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



i

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.



ii

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.



iii

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



vi

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



1

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,



3

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.



4

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,



5

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).



10

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)



11

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).



14

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



15

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).



16

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



17

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



18

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



19

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



20

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



21

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



22

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



23

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.



24

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.



25

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



26

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



27

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



28

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



29

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



30

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).



31

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.



32

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.



33

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



34

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.



35

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:



36

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



37

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



38

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.



39

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.



40

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



41

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.



42

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



43

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



44

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.



45

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)



46

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)



47

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)



48

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.



49

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



50

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.



51

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.



52

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.



53

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


-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



54

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


-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


15.73% 10.38% 5.09% 0.00% -4.89% -9.59% -13.99%



55

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.



56

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.



57

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).



58

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.



59

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.



60

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.



61

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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



72

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



73

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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