Valuing Real Options by Spreadsheet: Parking Garage Case ... - MIT

Valuing Real Options by Spreadsheet:Parking Garage Case ExampleRichard de Neufville, 1 L.M. ASCE, Stefan Scholtes, 2 and Tao Wang 3IntroductionA “real option” embodies flexibility in the development of a project. It represents a “right, but notan obligation” to take some course of action that may be advisable either if there is someunfortunate turn of events or some new opportunities. A “real option” thus represents either aform of insurance or a means to take advantage of a favorable situation. The use of real optionsoriginated in the field of finance (Myers, 1984) and has been developed for the use ofmanagement since the early 1990s (see for example Dixit and Pindyck, 1994; Trigeorgis, 1996;Amran and Kulatilaka, 1999; Copeland and Antikarov, 2001).Real options have more recently been applied to the design of infrastructure systems. Forexample, Leviakangas and Lahesmaa (2002) discuss their application to toll roads; and Ford et al.(2002) to strategic planning. Ho and Liu (2003) present a method for evaluating investments inconstruction technology; Zhao and Zheng (2003) provide an alternative approach and apply it toparking garages; Zhao, Sundararajan, and Tseng (2004) extend this work to highwaydevelopment; and de Weck, de Neufville and Chaize (2004) demonstrate how the use of realoptions could lead to major improvements in performance, on the order of 30%.However, real options have not been widely used in engineering practice. This is probably due tothe fact that the standard approaches to their analysis requires an understanding of financialtheory; advanced mathematical techniques (such as trinomial lattice and stochastic dynamic1 Professor of Civil and Environmental Engineering and of Engineering Systems, MIT, Cambridge,MA, 02139, U.S.A. (Corresponding author) Email: ardent@mit.edu2 Professor of Management Science, Judge Institute of Management, Cambridge University,Cambridge CB2 1AG, U.K. Email: s.scholtes@jims.cam.ac.uk3 Doctoral candidate, Engineering Systems Division, MIT, Cambridge, MA, 02139, U.S.A. Email:tao@mit.edu2

programming, Wang and de Neufville, 2004); and statistical data that are inaccessible to mostengineers. Moreover, even when practitioners are skilled in the use of the financial techniquesfor evaluating options, the results they produce are difficult to explain to the senior engineers andmanagers who are ultimately responsible for approving the configuration and design ofinfrastructure systems.To make the use of real options readily accessible to designers, this article proposes a simplespreadsheet model for estimating the value of real options in engineering systems. The modelhas three advantages compared to alternative procedures based on financial mathematics: ituses standard, readily available spreadsheet procedures; is based on data available in practice;and provides graphics that explain the results intuitively.Spreadsheet modelThis valuation of flexibility is based on standard discounted cash flow (DCF) analysis used toevaluate projects (see Riggs and West, 1986; de Neufville, 1990; White et al, 1998; DeGarmo etal, 2000). The process discounts future revenues and expenses to place them on a comparablebasis, typically the present. The sum of these discounted cash flows is the net present value(NPV). Engineers and managers regularly use computer-based spreadsheets, such as Excel®,to value projects.The process of estimating the value of real options using spreadsheets is simple and easy toexecute. Once the basic data have been placed in the spreadsheet, the calculations can be donein minutes. The authors have posted a version of the model at http://ardent.mit.edu/real_options.The process involves 3 steps:1. Set up the spreadsheet representing the most likely projections of future costs andrevenues of the project, and use the Data Table function to calculate its value for a rangeof design parameters to determine the optimum design for this deterministic case. The3

esult is the base case against which flexible solutions are compared, so as to derive thevalue of these alternative designs.2. Explore the implications of uncertainty by simulating ranges of possible scenarios (forexample, of the uncertain future revenues) using the Excel® random number generator,Rand(). Each scenario leads to a different NPV, and the collection of scenarios providesthe distribution of possible outcomes for a project. In general, a project that is worthwhileon average might turn out to be either unprofitable or highly profitable, depending on theactual circumstances. Use the Data Table function again to determine the best designwhen the future is uncertain, which is normally different than the one for the unrealisticbase case that assumes the future is known. (The difference is due to non-linearity in thedata, which means that the value of the project based on expected demand is not thesame as the expected value of the project based on actual values – Jensen’s Inequality,see Planetmath; Savage 2000)3. Explore the implications of various ways to provide flexibility by changing the costs andrevenues to reflect these design alternatives. The resulting expected values can becompared to the base case to define the value of flexibility. Moreover, the graphicaldisplay of the cumulative distribution of the results demonstrates the Value at Risk (VaR)or the worse cases that could occur. This information is often a key factor in decisionsabout the design of major projects.Practical DemonstrationAn application to a hypothetical design of a parking garage, inspired by Zhao and Tseng (2003),demonstrates the ease of use of the model. This situation was extrapolated from an actualproject in the Bluewater development in England (http://www.bluewater.co.uk/). It assumes thatthe car park is next to a new commercial center in a region that is growing as population expands.The basic data used are that:4

