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
Introduction: Problem

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: Objective

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.
Model and Assumptions

Price Model
dV
  dt   dz
V
Where:
V
dz
μ


is the market price of the property;
is the Wiener increment;
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

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.
Price Volatility

Historical prices series of residential property (SecoviRJ)

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
Model and Assumptions

Models for First and Second Periods

If investor chooses to enter into presale contract, he is required
to make first down payment P0.
Decision
0
V1
High
Abandon
V2
High
Continue
Continue
-P0
Decision 1
Low
-P1/(1+r)
Abandon
δ γ1/(1+r)
Low
Model and Assumptions

Partial View of Project Model
Decision0
V1
Decision1
up
Continua
-Pgto0
Down
Abandona
Continua
-Pgto1/(1+r)^1
V7
Down
Decision12
Continua
-Pgto7/(1+r)^7
V13
Down
Abandona
Perc*Pgac12/(1+r)^12
V8
Decision3
Continua
-Pgto3/(1+r)^3
Down
Decision8
Down
Continua
-Pgto8/(1+r)^8
V14
Down
V9
Abandona
Perc*Pgac13/(1+r)^13
Continu
-Pgt
Down
Decision9
Abando
P
V10
Decision
up
Continua
-Pgto9/(1+r)^9
Down
Continu
-Pgto
Down
Abandona
Perc*Pgac9/(1+r)^9
Decision14
V15
Down
Abandona
Perc*Pgac14/(1+r)^14
Abando
Per
Decision15
up
Continua
-Pgto14/(1+r)^14
Decision
Abandona
Perc*Pgac3/(1+r)^3
Abandona
Perc*Pgac8/(1+r)^8
up
V4
up
up
Decision13
Continua
-Pgto13/(1+r)^13
V3
Abandona
Perc*Pgac2/(1+r)^2
Abandona
Perc*Pgac7/(1+r)^7
up
Continua
-Pgto12/(1+r)^12
Continua
-Pgto2/(1+r)^2
up
Abandona
Perc*Pgac6/(1+r)^6
b
Down
Decision7
up
Continua
-Pgto6/(1+r)^6
Decision2
up
Abandona
Perc*Pgac1/(1+r)^1
Decision6
a
V2
up
V16
De
up
Continua
-Pgto15/(1+r)^15
Co
Down
Abandona
Perc*Pgac15/(1+r)^15
Ab
Model and Assumptions
Dec is ion0
V1
up
Continua
Dec is ion1
V2
up
Continua
Down
-Pgto0
Abandona
-Pgto1/(1+ r)^1
V7
Continua
a
Dec is ion7
Down
Abandona
-Pgto7/(1+ r)^7
Dec is ion12
V13
Continua
Dec is ion13
-Pgto12/(1+ r)^12
Abandona
Dec is ion18
-Pgto13/(1+ r)^13
V19
up
Dec is ion19
Down
Abandona
-Pgto19/(1+ r)^19
Abandona
Perc*Pgac18/(1+ r)^18
Continua
d
Dec is ion24
V24/(1+ r)^24-(Pgto24+ D24)/(1+ r)^24
Abandona
Perc*Pgac24/(1+ r)^24
Perc*Pgac19/(1+ r)^19
-Pgto9/(1+ r)^9
Dec is ion14
V20
V15
Dec is ion10
-Pgto14/(1+ r)^14
Dec is ion20
-Pgto20/(1+ r)^20
Abandona
Perc*Pgac20/(1+ r)^20
-Pgto10/(1+ r)^10
Dec is ion15
V16
-Pgto15/(1+ r)^15
Dec is ion11
Dec is ion21
-Pgto21/(1+ r)^21
Abandona
Perc*Pgac21/(1+ r)^21
-Pgto11/(1+ r)^11
Dec is ion16
-Pgto16/(1+ r)^16
V22
Dec is ion22
Perc*Pgac11/(1+ r)^11
V17
up
-Pgto22/(1+ r)^22
Abandona
Perc*Pgac22/(1+ r)^22
Dec is ion17
V18
up
Continua
Down
-Pgto17/(1+ r)^17
Down
Abandona
Perc*Pgac17/(1+ r)^17
V23
up
Continua
Down
b
Down
Abandona
Perc*Pgac16/(1+ r)^16
up
V12
up
Continua
Down
Abandona
Continua
Down
V11
up
Continua
Down
Perc*Pgac15/(1+ r)^15
V21
Perc*Pgac5/(1+ r)^5
Perc*Pgac10/(1+ r)^10
up
a
Down
Abandona
Abandona
Abandona
up
-Pgto5/(1+ r)^5
Continua
Down
Continua
Down
Continua
Down
V10
up
V6
up
Continua
Down
Perc*Pgac4/(1+ r)^4
Perc*Pgac9/(1+ r)^9
up
Dec is ion5
Abandona
Abandona
Perc*Pgac14/(1+ r)^14
up
-Pgto4/(1+ r)^4
Continua
Down
Abandona
Continua
-Pgto18/(1+ r)^18
-Pgto8/(1+ r)^8
-Pgto3/(1+ r)^3
Dec is ion9
Continua
Down
Perc*Pgac13/(1+ r)^13
Continua
c
V14
up
Abandona
Perc*Pgac12/(1+ r)^12
V9
up
V5
up
Continua
Down
Perc*Pgac3/(1+ r)^3
Perc*Pgac8/(1+ r)^8
Continua
Down
Dec is ion8
Dec is ion4
Abandona
Abandona
Perc*Pgac7/(1+ r)^7
up
-Pgto2/(1+ r)^2
Continua
Down
Abandona
Perc*Pgac6/(1+ r)^6
b
V8
up
V4
up
Continua
Down
Perc*Pgac2/(1+ r)^2
Continua
-Pgto6/(1+ r)^6
Dec is ion3
Abandona
Perc*Pgac1/(1+ r)^1
up
V3
up
Continua
Down
Abandona
Dec is ion6
Dec is ion2
Dec is ion23
V24
up
Continua
Down
-Pgto23/(1+ r)^23
Abandona
Perc*Pgac23/(1+ r)^23
Down
Model and Assumptions

