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Christopher CannaNovember 29, 2010

Urban Expansion Controls and Real Options Valuation

Low-density sprawl is one of the most defining features of city growth in the industrial and post-industrial era, and is often blamed on the failure of authorities to deal with the negative externalities of urban growth, including congestion/pollution, loss of public space and increased infrastructure burdens on local governments (Bluffstone, 435; Krugman). Attempts to control urban growth and mitigate its negative affects typically fall into one of two categories: price mechanisms (impact fees) and quantity mechanisms, (land-use restrictions and urban growth boundaries). Both of these mechanisms are designed to discourage sprawl by bringing the benefits of urban growth in line with its social costs. Price mechanisms are policies that directly increase the price of development so that it reflects social costs. Quantity mechanisms, on the other hand, directly proscribe density levels that are considered socially desirable.

Evidence of economically significant real option values in undeveloped land prices suggests that these policies are not as effective in areas where real options valuation is appropriate. By limiting future development alternatives these policies reduce uncertainty, and, therefore, the real option value in undeveloped land. As a result, a developer’s incentive to wait is reduced and development may accelerate, thereby mitigating the effectiveness of policy meant to curb development.

The Negative Externalities of Sprawl

The negative affects of urban growth are often lumped together under the general heading of “sprawl” and are at times difficult to identify and quantify. For example, the architectural homogeneity typical of sprawl greatly bothers some people, but not others (Bluffstone, 436). Despite this, three negative externalities of excessive urban growth are widely accepted: congestion/air pollution, loss of open space, and overburdened public infrastructure (Bluffstone, 437). These negative externalities result from market failures that allow individuals to avoid paying the full cost of their housing decisions.

When making housing decisions, developers and households receive benefits, such as profits and larger homes, by degrading public resources, such as open space and public infrastructure. This is represented in Figure 1 by the marginal benefit (MB) curve, which is downward sloping, because earlier migrants receive greater benefits than later migrants, such as lower land prices or better views. Social costs, like increased congestion and loss of public land, are represented by the marginal public cost (MPC) curve, which slopes upward to reflect increasing damages like the development of increasingly sensitive land. (Bluffstone, 435)

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In the absence of limiting public policy, developers and migrants would degrade public resources until they receive no net benefit, meaning until MB = 0 (Bluffstone, 436). At this point, however, social costs greatly exceed private benefits as is shown at point B. Ideally, development should only occur in a manner that maximizes social welfare meaning the intersection of the marginal benefit and marginal public cost curves, shown at point A. Despite differing opinions about its specific negative qualities, sprawl can be generally defined as urban development where marginal public costs exceed benefits, i.e. the space between points A and B.

When marginal public costs are higher than marginal benefits, it is because developers

and households do not account for the full social costs of their housing decisions. For example, when a household chooses a place to live that requires a long commute, it typically considers the private costs of that commute, like personal commute time and vehicle operating expenses. It often fails, however, to consider the social cost of its commute in terms of the time lost by others due to the presence of an additional car on the road, and air pollution caused by an additional tailpipe (Bluffstone, 437; Krugman). To the extent that public policy fails to internalize negative externalities, like congestion, it subsidizes sprawl by covering social costs for private actions.

MSC

MB

Impact Fee

Public Resources Lost

Ben

efits

and

Cos

ts $

0 A B

Figure 1: Marginal Benefits and Social Costs of Sprawl

Point A represents equilibrium between marginal benefits and marginal social costs and therefore represents maximum social welfare. At every point to the right of point marginal social costs exceed marginal benefits. In terms of urban expansion this area represents urban sprawl, or undesirable growth.

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Attempts to Correct Externalities

Price and quantity mechanisms are two policy options available to local governments interested in correcting market failures and changing the spatial pattern of urban growth so that the social costs of growth are nearer to equilibrium with its benefits.

Impact fees are a common price mechanism used to compensate for increased demand on public infrastructure, such as schools, roads, and police, caused by new development. For legal reasons, these fees do not typically represent the total social costs of new development (Bluffstone, 444). In theory, however, local governments could use development fees to force developers and households to factor social costs into their housing choices by setting fees at a level where marginal benefits equal social costs (See Figure 1). By internalizing social costs into the cost of development, any development below the equilibrium point would be discouraged. This process is analogous to gasoline taxes in Europe, which are set at a level that internalizes the negative externalities caused by driving, such as congestion and air pollution. As a result, individual drivers are discouraged from driving excessively and encouraged to use fuel-efficient vehicles (Bluffstone, 443).

