1. Optionality in Presale of Real Estate Developments Sergio Rozenbaum, Luiz Brandão, Alexandre Rebello and Graziela Fortunato 12th Annual International Conference on Real Options Rio de Janeiro, July 2008

2.  Presale of Real Estate units: Sale before completion  Reasons: Risk sharing To reduce liquidity risk For the investor: locks in the property price  Risks involved: Demand uncertainty Price Volatility Long turnaround time and low liquidity Investor Default Introduction

3.  Asia: Developers must complete a portion prior to presale Risk of receiving an inferior product tends to favor established developers and market concentration. Investor is penalized for default  Brazil Full project spec files with authorities prior to presale, reducing the risk to investor 50% received during construction and the rest upon delivery Investors in default are taking developers to court Introduction

4.  The case of Brazil Prior to 1990, investors forfeited all prior payments in case of default Consumer protection laws of 1990 required partial refund, but developers capped refunds at 15% to 20% of amounts paid. Some investors have been able to receive up to 90% refund by suing developers in court Recent court rulings have established that developers must a minimum of 70% of amounts received. This had the effect of establishing by law a strike price for the option to abandon a presale contract, creating an lawful abandon option for the investor.. Introduction: Problem

5.  To determine the value and incremental cost of this abandon option to a real estate developer  To determine the impact on real estate investment strategies.  The option to abandon is modeled as American Put with exercise period of 24 months, which is equal to the construction period.  The option to abandon represents an optimal stopping problem where the optimal decision is governed by  The option to abandon will be exercised whenever the market value of the unit less the remaining unpaid balance drops below the amount to be refunded by the developer, or: Introduction: Objective

6.  Let : P t be the contractual payment due in period t γ t the accumulated payments made up to period t-1, such that t = 1, 2, …n. δ he percentage of the accumulated payments γ t that will be refunded, 0 < δ < 0.90.  The solution to the optimal stopping problem can be described by the following Bellman equation where V is the market price of the unit, is the refund to be received in time t, and is the payment due at time t. Model and Assumptions

7.  In the continuation region, the term to the right of is the greater the two, and we have  Given that V(t) follows a GBM, we arrive at  This equation holds for V > V*, where V* is the optimal stopping value.  We solve this problem using the Cox, Ross and Rubinstein (CRR, 1979) discrete binomial model Model and Assumptions

8.  Price Model Where: Vis the market price of the property; dz is the Wiener increment; μ is the expected growth in the property’s value  is the volatility of the property value.  Option and Solution American Put Option Solved with 24 period discrete binomial CCR model Model and Assumptions

9.  Investor: Presale Purchase at time t = 0 50% total price paid during 24 month construction period as follows: 10% down payment at t = 0 4 semi annual payments of 4% at t = 6, 12, 18 and 24 24 monthly payments of 1% of total price. 50% refinanced upon completion and delivery of unit. Exposed to price volatility risk Will exercise option to abandon if market value at t = 24 drops below the balance still to be paid plus the amount to be refunded. Model and Assumptions

10.  Historical prices series of residential property (Secovi- RJ) Period: Jan/95 – Dec/05 Interval: Monthly basis Real values Area: Neighborhoods of Greater Rio Type: Studio, one, two, three and four bedrooms Price Volatility

13.  Models for First and Second Periods If investor chooses to enter into presale contract, he is required to make first down payment P 0. Model and Assumptions

14.  Partial View of Project Model Model and Assumptions

15.  Model of Periods 23 and 24 Continuation required further down payment installments Abandon entails receiving a portion  of accumulated payments  i up to period i. Model and Assumptions V 24 = V 23 u V 2 4 = V 23 d Continue -P 23 /(1+r) 23 V24 Abandon δ γ 23 /(1+r) 23 Decision 23 Continue V 24 /(1+r) 24 - (P 24 + D 24 )/(1+r) 24 Abandon δ γ 24 /(1+r) 24 Decision 24

16. Partial View of Tree

17. Option Value as function of region in % of property price Option Value as function of size in % of property price Results

18.  Option Value as function of region in and unit size (as % of property price 0%10%30%50%70%90% % of refund Region 18 Region 11 Region 9 Region 7 Region 1 0%10%30%50%70%90% % of refund 4 Rooms 3 Rooms 2 Rooms 1 Room Studio

19. Conclusion  The value of the option to abandon is high and can have a significant impact on the profitability of a real estate developer  For the average neighborhood of Rio, the option value for a refund rate of 70% was close to 10% of the value of the property.  This implies that the presale system may not reduce the risk to the developers as much as before  Developers may be saddled with illiquid property if there is a strong downturn in the market at the same time they may be called upon to refund investors as they exercise their option to abandon this unprofitable investment.

20. Conclusion  For developers, this information may allow them to mitigate their risks by offering alternatives that increase the option exercise cost to the investor, such as product customization  For the investor, this information is also valuable since it allows him to make optimal decisions and negotiate better conditions with the developers if necessary.  Model limitations includes low reliability of volatility estimates since price series refer to different properties due to lack of public records of real estate transactions.

21. O GLOBO 04/02/2009 “... the presale system may not reduce the risk to the developers as much as expected, since a more severe downturn in the real estate market, such as the subprime crisis in the United States, may not only saddle developers with illiquid property but also require them to refund buyers that are bailing out of the market. “One alternative developers can use to minimize this risk is to offer product customization such as customized kitchens, cabinets and closets, since these costs are non refundable and increase the exercise cost for the buyer”.

22. Optionality in Presale of Real Estate Developments Sergio Rozenbaum, Luiz Brandão, Alexandre Rebello and Graziela Fortunato 12th Annual International Conference on Real Options Rio de Janeiro, July 2008