REAL OPTION VALUATION IN REAL ESTATE DEVELOPMENT A CASE STUDY OF FREDERICIAC
Author: Anders Houe
[email protected] Academic advisor: prof. Stefan Hirth
[email protected]
Delivered February 2016 Master of Science in Finance Aarhus school of business and social science
Abstract Real option theory has long been of interest in the theoretical world but has, to some degree, failed to become widely accepted as a valuation approach for practitioners. Several studies indicate that the practical failure of real option theory is due to the expectation of a high degree of mathematical complexity, or due to a lack of a practical step by step approach, which both might look to be true at first glance. This thesis studies the different approaches to real option valuation and examines the use of this method in the real estate industry as a supplement to the dominant discounted cash flow method. Real option theory has been acknowledged for its ability to value flexibility in decades, which the more traditional valuation methods have failed to incorporate. Several authors proclaim that the traditional paradigm of using a net present value and not incorporating flexibility will lead to systematically undervaluing investment opportunities. The thesis starts by evaluating real option theory in relation to its theoretical context and its practical implications, before taking it into practice in relation to a long-term infrastructure development, in the form of a commercial real estate development “FredericiaC”. Real estate investments are characterized by large sunk costs and by great uncertainty, due to the length of the construction. This makes the initial investment decision very important, why a comprehensive appraisal approach is needed. This thesis uses the binomial lattice framework suggested by Cox, Ross and Rubinstein (1979) to calculate the option value embedded in the project. The relevant options are found to be sequential compound options, meaning that the execution and value of future options depend on previous options. In addition to the valuation of the case studied, real option analysis is briefly examined in relation to pricing “pre-sale” contracts, which is a contract that allows the developer to sell their units before completion. The thesis concludes that real option analysis indeed provides an additional value in comparison to the traditional discounted cash flow method when flexibility is included in a given project. However, the use of real option theory is not without challenges as it, all else equal, demands more work than traditional valuation methods as well as a more close consideration of the chosen analytical approach to satisfy its assumptions.
“In ten years, real option will replace NPV as the central paradigm for investment decisions” - [Tom Copland and Vladimir Antikeros 2001]
Table of content 1. Introduction .........................................................................................................................................................................................................4 1.1. Background .................................................................................................................................................................................................4 1.2 Problem statement and research question ....................................................................................................................................5 1.3 Delimitation ..................................................................................................................................................................................................6 1.4 Literature review: ......................................................................................................................................................................................6 1.5 Structure of the paper ..............................................................................................................................................................................8 1.6 Introduction to FredericiaC...................................................................................................................................................................9 2 Real estate development and common valuation practice ............................................................................................................ 10 2.1 The background of real estate developing .................................................................................................................................. 10 2.1.2Vacancy................................................................................................................................................................................................ 11 2.1.3 Rent ...................................................................................................................................................................................................... 12 2.1.4 Construction ..................................................................................................................................................................................... 12 2.1.5 Absorption ........................................................................................................................................................................................ 12 2.2 Risks and uncertainties in real estate development ............................................................................................................... 12 2.2.1 Development risk ........................................................................................................................................................................... 13 2.2.2 Time risk ............................................................................................................................................................................................ 13 2.2.3 Cost risk ............................................................................................................................................................................................. 13 2.2.4 Financing risk .................................................................................................................................................................................. 14 2.2.5 Building site risk ............................................................................................................................................................................ 14 2.2.6 Approval risks ................................................................................................................................................................................. 14 2.3.1 The cost approach ......................................................................................................................................................................... 15 2.3.2 The comparison approach ......................................................................................................................................................... 15 2.3.3 The income methodologies ....................................................................................................................................................... 15 2.3.4 The Financial approach/Discounted Cash flow approach........................................................................................... 16 3. Theoretical framework ................................................................................................................................................................................. 16 3.1 The discounted cash flow Model (DCF-Model) .......................................................................................................................... 16 3.1.2 Pros and cons of the DF approach ............................................................................................................................................... 18 3.2 Real option theory .................................................................................................................................................................................. 19 3.2.1 The basic framework of an option ......................................................................................................................................... 20 3.3 Value drivers ............................................................................................................................................................................................. 22 3.3.1. The value of the underlying risky asset .............................................................................................................................. 23 3.3.2. The volatility of the value of the underlying risky asset ............................................................................................. 23 3.3.3. The exercise price ......................................................................................................................................................................... 24 3.3.5. The risk-free rate of interest over the life of the option: ............................................................................................ 24 3.3.6. The dividend paid from the underlying asset .................................................................................................................. 24 3.4 Estimating the volatility ....................................................................................................................................................................... 25
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3.4.1 Logarithmic cash flow returns method ................................................................................................................................ 25 3.4.2 Logarithmic present value approach .................................................................................................................................... 25 3.4.3 GARCH approach (Generalized autoregressive conditional heteroskedasticity) ............................................. 25 3.4.4 Management assumption approach ...................................................................................................................................... 25 3.4.5 Market proxy approach ............................................................................................................................................................... 25 3.6 Common types of real options .......................................................................................................................................................... 26 3.6.1 Option to defer ................................................................................................................................................................................ 26 3.6.2 Option to alter operating scale (expand/contract) ........................................................................................................ 26 3.6.3 Option to grow ................................................................................................................................................................................ 26 3.6.4 Option to stage ................................................................................................................................................................................ 26 3.6.5 Option to abandon ......................................................................................................................................................................... 27 3.7 Approaches to value real options. ................................................................................................................................................... 27 3.7.1 The Classic (No arbitrage, market data) .............................................................................................................................. 27 3.7.2 The Subjective (No arbitrage, subjective Data) Approach .......................................................................................... 28 3.7.3 The Market Asset Disclaimer (MAD) Approach ............................................................................................................... 28 3.7.4 The Revised Classic (Two investment types) Approach .............................................................................................. 29 3.7.5 The Integrated (Two risk types) Approach........................................................................................................................ 29 3.8 Real option analysis methods............................................................................................................................................................ 30 3.8.1 Partial Differentiation equations: ........................................................................................................................................... 30 3.8.2 Simulations: ...................................................................................................................................................................................... 31 3.8.3 Binomial lattices: ........................................................................................................................................................................... 32 3.9 Advanced options ................................................................................................................................................................................... 34 3.9.1 Compound options ........................................................................................................................................................................ 34 3.10 Real option and its prevalence among practitioners and its shortcomings............................................................... 35 3.11 Real option in real estate .................................................................................................................................................................. 36 4. FredericiaC case study ............................................................................................................................................................................ 37 4.1 Project description ................................................................................................................................................................................. 37 4.2 Underlying drivers ................................................................................................................................................................................. 38 4.2.1 Costs..................................................................................................................................................................................................... 38 4.2.2 Income – Sale price and rent. ................................................................................................................................................... 39 4.3 Cost of capital ...................................................................................................................................................................................... 40 4.3.1 Risk free interest rate .................................................................................................................................................................. 41 4.3.2 Market risk premium ................................................................................................................................................................... 41 4.3.3 Beta ...................................................................................................................................................................................................... 41 3.4 Choice of discount rate ......................................................................................................................................................................... 43 4.5 Evaluation of the project ..................................................................................................................................................................... 44 4.5.1 Static NPV model ............................................................................................................................................................................ 44 4.5.2 Sensitivity analysis of the NPV valuation. ........................................................................................................................... 45
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4.6 Volatility ...................................................................................................................................................................................................... 46 4.7 Real option valuation of FredericiaC: ....................................................................................................................................... 47 4.7.1 Binomial lattice method .............................................................................................................................................................. 48 4.8 Case study results ................................................................................................................................................................................... 49 4.8.1 Sensitivity analysis ............................................................................................................................................................................. 50 4.8.2 Empirical comparison .................................................................................................................................................................. 51 4.9 Valuation of presale contracts. ......................................................................................................................................................... 52 4.9.1 Should a developer thus launch a presale? ........................................................................................................................ 53 5. Critique and reflections .......................................................................................................................................................................... 55 6. Conclusion and considerations: .......................................................................................................................................................... 56 7 References ..................................................................................................................................................................................................... 58
Table of Figure: Figure 1: Thesis structure ...................................................................................................................................................................................8 Figure 2: Uncertainty [Source: Own illustration based on [Wiegelmann 2012 – Väth 1998] ........................................... 13 Figure 3: Future flexibility [source: own creation] ............................................................................................................................... 19 Figure 4: Value of Put/Call options [source: Mun. 2006]................................................................................................................... 21 Figure 5: Comparative-static overview of financial option value drivers. [Source: Copeland & Antikkarov] ........... 22 Figure 6: Uncertainty increase value [source: Amran1999] ............................................................................................................ 23 Figure 7: Introduces the cone of uncertainty [source Amran1999] ............................................................................................. 24 Figure 8: The binominal tree and uncertainty distribution (Adopted from M. Amram 1999) ......................................... 32 Figure 9: 4 step valuation approach ............................................................................................................................................................ 37 Figure 10: Sensitivity analysis of construction costs and price movement in absolute values. Percentage change is shown in appendix .............................................................................................................................................................................................. 45 Figure 11: Absolute values: Sensitivity analysis of discount rates numbers in 000’. Percentage change is shown in appendix .................................................................................................................................................................................................................. 46 Figure 12: Option maturity to defer ............................................................................................................................................................ 48 Figure 13: Sensitivity analysis of profitability with changing Sq.m prices and volatility. ................................................... 50 Figure 14: Sensitivity analysis of real option analysis – Profitability .......................................................................................... 51 List of Tables: Table 1: Simple example where the DCF method is a great valuation tool [source: own creation] ............................... 18 Table 2: Simple example of a shortcoming of the DCF method [source: own creation] ...................................................... 18 Table 3: Analogies: Financial vs real options [Source: A. Brach 2003] ........................................................................................ 21 Table 4: Real option calculation methods [Kodukula 2006] ............................................................................................................ 30 Table 5: Techniques used in practice [Source Block 2007] .............................................................................................................. 35 Table 6: Table reason for not using real option valuation in practice [Source Block 2007] .............................................. 36 Table 7: Construction phase and total Sq.m ............................................................................................................................................ 37 Table 8: Peer group ............................................................................................................................................................................................. 42 Table 9: Industry average [source: data from Damodaran] ............................................................................................................. 42 Tabel 10: Input parameters for NPV ........................................................................................................................................................... 44 Table 11: Inputs to binominal lattice approach ..................................................................................................................................... 48 Table 12: Binominal lattice of phase I ....................................................................................................................................................... 49
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1. Introduction 1.1. Background Real option theory has gained a lot of publicity in the last decade and it is becoming an exciting area of finance, for both academics and practitioners. The present capital budgeting paradigm has long been dominated by the static discounted cash flow method, however not without critiques. The awareness of the shortcomings of the traditional discounted cash flow models goes back to Dean (1951) and Hayes and Garvin (1980), acknowledging that this method undervalues the investments by not considering the managerial flexibility. The real option theory arose partially due to this dissatisfaction of a lack of flexibility in traditional capital budgeting [Trigeorgis et al. 2001]. Real option valuation is the process of using option pricing theory, to capital budget decisions, Trigeorgis (1995) defines it as: “Similar to options on financial securities, real option involves discretionary decisions or, rights, with no obligations, to acquire or exchange an asset for a specified alternative price”. Consequently real options can be found in many real life situations, where uncertainty or risks are present, e.g. when leasing a car with the option to buy it or whether to invest in an asset or to wait. As the theory can be applied to many situations and cope with the shortcomings of the traditional techniques, it has gained popularity as a prominent valuation technique when uncertainty is a fundamental factor. This is particularly true for real estate development, where the investor, in many cases, has to take a passive stand regarding external risk factors. However, when the investor has the flexibility in the form of options to change the outcome of the project, in response to external factors, the option will have an additional value. The possibility to include the option value is what differentiates real option analyses from other valuation techniques. Real estate development plays a central role in modern economy, which can be inferred from a study conducted by INREV (2011) (the European Association for Investors in Non-Listed Real Estate Vehicles). This research shows the impact of European real estate economy, indicating that the commercial property sector contributed more to the economy than the European car and telecommunication sector combined. Investments in new commercial properties and refurbishment and developments of existing properties represented over 10 % of the total investments in Europe, which is equivalent to the Danish GDP [Giacomo et al. property finance 2014]. The long period of increasing house prices in the start of the new millennium, lead to a real estate boom. As a real estate developer has to bind a large amount of capital in assets, which have a long construction time before producing a cash inflow, the uncertainty of costs, benefits and risks need to be well forecast, which has proven to be a difficult challenge. This could be seen in the last financial crisis as the prices decreased due to an increased competition among the few projects offered. Many entrepreneurs worked with “turnkey contracts”, meaning a contract that sets a fixed price and time of delivery before completion. This furthermore have resulted in several bankruptcies among larger Danish contractors, which tells how important right assessments is, when valuating projects. Side 4 af 64
The term “Commercial real estate” implies investing with the intent to make an economic profit. It is easily seen, that investing in real estate has gained little attention comparing it to investments in the stock market. The information and attention to the stock market could create the impression that it is the best way to invest, which many investment textbooks likewise imply, as they often show charts of the relative performance of stocks, bonds and stock index, but seldom show the performance of the real estate market. [Timothy 2005] explains that real estate is an overlooked world for many investors, due to the lack of knowledge of how to invest, or wrong assessments of the requirements to do so. Understanding the real estate market and being able to properly asses the values of the properties is thus fundamental and have always been of key interest for people who want to invest in real estate. The traditional method of valuating real estate is as most corporate decisions, often based on the discounted cash flow and consequently a static approach. However, real estate development is not a static process, as the decision maker often has the ability to change the output over the time of construction. Real option theory can thus be used to provide a more flexible framework by including the value of the option imbedded in the given project. Real options can also be found in the “pre-sale” contract, which is a strategy developer uses, in order to sell their units before completion, and thereby attract capital and reduce their risk. These contracts gives the buyer a possibility to abandon the contract, by paying a forfeiture premium, which real option can be used to calculate. Real options are consequently highly relevant for the real estate industry as it might helps the decision maker to take a more informative investment decision. It also provides an option thinking environment that focuses on several scenarios rather than a static future.
1.2 Problem statement and research question The focus of this thesis is to evaluate the usability of real option theory in practice. The thesis will address the theory in relation to the real estate industry, in order to examine the use of real option theory relative to the prevailing paradigm of using a discounted cash flow approach. Likewise, parallels will be drawn between the different valuation approaches to see if real option theory provides any significant additional detail about the true value of the project, and whether this method is more difficult to implement in practice than the traditional methods. The thesis will further introduce the use of a pre-sale contract and the option embedded in these contracts, in order to see how the option might affect the structure of these contracts. The subject of the thesis is interesting from the point of view of a practitioner, as it evaluates the theory through a real-life case, and examines its usefulness in practice. The aim of this thesis is thus to answer the following problem statement:
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Can real option theory help the decision-maker in a real estate development project to make decisions that are more informative, compared to the more “traditional valuation methods”?
To answer this problem statement adequately, it is found necessary to examine and answer the following sub-questions: -
What are the challenges of using real option theory?
