Presale Contract and its Embedded Default and Abandonment Options

In an article titled “Fla. highrise has 32 stories, but just one tenant”, Christine Armario describes a situation in which many buyers exercised the default options of their presale contracts (Associated Press Writer—Sat, 1 Aug 2009, 3:37 p.m. ET). This article can be downloaded from http://​news.​yahoo.​com/​s/​ap/​20090801/​ap_​on_​re_​us/​us_​lonely_​highrise.

For an interesting article describing a developer’s abandonment decision, see Hubbie Smith, “Las Vegas Valley development is latest casualty of financial crisis”, Las Vegas Review-Journal (Nevada), 10 March 2009. This article can be downloaded from http://​www.​allbusiness.​com/​legal/​property-law-real-property-building-housing-codes/​12223056-1.​html.

The presale method has been used in many cities around the world, but is particularly popular in several Asian countries/regions such as Hong Kong, Taiwan, Korea, Singapore and Mainland China.

Many practices in real estate markets are associated with the use of options, see Grenadier (1995, 1996), Wang and Zhou (2006), Lai et al. (2007), and Buttimer et al. (2008).

Wang and Zhou (2000) and Wang et al. (2002), among others, also used a game-theoretical approach to model the seemingly irrational phenomena observed in real estate markets.

Geltner and Ling (2007) argue that construction cost is a major variable in the development industry information set and should be encompassed in an ideal real estate index.

Since the choice of a selling method will not affect a developer’s investment decision (nor the supply in the market), the use of a particular selling method will not affect the selling price of a property in the spot market. Given this, we do not need to explicitly model the determination of the spot price.

Note that \(\widetilde{c}\) measures the construction costs according to the blueprint. While in practice a developer might be allowed to substitute materials or change floor plans in some presale contracts, our model does not allow for this possibility. However, as long as the substitutions must be done with equal costs, allowing for this practice will not affect the conclusions of our paper.

An inclusion of the interest rate into our model will not change our model implications but will make the presentation of the result much more complicated.

This specification assumes that the future spot price and the construction cost follow uniform distributions. We had tried to use the normal distribution assumption instead; however, we cannot derive a closed-form solution under this assumption.

Wang and Zhou (2006) report that, historically, the construction cost volatility could be higher than the price volatility in certain periods.

It might not be realistic to assume that a developer can spend exactly the amount \(d\widetilde{c}\) during the first construction phase as the value of \(\widetilde{c}\) will not be realized until at the end of the first construction phase (or t = 1). However, instead of using \(d\widetilde{c}\), we can assume that the developer spends a fixed construction cost during the first-phase period (that is, \(d\overline{c}\)) and all our model implications will not change. The assumption of \(d\widetilde{c}\) simplifies the model presentation greatly.

For the analyses presented in this paper, the downpayment ratio and the first-phase construction ratio are assumed to be the same. We also conducted analyses allowing these two ratios to differ from each other. However, the mathematical presentation is much more complicated, while the implications of the model are exactly the same. Given this, we decided to report the result that uses only one ratio. The results of using two different ratios are available from the authors upon request.

It should be noted that we assume that the buyer will not receive a refund of the deposit when the developer abandons the project. In practice, depending on the developer’s strategies and contract enforceability, it is sometimes possible for the buyer to receive a full or partial refund. The inclusion of this refund parameter will not affect our qualitative conclusions (it only changes the magnitude of the cash flow under the abandonment scenario) but will significantly increase the mathematical presentation in our model. This is true because the refund option only takes effect when the developer abandons and not when he continues the project. Under this circumstance, we have to increase the number of equations to describe both scenarios. To simplify the presentation, we do not include the refund possibility in this paper. However, the results with a refund possibility are available from the authors upon request. Clearly, a refund privilege will decrease a developer’s incentive to abandon a project and hence reduce the value of an abandonment option.

It should be noted that we assume that the developers will lose nothing if they decide to abandon the property. In practice, there is a reputation cost to the developer or buyers might be able to go after the developer’s other assets (if there are any). The inclusion of this reputation parameter will not affect our qualitative conclusions unless the reputation cost is larger than the abandonment benefits (this is a trivial implication). However, to include the reputation cost into the model will significantly lengthen the mathematical presentation in our paper. This is true because the reputation cost only takes effect when the developer abandons the project and not when the developer continues the project. Under this circumstance, we have to increase the number of equations to describe both scenarios. To simplify the presentation, we do not include the reputation cost in this paper. However, the results with a reputation cost (which are the same as in this paper) are available from the authors upon request. It is clear that, with a reputation cost, it is less likely for a developer to abandon a project and hence will reduce the value of an abandonment option. When the reputation cost is high enough, the value of the abandonment option approaches zero.

We realize that the determination of the equilibrium presale price ignores two factors. First, we did not explicitly analyze the impact of the presale cost, defined as s in our model, on the presale price. The presale cost must be included in the model because, without it, the developer can offer a presale at any price without penalty. Second, the benefits of a presale contract are not modeled explicitly. Lai et al. (2004) and Chan et al. (2008) speculate that a presale contract can reduce the development risk and borrowing cost of a development project. In reality, a developer should share some of the benefits with a buyer (by lowering the presale price) to attract the buyer into the presale market. However, to include these two factors into our model requires us to make more behavioral related assumptions that will make the model more complicated. Given this, we simply assume that the presale benefit equals the presale cost, so that s = 0. It should be noted that, while this assumption (s = 0) simplifies our model development greatly, it also prohibits us from formally addressing interesting questions such as why a presale contract exists, what are the costs and benefits of presale contracts, and how can the costs and benefits be allocated. Clearly, intuition tells us that we are more likely to see presale contracts when markets have tight credit (or high interest rate), when developers have low equity and face high bankruptcy cost, and/or when buyers have low risk tolerance. We plan to address these important issues in a future research with a formal behavioral model.

Also see Lai et al. (2004) and Chan et al. (2008) for some of the possible incentives for using the presale method.

This result conforms to a personal experience of a co-author of this paper. After signing a contract to remodel a house with a large downpayment, the contractor abandoned the project once he discovered that the realized cost would be on the high end of his estimate. Of course, this developer offered a very low price because of the high downpayment received.

Lai et al. (2004) and Chan et al. (2008) argue that the presale method can reduce potential bankruptcy cost and financing cost when compared to the spot sale method. The benefit of using the presale method, therefore, can be shared by the developer and the buyer. If we include the benefits from a reduction in potential bankruptcy cost and financing cost into our model, it is possible that the result \(p_{p}^{\ast }>\overline{p}\) does not hold under this no-developer-abandonment condition.

See Eqs. 56 and 57 for the exact formulas on how to calculate these two probabilities.