• The immediate demand is for 750 spaces, and is expected to rise exponentially byanother 750 spaces over the next 10 years;• Average annual revenue per space used will be $10,000, and the average operatingcosts (staff, cleaning, etc.) will be about $2,000 per year for each space available (notethat the number of spaces used is often lower than the spaces available);• The lease of the land will cost $3.6 Million annually;• The construction will cost $16,000 per space for pre-cast construction, with a 10%increase for every level above the ground level;• The site is large enough to accommodate 200 cars per level; and• The discount rate is taken to be 12%.Additionally, economic analysis needs to recognize that actual demand is uncertain, given thelong time horizon. The case assumes that the additional future demand could be 50% off theprojection, either way, and that its annual volatility for growth is 10%.The designers can design the footings and columns of the original building so that additionallevels of parking can easily be added, as was the case for the Bluewater development. The caseassumes that doing so will add 5% to the total initial construction cost. This premium is the priceto get the real option for future expansion, the right but not the obligation to do so.Step 1: Table 1 represents the basic spreadsheet for calculating the NPV of the parking garageassuming that the demand for spaces grows as projected. This particular version is for 6 levelsthat provides 1200 spaces. Note that when demand grows beyond the capacity of the facility itcannot benefit from addition demand.The Data Table function in Excel® enables the analyst to compute the NPV for parking garageswith many different levels, provided that the cost of construction and the capacity in thespreadsheet has been expressed as a formula in terms of the number of levels, as it has in this5

case. Figure 1 correspondingly displays the NPV for various levels of design for the deterministiccase. As can be seen, the optimal design for this base case, that unrealistically assumes thatdemand is known in advance, is to build 6 floors. The NPV in this case is $6,238,417.[Table 1 and Figure 1 about here]Step 2: Recognizes the uncertainty in the forecast demand by simulating possible scenarios.The analysis applies the Rand() function and uses the Data Table functions to change the inputdemand. This example analysis ran 2000 scenarios, which took about 1 minute on a standardPC. Figures 2 illustrate the results for a 5-level design both in terms of a histogram representingthe probability distribution (PDF), and the associated cumulative probability diagram (CDF). Theexpected results for different levels of design appear in Figure 1.This analysis provides useful insights that motivate the use of flexibility. It shows that:• Uncertainty can lead to asymmetric returns. In this case, although the chance of higherand lower demands are equal, the upside value of the project is limited (because thefixed capacity cannot take advantage of higher demands) while the downside risks aresubstantial and can lead to great losses.• The expected value of the project when uncertainty is recognized is thus not equal to itsvalue in the deterministic case (as Figures 1 and 2a indicate).• The CDF in Figure 2b shows the Value at Risk (VaR), that is, the chance that a loss willexceed any specific threshold. It shows for example that there is about 10% chance thatthe losses from a 5-level parking garage would equal or exceed $4 million.[Figures 2 and 3 and Table 2 about here about here]Step 3: In this phase the analyst explores ways to limit the downside risk (VaR) and takeadvantage of upside potential. For example, the above analysis easily shows how the designers6