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What different types of real options exists?
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What different approaches to real option methods exists and which is best suited for real estate development?
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Why is real option theory not widely used as a valuation method?
1.3 Delimitation As the case study “FredericiaC” is a partnership between three actors, Fredericia municipality, Real Dania and a third partner, several conflicts of interest might arise due to different intentions of the actors. However, due to the extent of the thesis, the differences in intentions are not considered and profit maximization is assumed as the main goal of the project. As the intent of the paper is to examine real option theory and its usability in real estate development, no insight into the technical aspects of constructing such a project is described. Some theoretical papers argue that real option valuation is less effective in competitive markets. Triantis (1996) shows that the effect of competition on the value of a real option, is analogous to the dividend of a call option, as increased competition, like a higher dividend, will force the option holder to exercise their options earlier. However, competition and its effect on the option value will not be considered in this thesis as it is assumed that FredericiaC is in a scale without competition. The pre-sale system has gained little attention in literature terms, and will not be described in depth in this thesis. The inclusion of the topic is due to its interesting nature and because the contract is often applied in larger real estate development. Likewise, it provides an understanding of the wide usability of real option theories in the real estate industry.
1.4 Literature review: Real option theory has its origins from the groundbreaking seminar work by Black and Scholes (1973) and the extending mathematical framework of Robert Merton (1973) on the topic of pricing financial European options. Though the Black-Scholes pricing formula was applied immediately in pricing financial options, it took several years before anybody considered expanding the theory to the corporate finance. Stewart Myers introduced the term “Real option” in 1977, when he evaluated the use of financial option pricing theory in management decisions, by comparing call options and investment opportunities [Myers 1977]. Cox, Ross, and Rubinstein (1979) expanded the theory by
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introducing the binomial model, enabling a more simple valuation approach of options, which still functions as the most popular foundation for real option analysis today. Geske (1979) introduced the term compound option, which is an option to acquire another option. This, in many cases, is applied in real option theory, as projects are often carried out in stages. Real option theory in a long period of time was primarily of academic interest, where it was the subject of many studies dealing with flexibility and uncertainty. The topic gained significant interest in the beginning of the 1990s as industries realized that option theory could be utilized as a management tool to better assess the value added from flexibility and better understand uncertainty than the more stationary approaches [Adam Borison 2013]. Sheridan Titman [1985] was the first to apply real option theory to real estate development by valuing urban land, using it and the binomial model. His findings showed that uncertainty creates an incentive for the landowner to defer investments until the development value exceeds a specific threshold, such as the construction costs, or until expected profit reach a certain point. His work, therefore, shows that the value of vacant land is not only based on its best immediate use but includes the option value of delaying the use of the land to its alternative best use in the future. This also can explain why some urban lots remain vacant in developed areas. Williams [1991] confirmed Titman’s [1985] results and furthermore considered an option pricing model that incorporated the optimal time to abandon or develop and the optimal density of the development. In this model, he assumed that both the cash inflows and the costs of development follow a geometric Weiner processes. Titman [1985] also concluded that a higher volatility would increase the present value of a real option, just like a financial option. Laura Quigg [1993] was the first to empirically test the use of the real option pricing model in real estate, by using a large sample of land transaction in Seattle. She found empirical support for a model that incorporates the option to wait to develop land, and superior explanatory power of predicting the transaction prices. This result showed that the market price reflects an option premium of a mean of 6% for the option to wait with the investment. Though real option, theoretically, is well developed with empirical support, it is still not commonly used in capital budgeting for practitioners in several industries, including real estate development [Pomykacz 20013]. In the article “On Option-pricing models in real estate; A critique,” Shiller et al., (1987) discuss some of the problems applying real option theory to real estate investment. Their article raises a stimulating question, whether real option pricing models produce better results or create more uncertainties for the end users. This is because some of the assumptions and criteria for the models may be absent in real estate investment. They conclude that several options may be modeled, using option pricing techniques, but at the same time institutional and theoretical aspect of the real estate market must be kept in mind. This includes the longer transaction periods, and relative illiquid market, making it empirically difficult to apply the option-pricing models for real estate development, which will be discussed further in section 3.7-3.8.
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1.5 Structure of the paper The thesis follows a deductive approach, by studying and applying existing theory to a real case study. No hypotheses are made but the paper tests the proclaimed hypotheses from several real option authors, that real option theory adds a significant knowledge of the economic value of flexibility in a project. The first part of the thesis, address the process of investing in real estate and the common factors that an investor needs to keep in mind before investing. This section also discusses the common appraisal techniques in the real estate industry. The second part introduces the theoretical background in order to be able to carry out a real option analysis. This includes the traditional valuation method, the discounted cash flow, and a theoretical examination of option theory. The third part introduces the case study and uses the DCF analysis to value the project. A sensitivity analysis of the value is carried out in order to see how the value changes when altering the assumptions and estimates in the model. The real option analysis is then carried out with the use of the market asset disclaimer approach (MAD) and the binomial model. A sensitivity analysis of the real option valuation is likewise conducted to see how the most uncertain estimated parameters affect the value of the project. At last, a discussion of the use of sale before completion contracts are discussed and valued. The last section will give an overview, discuss real option as a valuation method, and conclude on the findings.
Real esate development and common valuation practice
● Historical background of real esate development ● Risk and uncertainty in real estate development ● Traditional valuation methods
Theoretical background
● Analysis of the DCF model ● The basic framework of an option ● Real option valuation ● Real vs. financial options
Valuation of case study value of presale option
● Underlying drivers ● DCF value of Fredericia C ●Sensitivity analysis ● Real option theory in "sale before completion"
Discussion and conclusion
● Discussion of the use of real option in practice ● Reflection & critique ● Conclusion and final remarks
Figure 1: Thesis structure
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1.6 Introduction to FredericiaC FredericiaC is an ambitious development project, with the purpose of transforming a 20 ha. brownfield site at the harbor of Fredericia into a new district, which will expand the area of the inner city by 25%. The project will consist of a mixed urban space of 265.000𝑚2 , that will blend residential, cultural and office space to get a dynamic and integrated environment. It is estimated to create 2.800 new work places and 1.000 new homes. Fredericia is located in the prosperous “triangle region”, in the center of Denmark towards the cost of Little Belt. This offers a unique location in terms of infrastructure and maritime environment. The planning phase of the project started in 2011 with an interdisciplinary parallel competition, allowing architect- and planning companies to submit ideas for a development plan. The development plan was public popularized in December 2012, with an estimated timeframe of 2025 years for the completion of the four construction phases. The first sod was officially turned in October 2015, with the construction of “Frederikshuset”, a 5.800𝑚2 building containing 41 social housings, 13 commercial real estates, and 600 m2 office space. The developers offer the commercial apartments before construction, which is a common procedure in many new development projects in Denmark. The strategic development plan as well as the timeframe is flexible, and the project is therefore able to adjust to the surroundings and conditions, which undoubtedly will change over the long construction period of the project. This long timeframe makes the project well suited for exercising several options such as defer, abandon, or switching which makes it an ideal case for studying flexibility in a real estate investment project. A static valuation method on the other hand is not expected to capture the managerial flexibility and ability to reduce downside risks and increase the possible upside potentials for expanding, re-developing or delaying the project. FredericiaC offers co-investors to be a part of the project. However, there is only one announced coinvestor so far, which might be due to the general uncertainty about the project and its profitability. Fredericia municipality and RealDania outlines and covers the non-revenue generating expenses of the project, such as the green areas, constructing canals, developing the promenades, streets and public spaces. The explanation of not having a third part investor included in these costs is because Real Dania and Fredericia municipality have other interests than pure profit maximization. RealDania provides philanthropic work to increase quality of life, through better living environments and Fredericia municipality also have other interest, such as becoming a dominant municipality in the triangular area, which this project can help them accomplish, profitable or not.
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The urban space on each cadastral may however, partly be developed at the co-investors request. FredericiaC has created a quality program to counter possible cooperation problems between the partners and as stated in the delamination, it is assumed that the purpose of the project is to maximize profits.
2 Real estate development and common valuation practice This chapter aims to give an overview of the process of investing in real estate development. An overview of the characters and conditions of the real estate market, together with the common valuation practices and their performances, will give an understanding as to whether real option theory can be a useful investment tool in this industry. To provide a framework for the case study, relations and remarks will be made when found relevant.
2.1 The background of real estate developing In order to understand the commercial real estate market, one should know its historical background. The commercial real estate market has had several volatile periods with booms and busts, where the last decade particularly has been notable in both increasing and decreasing directions. This development has particularly been true for larger cities where the prices have tended to be more volatile than in smaller cities. In the mid-2000’ the property prices increased sharply, with a nearly 20 pct. price increase, adjusted for the general increase in consumer prices. This increase was followed by a sharp decrease of 15% in 2009. Similarly, in 1982-1986, the commercial real estate market was seen as an investment tool to “beat the inflation” with a yearly property price increase of 11 pct. [See appendix 1]. This resulted in a massive overinvestment in commercial real estate development, and thus a massive oversupply of commercial properties. This overinvestment, as well as the contraction of credits of the monetary authorities, resulted in a collapsing of the real estate market. In general, the real estate market is highly influenced by several socio-economic conditions, such as loan opportunities, interest rates and the general income level of the target group. Other non-rational factors such as expectation and optimism in market development also have a great impact on the price development. The behavioral school of finance recognizes the problems with the “rational expectation” assumption. Xiao et Al. (2007) argue that there is empirical evidence that investors in the real estate market have replaced rational expectations with a “backwardlooking” expectation, resulting in future prices prediction based on extrapolation of past trends. (Kindleberger et al. 2005) describes this phenomenon well, as a replacement of rational expectation with clichés such as “the trend is your friend”, which reflects the view, that if prices have increased, they will continue to do so. The Danish Ministry of Business and Growth likewise has argued that
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optimism both nationally and internationally contributed to the price surge of real estate in mid2000. The future price trend of the real estate market is difficult to estimate. This is a fact which commercial real estate developers must accept. Several larger Danish stakeholders have developed their own macroeconomic models, of which the most acknowledged are the Danish Economic Councils “SMEC”, the National bank “MONA” and the governments “ADAM”. These relative complex models, however, also have had difficulty predicting the price trend of the real estate market. An example of this is the period from 1999-2005, where the real estate prices rose by 50 pct. but the models predicted an increase of 30-, 20- and 5-6 pct. respectively1. Investing in real estate development thus involves not only a significant degree of irreversibility but likewise uncertainty.
By nature real estate investments differs significantly from investing in financial assets or most other real assets, by their heterogeneity. No real estate investments are alike, whether it is investing in plots, office buildings, development projects or properties, as they contain individual utilities which make it hard to conduct a precise appraisal of their value. The main character of real estate development is that it is capital intensive, often large in scale and require extensive construction time with a long period without any cash inflow. The value of a real estate is closely linked to the geographical area, and in contrast to many other assets is nonmovable, making the location one of the most important attributes of the price. Much of the value depends not only on the project itself but also on external market conditions such as the demand for houses and the overall economy. When a real estate investor considers constructing a new project, he then has to ascertain and understand the surroundings and market conditions. When analyzing the market, the decision maker should focus on quantifiable indicators, from both the sales and rental market, in terms of their supply and demand. [Arnott et Al. 2006] Suggest four important parameters that one should study before investing: The vacancy rate, rent level, construction and absorption. These factors are very important and can have a great impact on the economic outcome of the project.
2.1.2Vacancy The vacancy rate refers to the percentage of non-occupied building space. The vacancy rate together with the market rent is a good indicator for the supply and demand in a given market. In order to compute the vacancy rate, the investor has to know the total stock of space and the amount of space occupied. It is important to understand that vacancy can occur due to the lumpy nature of the real estate markets, as supply is not added in infinitesimal units but often in larger scales in contrast to the demand, whereby temporary vacancy will naturally occur. It furthermore happens due to 1
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movements in termination of leasing periods and the proprietor’s option to wait for a better deal to show up. The real estate market, therefore, has a “natural balance rate” which is the average of the long run vacancy, telling if the market is in or out of balance. To put it in perspective, the vacancy rate of dwellings in Fredericia has approximately been 5 pct. for dwellings and 8 pct. for office space and retail premises. (See appendix 3)
2.1.3 Rent: The current market rent refers to the rent charged in the market. The rent rate is a good indicator of the market conditions but one has to keep in mind the differences in utilities that the rented space offers. The average rent for office space and rental premises in the South Jutland the last 5 years has been between 681-667 DKK and 740-796 DKK respectively2. 2.1.4 Construction The construction is the quantity of new construction, which is an important factor, as more construction will, all else being equal, lower the demand. 2.1.5 Absorption Absorption is the amount of additional space that is occupied within a year. Comparing these indicators gives an understanding as to how the demand and supply rates evolves. Other market factors that give valuable insight for a real estate developer, is the average square meter price and volume of premises and homes for rent/sale. It should be kept in mind that different real estates offer different utilities, but comparison gives an overall idea of the price range in the region. The average price pr. Sq.m. of dwellings in Fredericia municipality by October 2015 is 15.439 DKK based on the 414 properties for sale3.
2.2 Risks and uncertainties in real estate development Real estate development generally involves a significant uncertainty and risk. This is part due to the characteristics discussed in the earlier section of high sunk costs and fixed location, but also due to other factors, such as the unknown future demand and general economic situation of the target group. In general, risk has a negative association with unfavorable future outcome, but as risks and returns are inextricably linked, one should not only see risk as a negative factor but rather try to understand and cope with it, to get the right compensation. Risks are present in all stages of a property development. However, risk and uncertainty will be lower over time as the project 2 3
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unfolds. [Wiegelmann 2012] gives a great illustration of the flexibility during the construction phase, where flexibility is of great importance in the early construction phases. Costs
start of construction
Project initation
Project conception
Project realisation/managment
Construction phase II Completion
Time Project marketing/disposal
Usage
Figure 2: Uncertainty [Source: Own illustration based on [Wiegelmann 2012 – Väth 1998]
[Wiegelmann 2012] further defines six main risks in real estate development which will be described shortly below:
2.2.1 Development risk Development risk is the risk that the project does not generate sufficient income to cover the desired return, due to a lack of sale, or the necessity to sell at a lower price than expected. The development risk is often harder to forecast when a project is more unique than the norm, as misreading the market then is more likely.
2.2.2 Time risk Construction time is of great importance in real estate development. As long as the project is under construction it does not generate any cash inflow but, on the contrary, expenses in the form of cost of capital. This, in most cases, will reduce the return on the project when it is delayed.
2.2.3 Cost risk Though the cost of real estate development can be approximated by comparing it to similar projects, it is far from a fixed factor. Both internal factors such as construction time and external factors such as financial risks can have devastating consequences for entrepreneurs. This has been seen in several cases in recently, where a fixed contract has been made, with a low-profit margin which has resulted in insolvency, due to wrong cost estimates.
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2.2.4 Financing risk The developer often depends on external financing due to high upfront costs and a long period with no cash inflow. This means that they are affected by interest rates and their source of financial structure.
