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

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

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.

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

max ;refund market price remaining unpaid balance

max ;abandon continue

Let :

Pt be the contractual payment due in period t

γt the accumulated payments made up to period t-1, such that t = 1, 2, …n.

δ he percentage of the accumulated payments γt 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

1( , ) max ( , ), ( , ) ( , )

1F V t V t V t dt E F V dV t dt V

rdt

( , ) ( )V t t ( , ) ( )V t P t

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

1( , ) ( ) ( , )

1F V t P t dt E F V dV t dt V

rdt

2 21( , ) ( , ) ( , ) ( , ) ( ) 0

2 VV V tV F V t VF V t F V t rF V t P t

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

Regions Studio 1 Bed 2 Bed 3 Bed 4 Bed Average

Region 1 7.30% 6.20% 8.04% 8.22% 9.70% 7.89%Region 2 8.36% 9.18% 8.20% 12.39% 6.76% 8.98%Region 3 9.98% 10.25% 8.97% 8.11% 9.51% 9.36%Region 4 10.11% 9.32% 9.24% 9.62% 8.59% 9.38%Region 5 10.35% 10.60% 9.34% 9.09% 8.58% 9.59%Region 6 11.26% 9.31% 9.19% 9.76% 8.99% 9.70%Region 7 13.63% 7.92% 10.16% 9.82% 8.35% 9.97%Region 8 12.73% 8.93% 8.24% 9.18% 10.99% 10.01%Region 9 10.96% 10.04% 8.84% 11.31% 9.21% 10.07%Region 10 10.77% 11.81% 12.45% 10.02% 6.93% 10.40%Region 11 11.72% 15.42% 8.64% 9.20% 7.61% 10.52%Region 12 10.90% 12.12% 10.55% 10.55% 8.83% 10.59%Region 13 12.88% 16.93% 8.51% 7.13% 7.78% 10.64%Region 14 10.79% 9.87% 10.93% 11.74% 11.15% 10.90%Region 15 13.31% 12.89% 9.62% 7.63% 11.31% 10.95%Region 16 10.79% 12.72% 13.38% 9.55% 9.13% 11.11%Region 17 11.77% 15.30% 10.13% 9.45% 8.97% 11.12%Region 18 12.54% 12.03% 11.54% 9.92% 9.66% 11.14%

Average 11.12% 11.16% 9.78% 9.59% 9.00% 10.13%

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

V1 = V0u

V1 = V0d Continue

-P0

V1

Abandon

Decision 0

V2 = V1u

V2 = V1d 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 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

V24 = V23u

V24 = V23d

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

Option Value as function of region in % of property price

Option Value as function of size in % of property price

Results

0% 10% 30% 50% 70% 90%

Region 1 7.89% 2.0% 2.6% 3.9% 5.5% 7.7% 10.4%

Region 7 9.97% 3.8% 4.5% 6.2% 8.3% 10.7% 13.7%

Region 9 10.07% 3.9% 4.6% 6.3% 8.4% 10.8% 13.9%

Region 11 10.52% 4.3% 5.1% 6.9% 9.1% 11.5% 14.6%

Region 18 11.14% 4.9% 5.8% 7.6% 9.9% 12.4% 15.6%

Average 10.13% 4.0% 4.7% 6.4% 8.5% 10.9% 14.0%

Percentage of RefundVolatilityRegion

0% 10% 30% 50% 70% 90%

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

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

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

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

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

Size Percentage of Refund

Volatility

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

“ ... 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”.

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