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

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: Problem

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: Problem

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

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.

Introduction: Objective

Price Model

Where:V is 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

dVdt dz

V

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

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

Price Volatility

Models for First and Second Periods If investor chooses to enter into presale contract, he is required

to make first down payment P0.

Model and Assumptions

High

Low Continue

-P0

V1

Abandon

Decision 0 High

Low

Continue

-P1/(1+r)

V2

Abandon

δ γ1/(1+r)

Decision 1

Partial View of Project Model

Model and Assumptions

Continua

-Pgto10/(1+r) 1̂0

Abandona

Perc*Pgac10/(1+r) 1̂0

up

Down

Decision10

Continua

-Pgto9/(1+r) 9̂

V10

Abandona

Perc*Pgac9/(1+r) 9̂

up

Down

Decision9

Continua

-Pgto8/(1+r) 8̂

V9

Abandona

Perc*Pgac8/(1+r) 8̂

up

Down

Decision8

Continua

-Pgto7/(1+r) 7̂

V8

Abandona

Perc*Pgac7/(1+r) 7̂

up

Down

Decision7

Continua

-Pgto6/(1+r) 6̂

V7

Abandona

Perc*Pgac6/(1+r) 6̂

a

Decision6

up

Down Continua

-Pgto15/(1+r) 1̂5

V16

Abandona

Perc*Pgac15/(1+r) 1̂5

up

Down

Decision15

Continua

-Pgto14/(1+r) 1̂4

V15

Abandona

Perc*Pgac14/(1+r) 1̂4

up

Down

Decision14

Continua

-Pgto13/(1+r) 1̂3

V14

Abandona

Perc*Pgac13/(1+r) 1̂3

up

Down

Decision13

Continua

-Pgto12/(1+r) 1̂2

V13

Abandona

Perc*Pgac12/(1+r) 1̂2

b

Decision12

Continua

-Pgto4/(1+r) 4̂

Abandona

Perc*Pgac4/(1+r) 4̂

up

Down

Decision4

Continua

-Pgto3/(1+r) 3̂

V4

Abandona

Perc*Pgac3/(1+r) 3̂

up

Down

Decision3

Continua

-Pgto2/(1+r) 2̂

V3

Abandona

Perc*Pgac2/(1+r) 2̂

up

Down

Decision2

Continua

-Pgto1/(1+r) 1̂

V2

Abandona

Perc*Pgac1/(1+r) 1̂

up

Down

Decision1

Continua

-Pgto0

V1

Abandona

Decision0

Model and Assumptions

up

Down b Continua

-Pgto11/(1+r)^11

V12

Abandona

Perc*Pgac11/(1+r)^11

up

Down

Decision11

Continua

-Pgto10/(1+r)^10

V11

Abandona

Perc*Pgac10/(1+r)^10

up

Down

Decision10

Continua

-Pgto9/(1+r)^9

V10

Abandona

Perc*Pgac9/(1+r)^9

up

Down

Decision9

Continua

-Pgto8/(1+r)^8

V9

Abandona

Perc*Pgac8/(1+r)^8

up

Down

Decision8

Continua

-Pgto7/(1+r)^7

V8

Abandona

Perc*Pgac7/(1+r)^7

up

Down

Decision7

Continua

-Pgto6/(1+r)^6

V7

Abandona

Perc*Pgac6/(1+r)^6

a

Decision6

up

Down c Continua

-Pgto17/(1+r)^17

V18

Abandona

Perc*Pgac17/(1+r)^17

up

Down

Decision17

Continua

-Pgto16/(1+r)^16

V17

Abandona

Perc*Pgac16/(1+r)^16

up

Down

Decision16

Continua

-Pgto15/(1+r)^15

V16

Abandona

Perc*Pgac15/(1+r)^15

up

Down

Decision15

Continua

-Pgto14/(1+r)^14

V15

Abandona

Perc*Pgac14/(1+r)^14

up

Down

Decision14

Continua

-Pgto13/(1+r)^13

V14

Abandona

Perc*Pgac13/(1+r)^13

up

Down

Decision13

Continua

-Pgto12/(1+r)^12

V13

Abandona

Perc*Pgac12/(1+r)^12

b

Decision12

up

Down d Continua

-Pgto23/(1+r)^23

V24

Abandona

Perc*Pgac23/(1+r)^23

up

Down

Decision23

Continua