2.2.5 Building site risk The building site can constitute risks if it needs to be modified in order to be useable. This is especially the case when a project is undertaken on a maladjusted ground, or the possibility of polluted soil, or when there is uncertainty about how much support the ground can offer, and therefore what kind of construction can be built on it.
2.2.6 Approval risks A real estate development needs to be approved and in line with the official planning rules, this could mean a risk of delaying the process or may alter the desired construction.
2.3 Traditional valuation approaches in real estate development [Pagourtzi et al. 2003] defines valuation as, “The determination of the amount for which the property will transact on a particular date”. This is an important statement to keep in mind, as market value does not always equal market price, due to uncertainties surrounding the estimated value. The market value is an indicator of what the property would sell for in a competitive market, whereas the market price is what the property can actually be sold for, in the current market. For any valuation method to have validity, it is essential for it to produce correct estimates of the current market price. This is why valuation should quantify all the underlying benefits and liability factors, that affects the real estate value. In the literature of real estate valuation, one can find several models to estimate the market value of properties. A majority of these estimates rely on some form of comparison to assess the value of other similar real estate properties [Hatzichristos et al. 2003]. [Damodaran 2012] points out, that many real estate investors have previously developed and used their own valuation models. He found the traditional methods inadequate to value real estate, due to its different nature compared to other investment areas, such as financial assets. He also clarifies, however, that real estate and financial assets share many common characteristics and that the value of both assets should be determined by their cash flows, expected growth, and the uncertainty associated with the cash flow. Due to these similarities, valuation methods for financial assets are also applicable to value real estate. The choice of valuation method should depend on the individual project and whether the real estate is a development project or an existing building. The methods most commonly used in real estate appraisal are the NPV method and the residual analysis [Ratcliffe et al. & Fabozzi 2005]. [Giacomo et al. 2014] further states that
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real estate appraisal, are generally valued by three different methods: The cost approach, the sales comparison approach and the income capitalization approach. The sales comparison and income capitalization approach are most applicable to commercial real estate. The income capitalization approach often prevails, due to the nature of the real estate market, with its relative infrequent transactions and highly heterogeneous nature of the properties [Giacomo et al. 2014]. Though most real estate investment theories conclude that the income capitalization approach is the most sensible valuation approach, its assumption of “all-or-nothing” strategy and hereby lack of flexibility, is often discussed. [Brown et al. 2000] argues that this will likely increase the number of academic papers concerning real estate investment in the future as there is a broad consensus that managerial flexibility offers value in real estate development. The three common types of valuation approaches are described below.
2.3.1 The cost approach The cost approach is only relevant for existing buildings. This method surmises that the value of a property is determined by the expected cost of building a similar property at a similar location.
2.3.2 The comparison approach The comparison approach estimates the value of a project by observing sales prices of similar projects, with the assumption that no rational buyer will pay more for a similar asset with the same utilities. The value relies on a strong assumption - that the compared price is the right market value. The method includes the use of hedonic regression analysis to break down the value of a real estate by e.g. its number of bedrooms and Sq.m. This method requires data from similar properties to be valid, which is also problematic in real estate development, as every property is unique. The comparison methods are typically used when there is a liquid market.
2.3.3 The income methodologies [Giacomo et al. 2014] divides the income method into the two most used methods, the direct capitalization approach and the financial approach (Discounted cash flow analysis). These methods determine the value of a real estate investment, based on the assets ability to generate economic profit over its lifetime. The income methodology works particularly well when there are no comparable properties. The direct capitalization approach: This approach is often called the cap rate and is widely used in the real estate industry. The cap rate is the ratio of net operating income (NOI) to the current market value of the property. The net operation income is defined as the effective gross income minus operating expenses. 𝐴𝑛𝑛𝑢𝑎𝑙 𝑛𝑒𝑡 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑖𝑛𝑐𝑜𝑚𝑒
𝐶𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 = 𝐶𝑜𝑠𝑡 (𝑜𝑟 𝑣𝑎𝑙𝑢𝑒)𝑜𝑓 𝑡ℎ𝑒 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦 (2.1)
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The direct capitalization approach can, therefore, be used to calculate the value of a property by first estimating the cost of constructing the project and then estimating the expected cap rate. 𝑉𝑎𝑙𝑢𝑒 =
𝑁𝑒𝑡 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑖𝑛𝑐𝑜𝑚𝑒 𝐶𝐴𝑃 𝑟𝑎𝑡𝑒
(2.2)
If the net operation income increases with a certain pct. “g” into perpetuity, it is a general version of the Gordon valuation model and the value 𝑉 = 𝑁𝑂𝐼/(𝑟 − 𝑔) and the capitalization rate = r-g, Where g is the growth rate and r is the weighted average rate of return [Mc Donald 2015]. The cap ratio can thus be seen as the inverse of the price/earnings ratio, and tells how much return there is on an investment. The cap rate is a great tool to measure the value of existing real estate with known cash flows, but can also be used in real estate development. The cap rate is a very simple and easy method to apply, and it can produce a great valuation when the net operating income is stable. When the cash flow is not stable, however a financial approach, as the DCF would create a much better valuation.
2.3.4 The Financial approach/Discounted Cash flow approach This approach is a much more elaborate process than the direct capitalization approach, as all the future cash flows are discounted with a rate that embeds the risks to get a net present value. It is often described as the cornerstone for real estate valuation as well as the general paradigm for capital budgeting. It can also be used to form the foundation for a real option valuation, which is why this method will be described in details in section (3.1)
3. Theoretical framework The first part of this section describes the most used valuation technique, the net present value, followed by a reflection of its usefulness and shortcomings. The second part of the chapter introduces real option analysis and how to apply it. Capital budgeting is without a doubt an important task when considering an investment, as it gives insights into the profitability and risk. However, [Trigeorgis & Schwartz 2001] claims that there have always existed, to some extent, a gap between financial theory and strategic planning, resulting in a limited impact on financial valuation in the strategic planning of many companies. This is due to a gap between understanding financial theory and properly applying it. This chapter aims to form an understanding of real option theory, to be able to implement it in a real investment case.
3.1 The discounted cash flow Model (DCF-Model) The DCF-method has long been considered the central paradigm for corporate investment decisions. The method is used to calculate the net present value (NPV), which tells us how much value is gained or lost when investing in a given project. This is calculated by using the cash flows Side 16 af 64
that an investment generates, and comparing the costs and benefits of these flows. The DCF method gives a basis for comparison between investment opportunities, regardless of risk, as risk is imbedded in the discount rate. This means that the decision rule is simple, as one should choose to invest in the project with the highest NPV, if mutually exclusive, or accept all projects with a positive NPV. To calculate the NPV we first need to estimate the expected cash flows and the required rate of return. These estimates can be a challenge to get exact, and constitutes the main risks in using this method for valuation. The NPV can then be calculated by discounting all future free cash flows with a rate equal to the opportunity costs of capital. In mathematical terms, the NPV can be written as following: 𝑇
∑ 𝑡
𝐶𝑛 − 𝐼0 (1 + 𝑟)𝑛
(3.1)
Where 𝐶𝑛 is all future cash flows discounted with the rate r over the given number of time n, with the initial investment I, the cash flows, C, is accumulated by adding all the cash flows from the project and discounting them back to time 0. DCF=
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑖𝑛 𝑦𝑒𝑎𝑟 1 (1+𝑟)1
+
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑖𝑛 𝑦𝑒𝑎𝑟 2 (1+𝑟)1
+⋯
𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 𝑖𝑛 𝑦𝑒𝑎𝑟 𝑛 (1+𝑟)1
(3.2)
The required rate of return, r, also known as the hurtle rate or discount rate, can be calculated in different ways. It is the rate that investors require in return for lending cash and it depends on the riskiness of the investment, whereby a project with higher risk will require a higher costs of capital and vice versa. The cost of capital depends on the structure of the financing used, and is often a composite of cost of debt and equity which can be calculated as 𝐸𝑞𝑢𝑖𝑡𝑦
𝑑𝑒𝑏𝑡
Cost of capital = 𝐶𝑒𝑞𝑢𝑖𝑡𝑦 (𝐷𝑒𝑏𝑡+𝑒𝑞𝑢𝑖𝑡𝑦) + 𝐶𝑑𝑒𝑏𝑡 (𝑑𝑒𝑏𝑡+𝑒𝑞𝑢𝑖𝑡𝑦)
(3.3)
The cost of equity can be calculated, using the Capital Asset Pricing Model (CAPM). The cost of equity will consequently equal other investment opportunities with the same risk, (same beta β value). The cost of debt is more easy to calculate, as contracts of the promised interest are made. When the discount rate and cash flow is estimated, it is relatively straightforward to carry out the valuation by applying equation (3.1).
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3.1.2 Pros and cons of the DF approach To highlight the pros and cons of the DCF method, two fictive examples are illustrated with a cost of capital of 7%. First, consider an investment opportunity to buy a building for 100 million (m) today with a rent payment of 15m each year for four years and the possibility to sell the property after five years for 80m. Year Investment
0
2
3
4
5
15
15
15
15
80
14,02
13,10
12,24
11,44
57,04
-100
Cash flow Discounted Cash Flow Net present Value
1
7,847
Table 1: Simple example where the DCF method is a great valuation tool [source: own creation]
The decision rule is to undertake the investment as the NPV has a positive value. If the cash flows are forecastable, the NPV provides a great and easy understanding for the decision maker, that they should make the investment as it creates value. Let us consider another example of an opportunity to invest in an undeveloped plot in a new urban area under development. The plot costs 100m and it would be worth 110m in five years. The investment furthermore grants the investor with a permit to build a commercial real estate. If the investor estimates that the construction cost has a present value of 50m and a sell PV of 40m, the construction would not be undertaken and the PV of the undeveloped land would be 78.428m. Year
0
1
2
3
4
5
-100
0
0
0
0
0
Cash flow
0
0
0
0
0
110
Discounted Cash Flow
0
0
0
0
0
78,428
Investment
Net present Value
-21,572
Table 2: Simple example of a shortcoming of the DCF method [source: own creation]
The project, therefore, yields a negative NPV and the decision rule would suggest that the investor should not buy the land in the first place. However, investing in the plot gives the investor the possibility to develop the land, and it therefore creates some future flexibility. If the investor decides to invest in the plot, he buys the option to develop the land but not the obligation to do so. If in five years from now, the market development of the new urban area has had a much more favorable development than expected, and he would be able to sell the project with an NPV of above 71.57m, he should invest in the land and develop the project. The DCF approach, thus forces the investor to accept a pre-fixed cash flow and does not consider the flexibility. This simple example shows that the DCF require the decision-maker to commit to the expected future cash flows, and not consider the value of learning and flexibility.
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Figure 3: Future flexibility [source: own creation]
Even if the project has a positive NPV in year 0, the investor might choose to hold the plot and not develop it, if he thinks that the value of flexibility to choose what to develop is worth more than investing in whatever had the highest NPV at the time. This example shows the “Now-or-never” problem with the DCF method. The DCF-method is straightforward in some situations and performs very well when the project are rather passive and when the cash flow can be well specified. The decision rule and its ability to easily compare between different projects is furthermore a very favorable feature. However, one of the main disadvantages of the DCF analyzes is the lack of coping with the value of flexibility, which could be seen in the second example. The DCF assumes that the decision maker cannot make any adjustments along the lifespan of the project. This is a very strict assumption in many situations and particular in real estate development. The DCF approach also assumes that the discount rate accounts for all the risks in the project and is often kept constant over the duration of the project. This makes the model very deterministic, and less capable of reflecting the true risks in the project. [Copland and Antikarov 2003] goes as far as stating: “the NPV technique systematically undervalues everything because it fails to capture the value of flexibility”. Though NPV suffers from these restrictive assumptions it is still highly utilized. A larger study conducted by Graham and Harvey 1991 shows that 75% of the asked CFO’s uses NPV always or almost always in capital budgeting [See appendix 2].
3.2 Real option theory - “A misunderstanding you run into is the idea that it is somehow inappropriate to use option pricing techniques in a corporate setting when you’re dealing with non-treaded assets. You hear this again and again from very sophisticated people. And it represent a misunderstanding of what corporate finance is all about.” - Stewart Myers [Arnold et al. 2002] The application of option-pricing techniques to value real assets has been an important and revolutionizing way of valuating investment opportunities. The main idea behind real option theory
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is to explicitly incorporate flexibly in the valuation process, as flexibility offer value when there are uncertainties about the future outcome. This is because the decision-maker has the possibility to act in respond to market changes, and limit his losses by e.g. changing the input or abandoning a given project. He, therefore, has the ability to actively reduce the exposure to downside risk but likewise have the ability to improve the likelihood of upside benefits. As mentioned in the literature review, real option is an extension of financial option theory to valuate non-financial, real options. As for financial options, real options are defined as the right, but not the obligation to take action on an underlying asset in the future [Kodukula & Papudescu 2006]. Financial and real options share many similarities but have some key differences as whether the underlying asset is a real or a financial asset. The payoff structure of financial and real options are often similar, where a project that has the flexibility to e.g. be abandoned has the same payoff structure as an American put option. This gives the owner the right but not the obligation to sell the project in the future for a given exercise price. Many other real options share similar abilities with financial options, which lead to the foundation of the real option theory. As real option origins from financial options, it is useful to take a look at the concepts behind option theory.
3.2.1 The basic framework of an option Acquiring an option gives the holder the rights but not the obligation to buy (call option) or sell (put option) the underlying asset at a predetermined price, called the strike price, on or at a certain date. If the option can be exercised at any date before maturity, it is called an American type option but if the option can only be exercised at a particular date, it is called a European option. The value of the call option (C) is the difference between the value of the underlying asset (S) and the cost of exercising the option (K), and just the opposite for the put option. Since the option holder has the right, but not the obligation, the option will only be exercised when it is profitable otherwise, it will expire worthless. This can be written mathematically as: C = max [S − K; 0] (3.4) P = Max [K − S; 0] (3.5) Figures 4 shows the payoff charts of a put and call option. The vertical axes represent the value of the option and the horizontal axes are the value of the underlying asset.
