expected options future
payoffs to be discounted at the risk-free interest rate (i.e. with actual probabilities
replaced with risk-neutral ones) (Trigeorgis, 2001).
Mason and Merton (1985) and Kasanen and Trigeorgis (1994) further extend the
risk-neutral valuation to non-traded real asset, as the existence of a traded “twin
security” or a dynamic portfolio for non-traded asset would have the same risk
features. Such risk is closely correlated to the non-traded asset’s uncertainty, and can
be used as the non-traded asset’s risk factor. In a completed market, using this risk
factor can be sufficient for the real option valuation.
More generally, Constantinides (1978), Cox, Ingersoll, and Ross (1985), and Harrison
and Kreps (1979) have suggested the risk neutral valuation can be applied to pricing
of any contingent claim on an asset, traded or not, since the actual growth rate can
always be replaced with a certainty-equivalent risk-neutral rate.
2.2.4 Basic Option Pricing Models
Black and Schles (1973) and Merton (1973) originate the first model for option
valuation, which is derived from their seminal work. Cox, Ross and Rubinstein’s
(1979) later develop binomial tree approach that allows a more simplified valuation
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approach for options. Geske (1979) and Carr (1988) further build up models for
compound options.
Black-Scholes Model
The most fundamental and acknowledged option valuation model is the
Black-Scholes equation, developed by Black, Merton, and Scholes (1973). The model
is a breakthrough in option pricing theory, and has been widely used in valuation of
various financial asset valuations and real options.
Below is a review of Black-Scholes Model:
( )1 2( ) ( )fr T
tCall S d Xe dφ φ−= − ( )2 1( ) ( )fr TPut Xe d S dφ φ−= − − −
Where
20
1
1ln( ) ( )( )2f
S r TXd
T
σ
σ
+ +=
2 1d d Tσ= −
Inputs:
φ-- The cumulative standard normal distribution function;
S --The value of the underlying asset;
X – The exercise price or the cost of developing the intangible;
rf -- The nominal risk-free rate;
σ-- The volatility measure;
T -- The time to expiration or the economic life of the strategic option.
Assumptions of Black-Scholes Model are a) underlying asset’s price structure follows
a Geometric Brownian Motion with drift factor (μ) and volatility parameter (σ), and
this motion follows a Markov-Weiner stochastic process; b) there is an efficient
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market with no risk-less arbitrage opportunities, no transaction costs, no dividend
payout and no taxes; c) price changes in a continuous and instantaneous way.
Despite the widely application of the Black-Scholes formula in not only financial
options valuation but also real options areas, Black-Scholes model is still subjected to
the criticism that lacking of model flexibilities. It only works on European options
with a fixed decision date, but hard to provide valuation of American options, which
are more common in actual real option world. It is also hard to apply to valuation of
options with dividends payment and compound options. In addition, it is difficult to
explain due to the highly technical stochastic calculus mathematics. Nevertheless,
Black-Scholes is an exact, quick and easy numerical method and can provide a useful
gross approximation as a benchmark (Mun, 2002).
Binomial Tree Approaches
Binomial tree approach was first suggested by Cox et al. (1979), which is essentially
based on the risk-neutral valuation. It assumes that the time to the option’s maturity
can be divided into a number of sub-intervals in each of which there are two possible
price changes for underlying risky asset. One possible direction is upward movement
by a multiplication factor u with the risk-neutral probability p. One the other
possibility is downward movement by a multiplication factor d with the risk-neutral
probability 1-p. V is the value of the underlying asset; u and d are determined by
uncertainties of underlying asset value (i.e. tu eσ ∆= , td e σ− ∆= ).
uV (with probability p)
V
dV (with probability 1-p)
A risk-less hedge portfolio with one share of the underlying risky asset and a short
position in h shares of call option is then created (see below). Thus if the value of the
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underlying risky asset goes down, so does the value of the call option written on it,
but as we are in the short position, our wealth hence goes up; and if the hedge ratio is
exactly right, the loss on the underlying asset is exactly offset by the gain on the short
position of call option (Copeland and Antikarov, 2003).
uV-hCu
V- hC
dV-hCd
Under the assumption of no arbitrage opportunities, the present value of the portfolio
in the up state should be equal to present value of the portfolio in the down state (i.e.
V-hC(1+rf) = uV-hCu = dV-hCd).
Thus, we can solve h = [(u-d)V]/(Cu-Cd).
Substitute n into present value of the hedge portfolio V-hC(1+rf) = uV-hCu
And get (1 )1 f
pCu p CdCr
+ −=
+, where
(1 )fr dp
u d+ −
=−
.
And if continuous risk-free rate is used,fr te dp
u d
δ− −=
−. This p is the risk-neutral
probability.
This process can be continued repeatedly till period n, which create binomial tree of
underlying asset value as below (e.g. n=3).
Vu3 Vu2 Vu Vu2d V Vud Vd Vud2 Vd2 Vd3
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And the value of option can be resolved by applying a “roll-back” procedure in each
period back to the presence. For European options, the options value at each end node
is computed and discounted stepwise at risk-free interest rate back to time zero. For
American options, the opportunities of early exercise need to be checked by
comparing the immediate exercise payoffs with the expected payoff of keep holding
the option.
As mentioned above, the multiplication factor u and d are determined by uncertainty
of underlying asset value, captured by the volatility (σ); because of which the
binomial tree comprises up and down movements. Such up and down movements
generate the value of an option; the higher the volatility, the higher the u and d, and
thereby the higher option value; the more time-steps there is, the more accurate is the
result (Mun, 2002).
In contrast to Black-Scholes model, Binomial tree approach is much easier to operate
and explain; and even very flexible to be tweaked easily to accommodate most types
of real options problems (Mun, 2002). But in order to acquire a good approximation,
great computing power is requested.
Monte Carlo Simulation
Another major approach to value real options is simulation method, which imitate
thousands of possible combinations of uncertain variables to simulate the real-life
system. The variables (e.g. interest rates, staffing needs, revenues, stock prices,
inventory, discount rates) have a known or estimated range of values but are uncertain
values at any particular time or event (Mun, 2002). Monte Carlo simulation is one of
the simulations, proposed by Boyle (1977). It conducts with following steps: first,
determine the stochastic process that state variables would follow; second, simulate a
series of paths that affecting the option values assuming risk-neutral; third, for each
path, the payoffs of each paths can be calculated and average these to obtain the
expected payoff; finally, discount the expected payoff at risk-free rate and the option
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value can be estimated (Hull, 2006).
As Monte Carlo simulation allows state variables to follow different paths, it can be
used to deal with path-dependence options (Mun, 2002). Further, Monte Carlo
simulation is superior to binomial trees model and Black-Scholes model in terms of
application to option valuation with multiple uncertainties (Hull, 2006). But Monte
Carlo simulation has a major drawback that it is unable to adapt the early exercise
feature of American-style options.
Compound Option Models
Compound option is an option to acquire another option, which was first valued by
Geske (1979). A compound option can be simultaneous or sequential. Example of
simultaneous compound options can be exchange options (e.g. exchange one risky
asset for another or for several risky assets), which are valued by Margrabe (1978),
Stulz (1982) and Johnson (1987). A sequential compound options exists in multiple
phases project, the latter phases depend on the success of previous phases (Mun,
2002). Carr (1988) values a sequential compound option, involving an option to
acquire a subsequent option to exchange the underlying asset for another risky
alternative.
In a compound option analysis, the value of the option depends on the value of
another option. For example, exercise of the first option give the holder the right to
acquire the second option, and the second option gives the holder the right to buy or
sell the underlying asset. Thus, the value of the first option is dependent on the second
option. The typical compound model based on binomial lattice approach has three
valuation steps: first, value underlying asset value (underlying lattice); second, value
second option on the underlying asset (equity lattice); finally, value the first option
(valuation lattice) (Mun, 2002).