can reduce the VaR by creating smaller designs that lower the chance that demand will not fill thefacility. Using the available information, Figure 3 compares the cumulative distribution function ofNPV for 4-floor design and 5-floor design. In this case, the smaller design eliminates the chanceof really big losses, but at the cost of never making any substantial profit. Thus, although buildingsmaller provides good insurance against losses, it is not sufficient to make the project attractive.The analyst can explore options to take advantage of possible growth by building these designsinto the spreadsheet. This case considered the possibility of making the columns big enough tosupport additional levels, should demand justify expansion of the parking garage in later years.(This is exactly what was done in the parking structures for the Bluewater development.) Table 2shows the appropriately modified spreadsheet. It incorporates 3 additional rows for “Decision onexpansion”, “Extra capacity”, and “Expansion cost”. For this example, the “Decision onexpansion” is based on the criterion that the capacity is less than the demand for two consecutiveyears, and the assumed decision rule is to construct 2 extra floors or 400 spaces. (This is just anexample, other criteria and rules could be programmed in.)The value of this call option that permits expansion in the case of favorable demand is shown inFigure 4. The capability to add capacity adds greatly increases both the maximum value of theproject (up to almost $30 million) and its expected value (about $10 million). The estimated valueof the option is the difference between the expected value with the option ($10,517,140) and thatwithout (-$28,800), that is $10,488,340 in this case.Beyond the expected value of the option, the flexibility provided by building small at the start withthe option to expand has several further advantages. The spreadsheet approach to the analysisof the value of options brings these out, as the financial approaches to calculating only value donot. As Table 4 indicates, the flexible approach to the design of this facility:• Reduces the maximum possible loss, that is the Value at Risk;• Increases the maximum possible and the expected gain;7

• While maintaining the initial investment costs low.[Figure 4 and Tables 3 and 4 about here]ConclusionA spreadsheet model for the valuation of real options is easy to use and provides insight into theway that flexibility in design minimizes exposure to risk and maximizes the potential for gainunder favorable circumstances. Compared to alternative approaches that require advancedmathematics and financial concepts, and that focus narrowly on the expected value of an optionand ignore the ways options change the distribution of outcomes, the spreadsheet approach isboth much easier to use and more useful. Because the spreadsheet model for the valuation ofreal options rests on tools and data that are readily available to practicing engineers andmanagers, it should be accessible and useful to them.AcknowledgementsThe authors appreciate the advice of senior staff of Laing O’Rourke (UK) who worked with thelead authors on the application of the spreadsheet model, and its validation through practicalexamples, during the Cambridge-MIT Institute Workshop on Real Options in May 2004.ReferencesAmram, M. and Kulatilaka, N. (1999) Real Options - Managing Strategic Investment in anUncertain World, Harvard Business School Press, Boston, MA.Copeland, T. and Antikarov, V. (2001) Real Options - A Practitioner's Guide, TEXERE, New York,NY.DeGarmo, E. et al (2000) Engineering Economy, 11 th Ed., Prentice-Hall, Upper Saddle River, NJ.de Neufville, R. (1982) “Airport Passenger Parking Design,” ASCE Journal of UrbanTransportation, 108, May, pp. 302 – 306.8

de Weck, O., de Neufville, R. and Chaize, M. (2004) “Staged Deployment of CommunicationsSatellite Constellations in Low Earth Orbit." Journal of Aerospace Computing, Information, andCommunication, Mar., pp. 119-136.Dixit, A. and Pindyck, R. (1994) Investment under Uncertainty, Princeton University Press,Princeton, NJ.Ford, D., Lander, D. and Voyer, J. (2002) “A Real Options Approach to Valuing StrategicFlexibility in Uncertain Construction Projects,” Construction Management and Economics, 20, pp.343 – 351.Ho, S. and Liu, L. (2003) “How to Evaluate and Invest in Emerging A/E/C Technologies underUncertainty,” J. of Construction Engineering and Management, 129(1), pp. 16 – 24.Leviakangas, P. and Lahesmaa, J. (2002) “Profitability Evaluation of Intelligent Transport SystemInvestments,” J. of Transportation Engineering, 128(3), pp. 276 – 286.Myers, S. (1984) “Finance theory and financial strategy.” Interfaces, 14, Jan-Feb, pp. 126-137.Trigeorgis, L. (1996) Real Options: Managerial Flexibility and Strategy in Resource Allocation,MIT Press, Cambridge, MA.Planetmath.org “Jensen’s Inequality.” http://planetmath.org/encyclopedia/JensenInequality.htmlRiggs, J. and West, T. (1986) Engineering Economics, McGraw-Hill, New York, NY.Savage, S. (2000)”The Flaw of Averages,” San Jose Mercury, Oct. 8,http://www.stanford.edu/dept/MSandE/faculty/savage/FOA%20Index.htmWang, T. and de Neufville, R. (2004) “Building Real Options into Physical Systems withStochastic Mixed-Integer Programming.” 8 th Annual Real Options International Conference,Montreal, Canada. http://www.realoptions.org/papers2004/de_Neufville.pdfWhite, J. et al (1998) Principles of Engineering Economics Analysis, John Wiley and Sons, NewYork, NY.Zhao, T., Sundararajan, S., and Tseng, C. (2004) “Highway Development Decision-Making underUncertainty: A Real Options Approach,” J. of Infrastructure Systems, 10(1), pp. 23 – 32.Zhao, T. and Tseng, C. (2003) “Valuing Flexibility in Infrastructure Expansion.” J. of InfrastructureSystems, 9(3), pp. 89 – 97.9

