Existing Option Pricing Methods - Case Study Example

How can we use real options in the pricing of real e Standard financial options like puts and calls on stocks and financial indices are familiar terms and often, real options too have similar characteristics. However, real options are not derivative instruments, but actual options that involve choices that become available upon undertaking certain business activities. Existing option pricing methods are useful in valuing real options, but they are different in that a real option confers a right, but not the obligation, to undertake one or more specific actions at specified costs, spread out over a predetermined time period. Real options have been in existence since centuries and the earliest references are found in the story of Thales, a Greek philosopher. Thales predicted a bumper olive harvest and paid a large premium to local olive refiners for the right to hire their entire olive pressing facilities for a specified fee during that year's harvest season.'Thales however did not have the obligation to use the facilities and had the option to let his right lapse if he chose to do so, at the cost of losing the premium he had paid already. The bumper crop did take place and Thales exercised his real option. He allowed other producers to use the facilities he had got at a predetermined price, but at a large additional premium. Thales is said to have profited immensely by his use of the real option. Real options in real estate are best illustrated by examples. Consider a prospective home owner who identifies a dream home available at an attractive price. Several others too would have arrived at the same conclusion and may be ready to make competitive offers. The first homeowner however does not have his finances tied up and needs a fortnight to get it done. Waiting for a fortnight may push the dream home into another's possession, a situation that throws up the concept of a real option. The prospective owner could offer the seller a sum of money just to hold the property for the two weeks he needs to arrange the funds and buy the home at the offering price. If the funds don't come through or if he changes his mind, he loses the money paid, while the seller keeps the sum of money and can easily find another buyer from among the numerous others interested in buying the property. Just how much the sum paid should be involves putting a value on the real option. A similar situation may arise in the case of a real estate development company holding vacant land. The possession of vacant land confers a right or an option, but not an obligation, to develop a completed building at a future date. The value of vacant land is a consequence of this right to develop an asset, the completed construction, at a price, the cost of construction. The decision to build or not and when to build if at all, are subject to several uncertainties. The future value of the constructed building may be uncertain - if property values rise, the builder is more certain of profits, while lower values at a specified time may justify delaying construction by avoiding potential losses. Delaying the construction may make more information available, allowing for a change in land utilization, nature of the project, tenant mix, funding options etc. The option to wait itself becomes valuable. Thus the uncertainty by itself has value, and if that value can be quantified, the decision making process would become more accurate. Real options analysis thus assumes relevance and importance in real estate pricing by allowing a value to be put on uncertainty. The value of the real option increases when uncertainty about the future value of the built property increases. Thus, development of the property will take place when the value of the completed project exceeds the costs by a premium determined by a combination of uncertainty of asset value, irreversibility of the development and the choice of waiting. In many cases, projects that might have been dropped as unviable become attractive when associated real options are evaluated and quantified. In a sense, real option analysis provides a scientific alternative to intuition that is so prevalent on real estate ventures. The Black Scholes Model, developed by Fisher Black, Robert Merton and Myron Scholes is an important concept in modern financial theory and is regarded as one of the best ways of valuing options. Several variations of the original model are in use for specific applications. Real options are yet to become a standard method for evaluating real estate. It is somewhat new to the real estate business and there is much scope for developing suitable intuitive, thorough and transparent models. (Amram and Kulatilaka, 1999) The concept of putting a value on uncertainty or intangibles is by itself an idea that most people will get used to only over a course of time. There is no doubt that real options are a very useful tool for all real estate investments, but the actual methodology involves many aspects that individual investors may find difficult to understand, much less implement. Most literature on the subject illustrates the use of real options in deciding that an otherwise unviable project could be taken up. No examples of real options indicating a decision to drop a project are seen in commonly accessible literature. No hard proof of the actual veracity of the predictions based on real options analysis could also be found among published literature. Real options are of immense use to commercial real estate users. They enable them to fit real estate investment and management policies with primary management objectives, and to make choices from among site locations, forms of ownership and capital structures. Premature investment and missed opportunities can also be avoided. Traditional methods of evaluating a real estate business opportunity involve assessing the project's net present value (NPV). Cash flows over a period of time are forecast and discounted at required rates-of-return, which in turn depends on the risk associated with the cash flow. The present values of future cash inflows and the expected cost outflows are compared. Their difference is the NPV. If