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Value of a put option
(-/+)
Value of a Calloption
(+/+)
(-/+)
(+/+)
Underlying Value
Premium
Underlying Value
Premium
(-/-)
(+/-)
(-/-)
X
(+/-)
X
Figure 4: Value of Put/Call options [source: Mun. 2006]
The solid line is the payoff function, where the value of the call (put) option increase (decreases) with increasing value of the underlying asset, and goes to zero (max) for call (put) option as the value of the underlying asset approaches the costs of acquiring the option. The horizontal floor value is the premium, where the maximum loss is the cost of acquiring the option. The payoff structure of financial options can easily be related to a real business strategy, where the call option can be seen as the price for creating an opportunity and the put option as the price of abandoning it. If the opportunity does not create any value, the total cost would be the price of acquiring the option. If on the other hand the value of the option increases above the strike price, it would generate value. 3.2.2 Real versus financial options
In the previous section, we saw that financial and real option share many similarities like the payoff structure. This section will further elaborate their dissimilarities and their value drivers. As real option theory is based on financial options, it is logical that they share many characteristics. Both option values are determined by their generated cash flow, the uncertainty about the cash flow, and the growth in the cash flow. [Brach 2003] summarize the main mathematical analogies between financial and real options as: Financial option
Variable
Investment project/real option
Exercise price
K
Cost of acquiring the asset
Stock price
S
Present value of future cash flows from the asset
Time to expiration
t
Length of time option is viable Riskiness of the asset, variance of the best and worst 2
Variance of stock return
𝜎
Risk-free rate of return
r
case scenarios Risk-free rate of return
Table 3: Analogies: Financial vs real options [Source: A. Brach 2003]
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Though the concepts share many analogies there are also some significant differences. First, the financial market is often liquid in contrast to many real options. Financial markets, will, therefore be more informative and easier to hedge against, whereas the market price is harder to find in many real option investments, as there is often no regular trading with the underlying asset. In the financial market, the option holder will observe the movement of the underlying asset with no possibility to change its value. The option holder of a real option can use flexibility to alter the movement of the value of the underlying asset and thereby mitigate the downside risk while preserving or expanding the upside potential [A. Brach 2003]. Financial options will often have a known time to maturity, usually months, while real options most do not have a certain time of expiration. For instants, real estate development will often have an approximation deadline, rather than a fixed, because the construction period will always include uncertainty.
3.3 Value drivers Understanding what drives the value is essential to active manage options, in order to maximize their value added for the decision-maker. Like financial options, the value of real options depends on some basic variables. [Copeland & Antikkarov 2003] argues that the value of financial as well as real option depends on six key value drivers. Figure five, gives a comparative-static overview of how financial options are affected by their value drivers.
Figure 5: Comparative-static overview of financial option value drivers. [Source: Copeland & Antikkarov]
These value drivers likewise are embedded in real options, which will be described in the following:
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3.3.1. The value of the underlying risky asset An increasing (decreasing) value of the underlying asset has a positively correlated effect on the call (put) option. This is intuitive, as the potential higher cash flow will increase the value of the option for call options. In contrast, one can think of an insurance or abandon option, as a put option, where an increase in value will decrease the possibility that one would exercise the hedging opportunity [stellmaszek 2010], or abandon the project. An important difference between financial and real options is the possibility for a real option holder to affect the value of the underlying asset in contrast to a financial option holder.
3.3.2. The volatility of the value of the underlying risky asset [Copeland et al. 2003] argues, that increasing uncertainty will increase the value of an option as the option has a higher probability of exceeding the exercise price with a larger upside potential, with the same limited loss, namely the acquiring cost. [Amram 1999] points out that management has traditionally put a lower value on risky assets due to risk-aversion, but further argues that managers should try to understand the risk, and use their option to respond by positioning the
Value
investment in a way to take advantage of the uncertainty.
Managerial options increase value
Real Option view
Traditional view
Uncertainty
Figure 6: Uncertainty increase value [source: Amran1999]
[Stellmaszek 2010] deliberates his view of uncertainty, and draws attention to the fact that several real option guiding books for practitioners including Copeland (2003) and Amram (1999) overlook the fact that this uncertainty statement only holds for the risk factors, which an option is targeted at. E.g. if one increases the risk by ridiculing branding expenditure before the launch of a new product, it would not add value to the option but, on the contrary, make it less likely to be exercised. Thus, a positive correlation between uncertainty and real option only exist between the real option value and the uncertainties that the firm is hedged against because of the option.
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3.3.3. The exercise price: The cost of exercising the option has a negative (positive) impact on the call (put) option. This is intuitive as the possibility of exercising a call option, e.g. building a real estate, increases as the costs of construction decreases. In the case of a put option, one can see the value of the option to abandon a project would increase if the price of the project increases.
3.3.4. The time to expiration of the option: Time to expiration has a positive effect on both call and put options, as it allows the investor to learn more about the uncertainty before making a decision. Figure 7 shows how the outcome of an asset can evolve where the possible outcome grows larger with time, resulting in a greater change of the option to be exercised.
Possible future values
High
Range of possible future value Low
Today
Time
Two years
Figure 7: Introduces the cone of uncertainty [source Amran1999]
3.3.5. The risk-free rate of interest over the life of the option: The risk-free rate is the profit an investor could obtain by investing in a risk-free asset in the financial market. An increase in the risk-free rate will increase the time value of money, and therefore, the value of a call option, and opposite for a put option.
3.3.6. The dividend paid from the underlying asset: Cash flow losses have a negative correlation with call options, and will reduce the likelihood of it being exercised. This can be due to not fully committing to a project and, therefore, a loss to competitors. The opposite is applicable for put options.
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3.4 Estimating the volatility Many authors (e.g. Mun 2006, Copeland 2003) in real option theory argues that volatility is the most difficult parameter to estimate when evaluating a project using real options. The volatility describes the uncertainty of the cash flow from the underlying asset, and the lack of historical information on real option makes the volatility harder to calculate than in comparison to liquid traded assets such as stocks and commodities. Mun (2006) present five alternative methods to estimate the volatility which is described below.
3.4.1 Logarithmic cash flow returns method: This method is often used for liquid assets, such as stocks or commodities. The drawback of the method is that it tends to overestimate the volatility, and it cannot be used for negative cash flows. The advantages of the method are that no simulation is needed, and it is easy to compute. It is often used for financial assets but because of the fact that the natural logarithm of negative value does not exist, it does not fully capture the possible cash flows downside and may thus yield a wrong result.
3.4.2 Logarithmic present value approach: The logarithmic present value method uses the present value of all future cash flows and discounts it back to two present values, the present and one for the first period. The logarithmic ratio is then calculated. The method then uses a Monte Carlo simulation to create a distribution and the standard deviation which is the volatility real option analysis. The method is criticized for the use of a single discount rate as the main variable and require simulation.
3.4.3 GARCH approach (Generalized autoregressive conditional heteroskedasticity) The GARCH model can be used to estimate the cash flow volatility, however, hundreds of data points are required to obtain a good result with this approach.
3.4.4 Management assumption approach The management assumption approach is a subjective approach to estimate volatility. This is done by assuming that the present value follows a specific distribution and that this value varies according to a certain range. A simulation could be applied to examine the value based on the selected assumption.
3.4.5 Market proxy approach Market proxies are often used to estimate the volatility by using projects with similar characteristics. [Mun 2006] argues that this method is often misused because of the assumption that the risks inherent in the comparable projects are not necessarily identical to the ones in the specific project under review. Side 25 af 64
3.6 Common types of real options As discussed already, real option deals with a broad range of business opportunities. Many real options occur naturally in an investment process (option to defer, abandon) while others come at costs (option to expand). [Brach 2000] describes the six most common types of real options in most industries, which will be described in the following.
3.6.1 Option to defer The ability for an option-holder to postpone an investment derives its value from making a more informative decision when more information about the outcome is known. The option is an American option as it gives the owner the ability to delay the exercising of the option to a desired date. In relating to a real estate development, an investor might delay the project until price or demand uncertainty has been resolved. This option is common in real estate development and has been described in relation to real estate in several academic papers as Titman (1985) and Quigg (1993), where the optimal timing of development and defer value have been of interest. The defer option should be weighed against the value loss from not developing the project and the costs of having the option.
3.6.2 Option to alter operating scale (expand/contract) The option to expand grants the option holder the possibility to increase the investment if the market conditions are more favorable than expected. In contrast, if the market conditions turn out to be less favorable, a decreasing scale might be applied. An option to expand can be valued as an American call option, whereas a contraction is an American put option [Brach 2003]. Investing in real estate development embeds an option to expand/contract the project, e.g. by expanding or reducing the total amount of Sq.m if there are changes in market conditions. Altering real estate development, however, can pose certain difficulties when the project is started, which is why the option might not be as common in real-life situations.
3.6.3 Option to grow The option to grow is an American call option. A growth option will often require more initial outlay than the expected revenue and thereby give a negative NPV, where the value derives from creating future growth opportunities [Brach 2003]. An example of growth options are the investment in R&D or investing in land with the possibility of developing it at a later date.
3.6.4 Option to stage Larger projects often unfold over several stages instead of a single period. The staging of capital investment as a series gives the investor the ability to invest in increments. This allows the investor to wait to uncertainties are more resolved, and therefore, create valuable options whether to Side 26 af 64
abandon or continue at the given stage. A stage option is a compound option, meaning it is an option on an option, which is often seen in R&D projects and large-scale constructions [Trigeorgis 1995].
3.6.5 Option to abandon The option to abandon is an American put option giving the option holder the right to abandon the project in exchange for its resale value, e.g. in the event of declining market conditions or poor operation. This option is especially important in projects with a high capital requirement and a long time to completion, which is the case for many larger real estate developments.
3.6.6 Option to Switch Having the flexibility to switch input/output creates option value as it allows the investor to respond to market conditions. The value of a switch option is the costs saved, or the extra cash flow generated, by switching the process or product. E.g. if a real estate developer doing a project learns that it is more profitable to switch from building a resident property to a commercial property the flexibility to switch will indeed provide a value.
3.7 Approaches to value real options. When implementing real option valuation in practice, one can use several contradictory approaches. Thus, a practitioner has to decide which particular approach to rely on, as they again rely on different assumptions, which can have consequences for the usefulness of the results [Scialdone 2007]. [Borison 2003] states that there are five different ways to apply real option theory, which are:
The Classic (No arbitrage, market data) Approach
The Subjective (No arbitrage, subjective Data) Approach
The MAD ( Equilibrium-based subjective Data) Approach
The Revised classic ( Two investment types) Approach
The Integrated (Two risk types) Approach
The next sub-section will describe the pros and cons as well as the applicability of the different approaches.
3.7.1 The Classic (No arbitrage, market data) Approach The classic approach is the most direct application of the option pricing theory to real option theory. It relies on the assumptions and arguments underlying the Black-Scholes model (see appendix 4),
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and that the capital market is complete. The classic approach makes the standard replicatingportfolio assumption, meaning that a portfolio can be constructed to replicate the returns of the option, and, therefore, the option can be priced, based on the no-arbitrage arguments. The BlackScholes model likewise assumes that the geometric Brownian motion can describe the assets price movements. Several authors such as Amram (1999), Copeland et al. (2000), refers to this approach as it is easily applied in practice, due to its simplicity. However, there are no empirical evidence or arguments supporting that a replicated portfolio exist for an exactly specified investment [Scialdone 2007]. Many real assets, like real estate development, are infrequently traded which makes the no-arbitrage argument invalid. Due to these facts, a practitioner should be careful using this approach.
3.7.2 The Subjective (No arbitrage, subjective Data) Approach The subjective approach is similar to the classical approach, as it uses the standard option pricing tools from finance theory and relies on the standard replicated-portfolio, the no-arbitrage argument. This approach assumes, as the standard approach, that the dynamics of the value of the assets follows a geometric Brownian motion. However, the input parameters used in this model are subjectively estimated, and, therefore, does not rely on an explicit identification of a replicating portfolio, but still assumes that the assumption holds with subjective data. The classic and subjective approach yield different results, which of course is problematic. If there was a replicated portfolio for the investment in question, then the subjective approach might yield a very different result than the classic approach. The main critique of the classic approach, however, as Borison (2005) points out is, if there is no replicated portfolio, how can the arbitrage argument hold? The results are at a minimum questionable.
3.7.3 The Market Asset Disclaimer (MAD) Approach The marked asset disclaimer (MAD) has gained a prominent role as a real option analysis approach. This approach does not rely on a the traditional replicated-portfolio assumption but takes a step away from the financial theory as it responds to the weak assumptions for real option theory in the Black-Scholes methodology. The idea of the MAD approach is that instead of finding a market-priced financial option with the same payout structure, which can be nearly impossible for a real project, one should use the net present value of the project without flexibility as the underlying value. The approach further assumes that the price movements follows a GBM or a similar random walk. Copeland and Antikarov argue that this method is applicable to a much broader range of investments than approaches based on replicated portfolios. Borison (2005) criticizes the method of relying on subjective data for every input than the cost of capital, why arbitrage opportunities
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may be available. He further discusses that the method relies on the GBM, but the value of the underlying investment may, however, be driven by another evolution than random walks. He concludes with the claim that the MAD approach, as well as the classic and subjective approaches all have significant problems with inaccurate and inconsistent assumptions why they should be applied with caution.
3.7.4 The Revised Classic (Two investment types) Approach The revised classic approach states that the three above approaches are a “one-size-fit-all” solution, which not always hold in real options as the assumption underlying real options analysis are quite restrictive. The framework for this approach is to consider the two types of risks within projects, namely the public risk, which can be hedged, and the private risk, which cannot. If the project is dominated by market prices and public risks the classic real option with the Black and Scholes framework is applicable to a replicated portfolio can be made. If the project risks, on the other hand, are dominated by corporate-specific or private risks, a dynamic decision tree analysis should be applied. The approach does not consider which discount rate should be applied when using decision analysis. The major drawback of the method is, that in real-world involves a mix of public and private risks, why errors can occur if one assume that there only exist one type of risk.
3.7.5 The Integrated (Two risk types) Approach The integrated approach, as the revised classic approach, starts by identifying each risk as either being public or private but tries to address both risks. It then identify the replicating portfolio for the public risks and assign risk-neutral probabilities. The private risks are then assigned subjective probabilities, and the two risk can then be incorporated into a spreadsheet to calculate the cash flows. This approach’s main assumption is that markets are complete, why a “market to market” hedge can be used. Its assumes limited restriction and no assume of GBM, why Borison (2005) finds this method more accurate than the other approaches, but it requires more work and is harder to explain.
Although the approaches share a common goal, their assumptions differ significantly. Borison (2005) argues that the methods can yield very different values, why a practitioner should be caution when using real option. He further argues, however, that it would be unfortunate to avoid using real option analysis due to this reason as the potential contribution of real option can be of great importance. In the case study, the MAD approach will be applied, why its discussed assumptions of this method should be kept in mind.
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3.8 Real option analysis methods ROA literature suggests several approaches to solve real option valuations. [Kodukula et al. 2006] describes the three most commonly used methods to value options as Partial differential equations, Simulations, and Lattices. If the inputs and application frame are properly structured, the methods will yield the same result. The choice of method depends on the situation, and each technique and their commonly used methods will be described in the following with relations to real estate development, when relevant. Option value technique Partial differential equations
Specific method Closed form solutions using Black-Scholes and other similar equations Analytical approximations Numerical methods (e.g., finite difference methods)
Simulations
Monte Carlo
Lattices
Binomial trinomial Quardrinomial Multinomial
Table 4: Real option calculation methods [Kodukula 2006]
3.8.1 Partial Differentiation equations: The partial differential equations (PDE) can be divided into three categories: closed form solutions, analytical approximations, and numerical methods. The PDE is a mathematical equation that relates the changing option value to observable changes in market securities. They are solved by specifying boundary conditions that tell how the solution must behave at certain values of the asset (e.g. at known points and its value at the extremes). The PDE can be of great complexity when the option has complex features and is subject to several risk factors [Brandao et al. 2005]. In some cases, the PDE can be deduced to a closed-form solution, where the value of the option can be written as one equation where the inputs are of finite numbers. The Black-Scholes equation (1973) is by far the most popular closed form solution to value European options. The formula for the Black-Scholes is given below: 𝐶0 = 𝑆0 𝑁(𝑑1 ) − 𝑋𝑒 −𝑟𝑓𝑇 𝑁(𝑑2 ) 𝑑1 =
ln(𝑆⁄𝑋)+𝑟𝑓 𝑇 𝜎 √𝑇
+
1 2
𝜎 √𝑇
(3.6)
𝑑2 = 𝑑1 − 𝜎√𝑇 Where C is the call value, S is the value of the underlying asset, X is the exercise price, T is the time to maturity 𝑟𝑓 is the risk-free rate, σ is the annual volatility and N is the cumulative standard normal distribution of unit 𝑑1 and 𝑑2 .