TablesTable 1. Discounted Cash Flow Model (6 levels)Year0 1 2 3 19 20Demand 750 893 1,015 1,688 1,696Capacity 1,200 1,200 1,200 1,200 1,200Revenue $7,500,000 $8,930,000 $10,150,000 $12,000,000 $12,000,000Recurring CostsOperating cost $2,400,000 $2,400,000 $2,400,000 $2,400,000 $2,400,000Land leasing cost $3,600,000 $3,600,000 $3,600,000 $3,600,000 $3,600,000 $3,600,000Cash flow $1,500,000 $2,930,000 $4,150,000 $6,000,000 $6,000,000Discounted Cash Flow $1,339,286 $2,335,778 $2,953,888 $696,641 $622,001Present value of cash flow $32,574,736Capacity costs for up to two levels $6,400,000Capacity costs for levels above 2 $16,336,320Net present value $6,238,416Table 2. Discount Cash Flow Model for 4 level design with embedded expansion option (forone demand realization path)Year0 1 2 3 19 20Demand 820 924 1,044 1,519 1,647Capacity 800 800 1,200 1,600 1,600Decision on expansionexpandExtra capacity 400Revenue $8,000,000 $8,000,000 $10,440,000 $15,190,000 $16,000,000Recurring CostsOperating cost $1,600,000 $1,600,000 $2,400,000 $3,200,000 $3,200,000Land leasing cost $3,600,000 $3,600,000 $3,600,000 $3,600,000 $3,600,000 $3,600,000Expansion cost $8,944,320Cash flow $2,800,000 -$6,144,320 $4,440,000 $8,390,000 $9,200,000Discounted Cash Flow $2,500,000 -$4,898,214 $3,160,304 $974,136 $953,734Present value of cash flow $30,270,287Capacity cost for up to two levels $6,400,000Capacity costs for levels above 2 $7,392,000Price for the option $689,600Net present value $12,878,287Table 3. Results from the Spreadsheet ModelPerspective Simulation Option Embedded Design Estimated Expected NPVDeterministic No No 6 levels $6,238,416Recognizing Uncertainty Yes No 5 levels $3,536,474Incorporating Real options Yes Yes4 levels with strengthenedstructure$10,517,140Table 4. Comparison of Results with and without OptionsDesign With Options Without Options Comparison(4 levels, strengthened structure) (5 levels)Initial Investment $18,081,600 $21,651,200 Better with optionsExpected NPV $10,517,140 $3,536,474 Better with optionsMinimum Value -$13,138,168 -$18,024,062 Better with optionsMaximum Value $29,790,838 $8,316,602 Better with options10

FiguresExpected NPV ($, Millions)1050-5-10-152 3 4 5 6 7 8 9Number of FloorsTraditional NPVRecognizing uncertaintyFigure 1. Expected NPV for Different Design (Number of Floors)600Frequency5004003002001005-floor designSim ulated Mean6-floor designDeterm inisticResult0-17.8 -15.6 -13.5 -11.3 -9.2 -7.0 -4.9 -2.7 -0.6 1.6 3.7 5.9 8.0Figure 2a. Histogram or Probability Distribution Function for NPV’s (in $, millions) for 5-level design recognizing demand uncertainty compared to deterministic optimal design11

10.90.8Probability0.70.6CDF for Result of0.5Sim ulation Analysis (5-0.4floor)Implied CDF for0.3Result of0.2Determ inistic NPV0.1A l i (6 fl )0-20 -15 -10 -5 0 5 10Figure 2b. Cumulative Distribution Function for NPV’s (in $, millions) for 5 level designrecognizing demand uncertainty compared to deterministic optimal designProbability10.90.80.70.60.50.40.30.20.10-20 -15 -10 -5 0 5 105-Floor Design4-Floor DesignFigure 3. Reduction of Downside Risk by Designing Smaller…12

100.0%Probability90.0%80.0%70.0%60.0%50.0%40.0%30.0%20.0%Mean for NPVwithout OptionsCDF for NPVwithout OptionsCDF for NPVwith OptionsMean for NPVwith Options10.0%0.0%-30 -20 -10 0 10 20 30 40Figure 4. Option to expand adds significant value to design13