Compound option models are often applied to the valuation of phased investments
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with various real options embedded in. They are particularly adopted for the valuation
of projects that can switched to alternative states of operations, or the projects with
strategic interdependences values (Schwartz and Trigeorgis, 2001).
2.3 Summaries
In this chapter, the concept of real option and theory of real option valuation are
reviewed. Real option revolution raised as a response of dissatisfaction of traditional
NPV approach, where investment opportunities and management flexibilities are
ignored and investment are undervalued. There are various kinds of real options; each
realizes one or more types of investment management flexibilities. Numerous
literatures focuses on modeling valuation of different types of real options, from
which interactions among multiple real options embedded in a single project are
realized. The fundamental of real option valuation is risk-neutral valuation, based on
which, a variety of valuation models such as Black-Scholes, Binomial trees, Monte
Carlo simulation are developed. Strengths and drawbacks of each valuation models
are discussed.
Based on this general review of real option literatures, next chapter will focus on the
literatures of real option application in real estate area.
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Chapter 3 Application of Real Options in Real Estate
Investment
Real estate investments are characterized by low liquidity, slow payback and high
sunk costs, involving high uncertainties about demand, house price and land costs
(Rocha et al., 2007). Such characteristics are especially remarkable in emerging
markets. The application of real options theory in real estate investment analysis
considers a real estate development as an investment opportunity that reduces the
uncertainties in the real estate development and creates economic value on real estate
projects.
3.1 Real Options Commonly Exist in Real Estate Investment
Various real options exist in real estate development projects, examples are listed as
follow.
The most typical real option exist in real estate market is an option to wait. For
example, vacant land gives its owner the right but not the obligation to develop
property at any point in the future (Titman, 1985). Due to high uncertainties involved
in real estate development, landowner can defer the large scale construction and wait
until necessary market information available. Hence, it is an American call option,
whose main value is from the time value of the option that allows developer to gain
more knowledge and the risks it reduces for the investment. The longer the option life
time, the higher level of the uncertainty is associated in the real estate project. As time
passes, the project’s value is more certain. Developers can either proceed with the
construction if the market situation is favorable, or defer the construction to avoid
potential losses in case of adverse market situation. It thus performs as a mean of risk
management on irreversible investments, by which developers will not lose any thing
other than the option’s premium.
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Also construction of a real estate site is often divided into phases. A Time-to-Build
option can be realized here, where the initial phase of a project provides its
performance that can be responded for future phases designing. For large,
multi-building developments, time-to-build option reduces risks and capitalizes risk
management flexibilities. The larger the scale of the investment, the higher the
uncertainties, thus the time-to-build option is more valuable. Exercising the option of
building a previous phase offers another option to build a subsequent phase. Thus, it is
analogous to a compound call option. Similar to the option to wait, time-to-build
option also represents an approach of risk management in real estate investment.
When previous phase provides unfavorable performances or the market condition
turns extreme unfavorable, a developer can exercise the option to abandon or scale
the project back by selling a fraction of it. They are American put options that protect
the developer from further losses. Conversely, if the market situation provide positive
feedback, the option to expand provides developers the opportunity to scale up the
property development, and obtain the upside potential probability.
Option to switch can also be applied into real estate developments (e.g. in terms of
switching land intended use or operation modes). According to market demand
changes, developers often have the option to convert land use between industrial,
commercial and residential use. An example can be conversing an office building to
residential property, which is an option to converse with the value of the proposed
residential project as underlying asset and the value of office building as exercise
price (Barman and Nash, 2007). Real estate developers can also switch between
different modes of operation such as switching between construction materials for
cost saving.
Real option concept can also be applied to project financing in real estate
development. For a levered real estate project, its equity providers hold a call option
on the project with the outstanding value of debt as the exercise price; the option is in
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the money if the project value over the debt value, where the equity provider has a
positive payoff (Barman and Nash, 2007).
There is even an option to growth for the real estate developers. One real estate
project can set-up value chains with other valuable projects, thereby early real estate
projects could provide later growth opportunities for the development company.
Overall, a real world real estate project is normally phased, with other types of options
embedded in each single phase. The most common options exist in single phase are
time-to-build option, options to wait and options to abandon. A typical sequential
phased project is described by Rocha et al. (2007) with the following decision tree:
Rocha, K. Salles, L. Garcia, F. A. A, Sardinha, J. A. and Teixerira, J. P. (2007), “Real Estate and Real
Options—A Case Study” Emerging Market Review, 8, pp.67-79
3.2 Prior Research on Real Options Application in Real Estate
Various studies have applied real option theory and pricing models to real estate. The
earliest work is Titman (1985), who first proposed the analogy that holding vacant
land can be recognized as an option to develop a completed building at the future. By
investigating the reason of why lots of land in Los Angels leaved undeveloped,
Titman figures out that an option to wait is analogous to an American call that
contributes significantly to the value of land. Value of the call option is positive
related to the uncertainties of the proposed project cash inflows and its construction
costs. Thus, the vacant land value should enclose both the value of its best immediate
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use and the value of option if development is delayed or the land is converted into its
best alternative use in the future (Trigeorgis, 2001). In that sense, holding a vacant
land undeveloped is thus reasonable since deferral option added economic value to the
land. Williams (1991) confirms Titman’s results and expands the research on option to
abandon, optimal timing for development and optimal density for a property.
In addition to the real option application in land valuation, operation flexibilities and
opportunities to redevelopment are realized as real options, and their impacts on value
of real estate development project are discussed. Examples of these literatures include
Williams (1997) and Childs et al. (1996)’s discussion of repeated redevelopment
impacts on project value; Grenadier (1995)’s research on optimal tenant mix
determinants; Capozza and Sick (1994)’s study on conversion of property alternative
use; and Capozza and Li (1994)’s research on optimal intensity and timing for
investments. Literatures find that the values of those options are significantly
contributed to the value of land and developed properties, which explains the current
continuing patterns on investments in existing (already developed) real estate assets
(Ott, 2004). However, above researches examines only singular real options
embedded in real estate investment, whereas real world situation are much more
complex.
Numerous empirical studies conducted to test validity of the real-option model on
land valuation and real estate development decision-making. Quigg (1993), an earlier
empirical test on real option pricing models, studies 2700 land transactions in Seattle,
confirms the explanatory power of real option model in land transaction price
prediction, and finds that the deferral option represents 6% on average of the
theoretical land value. Ott and Riddiough (2000) and Ott and Yi (2001)’s empirical
study results also favors real option model prediction power and highlight the
importance of deferral option value in irreversible real estate investment. By studying
aggregate U.S. and regional commercial real estate data, they find real option model,
especially the uncertainty variable in it, significantly explains commercial real estate
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investment and development cycles. Another example of empirical test of real option
models on U.S. commercial real estate investment is Sivtanidou and Sivtanides (2000),
whose results consist with Ott and Riddough’s findings. Recent empirical works
includes Yao’s (2004) empirical testing of real options in Hong Kong residential
market, Bulan et al.’s (2004) empirical evidence in Vancouver, Canada between 1979
and 1998, and Yavas’s (2005) experimental paper.
Recent works in real option in real estate focus on the practical applications, due to
the significant gap between theory and practice. Ott (2004) tries to bridge this gap by
reviewing real options in real estate and demonstrates a practical application to
illustrated growth option valuation practice. Further, Masunaga (2007) explains the
reason that why real option approach is not fully used in real estate world is because
of the need for understanding the advanced financial theories. By doing experiment in
a real estate case, Masunaga compares real option analysis result with
engineering-based approach result (the valuation approach commonly used in real
estate world), concluded that real option approach though requires advance finance
knowledge but can obtain accurate valuation result, which is suggested to combine
with engineering-based approach. Barman and Nash (2007), stand on the same
argument with Masunaga, developed a streamlined “hybrid” model based on both the
traditional economic and the more recent engineering real options methodologies, and
demonstrated it with a case study. In addition, researchers realize that the existence of
multiple players in the same real estate investment will affect real estate investment
valuation and decision-making (e.g., Wang and Zhou (2006) and Schwartz (2007)).