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The advantage of the Black-Scholes equation is that it is easy to implement and very fast to calculate when the parameters are specified. The estimates are only valid under very restricted conditions. Given the dissimilarities between financial and real options described in section (3.2), one must be aware of the restrictions and assumptions before applying the theory in practice. [Triantis & Borison 2001] studied the prevalence of the black-Scholes formula in real option analysis, and found that most practitioners use this method as a quick and easy way to find a crude value for simple investment options, but applied binomial lattice or Monte Carlo simulation for more precise and complex investments. This is due the fundamental assumptions behind the Black-Scholes model, which is often violated when used in real option valuation. First, the formula assumes that the project has a constant volatility over its lifetime, which is a very simplistic assumption. It further assumes that the option only depends on one source of uncertainty, which is seldom the case for real option projects like real estate development. They might have development costs and other sources of uncertainty. The model assumes that the price of the underlying asset follows a continuous stochastic process, with a static drift and a given volatility as the Brownian motion: 𝛿𝑆 𝑆
= 𝜇(𝛿𝑡) + 𝜎𝜀√𝛿𝑡
(3.7)
The first part of the equation is the deterministic element and the second the stochastic where µ = drift, 𝛿𝑡 = time step, σ volatility, and an error term ε [Mun 2006]. This is not always the truth, as real option might have jumps or be mean reverting. The formula also has limitations as it can only be used to value European options and, therefore, does not consider early exercise.
3.8.2 Simulations: Monte Carlo simulation has long been a very important tool for asset pricing and risk management. The basic concept behind the Monte Carlo approach is to simulate a stochastic process for the variable of interest, a sufficient number of times and thereby, creating a distribution of the values. These values are drawn from a pre-specified probability distribution that is assumed to be known. The reason for the popularity of the Monte Carlo simulation is that it can generate scenarios where the estimates will converge to the true price, due to the law of large numbers. A simulation approach is particularly useful in valuing options when there is no closed-form solution since it can price more complex paths depending options. Under relatively general conditions, we can find the price of assets or derivatives as the discounted expectation of the future payoff in a risk neutral setting. One has to choose a process with a drift and simulate the value to the time horizon and calculate the payoff. The most common simulation approach is to apply a random walk, e.g. the geometric Brownian motion [Kodukula et al. 2006]. For every simulation, the value starts at 𝑉0 and simulates its value by 𝑉𝑡 = 𝑉𝑡−1 + 𝑉𝑡−1 (𝑟 ∗ 𝛿𝑡 + 𝜎𝜀√𝛿𝑡)
(3.8)
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Where V is the underlying asset value, σ is the volatility, ε is a simulated value from a standard normal distribution with mean zero and a variance of one (Papudescu 2006). The value can then be found by averaging the payoff and discounting it backward: (3.9)
𝑉 = 𝑒 −𝑟𝑡 𝐸(𝑉𝑇 ) Where t= time to maturity, E is the expectations operator
3.8.3 Binomial lattices: The Binomial option pricing method was first proposed by Ross and Rubinstein in (1979). The method is based on a simple discrete-time evolution of the option value, which fits well with real option valuation, as decisions can be modeled through time. The beauty of the model is its simplicity and easiness to understand with just simple mathematics, making it a great tool for practitioners. It is also widely used because it has the ability to value a variety of conditions which other valuation methods cannot. It is able to handle American options as well as Bermuda options that are exercised at predetermined dates. Fig 9 shows the possible path through the up and down movements. The figure shows how the binomial model is transformed into a probability distribution, which can be used to value the option.
(A) The Binomial Tree (B) Distribution of outcomes 𝑆
𝑁
𝑆
𝑆 𝑢𝑑
𝑆𝑑
𝑟𝑜 𝑎 𝑖𝑙𝑖𝑡
𝑆 𝑢2 𝑆𝑢
𝑟𝑜 𝑎 𝑖𝑙𝑖𝑡
𝑜 𝑖 𝑙𝑒 𝑢𝑡𝑖𝑟𝑒 𝑎 𝑒𝑡 𝑉𝑎𝑙𝑢𝑒
𝑡
𝑆 𝑑2
𝑇𝑜𝑑𝑎
𝑇𝑖𝑚𝑒
𝑎𝑡𝑢𝑟𝑖𝑡
𝑜
𝑖𝑔
Figure 8: The binominal tree and uncertainty distribution (Adopted from M. Amram 1999)
The binomial model assumes that the value for the next period (Δt), can increase or decrease by a certain probability. The up and down movements are each other’s reciprocals and can be stated mathematically as:
𝑢 = 𝑒 𝜎√𝛥𝑡 𝑎𝑛𝑑 𝑑 = 𝑒 −𝜎√𝛥𝑡
(3.10)
Where σ is the volatility of the movement and Δt is the change in time.
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Each step happens with the probability p (up move) or 1-p (down move) respectively. The value today of an option is the contingent claim on the underlying asset, where the value of the asset is a function of the probability of the best and worst case scenario. V = [q ∗ 𝑆 𝑢 + (1 − ) ∗ 𝑆 𝑑 ]
(3.11)
The binomial model can be applied in two ways, the risk-neutral probability, or by use of marketreplication portfolios [Mun 2006]. The market-replication portfolios use a portfolio of assets with the same risk, with the assumption of no arbitrage opportunity and the assumption that a possibility of using market assets to obtain the same payout structure exists. This makes sense for financial securities in a freely traded and liquid market, but is less realistic in real options, as real assets are often not as frequently traded. The risk-neutral probabilities approach, uses the risk-free rate when discounting the cash flow with a risk-adjusted probability. The two approaches yield the same results but the risk-neutral approach is more tangible and therefore more common in practice. The mathematical formula to calculate the risk-neutral probability is: =
(𝑟 −𝑏)(𝛿𝑡) 𝑒 𝑓 −𝑑
𝑢−𝑑
(3.12)
Where 𝑟𝑓 = risk-free rate and b is the dividend outflow in percent. The process of using binomial lattices requires the creation of a lattice for the underlying asset, and one for each option [Mun 2006]. The value of the underlying asset is simply calculated by multiplying it with the number of up and down steps, as calculated in equation 3.9. The movement in the lattice happens due to the volatility, where a volatility of zero, would result in a straight line and the value of an option would intuitively be zero. The valuation of the option lattice is carried out in two steps through a process called backward induction. First, the value of the terminal nodes is calculated as simply the value of executing the option or letting it expire worthless. 𝐶𝑖,𝑇 =Max [𝑆𝑖,𝑇 − 𝐾𝑇 ; 0]
(3.13)
The second step is to calculate the intermediate nodes by using the risk neutral probability: C= [𝑝 ∗ 𝐶 𝑢 + (1 − 𝑝) ∗ 𝐶 𝑑 )𝑒 [(−𝑟𝑓)(𝛿𝑡)] ]
(3.14)
The binomial method is very flexible and transparent making it easy to understand the steps in the valuation process. The disadvantage is that it can become computationally hard to estimate if it is very extensive and thus time-consuming. The binomial lattice is often the preferred method in real option practice due to its mathematical simplicity and transparency [Mun 2006].
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3.9 Advanced options This subsection will elaborate the concept of compound options as it is a key concept for many stage projects such as this case study. Real-life options are often more complex than simple as they consist of multiple options, in which different values may interact. Trigeorgis (1991) pointed out that the combined value of multiple real options may differ from the sum of the same options valued separately. He presented the value of different options (e.g. to expand and defer) and showed that the incremental value of an additional option, in the presence of other options, generally are less valuable than isolated, due to various typical negative interactions. In more complex option situations with multiple interacting options, the analytic solution (discussed in section 3.8.1) may not exist and even no partial differentiation equations to describe the underlying stochastic process either. In these cases, simulations and lattice approaches can be used (Trigeorgis 1995).
3.9.1 Compound options: Compound options are, as described in section 3.2.8, options whose value is contingent on other options. They are often found in R&D and larger real estate development projects such as FredericiaC, where each step relies on the previous step. Geske (1979) was the first to price a compound option, by pricing a call option on a stock seeing itself as a European call option on the value of a firm’s assets. The compound options are somewhat straightforward to value in the binomial approach but can also be calculated by a closed form solution as Geske did. The compound option model by Geske (1979) is based on the theory made in the Black-Scholes approach, with the assumption that under risk-neutral measures the underlying asset, V, follows a lognormal process. 𝑑𝑉 𝑉
(3.15)
= 𝛼𝑑𝑡 + 𝜎𝑑𝑧
The value of the call option as a compound option is a function of the underlying value V and the option S and t is the current time. C =𝑓 = (𝑆, 𝜏) = 𝑓(𝑔(𝑉, 𝑡), 𝑡). The compound option at maturity T’ can acquire, with a strike of E, the other option, S, on the underlying value V with a maturity T and exercise I. Geske provided a closed form solution to the value of a European compound option as: 𝐶 = 𝑉 𝐵( + 𝜎√𝑇 ′ − 𝑡, 𝑘 + 𝜎√𝑇 − 𝑡, 𝜌) − 𝐼𝑒 𝑟𝜏 𝐵( , 𝑘, 𝑝) − 𝐸𝑒 −𝑟𝑇
′ −𝑡
𝑁( )
(3.16)
Where N is a cumulative standard normal distribution and B (a,b,𝜌) is a bivariate cumulative normal distribution function of upper integral limits, a and lower of b, with correlation coefficient 𝜌 as being the √𝑇 − 𝑡. 𝑉
=
ln( ∗ )+(𝑟−½𝜎 2 )𝑇 ′−𝑡 𝑉 𝜎√𝑇 ′ −𝑡
(3.17)
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𝑘=
𝑉 𝐼
ln( )+(𝑟−½𝜎2 )𝑇−𝑡 𝜎 √𝜏
(3.18)
And V* is the schedule of asset value V on which the compound options should be exercised, which he obtain by solving S(𝑉 ∗ ) − 𝐸 = 0) Because this model calculates the value of a two-period compound models it is not useful in calculating compound options with several stages. It is furthermore only used to price a European option, which limits the method. The binomial model likewise can be used to price a compound option, where the procedure of 3.4.3 is used with a little modification. This process adds a lattice for each compound option, where the longest compound option is the underlying value for the following compound option. This method is preferable as it can handle several stages as well as American options.
3.10 Real option and its prevalence among practitioners and its shortcomings Though real option seems, at least theoretically, to be a good appraisal approach, it is not as widely used as some authors have expected. Real options advocates have, for a longer period claimed, that it is just a matter of time before the theory gets widely accepted in practice. Several studies, however, showed that there still is a large gap between practice and theory. According to a survey from Bain & Co. (2000), only 9 pct. of the 451 CFOs asked used real option as a valuation tool in decision making. Their survey from 2002 showed that approximately 25 pct. used real option analysis which, they likewise pointed out was surprising. Another study from the same year by Patricia A. (2002) of 204 “Fortune1000” CFOs indicated a much lower number of practitioners, 11.4 pct. Block S. (2007), likewise studied how many of the “Fortune1000” companies used real option analysis, where 14.3% of the 239 responding used real option analysis in their capital budgeting. A follow-up question of which methods were most applied showed, that the binominal lattices were the prevailing methods of choice and the Black and Scholes model was the least utilized method. Techniques for using real options Binomial lattices
16
Risk-adjusted decision trees
12
Monte Carlo simulations
9
Black-Scholes option pricing model
1
Other
2
Table 5: Techniques used in practice [Source Block 2007]
Upon asking the 279 companies not using real option, a large number indicated that top management has been hesitant to embrace the new approach, as the methodology cannot be conducted in a systematic manner. Though it should be mentioned, that 43.5% of the nonusers said
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that there is a good chance they will consider the use of real option in the future and 26.3% of the nonuser had a total rejection of the idea of using it in the future. Techniques for using real options Lack of top management support
42.7%
Discounted cash flow is a proven method
25.6%
Require too much sophistication
19.5%
Black-Scholes option pricing model
12.5%
Table 6: Table reason for not using real option valuation in practice [Source Block 2007]
Another common reason for not using real option was the assumption that the technique relies on a too sophisticated mathematic calculation and, therefore, has a lack of transparency. Real option theory also is a relatively new tool, compared to many of the traditional valuation methods. Even the DCF method took decades to become widely used. Changing the paradigm of capital investment does not happen as quickly as expected from Copland and Antikeros (2001) who proclaimed that real option would be the most used valuation method in ten years.
3.11 Real option in real estate As described in the literature review, real option theory since Titman’s article in 1985 has been of interest in the field of real estate development. Several authors have since theoretically and empirically showed that real option valuation can add to more informative investment decisions, than using more traditional valuation techniques. Real option theory, in general, is not widely used as an appraisal method in respect to the traditional DCF method as discussed in the previous section. Likewise, this also seems to be the case for the real estate development industry, where several real estate investment books and articles do not suggest real option valuation as a prominent or commonly used appraisal method. They suggest using the traditional methods, which are also more commonly used4. The nature of real estate development, however, makes a static decision-making process erroneous, as real estate development often takes place in several phases with different uncertainties and embedded options. Real option theory thus can help to shed light on the value of the many different options discussed in section (3.2.4), where the most common ones for real estate development are the options to abandon, expand, to stage and to defer.