NPV is zero or positive, the project goes through, and when it is negative, the project is dropped. Decisions based on NPV are isolated from the dynamics of the market. Cash flows may be different from originally anticipated, and new developments may open up new opportunities to capitalize upon or even to minimise potential losses. These are the real options in real estate pricing and investments. Real estate value with real options considered must then be worked out and finally linked to the NPV valuation to arrive at an overall valuation of the investment opportunity. (Ott: http://www.belkcollege.uncc.edu/real_estate/pdf/Real%20Option%20Review%20and%20Valuation.pdf) "Real property options are among the earliest modeled real options, with now six primary practical uses: planning, investment timing, leasing, operations, funding and industry strategy. Property research options are used in the early stages of design and planning. Investment options are essential models for deciding the time and density of land conversion and construction. Leasing options govern the alternatives and trade-offs between short-term and straight rentals, upward only arrangements, and general landlord and tenant terms. Operating options include tenant mix and space options, maintenance expenditures, and alternative use and upgrading decisions. Funding options cover the choices between debt and equity funding, including the many varieties in between, as well as the insurance, default and prepayment options in mortgages and mortgage-backed-securities. Finally, property industry strategy real options view patterns of the timing of innovation and new developments, in the context of competition and rent cycles". (Patel and Sing, 2005: http://www.rics.org/Property/Propertyappraisalandvaluation/review_of_practical_uses_real_property_options.html) The use of real options in real estate pricing can be illustrated by a case study reported by Steven H Ott, detailed as Appendix. (Ott: http://www.belkcollege.uncc.edu/real_estate/pdf/Real%20Option%20Review%20and%20Valuation.pdf) The case study illustrates all the nuances of the use of real options in pricing real estate. The reversal of a traditionally acceptable decision based on sound scientific principles is almost tantamount to making intuition scientific. In fact, development of real options valuation has even led to the justification of seemingly risky ventures and help explain the successes of many old unexpected successes. The values worked out indicate the limits of price flexibility available. However, it also illustrates that valuation of real options involves some elements of advanced mathematics, often beyond the capabilities of individual investors in real estate. Several assumptions have also to be made, and the margin of error in these assumptions is crucial. Another moot point is whether every possible scenario can be anticipated. It also remains to be proved how negative valuations of uncertainty and certainty of fall in value will be translated in real options analysis. Very few quantitative studies dealing with valuation of real estate projects using the real options method have been conducted or are available. Practical valuations have to be carried out extensively, covering all possible scenarios and validated over time to make the real options method more acceptable. Sheridan Titman has presented a model for pricing vacant lots in urban areas taking into account the possible building sizes and appropriateness of the constructed buildings at different points of time. It can be seen that as uncertainty about future prices increases, the real option becomes more valuable, but causes a decrease in building activity at the present period. The model also suggest a method to value houses that may be demolished for bigger buildings, and a method to determine the optimum time to pull down an old house to make way for a new and larger building. It goes so far as to claim that the model can predict the optimum conditions to renovate apartment houses or convert them. The mathematical processes involved in the model are complex, but the utility of the model in widely different conditions and situations make it an exciting method. (Titman, 1985: http://www.jstor.org/view/00028282/di950045/95p0050y/0) Despite the excitement, there are several problems associated with real options valuation. Estimating probabilities accurately is one, and gaining trust among investors as a valid method of valuation is another. However, investors have begun to take note of hidden value in assets and investments and the time factor in valuation. (http://www.investopedia.com/articles/03/012803.asp). Another danger inherent in the use of real options is the possibility of unscrupulous real estate developers manipulating calculations and assumptions to make an otherwise unviable proposal look attractive. It would be a mistake to discard real options in pricing real estate because of these inherent dangers. Attempts must certainly be made to overcome these shortcomings and make the concept acceptable and accessible to even individual investors. Two possible solutions suggest themselves. The first is the possibility of independent agencies on the lines of credit rating agencies that could evaluate real options for a fee, for any investor. The key factor here would be the credibility of the agency and its independence. Credibility will take time to get established since results alone can finally convince users about the real value of real options, something that may take years. The second option to make the use of real options widespread is much more easier to implement. Software incorporating all the possible scenarios and levels of optimism or pessimism can be developed. The software would need to guide the user in making a proper choice of possibilities. These possibilities may be chosen by the user according to individual perceptions and comfort levels and the actual calculations could be carried out quickly and accurately by the software. This option also allows a user to compare results of different scenarios by changing the parameters any number of times without actually making tedious calculations. The user has the satisfaction