Models are also developed for multiple real options interaction. For instance, Paxon
(2005) develops valuation model for up to eight different options. Based on the
numerical solutions, Paxon finds that increase in number of options reduces the
investment and abandonment triggers, and increases the values of the investment
option and total option values.
Yet, few papers put on directly applications of real option valuation for multi-phased
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real estate investment projects. Researches that focus on the emerging market
application are also very limited. However, it is the market with relative higher
uncertainties, where real option approach should be employed to reduce risks. One
example is Rocha et al. (2007), who study a two-phase residential housing in the west
zone of Rio de Janeiro in Brazil. Applying their model, Rocha et al. (2007) show that
real option application in emerging real estate market improves the risk management
of project by identifying the optimal strategy and timing for the construction phases.
3.3 Research in Real Option Application in Chinese Real Estate Market
In china, pioneers cities such Guangzhou, Shenzhen experiences a boom in real estate
market due to land reform since 1980’s (Chen and Wills, 1999). As one of the
emerging markets, real estate investments are especially associated with high
uncertainties. Despite that, the real option methodology does not introduced to real
estate investment analysis until recent years.
Most Chinese literatures theoretically realized the advantage of real option method
over Traditional NPV in capture the investment and operation flexibilities in Chinese
real estate market. Zhao (2006a) compares real option and NPV analysis in
commercial real estate investment, concludes NPV ignores the irreversibility,
uncertainty and flexibility involved in commercial estate investments, so that
undervalues the investment value and leads to incorrect investment decision. Liu and
Liu (2006) provide a case study on the comparison of real option and NPV analysis in
investment decision-making on real estate project, and draw the same conclusion with
Zhao (2006). Li et al. (2003) explain the various types of real options exist in real
estate investment, study on the strategies in investment decisions with consideration
of real options, and finally observed above discussion with an example of option to
wait. Zhao (2006b) studies the real option characteristics in real estate market and
conducts a framework for the commercial real estate investments. Nevertheless,
practical and empirical papers are not rich in real option research on Chinese real
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estate market.
Different from real options literatures in Europe and US, researches on multi-phased
investments in Chinese real estate market are limited. The only example is Zeng and
Qiu (2006), who provide a real option model for a three-stage real estate investment
and development project, state that each stage of the three stages (land obtain,
construction and sales) in real estate development gives the option to conduct the next
stage.
Regards to the real option valuation applied in real estate investment, Black-Scholes
models are commonly used in real estates real option research (e.g., Xiang and He
(2002) and Yang and Zhang (2005)). Only few papers focus on the binomial tree
method application in valuing real options in real estate area. For instance, Sun (2006)
builds up a binomial model for real estate investment and applies it in his case study.
Hence, it can be concluded that although Chinese real estate market is more volatile
than developed market, Chinese literatures about real option application are still
constrained on theories, lack of empirical and practical studies, especially for the
phased real estate investments. And most of the case studies are conduct the valuation
with Black-Scholes models, but few apply binomial tree method to the real option
evaluation, despite better model flexibility of binomial approach on capturing real
option characteristics (refer to 2.3.3).
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3.4 Summaries
Regardless the enormous theoretical contributions, current real option research in real
estate constrained in singular real option valuations, multi-phased real option models
are limited. Moreover, there is a notable gap between theory and practice, especially
in emerging real estate markets, which is probably because of the requirement of
advance finance knowledge when applying real option analysis. Hence, the literature
of real options in real estates lacks practical value (Lucius, 2001). Recent papers thus
much more focus on the practical applications in order to bridge the gap. Nevertheless,
fewer researches pay attention to emerging market applications. In Chinese real estate
market, as one of the major emerging market, real option analysis should have been
applied into real estate investment valuation for risk management. However,
researches on Chinese real estate market in application of real option theory are still
restricted in theoretical framework with limited practical examples, particularly in
multi-phased investments. Even in practical examples, binomial method is rarely used
for valuation, which would actually offer a more accurate valuation result.
Hence, in the following chapters I try to provide a practical application of binomial
tree method to a phased real estate investment project in Guangzhou China, observe
the importance of investment flexibilities in adding value to real estate project and
reducing uncertainties.
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Chapter 4 Case Study
In the following two chapters, methodology of case study will be used to provide
insight for real option analysis applied in a real estate investment project. The
objective is to show the importance of the real option in adding value to the whole
project, accounting into the uncertainties involved in the project. For the real option
analysis in this case, binomial trees approach is chosen for real option valuation, due
to its model flexibility and computation accuracy compared with other methods.
The case is referred to a real estate project located in Guangzhou, one of the boom
emerging real estate markets in china for recent ten years. It is a case that usually
exampled for real estate development planning, where traditional NPV is used as
investment appraisal method. However, without considering the investment flexibility,
some of project value was neglected by the developer. This chapter is going to
introduce the background and statement of the case, and the real option analysis for
the case will be conducted in next chapter.
4.1 Case Background3
In 2001, Guangzhou City Construction & Development Property Holdings Co., Ltd.
(GCCDP) was considering to purchase a land in Haizhu District, Guangzhou, with a
land cost of RMB ¥480 million, develop it into residential housing property “Jiangnan
New Village”. The whole project will take 6 years to build. If the development is
success, the property will be the present largest residential property development in
Guangzhou.
The real estate market in Guangzhou thrived since 1990’s. It grew fast from 2000, in
3 All the figures and background information about Haizhu District and Jiangnan New Village are sourced from Jia, S. (2005), Real Estate investment project planning—Theory, Practice and Case Study, Guangdong Economic publishing, Guangzhou.
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which year real estate development investment was 356.05 million RMB, 20.33%
more than the investment amount in 1999. Haizhu District is one of the most boom
districts in real estate investment and development. During three quarters of 2000,
there was1,080,000m2 housing property sold in Haizhu District, which was the
highest deal amount in Guangzhou, about 25% of overall sales. The land GCCDP
considered to purchase is located on a traffic conjunction of main streets, with other
residential housing properties and many colleges and schools surrounded. But the
security, noise and pollution become the weakness of the development. More
important, it will face the threats of intensive competition from other residential
properties, such as Haifu Garden and Fujing Garden. Hence, the treats and
environment determined that the land can not be used as luxury property development
but intends to be built as a residential property for middle classes. Nevertheless,
middle classes are more sensitive to price, therefore the demand is very elastic and
involve more uncertainties regarding Chinese economic environment. In addition, the
project is going to be the largest residential development property, so that faces much
higher risks than any other middle class residential property developments.
The developer Guangzhou City Construction & Development Property Holdings Co.,
Ltd. is one of the leading real estate developers in Guangzhou, opened in 1978.
Through asset restructuring with Yuexiu Enterprise (Holdings) Ltd. in 2002, the
company was listed in Hong Kong Exchanges in the name of Guangzhou Investment
with total capital assets of RMB 21 billion. GCCDP has developed more than 40
residential areas over the years, in which Jiangnan Village was one of the earlier
development and operating property. Other projects include 5.2 sq.km Tianhe
Construction Section (integratedly developed for the sixth national games and
collaboration in the implementation of the strategy of shifting the center of
Guangzhou eastward), Ershadao Islet Villa Complex (the most luxurious complex in
Guangzhou) and Glade Village and Southern Le Sand (GCCDP, 2007). From the
position of present time, Jiangnan Village offered a growth opportunity for GCCDP to
become an integrated enterprise with a robust brand. In addition, the first Real Estate
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Investment Trusts (REITs) in mainland China also went public under the name of
GCCDP.