Unlike price mechanisms, quantity mechanisms directly affect the type of development allowed by legally proscribing an intensity of land-use in line with marginal social costs. An urban growth boundary is a well-known example of a quantity mechanism used to control urban growth. Urban growth boundary’s attempt to redirect growth away from rural land and toward existing urban areas by limiting the maximum density allowed in rural areas (Cunningham, 343). For example, Washington state requires certain counties, including Seattle’s King County, to create boundaries segregating areas for high density urban use and low-density rural use. A maximum allowable density of one residence per five acres is allowed in rural areas, and a maximum density of one residence per 80 acres is allowed in forest/resource areas (Cunnignham, 346).

By limiting allowable housing density in rural areas, undeveloped agricultural land becomes relatively more profitable, which may prevent housing development from occurring. However, even if development proceeds, these restrictions ensure that it takes a form the local government has deemed an appropriate balance between benefits and social costs. Impact fees cannot achieve this level of effectiveness, because they ultimately allow undesirable development provided a household is willing to pay the monetary cost for their actions. Conversely, a potential downside of quantity mechanisms is that they are very inflexible in the face of demand shocks and can greatly increase the price of land in side the growth boundary (Guthrie, 67).

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Real Options Valuation and Urban Growth Management

A real options approach to the valuation of undeveloped land has important consequences for local policy meant to control urban growth, because real options considerations can potentially cause developers to behave in ways that reduce the effectiveness of these policies.

Real Options Approach Definition

The real options approach to investment differs from traditional discounted cash flow approaches, because it accounts for the irreversibility of many investment expenditures and the ability of investors to delay investment decisions in order to gain more information (Pindyck, 1110). Irreversible investments are very similar to financial call options, which provide an option holder with a right, but not an obligation, to pay an exercise price for an asset during a specified time period. Exercising the option is irreversible, because, while the option holder can sell the underlying asset to another investor, they cannot get back the option or the money spent to exercise it (Pindyck, 1110).

Both financial call options and real options derive their value from uncertainty about the future value of an underlying asset. If an asset’s future value is unknown, an option allows an investor to wait and only exercise the option if the value of the underlying asset is above the exercise price. If the value is below the exercise price the investor will choose not to exercise

Table 1: Discounted Cash Flow Approach (DCF)

Year 1 2

Construction Cost -$1,200,000

NOI $1,500,000

PV -$1,090,909 $1,239,669

NPV $148,760

Table 2: Real Options Approach (ROA)

Year 1 2

Construction Cost -$600,000

NOI $1,000,000

PV -$545,455 $826,446

NPV $280,992

ROA-DCF $132,231

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the option, and will only lose the amount spent to obtain the option (Pindyck, 1111). Accordingly, the value of an option increases as volatility in the price of the underlying asset increases, because volatility increases uncertainty and the likelihood that an asset’s value will exceed the exercise price.

To demonstrate the value of the real options approach compared to straight line discounting in real estate, consider a simple two period situation where a developer is trying to decide whether to or not to develop a piece of land under the following conditions:

• The development will cost $1.2million to construct. • After construction, there is a 50% chance NOI will be $2,000,000 and a 50%

chance it will be $1,000,000. • The developer wants a 10% return.

Under the typical discounted cash flow approach to investment, the project would have a positive net present value of $148,760 (See Table 1). Because the expected value of the development is greater than the cost of construction, the developer would decide to commence construction immediately.

This conclusion is incorrect, however, because the developer has not accounted for the opportunity cost of investing now instead of waiting and only investing if NOI is $2,000,000. To determine this cost, assume the developer waits one year and develops their property only if NOI is $2,000,000 (See Table 2). In this situation the net present value is $280,992, or $132,231 higher than if the developer had not waited. This difference represents the value of waiting, i.e. the value of the real option. If the developer had not considered the value of waiting he would have effectively lost $132,231.

It should be noted, however, that the real options approach is only applicable if the option to wait is truly present. If the developer faces a situation where they can only choose between investing now or never investing, the straight-line discounted cash flow approach would be appropriate (Pindyck, 1111). For example, competition between developers can erode the value of the real option by forcing developers to act quickly before a competitor preempts them (Bulan, 248). Developers must therefore have some flexibility in timing their development to derive real option value.

Obviously, another condition required in order for the real options approach to be applicable is uncertainty about the future value of an underlying asset. In the example provided above, that asset is a project with two potential cash flows. If there were no uncertainty about future cash flows then the developer would have no reason to delay construction, provided the expected cash flows exceed costs, because waiting will not provide additional, or valuable,

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information. These two conditions mean that the real options approach is most valuable when investors face a highly uncertain environment and possess a high degree of flexibility.

