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Optimal Phasing and Inventory Decisions for Large-Scale Residential Development Projects

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Abstract

Land developers in select economic environments have been found to build in large increments and hold substantial amounts of inventory despite their ability to mitigate risk by phasing the production of residential lots. Such behavior was observed in numerous metropolitan areas throughout the southeastern and southwestern United States in the years leading up to financial crises, resulting in inventories of tens of thousands of lots in cities such as Atlanta, Las Vegas and Orlando, just to name a few. The model presented in this paper explores the rationale behind the choices made by developers in these markets and others by extending the real options framework to concurrently estimate optimal phasing and inventory decisions for large-scale residential development projects. Modeled interactions between several variables indicate that full development, smooth phased development and lumpy development can all be optimal under different market conditions, with each pattern feeding back into inventory levels and lot pricing.

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Notes

  1. The Atlanta Journal-Constitution reported over 150,000 vacant residential lots existed in the Atlanta metropolitan area in 2008 (August 8, 2008), while the Dallas Business Journal reported over 100,000 existed in the Dallas-Fort Worth metropolitan area at approximately the same time (August 17, 2008). More recently, inventories of developed lots exceeding 8–10 years of supply have been reported in metropolitan areas throughout Florida (Jacksonville Business Journal, November 19, 2010; Orange County Growth Management Department Outlook Report, October 2009). The Las Vegas Sun (March 1, 2009) reported developed residential lots selling for less than the replacement cost of the land improvements alone in subdivisions throughout Las Vegas and Phoenix due to dramatic oversupply that existed in 2009.

  2. Early theoretical studies completed by Hayashi and Trapani (1978) and Tompkinson (1979) attempt to quantify the benefits of holding inventory in the homebuilding industry when faced with uncertain demand, while considering the offsetting effects of carrying costs. The optimal inventory level for speculative homebuilders is identified in the former study by minimizing lost revenue and in the latter by minimizing construction costs. Demand is assumed exogenous in both models. These studies offer a foundation to begin examining optimal development strategies for residential land developers, but fall short of considering optimal phasing and inventory decisions concurrently in an uncertain economic environment.

  3. An empirical study completed by Sirmans et al. (1997) found evidence that single-family houses sell at a discount in the first phase of a subdivision, with prices increasing over subsequent phases as uncertainty is resolved.

  4. Titman’s (1985) seminal work examined the option to develop a parcel of land in a two-period setting, where both revenues and construction costs were presumed uncertain and development was anticipated to occur in an all-or-nothing manner. As expected, market volatility was found to increase the value of the development option, thereby increasing the opportunity cost of moving forward with a project immediately.

  5. Williams (1993) emphasized key differences between real options and more traditional financial options by modeling real estate development decisions in an environment where multiple firms facing uncertain demand and limited production capacity simultaneously invest in a land-constrained market knowing their choices will impact the decisions of other developers and ultimately market prices. Grenadier (1996) employed a similar equilibrium framework, allowing for simultaneous or sequential development by two competitive firms, to explain bursts of construction activity in volatile markets and prolonged periods of overbuilding in areas experiencing declining demand. Wang and Zhou (2006) extended the analysis by allowing for both sequential development and competition among multiple firms. The conclusions drawn in the theoretical models described are supported by numerous empirical studies. See Quigg (1993); Holland et al. (2000); Sivitanidou and Sivitanides (2000); Plantiga et al. (2002); Sing and Patel (2001); Cunningham (2006); Schwartz and Torous (2007); Towe et al. (2008), and Bulan et al. (2009).

  6. Cortazar and Schwartz (1993) consider phasing and inventory concurrently in an operations management setting by examining the compound real option created by a firm’s ability to engage in one stage of a sequential production process in order to create an option to engage in a second stage. They found optimal work-in-progress inventory levels increase with market volatility, despite inventory carrying costs, in order to reduce the risk of production bottlenecks in the event demand for finished goods spikes in the future. While informative, this model is not directly applicable to real estate development because the authors expect inventory to be held only to address inefficiencies in the production process, rather than to take advantage of economies of scale in construction, pricing power, and/or signaling effects. Appropriately specified real estate development models must also accommodate “time-to-build” constraints resulting from lengthy construction cycles, as well as supply constraints that exist when a developer controls a finite amount of land.

  7. Note that at any time t, the percentage of the total lots held in inventory plus percentage of the total lots sold plus the percentage of the lots remaining equals 1, i.e., \( {I_t} + {J_t} + {K_t} = 1 \). Thus, knowing any two of these auxiliary state variables provides the value for the third.

  8. Using Ito’s Lemma, the process for θ in the physical measure is \( d\theta /\theta = ({\mu_P} + \kappa (\ln \bar{\theta } + \alpha t - \ln \theta ))dt + \sigma \;dz \).

  9. The incoming inventories at time t = 1 nodes are I 1  = x 0 and J 1  = 1-x 0; for each of these nodes, the stored optimal values of x 1 and X 1 are returned and the incoming inventories at time t = 2 are updated \( {I_2} = {I_1} - {X_1} + {x_1} \) and \( {J_2} = {J_1} - {x_1} \). Given these inventories, for each node at time t = 2 the stored optimal values of x 2 and X 2 are returned and the inventories at time t = 3 are updated, etc. Because of the path dependency of the optimal strategies, the number of states grows exponentially with time: if the tree is constructed with k time steps over each phase then there will be \( {(k + 1)^t} \) states at time t. To compute the expected amounts to sell and develop each phase the true probabilities of the states and in particular the true probabilities of the nodes in the tree for ln θ must be found.

  10. Units represent a percentage of a project of any size.

  11. Elasticities for new residential construction are historically between 4 and 13 according to existing research. See Malpezzi and Maclennan (2001) and Green et al. (2005).

  12. Other levels of β were analyzed with similar results.

  13. This inventory cost is chosen because it best demonstrates the effects of varying the volatility level.

  14. Although most carrying costs are not expected to vary dramatically across geographic areas, property taxes in some jurisdictions are considerably higher than others. The U.S. Census American Community Survey (2008), for example, identifies property taxes in several counties surrounding Chicago, New York and San Francisco with property taxes 300% to 600% higher than the national average. The cost of holding undeveloped land for extended period of times may be extremely costly in these parts of the country, as compared to many parts of the Midwest or Southern United States.

  15. Galster (2001) noted that consumer preferences for homogenous neighborhoods, coupled with restrictive land use regulations, limits diversity in the housing stock in small geographic areas. This may reduce the importance of signaling effects in areas that already have observable characteristics due to previous residential development activity. However, signaling effects may be more important to buyers considering housing on the urban fringe who cannot look to surrounding subdivisions to predict the future characteristics of the area.

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Acknowledgements

Special thanks to Richard Buttimer, Francois Viruly and Walter Torous, as well as the participants of the 2010 American Real Estate Society Annual Meeting and the 2011 American Real Estate and Urban Economics Association Annual Meeting, for the feedback provided during the development of this paper.

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  1. Belk College of Business, University of North Carolina Charlotte, Charlotte, NC, 28223-0001, USA

    Steven H. Ott, W. Keener Hughen & Dustin C. Read

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  1. Steven H. Ott
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  2. W. Keener Hughen
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Correspondence to Steven H. Ott.

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Ott, S.H., Hughen, W.K. & Read, D.C. Optimal Phasing and Inventory Decisions for Large-Scale Residential Development Projects. J Real Estate Finan Econ 45, 888–918 (2012). https://doi.org/10.1007/s11146-011-9299-y

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