4.2 Case Statement—Jiangnan New Village4
If GCCDP decide to purchase the land, the residential property “Jiangnan New
Village” would be developed, with a gross land area of 106,690 m2, and building area
of 352290m2 (including 12 mid-high units, 8 low units and 8 high units residential
houses). The project starts on January 2002, and expected completed at the end of
2007, with duration of 6 years.
The project involves 3 Phases including initial investment setting up and building
constructions:
Phase I —initial launch phase (from Jan. 2002 to Dec. 2002, duration 1 year,)
The first phase involves the initial investment and preparation including market
research, sales planning, and initial investment feasibility analysis; building design;
land acquiring, document and permission obtaining. It is expected to cost an initial
expenditure with a present value of RMB ¥ 109.2452m (see Appendix 1).
Phase II—1st stage construction phase (from Jan. 2003 to Dec. 2004, duration 2
years)
In the first construction stage, the construction plan contains 12 mid-high residential
units, 6 low residential units, and nursery school, Central Park and other basic
facilities, with building area of168435.56m2. The total construction cost for this phase
is expected to have a present value of RMB ¥496.4299 (Appendix 2). Sales plan
begins from phase II, in which 40% of mid-high units is planning to be sold in 2004
4 The case is quoted from Jia, S. (2005), Real Estate investment project planning—Theory, Practice and Case Study, Guangdong Economic publishing, Guangzhou. And all the relevant data are quoted from the book.
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with a price of ¥5200/m2 (refer to Appendix 3). Further sales are planned to be
conducted in Phase III.
Phase III—2nd stage construction phase (from Jan. 2005 to Dec, 2007, duration 3
years)
Second construction stage contains 8 high residential and commercial units, 2 low
residential units, with 16970414m2 building area. A construction cost with a present
value of RMB ¥393.1843m is needed for phase III (Appendix 2). Sales activity are
mainly planned to be conducted in this phase. 40% of mid-high units and 40% of low
units are expected to be sold in 2005 with a price of ¥5200/m2 and ¥5400/m2
respectively. And in 2006, it has the budget to sale rest of the mid-high units and 40%
of low units and 60% of high units. High units sold in a price of ¥5600/m2. Rest of the
property (20% of low units and 40% of high units) are planned to be sold in 2007 (see
Appendix 3).
When constructions completed, the residential property will be operated and managed
for 20 years by GCCDP, after which the property is proposed to be resold. The total
project is expected to generate a cash flow with a present value of RMB
¥1,061.894282m (see Appendix 2). And the investment appraisal of Jiangnan New
Village was done by traditional net present value approach, with the net present value
of is RMB ¥150.4934m (refer to Appendix 2).
4.3 Real Options Identification
To identify the real options embedded in the project, we need to look the project
closely phase by phase. Below is a summary of the case project phases:
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Time-to-Build Option
By showing above, we can see that each phase can be seen as an option on the value
of subsequent phases by investing the construction cost required to proceed to the
next stage. Such an option gives the real estate developer the flexibility to conduct the
next phase construction. For example, after the initial launch phase, the GCCDP does
not have to start the construction immediately, but can decide what to do according to
the first phase result. The success of the initial launch provides an option to conduct
the 1st stage construction phase. Similarly, 1st stage construction phase also provide
such an option to carry out 2nd stage construction. As well, the investment of initial
launch opens the opportunity to conduct the later two construction phases.
Nevertheless, exercises of investment in each phase are not obligations.
Hence, there is a sequential compound option exists in this three-phase real estate
development project, composed by three simple European call option at each phase.
The exercise of previous option gives the right to buy the subsequent option. The
value of option in phase II is based on the option in phase III, and the option value in
phase I is compound on phase II option value. The exercise price for each simple call
option is the construction costs for each phase.
0 1 2 3 4 5 6 7
Initial Launch
1st Stage Construction 2nd Stage Construction
RMB ¥109.2452m
RMB ¥496.4299m
RMB ¥393.1843m
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Abandon option
In addition to the compound deferral option, it can be recognized that an abandon
option exist during the whole project, which can be exercised any time before the end
of the project. In the case of the extreme unfavorable market situation, such an option
allows GCCDP to abandon the project at the salvage value of the project, and thus
limit the downside loss. This is an American put option alive during entire project
periods.
Both types of options would mitigate the risks faced by Jiangnan New Village’s
development, and can be seen as risk management flexibilities that can be employed
by GCCDP.
4.4 Valuation Model Choice
4.4.1 Real Option Model
For the real option valuation conducted in the following chapter, binomial trees
approach is chosen as the valuation model. This is mainly because of its advantage in
the model flexibility. Other real option valuation models like Black-Scholes are lack
of such flexibility in easy adaptation in various type of real options, such as American
real options (as it requires a fixed decision date) and options with dividends payment
(refer to section 2.2.3). Nevertheless, the abandon option identified above is an
American put option that cannot apply Black-Scholes for valuation. Black-Scholes
cannot capture the value of complicated compound real options either. But in this case
study and most real estate investment projects are not single existed but compounded
by phases, which are easier to be captured by Binomial Tree approach. Binomial
models also have the advantages of easy explanation and operation. In practice, most
real estate developers are lack of financial options knowledge, whereas the binomial
tree is easy to understand and managed, and is a relative practical valuation method
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compared with Black-Scholes Model, which requires specific financial knowledge for
understanding. Other methodologies such as Monte Carlo simulation are either
difficult to explain in theory or complicated in technical application, hence are not
considered as appropriate valuation methodology.
4.4.2 Expanded NPV Framework
After the valuation of real option, the Expanded NPV framework will be applied to
calculate the expended project value with each option. Trigeorgis (1996) propose an
expanded or strategic NPV criterion which does not only reflect NPV of project cash
flow, but also the real option values by adding them on traditional net present value.
Namely, Expanded (strategic) NPV equals Static (passive) NPV of project expected
cash flows plus Value of flexibilities (real options) embedded in the project
(Trigeorgis, 2001). By applying such a framework, the effect of real option analysis
on project valuation can be directly illustrated.
To sum, under the framework of the expanded NPV rule, the real option will be
analyzed by Binomial Trees Approach. All the data (including NPV and cash flows of
the project, construction costs) are quoted from Jia’s (2005) book on real estate
investment project planning. Some assumption will be made for the project valuation
in the next chapter.
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Chapter 5 Real Options Valuation and Analysis
5.1 Time-to-Build Option
This is a sequential compound option composed by three European call options. The
exercise of phase I option (C1) give the Jiangnan New Village’s developer the right to
buy another call option (C2), and which also offer a right to buy phase III option (C3).
C2 is active only after the exercise of C1 and C3 is alive only when C2 is exercised.
Hence, from an economic point of view, the third option chronologically is the first
option (Copeland and Antikarov, 2003). The underlying asset for C1 is based on C2,
which is, on the other hand, based on the value of C3.
5.1.1 Parameters Estimation
Underlying asset
As I stated above, the time-to-build option is a sequential compound option, and value
of C1 is based on C2, and value of C2 is based on C3. Thus, the underlying asset for
phase I option is the option value of C2 at the exercise date of C1; the underlying asset
for phase II is the option value of C3 at the exercise date of C2; whereas, the
underlying asset for phase III option is the value of cash flows that generated by this
real estate project at the date of C3’s exercising. The present value of these cash
inflows can be derived from the net cash flows of the Jiangnan New Village (See
Appendix 2), which is RMB ¥1,061.894282 million (i.e. sum of the present value of
cash inflows).