Affect of Real Options on Price and Quantity Mechanisms

Both quantity mechanisms and price mechanisms reduce the option value in undeveloped land at the urban periphery by reducing uncertainty about appropriate development intensity and future asset prices. As a result, they can accelerate development, because the value of waiting has been diminished. The erosion of real option value therefore works against the goal of reducing development, and reduces the effectiveness of price and quantity mechanisms in terms of controlling urban growth.

Urban growth boundaries reduce the value of real options in rural areas outside the boundary by directly reducing uncertainty about future optimum uses for undeveloped land (Cunningham, 343). They do this by restricting the development intensity possible on an undeveloped parcel. For example, prior to the implementation of a growth boundary, a developer with a 5-acre parcel might be able to build 10 residences on their land. After the imposition of the boundary, however, they can only build one residence. Assuming these are the developer’s only two options, and both would generate a profit, the removal of the ability to build 10 residences would prompt the developer to begin construction on the single residence, because there is no longer any reason to wait and gain more information.

Empirical evidence from King County in Washington state demonstrates this effect (Cunningham, 357). Cunningham found that the imposition of an urban growth boundary reduced the value of real options and as a result spurred development. In the absence of real option considerations, he estimates the growth boundary would have reduced development by 42% - 48% in rural areas outside the boundary. The erosion of real options value, however, diminished its effectiveness to a 28%-39% reduction in development.

Conversely, a growth boundary could potentially delay development in interior areas by increasing uncertainty about the appropriate level of development intensity. Growth boundaries like the one in King County are meant to focus development into urban areas, but their effectiveness and the amount of increased demand may be unclear to developers who will find value in waiting to see if land could be developed more intensely than would be possible in the absence of a growth boundary. This further reduces the effectiveness of growth boundaries as interior development is delayed and exterior development accelerated.

The effectiveness of impact fees is similarly reduced by real options considerations, because impact fees reduce uncertainty. Unlike growth boundaries, impact fees work by directly increasing the cost of development to a point where undesirable developments are economically unfeasible. For example, if a developer only has a choice between developing 10 houses on a

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5-acre property, or developing one house on the same 5 acres, development fees may make developing 10 houses unprofitable by forcing the price above what a potential household would be willing to pay for a half-acre lot. Depending on local market conditions, however, and the type of development at which the impact fee is targeted, the developer may still find it possible to sell a single home on 5-acres. With his development opportunities limited by the impact fee, the developer may decide there is no longer value in waiting and begin construction. In this example impact fees have the same affect as a pre-development tax increase, which has been shown to accelerate land conversion and reduce capital intensity and the value of undeveloped land (Capozza, 898).

Conclusion

In areas where significant real option value is reflected in the price of undeveloped land, price and quantity mechanisms are less effective at limiting development than would otherwise be the case, because these mechanisms reduce the value of waiting and therefore spur more immediate development at the urban periphery. Real options increase the value of undeveloped land if a developer has flexibility in timing development and future project values are uncertain. The combination of these factors creates real value reflected in land prices, because developers can wait for additional information and only choose to exercise their option to develop if asset prices are sufficiently high. Price and quantity controls on development reduce uncertainty by limiting the options available to developers, and as a result reduce the value of delaying development and encourage more immediate construction. This diminishes the impact of regulation meant to reduce new construction, and should be incorporated into policy design by local authorities who want to combat the negative externalities of excessive urban development like congestion, loss of open space and overburdened infrastructure.

Bibliography

Bluffstobne, R., M. Braman, L. Fernandez, T. Scott, and P. Lee (2008): “Housing Sprawl and the Use of Development Impact Fees: The Case of the Inland Empire,” Contemporary Economic Policy, 26(3), 433-447.

Brueggeman, W. B. and J. D. Fisher (2011): Real Estate Finance and Investments. McGraw Hill Irwin, New York, NY, 14th ed.

Bulan, L., C. J. Mayer, and C. T. Somerville (2009): “Irreversible Investment, Real Options, and Competition: Evidence from Real Estate Development,” Journal of Urban Economics, 65(3), 237-251.

Cunningham, C. R. (2007): “Growth Controls, Real Options, and Land Development,” Review of Economics and Statistics, 89(2), 343-358.

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Capozza, D. R., and Y. Li (1994): “The Intensity and Timing of Investment: The Case of Land,” American Economic Review, 84(4), 889-904.

Capozza, D. R., and Y. Li (2002): “Optimal Land Development Decisions,” Journal of UrbanEconomics, 51(1), 123-142.

Guthrie, G. (2010): “House Prices, Development Costs, and the Value of Waiting,” Journal of Urban Economics, 68(1), 56-71.

Krugeman, P.R. (2001): “Nation in a Jam,” Op-ed: 13 May, New York Times

Pindyck, R. S. (1991): “Irreversibility, Uncertainty, and Investment,” Journal of Economic Literature, 29(3), 1110-1148.