Model of Periods 23 and 24


Continuation required further down payment installments
Abandon entails receiving a portion d of accumulated payments
gi up to period i.
Decision 23
V24
Decision 24
High
Continue
Continue
-P23/(1+r)23
Low
V24/(1+r)24 - (P24 + D24)/(1+r)24
Abandon
Abandon
δ γ23/(1+r)23
δ γ24/(1+r)24
Partial View of Tree
V3
Decision2
up
Continua
[19.3688]
-0.9759
Abandona
52%
V2
Decision1
up
Continua
[14.4535]
[-1.2167]
9.7712
[14.4535]
V3
-0.9879
Decision2
52%
[19.3688]
Down
Continua
[9.1249]
-0.9759
Abandona
48%
[9.1249]
[-1.2167]
9.7712
Abandona
V1
Decision0
Continua
[10.4180]
[-1.0563]
8.9437
[10.4180]
V3
-10.0000
Decision2
up
Continua
[9.1249]
-0.9759
Abandona
52%
V2
Decision1
Down
Continua
[6.0433]
[-1.2167]
9.7712
[6.0433]
V3
-0.9879
Decision2
48%
[9.1249]
Down
48%
Continua
[2.7027]
[2.7027]
-0.9759
Abandona
[-1.2167]
9.7712
Abandona
[-1.0563]
8.9437
Abandona
[0.0000]
Model and Assumptions

Partial View of Project Model
Results

Option Value as function of region in % of property price

Option Value as function of size in % of property price
Size
Studio
1 Room
2 Rooms
3 Rooms
4 Rooms
Volatility
11.34%
11.30%
9.30%
9.24%
8.70%
0%
5.1%
5.1%
3.2%
3.2%
2.7%
10%
6.0%
5.9%
3.8%
3.8%
3.3%
Percentage of Refund
30%
50%
7.8%
10.2%
7.8%
10.1%
5.5%
7.4%
5.4%
7.3%
4.8%
6.6%
70%
12.7%
12.6%
9.7%
9.6%
8.8%
90%
15.9%
15.8%
12.7%
12.6%
11.7%
Results

Option Value as function of region in and unit size (as %
of property price
4 Rooms
Region 18
3 Rooms
Region 11
2 Rooms
Region 9
1 Room
Region 7
Studio
Region 1
0%
0%
10%
30%
50%
% of refund
70%
10%
30%
50%
90%
% of refund
70%
90%
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 incorporaor. 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.