Exercise price
For real options, option is exercised when investment is made, and the exercise price
is the cost of making investment on the project. Hence, the construction costs for each
phase in Jiangnan New Village project are assumed to present the exercise prices for
the single option in each phase. Those are RMB ¥109.2452m for phase I, RMB
¥496.4299m for phase II and RMB ¥393.1843m for phase III respectively.
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Time to Maturity
Assume year 0 is 2001, when the company has to make the decision of Jiangnan New
Village investment. For the option to develop phase III, the time to maturity (T3) is
equal to the development time of phase III in 2005, which is 4 year from year 0. And
for the phase II option, the time to expire (T2) is 2 years from year 0. Phase I then has
a time to maturity (T1) of 1 year from year 0. But it has to be noticed that Phase III
option is not alive until the exercise of the Phase II option, as well as for Phase II
option that can only exercised after phase I has successes launched.
Volatility estimation
Many different methods are available to estimate the volatility in real option,
including logarithmic cash flow returns, logarithmic present value approach and
GARCH approach (Mun 2002). In this dissertation, logarithmic present value of
returns approach is adopted. Six years history stock price of GCCDP5 is assumed
having the same volatility with Jiangnan New Village development cash flows, and
has been used to derive the volatility. Namely, the volatility is measured as standard
deviation of the logarithmic GCCDP history stock prices by the formula
1)( 2
−−
= ∑n
RRσ where )/ln( 1−= tt PPR . The daily standard deviation is then
annualized by the formula dailyannualized yearsnSQRT σσ ×= )/( to get the annual
volatility. Detailed calculation of the volatility estimation is illustrated as below
(Table 5.1).
As shown, a result of 41.43% annualized volatility was obtained from this process for
Jiangnan New Village project, and assumed to be constant over the entire project life.
5 Quoted from Yahoo! Finance (2007), trading code 0123
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Table 5.1 Volatility Estimation
Date Close pt/pt-1 r=ln(pt/pt-1) r-r' (r-r')2
18-Sep-07 2.76 1.01845018 0.018282045 0.017268974 0.000298217
17-Sep-07 2.71 1.08835341 0.084665924 0.083652854 0.0069978
14-Sep-07 2.49 0.95402299 -0.047067511 -0.048080582 0.002311742
13-Sep-07 2.61 1.12017167 0.113481954 0.112468883 0.01264925
12-Sep-07 2.33 1.02192982 0.021692825 0.020679754 0.000427652
11-Sep-07 2.28 1.01785714 0.017699577 0.016686506 0.000278439
10-Sep-07 2.24 1 0 -0.001013071 1.02631E-06
7-Sep-07 2.24 1.00900901 0.00896867 0.007955599 6.32916E-05
6-Sep-07 2.22 1.01369863 0.013605652 0.012592581 0.000158573
- - - - - -
- - - - - -
- - - - - -
10-Jan-02 0.67 1 0 -0.001013071 1.02631E-06
9-Jan-02 0.67 0.98529412 -0.014815086 -0.015828157 0.000250531
8-Jan-02 0.68 0.97142857 -0.028987537 -0.030000608 0.000900036
7-Jan-02 0.7 1.04477612 0.043802623 0.042789552 0.001830946
4-Jan-02 0.67 1.046875 0.045809536 0.044796465 0.002006723
3-Jan-02 0.64 1 0 -0.001013071 1.02631E-06
2-Jan-02 0.64 1.03225806 0.031748698 0.030735627 0.000944679
1-Jan-02 0.62
r'= 0.00101307 sum 1.029294152
n= 1475 variance 0.0006983
n/6 245.833333 S.D.Daily 0.026425366
SQRT(n/6) 15.6790731 S.D.Annualized 0.414325245
Where S.D Annualized =SQRT(n/6)*S.D.Daily
Risk-free rate
The interest rate of government bond with correspond life time to option’s time to
maturity can be used for estimation of the risk free rate. In this case, it is assumed to
be 3.78%, which refers to 5 year government bond interest rate in 2001 quoted from
The People’s Bank of China. It is also assumed that the risk-free rate is constant and
continuous.
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5.1.2 Time-to-Build Option Valuation
Based on the assumption stated above, an 8 time-step binomial tree is developed for
the valuation of this time to build option. As analyzed in last section, the third option
chronologically is the first option from the economic point of view. Thus the valuation
process starts from the estimation of Phase III value and calculated backward to Phase
I option.
Underlying asset value tree
To value the phase III option value, its underlying asset, the returns of Jiangnan New
Village has to be estimated first. It has a present value of RMB ¥1,061.894282m,
which has two possibilities at each time-step: increase by up state multiplier u, with
risk-neutral probability p; or decrease by the down state multiplier d, with risk-neutral
probability of 1-p. All the values are presented in ¥m.
Table 5.2 Inputs
present value of cash inflows 1061.894282 u 1.340382
Risk-free rate 0.0378 d 0.746056
Time to expiry 4 a 1.0191
time steps 8 p 0.4594
sigma 0.4143 1-p 0.5406
Delta t 0.5 Exp(-r delta t) 0.9813
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Table 5.3 Estimation of underlying asset value
Y0 Y1 Y2 Y3 Y4
Vu8
11063.91694
Vu7
8254.30389
Vu6 Vu7d
6158.17464 6158.174637
Vu5 Vu6d
4594.3444 4594.3444
Vu4 Vu5d Vu6d2
3427.6391 3427.63915 3427.639149
Vu3 Vu4d Vu5d2
2557.211 2557.2115 2557.21146
Vu2 Vu3d Vu4d2 Vu5d3
1907.823475 1907.8235 1907.82348 1907.823475
Vu Vu2d Vu3d2 Vu4d3
1423.343542 1423.344 1423.3435 1423.34354
V Vud Vu2d2 Vu3d3 Vu4d4
1061.894282 1061.894282 1061.8943 1061.89428 1061.894282
Vd Vud2 Vu2d3 Vu3d4
792.2328184 792.2328 792.23282 792.232818
Vd2 Vud3 Vu2d4 Vu3d5
591.0502102 591.05021 591.05021 591.0502102
Vd3 Vud4 Vu2d5
440.9567 440.95668 440.956677
Vd4 Vud5 Vu2d6
328.97847 328.978465 328.9784651
Vd5 Vud6
245.43643 245.436425
Vd6 Vud7
183.109368 183.1093681
Vd7
136.60988 Vd8
101.9186489
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Phase III Value
Based on the underlying asset value tree, value of phase III option C3 can be derived.
The payoffs at the time to expiration of the option are MAX (0, ST-X), where X is the
construction cost of phase III, equal to RMB ¥393.1843m. Using the risk-neutral
valuation ( ) [ ( ) (1 ) ( )]r tC t e pCu t t p Cd t t− ∆= + ∆ + − + ∆ and apply the roll back
procedure until year 2 when C3 becomes alive, the value of C3 is then derived. As C3
is not available until year 2, the option values before year 2 are zero. At nodes C3u2d6,
C3ud7 and C3d7, the zero call option values imply that at these economic states the
market situation is not favorable enough to proceed phase III, thus the phase III
construction should be either deferred or abandon.