4
E.g. ”the real Estate Investment handbook” – Timothy & singer, “Real estate investment” – Brown & Matysiak, “Property finance” – Giacomo & Mazza”
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4. FredericiaC case study This section will value FredericiaC by following the four-step process suggested by Copeland et al. (2003), which rely on the MAD approach discussed in section (3.7.3). This step- by step method, have gained wide recognition and is often referred to by other authors5 as being a great practical approach. It starts by calculating the static NPV then add the value of the flexibility, which will give an understanding as to whether real option analysis provides a better assessment of the true value of the project. Sensitivity analysis is likewise conducted in order to see how the value changes when the estimates and assumptions behind the model change. Lastly, the use of real option in a pre-sale contract will be discussed. 𝑅𝑂𝐴 = 𝑡𝑎𝑡𝑖𝑐 𝑁 𝑉 + 𝑜𝑝𝑡𝑖𝑜𝑛 𝑣𝑎𝑙𝑢𝑒 ( 𝑙𝑒𝑥𝑖 𝑖𝑙𝑖𝑡 )
Compute base case present value without flexibiltiy with the DCF valuation method
Model the uncertainty using event trees
Indentify and incorporate managerial flexibilities, creating a devision tree
Conduct the real option analytsis
Figure 9: 4 step valuation approach
4.1 Project description To apply real option theory to FredericiaC, several assumptions have to be made. The construction of the project will be carried out in phases. In order to get a natural transition zone from the existing town to the newly developed area, the construction starts geographically from the west end of the city to the east. The project is thus divided into four sequential stages, where each stage can be started as soon as the previous stage is completed. There is an estimated construction period of 2025 years, but the individual stages have not yet been assigned a specific timeframe. The construction time thus is assumed to be 23 years, and the construction duration of each phase is calculated, based on the total number of Sq.m. of the individual stages. As the project both include dwellings, retail offices, and cultural space, it will be assumed that the dwellings and retail price movement will correlate perfectly. The office space is expected to be leased out with a constant growth rate in price. # 2 Dwellings Retail Office space Culture Total area Construction time
Phase 1 30.431 12.443 8.657 10.785 62.317 5
Phase 2 17.931 2.386 15.391 4.000 39.709 3
Phase 3 86.637 170 19.988 3.500 110.296 10
Phase 4
45.961 6.714 52.676 5
Total area 135.000 15.000 90.000 25.000 265.000 23 Years
Table 7: Construction phase and total Sq.m
5
E.g. ”Real Option Valuation” Shockley R.
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The construction of FredericaC started in October 2015, with the first sub-part of phase one. It will be assumed, however, that the phase is not started yet, to value the decision whether to start the project or defer it at the beginning. The construction, as described earlier is carried out in stages and it is assumed that one-half of the project area of phase one and four is sold after 3 years of construction while the rest is sold at completion. For phase 2 it is assumed that it is sold at completion, and for step 3, it is assumed that it is sold equally over three phases of the 10-years of construction time.
4.2 Underlying drivers In order to forecast the potential cash flow and calculate the static NPV one must identify the underlying drivers that affect the value of a real estate development. These drivers can be deduced to be income or costs related. The income is by far the most uncertain parameter, making it ideal for a sensitivity analysis. The cost of construction is more predictable as several similar projects can be used to estimate the costs.
4.2.1 Costs The expected construction costs for the FredericiaC is disclosed, why an estimate based on similar projects has to be used. Ramboll (a larger Danish construction company) has made a draft of the average cost of constructing, based on experiences and key figures from V&S prisdata [Nybyggeri husbygning 2013]. Their data indicate an average square meter price of 13.262 DKK of high quality dwellings and 17.881 DKK for retail and office premises without internal costs. Licitationen (a construction industry newspaper) in collaboration with Byggeriets Evaluerings Center has gathered information about construction costs from newly developed constructions. Their figures indicate similar building costs for both dwellings, office and retail space when including internal building costs of approximately 16.000 DKK pr. Sq.m. [V&S 2013] Suggest that the construction costs should be geographically adjusted which will lower the construction costs for the FredericiaC with 5%. It furthermore depends on the size of construction, and [V&S 2013] suggest a rule of thumb of a 6-7% increase (decrease) of the building costs, when the project Sq.m is doubled (halved). Due to the size and economy of scale of this project, it is assumed that the construction costs are furthermore reduced 5% in relation to the general average costs. It is assumed to be 17.500 DKK pr. Sq.m. for high quality construction given a construction costs of 15.750 DKK Sq.m. The building costs, since 2005 have had an annual growth rate of 2,473% [see appendix 5]. This will be used to forecast the price trend of the construction costs during the construction period. The construction costs are assumed to be paid at the beginning of each year, and the cost is presumed to be linear in nature and thus follow the development of the constructed square meters.
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4.2.2 Income – Sale price and rent. The typical method to estimate the sale price is by comparing it with similar assets which offer similar utilities. One might use the sale history to find an average sale price, but the heterogeneous nature of real estate makes this difficult to apply. The current average price pr. Sq.m. in Fredericia is 15.654 DKK with an average transaction price of 11.667 DKK [See appendix 6]. The first subproject of phase I has been started with an average price of 21.729 DKK for dwellings which is significantly higher (almost double) than the average transaction price in Fredericia. As discussed earlier, location is of great importance on the price and FredericiaC is at a unique location, close to the sea front, making it more expensive that the average of Fredericia. The construction quality is above average too. The prices of the first dwellings in a new area are often lower, in order to attract first movers and to make the area popular. [Realproject.dk] estimates that new projects in new locations are often sold with a 10% discount compared to a similar estate. This might be the case for the first sub-section of phase one. The average price reduction for Fredericia is 4.9% of the original sale price, which is also assumed realistic in FredericiaC. The expected sale price for dwellings, therefore, is set to be 23.000 DKK/𝑚2 6 . Due to the location closer to the harbor, the price is expected to increase with 1.000 DKK/𝑚2 in each phase, in addition to the average growth rate. An accurate estimate of the price movement for the sales price is pivotal in order to calculate a reliable NPV as it was highlighted as the most uncertain variable. The historical price movement for condominiums in Fredericia, on the average, has had a growth rate of 3.85 pct. over the last 22 years. The return distribution of real estate is a much discussed topic without a clear conclusion but with a general assessment of evolving according to a geometric Brownian motion. Lai (2004) finds evidence in favor of this process and Kuo (1996) further clarifies that most real estate literature typically assumes this evolution. To test if the return distribution of the data from Fredericia follows a GBM its assumptions are tested in appendix 7. An Augmented Dickey-Fuller test concludes that the process is a random walk, and the assumption of normally distributed log-returns likewise are satisfied. The log-returns, however, suffers from homoscedasticity in several lags, which violate the Gauss-Markov assumption. Other empirical real estate studies likewise find problems with the geometric Brownian motion assumptions. As an example, Bulan et al. (2009) find empirical evidence of short-run positive serial correlation and long-run mean reversion. A small sample size might lead to a significant bias in the autocorrelation estimation, why it has been chosen to assume a geometric Brownian motion as the price movement. A Monte Carlo simulation of 50.000 iterations of the expected growth rate following a geometric Brownian motion is conducted, which indicates an average growth rate of 3.9 pct., close to the historical rate of 3.85 pct., and will be used in the
6
It is expected that the first sub-part of phase I is sold at a price of 10 % below the average of phase I = 23.000 DKK Sq. M
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case study. The office premises is expected to be sold at completion and the first office space is offered at a presale price of 18.846 DKK/𝑚2 . As the costs of raising office buildings and dwellings are similar, it is assumed that the office space will be sold, at the same Sq.m. price as dwellings on the average. The average price of rental premises in the south Jutland has been rather stable between 740-796 DKK/𝑚2 in the last 5 years7. Because of the location and the quality of this project, it is expected to be leased at a price of 1.000 DKK. Sq.m. The operation costs of the rental premises are announced to be 190 DKK Sq.m./yearly. The retail premises are expected to be leased out at a current rate of 810 DKK after operating expenses, with a growth rate of 2%. The rental premises are expected to be leased for 15 years, and a terminal value is calculated thereafter. The terminal value can be calculated using several approaches, involving some assumptions about the long-term cash flow growth or a resale rate. A common approach is to use the Gordan growth model to evaluate the terminal value with an assumption of a constant growth rate. [Timothy 2005] suggests that one should find the terminal value of a real estate by dividing the cash flow in the last year with the capitalization (cap) rate, or the discount rate. This approach, therefore, will be applied in the calculation, with a rate of 6.9%.
4.3 Cost of capital The cost of capital is the cost of the debt and equity a company has acquired, in order to run its operation, and it, therefore, depends on the capital structure of the firm. The cost of capital can be seen as the best expected return in the market for assets with similar risks. As FredericiaC is a partnership between Fredericia municipality, RealDania and third partners, the cost of capital will be assumed to be purely equity financed. This means that instead of using the WACC, the cost of capital will be estimated by the cost of equity. The cost of equity can be calculated using several different approaches. The most commonly used methods include the arbitrage pricing theory (APT) the Fama-French model and the most common approach which is the capital asset pricing method (CAPM). To calculate the cost of capital we need to estimate three parameters, namely the risk-free rate, the market risk premium and the company’s beta. The CAPM model postulates that the expected return can be calculated by the following formula: 𝐸(𝑅𝑖 ) = 𝑟𝑓 + 𝛽𝑖 [𝐸(𝑅𝑚 ) − 𝑟𝑓 ]
(4.1)
Where 𝐸(𝑅𝑖 ) is the expected return, 𝑟𝑓 the-risk free rate, 𝛽𝑖 the sensitivity of the stock to market development and 𝐸(𝑅𝑚 ) the expected return on the market.
7
oline.dk
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4.3.1 Risk free interest rate The risk-free rate is defined as the rate an investor can save and borrow though borrowing in reality often require a higher rate than the saving rate. The risk-free rate forms the basis for the discount rate, and it should include inflation and the time value of money. In reality, there are no truly riskfree investments but the risk-free rate is generally determined by the government treasure securities [Demarzo et al. 2014]. The maturity of the bond should be chosen in relation to the investment period as the cash flow. However choosing a bond with a maturity above 10-years might be misleading due to illiquidity [Koller 2010]. The risk-free rate for a Danish 10 year bond is currently 0.4%, which is very low in relation to historical figures. The government bond has been volatile why an approximation of the average rate from 2005- 2015 of 2.7% is applied and kept constant over the period of the project [see Excel Rf_rate].
4.3.2 Market risk premium The market risk premium is the market return minus the risk-free rate (𝑅𝑚 − 𝑅𝑓 ). Generally, there are three different ways to estimate the risk premium [Danish national bank 2003]. The historical approach, the forward-looking theoretical approach and a survey approach where investors are asked to assess their risk premium. The most common approach is to calculate the historical average excess return of the market of a broad stock index, such as the S&P 500, or the Copenhagen stock exchange. The historical approach is widely used but has certain challenges. First, the selected period and time horizon affect the estimate. Second, it takes much data to produce accurate estimates, and older value might not be a good indicator of the future value, which creates a tradeoff. Denmark has had a risk premium of respectively 2.2%, 5.2%, and 7.2% for the periods 1970-1982, 1983-2002 and 1983-2002 (Nationalbanken 2003). According to [Berk et al. 2014] the S&P 500 excess returns from 1962-2012 has had an average of 7.7% whereas the period 1962-2012 has been 5.5% compared to a 10-year U.S treasury bond. From the figures it shows that the period chosen has a great effect on the estimate. The market return for the case study is based on the average of the S&P 500, and the risk premium can thus be calculated by 𝑅𝑚 − 𝑅𝑓 = (6.6%-2.7%)= 3.9%.
4.3.3 Beta The beta value indicates how sensitive the company is to changes in the volatility of the market. Therefore, it is a company specific symmetric risk that cannot be diversified. The beta value of the market is by definition one. Companies with a higher (lower) beta are more (less) volatile and expects a greater (lesser) required return than the market. The raw beta value empirically can be
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estimated using an OLS regression, where the most common one is to regress the historical stocks return against the historical market return: (4.2)
𝑟𝑖 = 𝛼 + 𝛽 𝑟𝑚 + 𝜀
When estimating the raw beta value, several terms must be kept in mind. First, one must specify the return period. [Koller 2010] suggest using data from a period of 5 years as a company might change risk structure over time and a longer period will not reflect the present beta. However, including fewer years will reduce the accuracy. Second, the return interval has to be specified. Too many intervals will increase bias in beta due to non-trading bias, but increasing the number of observations will make the estimate more precise [koller2010]. Because the project does not have a beta value, a peer group has been determined as a benchmark, with the assumption that their business has the same risk level as FredericiaC. The beta of the peer group is estimated using OLS where the returns are regressed against the market return of the S&P 500 with 10-years of data. [see appendix 7]. To calculate the beta unleveraged we can use the following formula 𝐵 = Peer group
Beta
𝐵𝐿
(4.3)
𝐷 𝐸
[1+(1−𝑇)∗( )]
Debt/equity ratio
Beta unlevered
Return of equity
TK Development
1,032
1,079
0,570428374
6,72%
Per Arfsleff
0,424
0,591
0,293764434
4,35%
1,2
0,798
0,750782065
7,38%
NCC Table 8: Peer group
[Koller 2010] suggest using a wider range of companies from the same industry to improve the precision of the beta estimate. As long as the estimation errors are uncorrelated, we would get a good indicator for the beta of the industry by taking the industry median. The data from the industry betas are retrieved from [www.stern.nyu.edu] comparing the European real estate firms cost of capital from 2015. Industry average: Industry
Number of Beta firms
D/E Ratio Tax rate
Unlevered beta
R.E.I.T.
117
0,97
64,40%
3,27%
0,60
Return on equity 6,5%
Real Estate (Development)
48
0,91
126,42%
7,71%
0,42
6,2%
Real Estate(General/Diversified)
73
0,88
144,28%
10,35%
0,38
6,1%
Average
79,33333
0,92
111,70%
7,11%
0,47
6,29%
Table 9: Industry average [source: data from Damodaran]
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The average cost of capital for the industry is 6.29%, which is similar to the average of the peer group. FredericiaC is expected to be unleveraged and thus do not have the financial effect of debt. However, both the peer group and the industry have some diversification by investing in several projects, which FredericiaC does not. Taking this fact into consideration, a beta value equal to 0.92, the average of the industry seems right. The cost of capital can then be calculated as 0.027+0.92*(0.067-0.027) = 6.88% which is similar to the required rate of return for the industry.
3.4 Choice of discount rate The choice of discount rate is an important topic as minor changes can have major impact on the outcome of the calculations. Mun (2006) and Brigham & Daves (2012) discuss the benefits of using multiple discount rates, with the idea that the riskiness of the individual cash flows should be reflected in the discount rate. Mun (2006) suggests that the costs should be discounted at a rate equal to the risk-free rate, or at a bit higher, while the income should be discounted at the appropriate risk-adjusted discount rate. This of cause makes it interesting to see how common multiple discount rates are, and how sensitive the interest rate assumptions are for the calculation. A study from Block (2003) showed that over 50% of the companies asked used a single discount rate based on WACC for all projects and only 14% used objective measurements to determine their discount rates. Therefore, multiple discount rates are not commonly used in the corporate world. Other authors8 argues that using several discount rates can be a great idea when there are strong reasons to do so but one should not routinely discount costs at a risk free cash flow. Lewis et al. (2009) recommend using the current practice of applying one discount rate to both cost and income. Trigeorgis (1995) likewise discuss the topic with the conclusion that it is obvious that risk may vary from different components of the cash flows, but in practice it is difficult to calculate. He elaborates that there is no single answer as to how many rates and how much effort one should put on estimating each rate to make a good analysis. The more sensitive the analysis is to the choice of discount rate, the more attention should be put on the estimates. A larger amount of real option literature does not discuss this topic but uses the traditional method. Though it makes sense to use a risk-adjusted discount rate for the income, the costs does not seem to be risk-free and known with certainty, why a rate for this should also be calculated. A discount rate for the costs is calculated as the (cost of capital + the risk free rate divided by two), yielding a rate of 4.5%, as the costs is surely less risky than the expected return which is discounted by 6.29%.