-Pgto22/(1+r)^22

V23

Abandona

Perc*Pgac22/(1+r)^22

up

Down

Decision22

Continua

-Pgto21/(1+r)^21

V22

Abandona

Perc*Pgac21/(1+r)^21

up

Down

Decision21

Continua

-Pgto20/(1+r)^20

V21

Abandona

Perc*Pgac20/(1+r)^20

up

Down

Decision20

Continua

-Pgto19/(1+r)^19

V20

Abandona

Perc*Pgac19/(1+r)^19

up

Down

Decision19

Continua

-Pgto18/(1+r)^18

V19

Abandona

Perc*Pgac18/(1+r)^18

c

Decision18

up

Down a Continua

-Pgto5/(1+r)^5

V6

Abandona

Perc*Pgac5/(1+r)^5

up

Down

Decision5

Continua

-Pgto4/(1+r)^4

V5

Abandona

Perc*Pgac4/(1+r)^4

up

Down

Decision4

Continua

-Pgto3/(1+r)^3

V4

Abandona

Perc*Pgac3/(1+r)^3

up

Down

Decision3

Continua

-Pgto2/(1+r)^2

V3

Abandona

Perc*Pgac2/(1+r)^2

up

Down

Decision2

Continua

-Pgto1/(1+r)^1

V2

Abandona

Perc*Pgac1/(1+r)^1

up

Down

Decision1

Continua

-Pgto0

V1

Abandona

Decision0

Continua

V24/(1+r)^24-(Pgto24+D24)/(1+r)^24

Abandona

Perc*Pgac24/(1+r)^24

d

Decision24

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

High

Low

Continue

-P23/(1+r)23

V24

Abandon

δ γ23/(1+r)23

Decision 23

Continue

V24/(1+r)24 - (P24 + D24)/(1+r)24

Abandon

δ γ24/(1+r)24

Decision 24

V3

-0.9759

[19.3688] Continua

9.7712

[-1.2167] Abandona

Decision2

52%

[19.3688] up

V3

-0.9759

[9.1249] Continua

9.7712

[-1.2167] Abandona

Decision2

48%

[9.1249] Down

V2

-0.9879

[14.4535] Continua

8.9437

[-1.0563] Abandona

Decision1

52%

[14.4535] up

V3

-0.9759

[9.1249] Continua

9.7712

[-1.2167] Abandona

Decision2

52%

[9.1249] up

V3

-0.9759

[2.7027] Continua

9.7712

[-1.2167] Abandona

Decision2

48%

[2.7027] Down

V2

-0.9879

[6.0433] Continua

8.9437

[-1.0563] Abandona

Decision1

48%

[6.0433] Down

V1

-10.0000

[10.4180] Continua

[0.0000] Abandona

Decision0 [10.4180]

Partial View of Tree

Partial View of Project Model

Model and Assumptions

Option Value as function of region in % of property price

Option Value as function of size in % of property price

Results

Size Volatility 0% 10% 30% 50% 70% 90%

Studio 11.34% 5.1% 6.0% 7.8% 10.2% 12.7% 15.9%

1 Room 11.30% 5.1% 5.9% 7.8% 10.1% 12.6% 15.8%

2 Rooms 9.30% 3.2% 3.8% 5.5% 7.4% 9.7% 12.7%

3 Rooms 9.24% 3.2% 3.8% 5.4% 7.3% 9.6% 12.6%

4 Rooms 8.70% 2.7% 3.3% 4.8% 6.6% 8.8% 11.7%

Percentage of Refund

Results

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

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.

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.

O GLOBO 04/02/2009

A venda de apartamentos em lançamentos imobiliários, em uma época de grande turbulência financeira, é um risco muito grande para o incorpora-or. A inclusão da decoração pode ser uma ação de marketing,mas também pode ter sido adotada como proteção a uma futura devolução.

“De posse dessa informação, uma das alternativas para estes incorporadores possivelmente poderia ser o de criar condições que tornem a opção de abandono menos atrativa, através da oferta de customização do imóvel ou a inclusão de produtos específicos de maior valor agregado como cozinhas e armários planejados, cujos custos não são passiveis de devolução no caso de desistência.” Texto do artigo.