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Table 5.4 Phase III option value Tree
Y0 Y1 Y2 Y3 Y4
C3u8
10670.73264
C3u7
7868.48099
C3u6 C3u7d
5779.57531 5764.990337
C3u5 C3u6d
4222.8334 4208.5215
C3u4 C3u5d C3u6d2
3063.0838 3049.03982 3034.454849
C3u3 C3u4d C3u5d2
0 2185.7005 2171.38856
C3u2 C3u3d C3u4d2 C3u5d3
0 1543.2681 1529.22415 1514.639175
C3u C3u2d C3u3d2 C3u4d3
0 0 1051.8325 1037.52064
C3 C3ud C3u2d2 C3u3d3 C3u4d4
0 0 702.42399 683.294956 668.709982
C3d C3ud2 C3u2d3 C3u3d4
0 0 430.30737 406.409917
C3d2 C3ud3 C3u2d4 C3u3d5
0 260.4167 230.519965 197.8659102
C3d3 C3ud4 C3u2d5
0 125.24432 89.1946102
C3d4 C3ud5 C3u2d6
66.073142 40.2074237 0
C3d5 C3ud6
18.124827 0
C3d6 C3ud7
0 0
C3d7
0 C3d8
0
Max (0, ST -X)
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Phase II Value
Using the values of phase III option at year 2 as underlying asset, value of phase II
option is then calculated. The payoffs at year 2 are MAX (0, C3-X2), where X2 equal
to Phase II construction cost, RMB ¥496.4299m. Similar to Phase III option, Phase II
option will not be valuable until the exercise of Phase I option. Thus, the option
values of Phase II in Y0 are zero. Again, zero call option value at nodes C2ud3 and
C2d4 imply that Phase II construction will not be defaulted.
Table 5.5 Phase II Option Value Tree
Y0 Y1 Y2
C2u4
2566.6539
C2u3
1712.346
C2u2 C2u3d
1080.207081 1046.8382
C2u C2u2d
0 581.1757
C2 C2ud C2u2d2
0 311.2451753 205.99409
C2d C2ud2
0 92.85865
C2d2 C2ud3
41.85911296 0
C2d3
0
C2d4
0
Compound Option Value
After obtained the value of C2, phase I option value can then be calculated, with the
payoff function of MAX (0, C2-X1), where X1 is the initial launch cost RMB
¥109.2452m. Note that Phase I option will not be exercised at the node C1d2 with a
value of zero, which means at that economic state the overall project will not
conducted then.
MAX (0, C3-X2)
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Table 5.6 Compound Option value Tree
Y0 Y1
C1u2
970.9618814
C1u
544.8530666
C1 C1ud
293.91641 201.9999753
C1d
91.05817689
C1d2
0
Finally, the value of compound option is derived as RMB ¥293.9164m, which is the
strategic value of considering the time-to-build option. Such a value can be added on
the project’s net present value based on Trigeorgis’s (1996) “expanded NPV” rule6:
Expanded NPV of Jiangnan New Village = NPV without investment flexibilities
+ Value of time to build option
=RMB ¥150.4934m + RMB ¥293.9164m
=RMB ¥ 444.4098m.
5.2 Option to Abandon
As the option to abandon can be exercised at any time before the project complete, it
is an American put option based on the project which provides the opportunity for
GCCDP to control the downside loss.
5.2.1 Parameters Estimation
Underlying asset
The underlying asset for this American put option is simply the Jiangnan New Village 6 “Expanded (strategic) NPV= Static (passive) NPV of expected cash flows + Value of options form active management” (Trigeorgis, 1996, p124).
MAX (0, C2-X1)
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cash inflows, with the present value of RMB ¥1,061.894282m.
Exercise price
For option to abandon, the exercise price would be the salvage value (i.e. the resale
value on the secondhand market) of the project. In this case, it is assumed the salvage
value is the land price RMB ¥480m (i.e. assume the project can be sold at its land
price at any time during the project life time if abandon).
Time to maturity
As analyzed in last chapter, this option to abandon will not expired until the end of the
project, and the project starts in one year from now (2001) having a building period of
6 years, hence, the option has a time to maturity of 7 years.
Volatility
As the underlying asset is still Jiangnan New Village cash inflows, the annualized
volatility 41.43% also represent the volatility for this real option, which is again
assumed to be constant over the project life.
Risk-free rate
The risk-free rate here is also assumed to be 3.78%, as there is no precise correspond
7-year government bond available for guidance of the risk-free rate. Again, the
risk-free is assumed to be constant and continuous.
5.2.2 Abandon Option Valuation
Based on the assumptions made above, a 7-step binomial tree is built to value this
American put option. Here 7 time-steps is chosen for time conservation.
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Table 5.7 Abandonment Option Value Tree
Initial stock price 1061.894282 Delta t 1
Exercise price 480 u 1.513311052
Risk-free rate 0.0378 d 0.660802681
Time to expiry 7 a 1.0385
sigma 0.4143 p 0.4431
time steps 7 1-p 0.5569
Exp(-r delta t) 0.9629
Y0 Y1 Y2 Y3 Y4 Y5 Y6 Y7
19300.951
0.0000
12754.12019
0.0000
8427.96 8427.9568
0.0000 0.0000
5569.22 5569.216455
0.0000 0.0000
3680.15 3680.15 3680.1532
0.0000 0.0000 0.0000
2431.86 2431.86 2431.855076
7.6994 0.0000 0.0000
1606.98 1606.98 1606.98 1606.9764
28.7333 14.3573 0.0000 0.0000
1061.89 1061.89 1061.89 1061.894282
63.5790 47.4544 26.7725 0.0000
701.70 701.70 701.70 701.70259
95.6986 77.0675 49.9234 0.0000
463.69 463.69 463.6869513
140.6992 122.4110 93.0937
306.41 306.41 306.40558
201.0541 188.5463 173.59442
202.47 202.473629
277.5264 277.5264
EARLY 133.80
EARLY 133.79512
346.2049 346.20488
EARLY 88.41217184
391.5878
EARLY 58.423
421.577
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Different from the European option, this option to abandon can be early exercised at
each node if the value of X-ST is bigger than the value derived by risk-neutral
valuation process. As shown above, it is better to early abandon the project in year 4 if
the project value goes down to RMB ¥202.4736m, since payoff by exercising the
American put option (X-S4=277.526371) is higher than the value derived from
risk-neutral valuation (i.e. e-rΔt(Pud4*p+Pd5*(1-p)=266.093922). With the flexibility
of early exercise, the abandonment option creates a value of RMB ¥63.5790m, adding
which the project’s net present value becomes RMB ¥214.0724m:
Expanded NPV of Jiangnan New Village = NPV without investment flexibilities
+ Value of abandonment option
= RMB ¥150.4934m + RMB ¥63.5790m
= RMB ¥214.0724m.
5.3 Result Analysis and Further Discussion
The result of above real options valuation indicates that the inclusion of real options
can affect project value drastically. The time to build option and the option to abandon
add on the Jiangnan New Village net present value by RMB ¥293.92m and RMB
¥63.58m individually. Such dramatic strategic values have managerial implications
for Jiangnan New Village’s developer GCCDP. As the risk of emerging real estate
market is relatively high compared with other markets, consideration of time-to-build
and abandonment opportunities can reduce the corresponding uncertainties involved,
taking of the upside potential gains and limit the downside losses. For instance, if the
real estate economic is declined, these options allow GCCDP either not default the
next phase, or simply abandon the project in any point of time at a salvage value.
Such real options mitigate the high uncertainties involved real estate developments.
GCCDP should have realized these opportunities of risk management and the
economic values they created, taking them account into the investment appraisal of
Jiangnan New Village.
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In terms of the combined effect of these two real options on Jiangnan New Village
project, possible interactions between them have to be taken into consideration.
Trigeorgis (1996) suggested that managerial flexibility embedded in investment
projects typically takes the form of a collection of real options, and interactions may
occur among real options, thus present in combination generally make their individual
values non additive. Such an interaction is obvious in our example of the
time-to-build compound option, where the presence of subsequent option (Phase II
and Phase III options) increases the value of the effective underlying asset for earlier
options (Phase I option) (Trigeorgis, 1996). Hence, the time to build option and option
to abandon are theoretically non additive, but interacted affect Jiangnan New Village’s
project value. For instance, an earlier abandonment may eliminate the project, and
therefore kill the later options (e.g. Phase II or Phase III options)7. Nevertheless, the
combined strategic values these real options afford may be still as economically
significant as the value of the project’s expected cash flows (Trigeorgis, 1996).