8
E.g. N. Lewis et al., L. Trigeorgis g
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4.5 Evaluation of the project In the previous section, all the necessary inputs for calculating the static net present value have been estimated, which is summarized in fig. 10. 4.5.1 Static NPV model Input Parameters for NPV calculation Income parameters Sale price
23.000-26.000 DKK/Sq.m
Rent price
810 DKK/Sq.m
Vacancy rate
9%
Expected growth in sale price
3,945%
Expected growth in rent price
2%
Construction parameters Construction costs
15.750 DKK/Sq.m
Expected construction growth
2,47%
Risk free rate r
2,70%
Beta β
0,92
Market risk premium
3,90%
Cost of equity
6,29%
Tabel 10: Input parameters for NPV
𝑁 𝑉 = 𝑉𝑏𝑒𝑛𝑒𝑓𝑖𝑡𝑠− 𝑉𝑐𝑜𝑠𝑡𝑠 NPV of FredericiaC = 𝑉𝑃ℎ𝑎𝑠𝑒 𝐼 + 𝑉𝑃ℎ𝑎𝑠𝑒 𝐼𝐼 + 𝑉𝑃ℎ𝑎𝑠𝑒 𝐼𝐼𝐼 + 𝑉𝑃ℎ𝑎𝑠𝑒 𝐼𝐼𝐼𝐼 NPV:
𝑎 𝑒 𝐼−46.705.643 +
𝑎 𝑒 𝐼𝐼3.678.882 +
𝑎 𝑒 𝐼𝐼𝐼46.444.797,16 +
𝑎 𝑒 𝐼𝐼𝐼𝐼92.243.921
= Total NPV of 96.661.958 DKK The total NPV of the project is the combined NPV of each of the 4 phases. The calculation can be seen in appendix 9, and to see the full calculation with all the phases a referral is made to excel [NPV_GBM]. The NPV of the project is 96.661.958 DKK which by the NPV rule means, that the project should be undertaken. However, the NPV, in comparison to the scale of the project is not very far from a break-even. Furthermore, it is notable that the first phase of the project has a highly negative value, which might influence the decision maker as the profitability relies on the fact that later phases will become more profitable. It is, therefore, interesting to use a sensitivity analysis to see how the value of the project varies with changes in the underlying assumptions.
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4.5.2 Sensitivity analysis of the NPV valuation. Because the NPV valuation solely relies on a set of fixed input parameters, it is important to see, what will happen if changes in these parameters occur. The sensitivity thus allows us to see the effect of the errors in the estimated calculation. First, a dynamic version of the discounted cash flow analysis is calculated with a Monte Carlo simulation of 50.000 trials with a static expectation of future growth rate based on the historical rate, but with a standard deviation of 12.8% (std. is calculated in section 4.3). The simulation is used to calculate a distribution of many future outcomes which indicates that the project has a 67.9% chance of being a positive investment (Appendix 10). Then an NPV is calculated with the assumption that the sale price follows a geometric Brownian motion. This indicates a higher expected payoff of 96.661.958 DKK and a 75.9% chance of break even. The simulation, therefore, shows that the expected NPV is highly depending on the assumptions of the price movements of the underlying drivers. The estimated price and discount rates are considered the most uncertain estimates in the NPV analysis. This is because there is a great uncertainty of demand because there is a lack of comparable projects in the same geographical area. Also, the cost of capital has a large impact on the value of the project. A sensitivity of both the price and construction costs is shown in fig. 11. The analysis show that even a small reduction in the estimated sale price will have a high impact on the profitability of the project and the calculations shows that a small reduction (3.3%) in the expected sale price, holding the construction costs fixed, will make the project unprofitable according to the NPV method. costs Price -10% -9% -8% -7% -6% -5% -4% -3% -2% -1% 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10%
20.700 20.930 21.160 21.390 21.620 21.850 22.080 22.310 22.540 22.770 23.000 23.230 23.460 23.690 23.920 24.150 24.380 24.610 24.840 25.070 25.300
-5% 14.963 -41.117.117 -11.949.431 17.218.254 46.385.939 75.553.624 104.721.309 133.888.995 163.056.680 192.224.365 221.392.050 250.559.735 279.727.421 308.895.106 338.062.791 367.230.476 396.398.162 425.565.847 454.733.532 483.901.217 513.068.902 542.236.588
-4% 15.120 -71.896.672 -42.728.987 -13.561.302 15.606.384 44.774.069 73.941.754 103.109.439 132.277.124 161.444.810 190.612.495 219.780.180 248.947.865 278.115.550 307.283.236 336.450.921 365.618.606 394.786.291 423.953.976 453.121.662 482.289.347 511.457.032
-3% 15.278 -102.676.228 -73.508.542 -44.340.857 15.606.385 13.994.513 43.162.199 72.329.884 101.497.569 130.665.254 159.832.939 189.000.625 218.168.310 247.335.995 276.503.680 305.671.365 334.839.051 364.006.736 393.174.421 422.342.106 451.509.791 480.677.477
-2% 15.435 -133.455.783 -104.288.098 -75.120.413 15.606.386 -16.785.042 12.382.643 41.550.328 70.718.013 99.885.699 129.053.384 158.221.069 187.388.754 216.556.440 245.724.125 274.891.810 304.059.495 333.227.180 362.394.866 391.562.551 420.730.236 449.897.921
-1% 15.593 -164.235.338 -135.067.653 -105.899.968 15.606.387 -47.564.598 -18.396.912 10.770.773 39.938.458 69.106.143 98.273.828 127.441.514 156.609.199 185.776.884 214.944.569 244.112.254 273.279.940 302.447.625 331.615.310 360.782.995 389.950.681 419.118.366
0% 15.750 -195.014.894 -165.847.209 -136.679.524 15.606.388 -78.344.153 -49.176.468 -20.008.783 9.158.903 38.326.588 67.494.273 96.661.958 125.829.643 154.997.329 184.165.014 213.332.699 242.500.384 271.668.069 300.835.755 330.003.440 359.171.125 388.338.810
1% 15.908 -225.794.449 -196.626.764 -167.459.079 15.606.389 -109.123.709 -79.956.023 -50.788.338 -21.620.653 7.547.032 36.714.718 65.882.403 95.050.088 124.217.773 153.385.458 182.553.144 211.720.829 240.888.514 270.056.199 299.223.884 328.391.570 357.559.255
2% 16.065 -256.574.005 -227.406.320 -198.238.634 15.606.390 -139.903.264 -110.735.579 -81.567.894 -52.400.208 -23.232.523 5.935.162 35.102.847 64.270.532 93.438.218 122.605.903 151.773.588 180.941.273 210.108.959 239.276.644 268.444.329 297.612.014 326.779.699
3% 16.223 -287.353.560 -258.185.875 -229.018.190 15.606.391 -170.682.819 -141.515.134 -112.347.449 -83.179.764 -54.012.079 -24.844.393 4.323.292 33.490.977 62.658.662 91.826.347 120.994.033 150.161.718 179.329.403 208.497.088 237.664.773 266.832.459 296.000.144
4% 16.380 -318.133.116 -288.965.431 -259.797.745 15.606.392 -201.462.375 -172.294.690 -143.127.005 -113.959.319 -84.791.634 -55.623.949 -26.456.264 2.711.422 31.879.107 61.046.792 90.214.477 119.382.162 148.549.848 177.717.533 206.885.218 236.052.903 265.220.588
5% 16.538 -348.912.671 -319.744.986 -290.577.301 15.606.393 -232.241.930 -203.074.245 -173.906.560 -144.738.875 -115.571.190 -86.403.504 -57.235.819 -28.068.134 1.099.551 30.267.237 59.434.922 88.602.607 117.770.292 146.937.977 176.105.663 205.273.348 234.441.033
Figure 10: Sensitivity analysis of construction costs and price movement in absolute values. Percentage change is shown in appendix
As the discount rates have a great impact on the results, a sensitivity analysis of the costs of capital applied to the capital inflows and the discount rate to the costs has been conducted. The figure
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below shows the cost of capital and its absolute effect with an increase of 0.5% and a decrease of 0.2% and its corresponding effect on the value of the project. Cost of capital Discount r Cost R-f rate 3,50% 0,00% 0,50% 1,00% 1,50% 2,00% 2,50%
2,70% 3,50% 4,495% 5,00% 5,50% 6,00% 6,50% 7,00%
-1,00% 0,80% 5,29% 5,49% -112.859.380 -195.523.275 173.099.837 90.435.942 484.603.804 401.939.910 626.331.509 543.667.614 756.980.137 674.316.242 878.787.171 796.123.276 992.464.812 909.800.917 1.098.661.163 1.015.997.268
-0,60% 5,69% -275.554.668 10.404.549 321.908.517 463.636.221 594.284.849 716.091.883 829.769.524 935.965.875
-0,40% 5,89% -353.050.235 -67.091.018 244.412.949 386.140.654 516.789.282 638.596.316 752.273.957 858.470.308
-0,20% 6,09% -428.102.745 -142.143.528 169.360.440 311.088.144 441.736.772 563.543.806 677.221.447 783.417.798
0 6,29% -500.801.226 -214.842.009 96.661.958 238.389.663 369.038.291 490.845.325 604.522.966 710.719.317
0,50% 1,00% 6,79% 7,29% -672.800.960 -831.857.381 -386.841.744 -545.898.165 -75.337.776 -234.394.197 66.389.928 -92.666.493 197.038.557 37.982.136 318.845.591 159.789.169 432.523.232 273.466.811 538.719.583 379.663.161
1,50% 7,79% -979.095.187 -693.135.970 -381.632.003 -239.904.298 -109.255.670 12.551.364 126.229.005 232.425.356
2,00% 8,29% -1.115.531.544 -829.572.327 -518.068.360 -376.340.655 -245.692.027 -123.884.993 -10.207.352 95.988.999
2,50% 3,00% 8,79% 9,29% -1.242.087.141 -1.359.596.034 -956.127.924 -1.073.636.817 -644.623.957 -762.132.850 -502.896.252 -620.405.145 -372.247.624 -489.756.517 -250.440.590 -367.949.483 -136.762.949 -254.271.842 -30.566.598 -148.075.491
3,50% 9,79% -1.468.814.424 -1.182.855.207 -871.351.240 -729.623.535 -598.974.907 -477.167.873 -363.490.232 -257.293.881
Figure 11: Absolute values: Sensitivity analysis of discount rates numbers in 000’. Percentage change is shown in appendix
The sensitivity analysis shows the importance of correct estimates, as small changes can have a large impact on the profitability. This is especially true for a project that spans several years. Using a discount rate similar to the cost of capital for the cost of the project will make it look much more valuable as the costs would be considerably lower. Conversely using a discount rate at the risk-free rate will have the opposite effect. The use of discount rates is a rather debated topic, and the analysis shows that a single wide discount rate of a company, instead of multiple ones, can lead to misleading decision information.
4.6 Volatility Volatility is a fundamental parameter for option valuation. As discussed earlier, real option projects often have limited historical data for the underlying price movement, making it hard to estimate the volatility. (Antikarov 2003) argues that a wrong specification of the volatility is a common mistake due to this fact. Because volatility tends to be persistent, a historical estimate provides a reasonable forecast for the volatility in the future, when available. (Berk et al. 2014). Section 3.5 elaborates on some of the most common approaches to assess volatility. However, when multiple sources of uncertainties are present, a Monte Carlo simulation can be used to calculate the total volatility of the project. In this case, the square meter price is identified as the volatile underlying parameter, and to calculate its volatility, the historical price movements for Fredericia municipality in the period of 1992-2015 has been used9. The long data period has been chosen due to the length of the construction period, and the options maturity embedded in the construction. This will also make the estimate less affected by the phenomena of volatility clustering. The historical quarterly data for the Sq.m price fluctuation of apartments show a volatility of 10.9% and an annual volatility of (10.9%∗ √4)= 21.8% for the last 23 years. The annual data indicate an annual volatility of 12.70%, which makes sense, as less frequent data tend to mask interim volatility. But due to the small sample size of apartments, the volatility for all types of dwellings in Fredericia have been calculated as a supplement, with a volatility of 7.4% in the same period. This is close to 9
Data from Realkreditforeningen.dk
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the average Danish volatility of apartments from 2000-2015, which have had a quarterly volatility of 3.2% and an annualized volatility of 6.5%. Other real estate literature suggest a bit higher numbers, Bulan et al. (2007) used a GARCH model to estimate the volatility of 1214 condominium developments and found a standard deviation of 15.7%-20%. Brown et al. (2000) use data from the investment property Databank of 13,500 properties, with a yearly standard deviation of 13.14%. Frederica’s price fluctuations have been higher than the average historically and it is therefore considered that the volatility of the price will match the volatility of 12.7% calculated from the annual data. It is further assumed that the volatility will be constant over the construction time of the project.
4.7 Real option valuation of FredericiaC: The NPV calculated in section 4.1 is the value of the project without flexibility. The long period of the construction phase creates a greater degree of uncertainty about the possible profitability. The management can actively affect this by exercising the options embedded in the project. Several options have been identified for a real estate development, which is also the case for FredericiaC. These options include the possibility to defer the investment and abandon the project. The options embedded in FredericiaC furthermore has been identified as four sequential compound options as the project is constructed in four phases. That the option is sequential means that the later phase of the construction is depending on the successful completion of previous one. Only the most relevant options should be included as more options might increase a lack of transparency more than actually creating value. Antikarov (2003) argues that too many options will overcomplicate the analysis which is a common mistake in practice. The set of realistic options can often be reduced to a few. Nalin Kulatilaka (2001) further claims: “You can make any project look good if you build in enough options”, but these options needs to be relevant and companies should only include the ones they will act on. For FredericiaC, it is assumed that the most relevant ones will be to abandon or defer the project. The deferral options maturity often depends on the given permits from the municipality. It is assumed that each phase can be deferred according to the phases construction time of the phase, so the longest construction phase has the longest defer maturity. Fig 14 shows the four options and their respective maturities. Each option is acquired at the first time the previous phase can be completed and option 𝐶2 is thus acquired in year 2020, 𝐶3 2023 and 𝐶4 2033. Each compound option is in an American option, meaning that they can be exercised and therefore abandoned or deferred before maturity. To calculate the compound option, the longer-term option needs to be calculated first, because the compound option is based on another option.