of arriving at an own decision. The issue of credibility could be overcome by this route. Payment based use of the software could be made available through a webportal and users need not have to reveal sensitive commercial information since names and locations would not be necessary for such use. Once the concept proves its utility, there is no doubt that real options will play an important part in deciding prices of real estate. "As property investors gradually embrace modern financial concepts it is clear that real estate valuation theory will have to change. One of the most promising areas that could have an important implication on the further development of valuation is the application of the real options paradigm". (Lucius, 2001) Appendix: CASE STUDY "Description of the Project: The project is situated in Charlotte, North Carolina. About 200 units designed with busy professionals in mind, were planned, spread out over more than 20 acres. A Charlotte regional development firm was attempting to replicate a successful project in Atlanta, Georgia, with a high concentration of similar busy professionals. Considering the similarities between the demographic profile of Atlanta and Charlotte, the chances of success were considered quite high. Land was to be developed into lots ready for building, and sold to homebuilders. Added impetus came from the developer's belief that success in Charlotte could be the precursor for more identical projects in the nearby areas. The know-how got from the Charlotte project and the flexibility thus acquired would be a real option. Actually, it would be a growth option since success would create a right, but not an obligation to develop more such projects elsewhere. The project faced several uncertainties on several counts. The cost of developing the land for the purpose was uncertain because this was the first project of its kind in Charlotte. Reasons were excessive earth moving, greater design difficulties, closer tolerances and utility conflicts, which made the lot-to-finished home price ratio an unprecedented 30% or $30,000 per lot. Timing and sale price were uncertain since the builder who was to purchase the lots was new to Charlotte and lacked prior acceptance. Being a special type of project, finding an alternate builder would be difficult if the first builder abandoned the project. Product demand was also uncertain, being a new type of housing product. These multiple uncertainties prompted the developer to want to quantify them and consider the value of the growth option in the financial analysis and the decision making process. This was achieved by valuing the project using the traditional NPV method first, and then the value of the growth option, after which the two were linked to arrive at the overall valuation. NPV analysis calculates the expected net present value of the project assuming that there are no real options. The expected NPV is arrived at by calculating the present value for each of the potential outcomes (scenarios) and then using the associated subjective probabilities for each scenario to calculate an expectation. Since the outcome of the project is highly uncertain, scenario analysis helps quantify the associated risks or uncertainties of the project. It also allows for the calculation of the variance of the values, as these variances will be needed for calculating the value of the growth option. The probabilities and explanations of the scenarios for the project are shown below: Probability Distribution Table for the Project Scenario Probability weight Explanation Very Optimistic 15% Project is very successful Optimistic 20% Project is successful Base Case 30% Project meets basic revenue and cost expectations Pessimistic 20% Project performs below expectations Very Pessimistic 15% Project is very unsuccessful The project's expected revenues and costs for each scenario are calculated. The project's NPV is the difference between the present value of its future cash inflows, and the present value of the project's expected cash outflows (costs). Both inflows and outflows are discounted at a rate that reflects the systematic risk of these expected future cash flows. The summary of the present value of revenues and costs as well as the corresponding probability-weighted expected NPV calculation for the project are given below: Present Value Calculation of Revenues and Costs for the Project Scenario Probability Weight PV of Lot Sale Revenues PV of Development Costs Very Optimistic 15.00% $6,409,826 $3,346,165 Optimistic 20.00% $4,273,217 $3,691,101 Base Case 30.00% $4,138,809 $3,990,728 Pessimistic 20.00% $2,574,837 $4,241,336 Very Pessimistic 15.00% $1,685,679 $4,495,500 Expected Present Value $3,825,579 $3,959,956 An annualized discount rate of 11.5% was used in calculating the present value of the lot sale revenues. An annualized discount rate of 6%, the risk-free rate, was used in calculating the present value of costs. The traditional NPV for the project is thus -$134,377 ($3,825,579 - $3,959,956). The project would thus have to be rejected under the traditional NPV decision rule. However, if the project were to be successful, the developer would be able to replicate the project, and this opportunity confers an additional value on the project, the value of the real option or the growth option in this case. After calculating the value of the option, the NPV and option analysis can be linked to ascertain the overall valuation of the project. Real Options Analysis - Valuation of the Growth Option Since options on real assets behave similarly to options on financial assets, the value of real options can be ascertained using similar valuation methodologies used for options on financial assets. Because in this case the value of the completed project and the development costs are uncertain, the growth option was valued using a variant of the Black-Scholes Option Pricing Model; specifically, the formula for an exchange option was used. The growth option attached to the project, denoted as G, will be valued using the standard exchange-option formula: G = S0N(d1) - X0 N(d2) where, S0= the time-zero expected present value of the replicated project's cash inflows. X0= the