Furthermore, although it was not taken into consideration in real option analysis
above for simplicity purpose, there are much more other options exist in such a real
estate development project. For instance, the project is actually not fully financed by
the developer, but 33% of the investment was financed by debt. Hence, there could be
an option to optimal real estate project financing option exist for the developer, which
could maximize the developer’s profit from the project investment. Also, Jiangnan
New Village is one of the most important residential projects that GCCDP has
developed, the success of the project generate enormous intangible income to GCCDP,
brand effect for instance. Thus, the development of Jiangnan New Village can be
realized as a growth option for GCCDP’s future expansion. And it is true that after
7 Nevertheless, this probably may not be the case under the assumptions of this dissertation. As the estimated salvage value is relative low to the underlying asset value, the early exercise of abandonment option would occur only after year 4 and only in the situation when the underlying asset goes down to ¥202.47m. While, in the same situation in year 4, the Phase III option will not exercised as its value down that state is already zero. Moreover, the two options are opposite in types (one is compound call option, and one is American put option). Thus, the option interactions are small and simple additivity could be a good approximation of combined option value (Trigeorgis, 1996). Therefore, the additive value ¥357.50m (time to build option value ¥293.9164m+ abandonment option value ¥63.5790m) may still be a reasonable approximation of the combination effect on Jiangnan New Village net present value.
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constructing the Jiangnan New Village, GCCDP developed Tianhe Construction
Section in the following year, Ershadao Islet Villa Complex and Glade Village and
Southern Le Sand in 2005. And it also published the first Real Estate Investment
Trusts (REITs) in mainland China in 2005.
All these real options together with time to build option and abandonment option I
analyzed above, taking the form of collection of real options, interact among each
other and enhance the value of the real estate investment project value. Although the
interactions among these various real options may generally reduce the single real
option value in isolation, and the combined value may declines as more options are
present (Trigeorgis, 1996), the overall effect of these real options is still noticeable
and economically considerable to real estate investment decisions. Therefore, as
shown in this case study, the application of the real option analysis in real estate is
important in investment decision, or even decisive in the developers’ business
strategic expansion. Particularly in Chinese real estate market, an emerging market
with high uncertainties related to demand, land price and government policies,
application of real option analysis is even more imperative.
5.4 Sensitivity Analysis
As all the parameters for the real option valuation in the case study are estimated and
using assumptions, different estimation will lead to changes on the real option value,
and therefore lead to a different investment decision. Hence, sensitive analysis is used
to find the most crucial parameters contribute to the variation of the real option values.
By doing which the real estate developer can better understand the project they
developed and management flexibilities on it, thereby make a better investment plan.
As the estimation of volatility and risk-free rate are both rough in this case study, they
are chosen as the critical parameter examined.
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5.4.1 Volatility Sensitivity Analysis
Volatility is a critical parameter for real options’ values. It is estimated using history
stock price data in this case study, assuming that the developers stock prices would
represent the similar risk level to the real estate project they developed. In order to see
how volatility changes could affect the value of the options, the range of volatility
variation from -30% to 30% is chosen.
Table 5.8 Volatility Sensitive Analysis
Volatility 29.00% 33.14% 37.29% 41.43% 45.57% 49.72% 53.86%
Percentage change of volatility
-30% -20% -10% 0% 10% 20% 30%
Time to Build Option value
234.2330 253.5220 273.4865 293.9164 314.3385 334.7231 354.9369
Percentage change of option value
-20.31% -13.74% -6.95% 0.00% 6.95% 13.88% 20.76%
Abandonment Option Value
19.2987 33.3065 48.2777 63.5790 78.9970 94.3936 110.1996
Percentage change of option value
-69.65% -47.61% -24.07% 0.00% 24.25% 48.47% 73.33%
Figure 5.1 Relationship between Volatility and Real Opiton Value
050
100150200250300350400
29.00
%
33.14
%
37.29
%
41.43
%
45.57
%
49.72
%
53.86
%
Volatility
Rea
l Opt
ion
Valu
e
Time to Build OptionValueAbandonment OptionValue
As shown above, there is a positive relationship between volatility and the options
value. Moreover, volatility seems to have quite significant influences on the option
value. For example, 30% increase or decrease will lead about 20% up or down of
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time-to-build option value. And the change effect is more apparent on abandonment
option’s value, where the same growth (30%) in volatility will increase the value of
abandonment option by 73.33%.
5.4.2 Risk-free Rate Sensitivity Analysis
The risk-free interest rate used in this case study is 5-year government bond interest
rate, which is not exactly matched the options’ life periods. Risk-free interest rate
sensitivity analysis therefore exams the impact of risk-free interest rate variation on
the option value. The analysis conducts by assuming that the variations of the
risk-free interest rate change between -30% and 30%.
Table 5.9 Risk-free Interest Rate Sensitive Analysis
Risk-free interest rate
2.65% 3.02% 3.40% 3.78% 4.16% 4.54% 4.91%
Percentage change of risk-free interest rate
-30% -20% -10% 0% 10% 20% 30%
Time to Build Option Value
279.8032 284.4234 289.1696 293.9164 298.6631 303.4091 308.028
Percentage change of option value
-4.80% -3.23% -1.62% 0.00% 1.61% 3.23% 4.80%
Abandonment Option Value
73.5782 70.1769 66.8138 63.5790 60.4690 57.4806 54.6843
Percentage change of option value
15.73% 10.38% 5.09% 0.00% -4.89% -9.59% -13.99%
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Figure 5.2 Relationship between Risk-free Rate andReal Option Values
0
50
100
150
200
250
300
350
2.65%
3.02%
3.40%
3.78%
4.16%
4.54%
4.91%
Risk-free interest rate
Rea
l Opt
ion
Valu
e
Time to Build OptionValue Abandonment OptionValue
As illustrated in Table 5.8, the effect of change in risk-free interest on real option
value is relatively less significant than the effect by change in volatility. For instance,
30% increase in risk-free interest rate lead to only 4.8% increase in time to build
option value. Again, the abandonment option value is more sensitive to the risk-free
rate changes than the time to build option, 13.99% value decrease with 30% increase
in risk-free interest rate. It is also found that there is a positive relation between
risk-free interest rate and the time-to-build option value, but it is negative correlated
between risk-free interest rate and abandonment option.
Overall, the sensitivity analysis on volatility and risk-free interest rate indicates that
volatility has relatively significant effects on the value of real options. As real estate
investment concerning more uncertainties than other kinds of investments due to the
characteristic of capital intensive, slow payback, high sunk costs and uncertainty in
demand and prices (Rocha et al., 2007), careful consideration should be taken when
applying real option valuation models to real estate investment.
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5.5 Limitations
5.5.1 Oversimplified Model Assumptions
The result derived using binomial tree models above may be imprecise due to the
simplified model assumptions I have made.
First of all, the assumption of constant and continuous volatility may be subjected to
criticisms. As sensitivity analysis suggested, volatility is the most important
parameters that could lead to significant variations of real options value, the
estimation of volatility is vital in obtaining accurate values of real options. However,
due to time constraints and absent of software resources, a simpler estimation method
was applied in Jiangnan New Village case. Monte Carlo Simulation, if applied, may
obtain a better estimation of volatility in the aspect of accuracy. Moreover, the
assumption of constant volatility over the option life time may be unrealistic, as the
volatility may change or even unknown in a real world context.
Similarly, the assumption of constant and continuous risk-free interest rate does not
reflect the real world situation either. Like volatility, Risk-free interest rate could
fluctuate over the real option life time, and in most cases it is not continuous but
discrete. More importantly, as non-existence of government bonds with the exactly
paralleled life time to the real options, the estimation of using 5-year Chinese
government bond interest is not accurate. This, as sensitivity analysis showed, will
lead to a considerable error in estimation of real option value.