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Maturity of defer options Maturity of option phase I Maturity of option phase II Maturity of option phase III Maturity of option phase IIII 2015
2018
2024
2030
2042
Figure 12: Option maturity to defer
4.7.1 Binomial lattice method To assess the value of the options imbedded in the project, the lattice approach developed by Cox, Ross and Rubinstein (1979) will be applied, as it is recommended for projects with multiple options. As discussed earlier, the lattice approach applies several lattices, one for the underlying asset and one for each option value. The lattice for the underlying asset (V) starts at 𝑇𝑜 with the present value of the expected future cash inflow. The up and down movements then are multiplied with its respective factor to calculate the value for next period. The up and down movement and the risk neutral probability is calculated by the following equations: 𝑢 = 𝑒 𝜎√𝛥𝑡 𝑎𝑛𝑑 𝑑 = 𝑒 −𝜎√𝛥𝑡 And 𝑝 =
𝑒 (𝑟𝑓−𝑏)(𝛿𝑡)−𝑑 𝑢−𝑑
(4.4)
By deferring the project an additional year, the investor loses their dividend. The dividend “b” is set to equal the opportunity cost of capital of 6.29%, which is the expected payoff if the investor chooses to invest in another asset with similar risk. In addition, the construction costs of the project will increase in the future which can also trigger an early commitment. It is further assumed that the options can only be exercised once a year (δt). The cost and value of abandoning the project are expected to even out. The inputs for the option valuation can be seen in table 11 below. Inputs for binominal lattice Annual risk free rate (𝑟𝑓 ) Annual standard deviation (δt) Number of steps per year
2,70% 12,70% 1
Up movement (u)
1,135
Down movement (d)
0,881
Dividend (b) Risk neutral probability (p)
6,29% 32,98%
Table 11: Inputs to binominal lattice approach
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The valuation lattice for the options is calculated using backward induction. This means that the value of the subsequent phase and its embedded option is calculated, based on the longer-term option. The longest lattice 𝐶4 is calculated first and the following lattice is calculated with the longer lattice as its underlying value, carried out to the present time. The method uses two steps, starting with calculating the terminal node (t=T), as the value of executing the option or letting it expire worthless: 𝐴𝑋[𝑉𝑇 − 𝑋; 0] For phase I at the terminal node the value is equal to 𝐶1 (𝑉3,0 )= Max[2.176.096.473-819.133.861;0]. The intermediate nodes thereafter can be calculated as the maximum between starting the construction, exercising the option to defer or abandoning the project. (4.5)
𝐴𝑋[𝑉𝑇 − 𝑋; 0]; [[𝑝]𝑢𝑝 + (1 − 𝑝)𝑑𝑜 𝑛]𝑒 −[(𝑟𝑖𝑠𝑘𝑓𝑟𝑒𝑒)(𝛿𝑡)] 𝐶1 (𝑉2,0 )=Max[1.680.290.604-819.133.861;(1.335.762*32.98%+(132.98%)*80.295.226)*𝑒 0,027 ); 0]
4.8 Case study results: The Real option lattices can be seen in appendix 11. Due to the long maturity of the construction and the extensive size of the calculating, only phase one is shown below10. Phase I 0 1 2 3
2015 0 150.105.993
2016 1 450.735.586 8.276.129
2017 2 861.156.742 25.778.550 -
2018 3 1.335.762.770 80.295.226 -
Table 12: Binominal lattice of phase I
The value of the real option valuation, and thus the total project value, can be seen from the final node in phase I, which indicates that the project is worth 150.105.993 DKK, including flexibility. This makes the options embedded in the project worth 53.444.034 DKK and the results thus show that the option is worth more than the project itself. Comparing the traditional DCF and the real option analysis expresses the value of including flexibility, resulting in a much more informative decision for the decision-maker. The results further show that including real option can lead to a noteworthy different view of the value of a given project. In this case, Real option analysis increases the value of the project from 96.7 million to 150.1 million, 55.3%. This result confirms Trigeorgis (1993) and Copland & Antikarov (2003) who proclaimed that the DCF analysis undervalues 10
See Appendix 12 for the binominal lattices.
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investment opportunities relative to real option theory, as it fails to incorporate uncertainty and flexibility. The numbers in grey color in the binomial lattice indicates that the given state should be deferring, whereas the dark gray means abandon and the white indicate construct. We can see from the analysis that the option value of deferring phase one is higher than the value of starting the project right away. Whether the project should be deferred in 2016 depends on the given conditions, where worse conditions indicate defer, and better market conditions indicate construct. The given actions that the managements need to take thus depends on the development of the market movement. If the valuation of the project was solely based on the NPV method, the project should be undertaken right away, while the ROA indicates that one should wait and react to the changing market conditions.
4.8.1 Sensitivity analysis The results from the ROA like the result from the static NPV depends on the assumptions made about the inputs. The real option analysis is highly depending on the volatility, why a sensitivity analysis of the volatility and the price movement is presented, to see how the value of the project will react to movement in these factors. Price
Volatility -5% 21850 -4% 22080 -3% 22310 -2% 22540 -1% 22770 0% 23000 1% 23230 2% 23460 3% 23690 4% 23920 5% 24150
Price
Volatility -5% 21850 -4% 22080 -3% 22310 -2% 22540 -1% 22770 0% 23000 1% 23230 2% 23460 3% 23690 4% 23920 5% 24150
-5% 7,70% 28.804.387 36.531.609 44.258.830 51.986.052 67.494.273 96.661.958 125.829.643 154.997.329 184.165.014 213.332.699 242.500.384
-4% 8,70% 40.358.389 48.902.038 57.445.687 65.989.337 74.532.986 96.661.958 125.829.643 154.997.329 184.165.014 213.332.699 242.500.384
-5% 7,70% -81% -76% -71% -65% -55% -36% -16% 3% 23% 42% 62%
-4% 8,70% -73% -67% -62% -56% -50% -36% -16% 3% 23% 42% 62%
Sensitivity analysis ROA: Absolut value -3% -2% -1% 0% 9,70% 10,70% 11,70% 12,70% 52.566.252 65.242.122 78.263.431 91.545.991 61.772.230 74.999.521 88.489.772 102.178.264 70.978.207 84.756.921 98.716.113 112.810.537 80.184.185 94.514.320 108.942.454 124.659.634 89.390.162 104.271.720 120.187.200 137.382.813 98.596.140 114.835.874 132.394.693 150.105.993 125.829.643 126.446.175 144.602.187 162.829.172 154.997.329 154.997.329 156.809.680 175.552.351 184.165.014 184.165.014 184.165.014 188.275.531 213.332.699 213.332.699 213.332.699 213.332.699 242.500.384 242.500.384 242.500.384 242.500.384 Sensitivity analysis ROA: Percentage change -3% -2% -1% 0% 9,70% 10,70% 11,70% 12,70% -65% -57% -48% -39% -59% -50% -41% -32% -53% -44% -34% -25% -47% -37% -27% -17% -40% -31% -20% -8% -34% -23% -12% 0% -16% -16% -4% 8% 3% 3% 4% 17% 23% 23% 23% 25% 42% 42% 42% 42% 62% 62% 62% 62%
1% 13,70% 105.029.980 116.018.961 128.405.345 141.580.339 154.755.333 167.930.327 181.105.321 194.280.314 207.455.308 220.630.302 242.500.384
2% 14,70% 118.671.659 131.534.972 145.110.832 158.686.692 172.262.552 185.838.412 199.414.272 212.990.132 226.565.992 240.141.852 253.717.712
3% 15,70% 134.130.860 148.066.310 162.001.760 175.937.210 189.872.659 203.808.109 217.743.559 231.679.009 245.614.459 259.549.909 273.485.359
4% 16,70% 150.516.672 164.777.811 179.038.949 193.300.087 207.561.225 221.822.363 236.083.502 250.344.640 264.605.778 278.866.916 293.128.054
5% 17,70% 167.074.587 181.633.228 196.191.870 210.750.511 225.309.153 239.867.794 254.426.435 268.985.077 283.543.718 298.102.360 312.661.001
1% 13,70% -30% -23% -14% -6% 3% 12% 21% 29% 38% 47% 62%
2% 14,70% -21% -12% -3% 6% 15% 24% 33% 42% 51% 60% 69%
3% 15,70% -11% -1% 8% 17% 26% 36% 45% 54% 64% 73% 82%
4% 16,70% 0% 10% 19% 29% 38% 48% 57% 67% 76% 86% 95%
5% 17,70% 11% 21% 31% 40% 50% 60% 69% 79% 89% 99% 108%
Figure 13: Sensitivity analysis of profitability with changing Sq.m prices and volatility.
The sensitivity analysis shows that both the volatility and Sq.m price have a great impact on the value of the project. We can see that the options imbedded in the project are of greater value when the volatility increases, and lesser when it decreases. The value of the options becomes insignificant in the light grey area because the volatility is too low to make the project worth deferring or abandon. The project will thus be constructed right away, as this will give the highest payoff under these conditions. If the volatility falls to the general volatility of Danish apartments over the last 10 years (6.5%), there would be no value in the flexibility, as the value of the projects with flexibility Side 50 af 64
would equal the value of the static NPV. However, if the volatility on the other hand, behaves as the expected volatility of Matysiak et al. (2000) or Bulan et al. (2007), the value would increase significantly.
Figure 14: Sensitivity analysis of real option analysis – Profitability
4.8.2 Empirical comparison A research by Bulan et al. (2007) of 1214 condominium developments in Canada in the period of 1979-1998, showed that an increase in idiosyncratic and systematic risks lead developers to delay their investments. They found empirical evidence that a one-standard deviation increase in the return volatility lead to a reduction of investment by 13 percent. The negative relation between volatility and investment is also expected in the CAPM model, which tells that greater volatility will lead to a lower investment level due to an increase in the required rate of return of the investors. In order to separate the impact of the models, real options and CAPM, they decompose the volatility of condominium returns into idiosyncratic and market risk components. They find evidence that volatility has little impact in a competitive environment and that idiosyncratic risk has nearly no impact on the timing of investment. This likewise gives evidence to the advantages of real option models over the simple risk aversion of the CAPM model. Their research, therefore, shows that the real option framework is better to describe the profitability as well as the behavior of a real estate investment over the alternative models.
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4.9 Valuation of presale contracts. Larger building projects such as FredericiaC often use the strategy, “Presale System”, which means that they sell units before completion. This strategy reduces the risk and uncertainty for both parties as well as secure capital and loans to build the project. Thus, this opportunity is often of great importance, when constructing larger projects. The risk sharing secures the constructor, at least, a portion of the sale proceeds in the form of a down payment. We know from previous discussions that the value of a call option increases with an increase in uncertainty. This is also the case for the developer’s option to presale the apartment, if they want to reduce their risk. These sales contracts are therefore interesting in a case such as FredericiaC, where the demand is hard to estimate due to lack of similar assets in similar locations. By selling a contract before construction, the investor will reduce their dependence on the market condition and thus be better off if the market conditions worsen, but worse of market condition becomes more lucrative. The real option theory has shown that there are at least three ways to deal with risks associated with demand uncertainty. First, as described in the literature review, Titman (1985) showed the value of the option to delay the project, which was also examined in the case study. Second, the developer can construct in phases, where Sirmans et al. (1997) showed empirical evidence that risk-averse investors would increase the price by time as the early buyer faces more uncertainty about the project than later buyers do. The third method is to sell units before construction. This method is popular in many countries, including Denmark. Though the method is very popular in practice, little attention to the value and risk of a presale strategy can be found in the literature [lai et al. 2004]. A presale contract comes with a down payment, where the buyer pays a certain amount at a specified time of the project. This down payment can be seen as the cost of a call option for the purchaser, to later buy the apartment. If the buyer decides not to honor the contract, a forfeiture charge has to be paid. The constructor, therefore, is selling an option to the buyer to purchase the project at a fixed exercise price but require a premium if the buyer defaults to their obligation. To analyze the value of a presale contract, the structure of [Lai et al. 2004] is applied. They find empirical evidence that property prices follows a geometric Brownian motion: 𝑑𝑆 = 𝜇𝑆𝑑𝑡 + 𝜎𝑠 𝑆𝑑𝑊𝑠 Where μ is the risk-adjusted expected growth rate of the property price and σ is the standard deviation of the return on the asset. Their framework assumes that the buyers are risk neutral and thus, are indifferent between buying the house now or at completion. Lai et al. (2004) comes up with a closed-form solution in a two-payment case, where the buyer pays a down payment of 𝑄1 at time t=1 and can either pay the rest of the amount 𝑄2 at t=T to obtain ownership of the apartment, or pay a forfeiture charge to not comply to the contract of buying the apartment. It is assumed that the buyer is rational and will only pay the last payment if “𝑆𝑇 > 𝑄2 − Side 52 af 64
𝐴”, where S is the price of a similar asset and A is the forfeiture charge. The conditions for the calculations of the option price “C” can be seen in appendix 13. 𝐶(𝑆𝑡 , 𝑡) = 𝑆𝑡 [𝑁(𝑑 + 𝜎√(𝑇 − 𝑡) − ( Where d=
− 𝜂)𝑁(𝑑) − 𝜂]
(4.6)
−𝐿𝑛(𝑀−𝜂)−½ 𝜎2 (𝑇−𝑡) 𝜎 √𝑇−𝑡
Where M is the percentage of the expected spot price of the final payment, 𝜂 is the forfeiture charge of the expected spot price and N is the normal distribution. The value of the presale option for the purchaser at time t is then a function of the current property price and the present value of the last payment if paid, minus the possibility of paying the forfeiture charge. The presale option is different from a financial call option, as the premium/down payment can be deducted from the purchase price when it is exercised. To put the theory into practice, we can assume a contract to buy an apartment in phase one with 100 Sq.m and a square meter price of 23.000DKK. At time t=𝑡1 the buyer has to pay a down payment but gets the option to defer the second payment if the value gets below the forfeiture price plus the down payment. We can assume a forfeit charge of 5%, which the buyer has to pay if he does not pay the second payment. We can further assume that the second payment is 95% of the payment depending on the expected future spot price at the last payment. The value of the call option C(𝑆𝑡=1 , 𝑡) is the amount that the developer will require as the down payment, in order to have no arbitrage opportunities. The value of the option can thus be calculated using formula (4.6) and the option with a one year to maturity will thus have a value of 142.716 DKK. By increasing the forfeiture charge, we can see that the price of the call option decreases, which is due to the buyers fear of default.
4.9.1 Should a developer thus launch a presale? There are two significant benefits of selling apartments before completion for the constructor. First, it is often discussed that the constructors are risk-averse in the beginning, meaning that they would rather reduce uncertainty and are often willing to pay a price to avoid it. By selling the apartment before completion, the developers are less exposed to uncertainty. A developer will also have the benefit of not getting into financial distress, which in itself can also lead to significant costs. There would also be benefits in reducing marketing and caring costs by selling faster. To see if a developer should offer a presale contract we need to look at the expected payoff to the developer. The value of a pre-sale contract to the developer can be written as: V=𝑄+
𝐸(𝑆𝑇 ) = 𝐶(𝑆𝑡 , 𝑇1 ) +
𝑆𝑡1 𝑒 𝑟𝑓(𝑇−𝑡1)
(4.7)
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If the buyer defaults, the developer will receive the forfeit charge and resale the apartment at the current spot price. If the buyer does not default, the constructor will receive the second payment.
The payoff is analogous to having a synthetic option with different payoff patterns:
Scenarios
Payoff
𝑆𝑇 < 𝐶
η𝑆𝑡 𝑒 −𝑟𝛼
Not even resale is suitable.
𝑆𝑇 − 𝐶 + η𝑆𝑡 𝑒 𝑟𝑓(𝑇−𝑡)
Resale when default occurs
C