time-zero present value of the cash outflows, i.e., the expected development costs required to replicate the project. N is the cumulative standard normal distribution function. = the length of time that the firm can defer a decision with respect to commencing an investment in the replicated project. , is the standard deviation of the ratio of revenues to costs. = the annualized standard deviation of the return on the value of the replicated project, S. = the annualized standard deviation of the return on the value of the costs, X. = the correlation between the return on value, S, and the return on costs, X. The present values of cash inflows and costs for the project calculated earlier are: S0= $3,825,579 X0= $3,959,956 corresponds to the amount of time in years that the firm has to exercise the growth option. If the time frame to complete the initial project is 3 years, a minimum of 3 years is needed to determine demand for the lots and the financial success of the project. The maximum time to exercise the option is usually finite due to competitive forces that can enter the market. For this project, 5 years is the "window of opportunity" estimated to be available to exercise this option. Standard deviations for the returns on revenues and costs are obtained by calculating internal rates of return (IRR's) on the cash flows for each scenario. The initial cash flow in the calculation of IRR assumes that revenues and costs can be theoretically "purchased" (i.e., a cash outflow is incurred) for their time zero expected values, i.e., S0 = $3,825,579 and X0 = $3,959,956. Subsequent cash flows are than based on the projected revenues and costs for each scenario. Once the IRRs are determined for the scenarios, annualized standard deviations for these returns can be calculated. A summary of the IRR's is shown in Tables 1 and 2 Table 1 Inputs for the Calculation of the Annualized Standard Deviation of the Return on Completed Project Value Scenario Probability IRR Very Optimistic 15.00% 32.86% Optimistic 20.00% 26.83% Base Case 30.00% 14.24% Pessimistic 20.00% -2.11% Very Pessimistic 15.00% -16.28% Expected Revenue IRR 11.70% Table 2 Inputs for the Calculation of the Annualized Standard Deviation of the Return on Development Costs Scenario Probability IRR Very Optimistic 15.00% -7.32% Optimistic 20.00% 0.47% Base Case 30.00% 6.59% Pessimistic 20.00% 11.24% Very Pessimistic 15.00% 15.72% Expected Cost IRR 5.58% The net revenues from the sale of the lots are based on market demand for the built housing product; therefore, these revenues are not related to the costs of developing the lots for sale. Thus, it is assumed that the correlation between the return on value and the return on costs, ', is 0. After obtaining values for d1 and d2, the respective values are used to obtain values for N(d1) and N(d2). N(d1) and N(d2) represent areas under a standard normal distribution function. The values of the normal distribution are obtained from statistic textbooks or found using an Excel spreadsheet program. Calculating the Value of the Growth Option Table 3 shows all of the necessary inputs to obtain a valuation of the growth option along with the final calculated value of the growth option. Note that after calculating the standard deviation of the return on revenues and costs using the data from Tables 1 and 2, the result must be annualized by dividing by the square root of the time for initial project completion (3 years). The value of the option based on the underlying assumptions and the corresponding inputs is $296,142. Table 3 Growth Option Valuation Model for the Project Present Value of Sales Revenues $3,825,579 Present Value of Costs $3,959,956 Time to exercise the option T 5 years Annualized Standard Deviation of Revenues 9.49% Annualized Standard Deviation of Costs 4.18% Correlation between Revenues and Costs ' 0 Standard Deviation of the ratio of revenues to costs 10.37% d1 -.0329 d2 -.2648 N(d1) .4869 N(d2) .3956 Calculated Value of the Growth Option G $296,142 The final present value of the development project, including the growth option, is found by simply summing the traditional NPV value and the value of the growth option. Table 4 summarizes this calculation. Table 4 Linking the Growth Option to NPV analysis NPV of Project without growth option -$134,377 Value of growth option $296,142 NPV including growth option $161,765 The Investment Decision It is seen that the option value is approximately 8% of the completed project value. While the traditional NPV of the project is negative and indicates that it should be rejected, the inclusion of the growth option in the analysis changes this decision since with the growth option, the project has a positive NPV. In this case, the development and investment in the new project provides the developer with valuable information that may be able to be used to undertake an additional positive NPV project. The value of this future investment opportunity overcomes the initial project's negative NPV." (Ott:http://www.belkcollege.uncc.edu/real_estate/pdf/Real%20Option%20Review%20and%20Valuation.pdf). Works Cited Amram, Martha and Kulatilaka, Nalin (1999). CSFB: Real Options. Harvard Business School Press. Ott, Steven H. Real Options and Real Estate: A Review and Valuation Illustration. Belk College of Business Administration University of North Carolina at Charlotte. http://www.belkcollege.uncc.edu/real_estate/pdf/Real%20Option%20Review%20and%20Valuation.pdf (accessed January 5, 2007). Patel, Kanak and Sing Tien Foo, 2005. A review of the Practical Uses of Real Property Options. http://www.rics.org/Property/Propertyappraisalandvaluation/review_of_practical_uses_real_property_options.html (accessed January 6, 2007). Titman, Sheridan: 1985. Urban Land Prices under uncertainty. The American Economic Review: 75 (No.3): 505-514. http://www.jstor.org/view/00028282/di950045/95p0050y/0 (accessed January 7, 2007). Pin Down Price with Real Options. 2006. http://www.investopedia.com/articles/03/012803.asp (accessed January 2, 2007). Lucius, 2001. Real Options in Real Estate Development: Journal of Property Investment and Finance, Volume 19, Number 1, pp. 73-78(6): Emerald Group Publishing Limited. Read More