Regards to the assumption of salvage value, for calculation simplicity, it was assumed
to be the land cost. But issues like depreciation and inflation may occur during real
option life time were ignored. Thus the exercise price for the abandonment option
may be misestimated, thereby, the option value.
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Other over simplified assumptions such as no dividend payout, no arbitrage
opportunities, no transaction costs, and instantaneous exercise, that may not be
possible to achieve in the real world, should also be taken into consideration for a
critical view of the result’s accuracy.
In addition, for time conservation, 8-time-step and 7-time-step were applied in the
binomial tree model. But as argued by Mun (2002), the more time steps are applied,
more accurate is the result. Thus, 20 or even 50 time steps could be still far away from
an accurate answer. Lots of software have been designed and applied to run higher
time-step valuations in order to obtain accurate real option values.
In sum, all these unrealistic and oversimplified assumptions could affect the accuracy
of real option valuation, thereby influence on the investment decisions.
5.5.2 Limitations of the Real Options Approach
As the analogy between real options and call options on stocks is not exact (Trigeorgis,
1996), the limitation of real option approach may also lead to result inaccuracy.
Initially, the underlying asset, Jiangnan New Village, is a unique asset, which does not
trade in a liquid market. The value thus cannot be accurately assessed until it is
marketed, as well as the variance (i.e. the risk) for it. Second, the real option analysis
above ignores the possibilities that other real estate developers may also intend to
acquire the land and make similar investment. But actually as stated in background
section of Chapter 4, the investment of Jiangnan New Village was facing intensive
competition since Haizhu District is one of the most boom real estate development
areas. Such a competitive interaction may have impact on the real option values
(Trigeorgis, 1996).
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In addition, much more complex circumstances exist in real world, such as
independent investments act as strategic links, or intensive competition involves in
acquiring the real options. These complicated situations may sometimes be neglected
by real option approach, or it is unable for real option approach to offer a specific
value of a package of real options including the interaction effect due to the
calculation complexity.
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Chapter 6 Conclusion
Real estate investments, like other irreversible investments, face high uncertainties
about demand, housing price and land costs. The investment circumstances are
particularly risky in emerging markets, like Chinese real estate market. Real option
approach, compared with traditional NPV method, better captures the investment
opportunities and management flexibilities in real estate investment decision-making
and performs as risk management against high uncertainties involved in real estate
development. Realization of the economic values of these investment opportunities
and management flexibilities can help real estate developers both utilize the
investment opportunities and mitigate potential downside losses.
The aim of this dissertation is to give an insight of how real option valuation is
applied in the real estate investment appraisal, to value the decision options embedded
in the investment projects, to improve the economic analysis of real estate
investments and support the decision-making by managing the different options and
uncertainties embedded in the project.
To achieve the objectives above, a case study of Chinese real estate investment project,
Jiangnan New Village in Guangzhou Haizhu District, has been conducted under real
option analysis. The case was chosen as an emerging market example, where relative
high uncertainties about demand, land costs and government policies may be involved.
Analysis of Jiangnan New Village developing phases identifies two kinds of options,
time-to-build option and the option to abandon. Valuations of these two real options
are conducted using binomial tree approach, considering that complexities of the
compound options and early exercises barrier the application of other real option
valuation methods, like Black-Scholes Model. Time-to-build option is considered as a
compound call option composed by three simple European calls, and the valuation is
conducted from the calculation of the third option chronologically to the first option.
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Option to abandon is valued simply as an American put option with life time
throughout entire project life.
The result suggests that the two options can perform as protection for the project
against the high risk it face, and create significant economic values that can be added
on to the original project net present value. This would have implications for
investment decision-making that the real estate developer of Jiangnan New Village
should have realized these operating flexibilities as risk management strategies, and
taken them into the consideration of investment appraisal. The possible interaction
effects between the two real options were commented. Limitations on estimation of
accurate real option values were discussed in aspect of both oversimplified model
assumptions and the inherent weakness of real option approach. Further sensitivity
analysis was also conducted, and concludes the substantial influence of volatility on
accurate real option price estimation.
Besides the Time-to-Build option and the option to abandon, GCCDP, the developers
of Jiangnan New Village was suggested that other investment opportunities and
operating flexibilities such as option to optimize capital structure and growth option
can be recognized from this project. All such investment opportunities and flexibilities
take form of a collection of real options interacted affecting the value of the real estate
investment project, adding significant economic values on it.
Nevertheless, real options approach is still underdevelopment. Gaps between real
option theory and practical application are still significant. Reasons for it include the
complexities of actual market situation, with various real options and competition
interacted, and the high request of technique knowledge by real option valuation
models but knowledge lacks of practitioners. Thus the application of real option in
actual market place may still be the most focused researching area.
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Appendices Appendix 1 Analogy between Real Options and Financial Options
Stock Call Option Real Option
Underlying assets Current value of stock
(Gross) PV of expected cash flows
Exercise price Exercise price Investment cost
Time to maturity Time to maturity Time until opportunities disappear
Volatility Stock value uncertainty
Project value uncertainty
Risk-free rate Riskless interest rate
Riskless interest rate
Source: Trigeorgis, L. (1988), “A conceptual Options Framework for Capital Budgeting,” Advances in Futures and Options Research, Vol. 3, pp. 145-167
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Appendix 2 Jiangnan New Village Investment Cash Flows, NPV and Construction Costs
Years 2002 2003 2004 2005 2006 2007 ¥m ¥m ¥m ¥m ¥m ¥m
cash inflow sales revenue 0 0 246.11 345.164 626.972 295.336 0 0 246.11 345.164 626.972 295.336 discount rate (r=8%) 1.08000 1.1664 1.259712 1.36048896 1.46932808 1.586874323 pv 0 0 195.3700528 253.7058441 426.706608 186.1117769 Sum cash inflow pv 1061.894282 cash outflow construction cost -109.2452 -131.034 -365.3959 -176.556 -199.288 -17.3403 land tax 0 0 -2.4611 -3.45164 -6.26972 -2.95336 tax on sales revenue 0 0 -15.332653 -21.503717 -39.06036 -18.39943 income tax 0 0 -11.4755 -18.9742 -30.9883 -14.5465 -109.2452 -131.034 -394.665153 -220.485557 -275.60638 -53.23959 net cash flows -109.2452 -131.034 -148.555153 124.678443 351.36562 242.09641 cumulated net cash flow -110.782 -241.816 -390.371153 -265.69271 85.67291 327.76932 discount rate (r=8%) 1.08000 1.1664 1.259712 1.36048896 1.46932808 1.586874323 pv of Net CF -101.152963 -112.34053 -117.92787 91.64237761 239.133537 152.5618044 pv of cumulated net CF -102.575926 -214.91646 -332.844331 -241.201953 -2.0684163 150.493388 r (project wacc) 0.08 after tax NPV Source: Jia (2005) Real Estate investment project planning—Theory, Practice and Case Study, Guangdong Economic publishing, Guangzhou Estimation of underlying asset and construction costs Sum of PV (S0) 1061.89428 Construction Costs phase I (X1) -109.2452 phase II (X2) -496.4299 phase III (X3) -393.1843
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Appendix 3 Sales Plan for Jiangnan New Village
2002 2003 2004 2005 2006 2007 Sales area m2 47328.77 47328.77 23664.38 Mid-High units
Sales proportion 40% 40% 20%
Sales area m2 9069.46 9069.46 4534.73 Low units
Sales proportion 40% 40% 20%
Sales area m2 79107.76 52738.5 High units
Sales proportion 60% 40%
Source: Jia (2005) Real Estate investment project planning—Theory, Practice and Case Study, Guangdong Economic publishing, Guangzhou
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