Transcript Real Options Valuation - IAG PUC-Rio

Real Options:
The Via Dutra Case
Luiz Brandao
The University of Texas at Austin
[email protected]
Class Web Site
www.mccombs.utexas.edu/faculty/luiz.brandao
Austin, Texas
Via Dutra Case
Via Dutra

Brazil is about the
size of the USA.

Roadways account
for over 60% of
total freight
transportation,
compared to 26% in
the USA.

Quality of roads is
poor.
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Federal Highway Network of Brazil
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Privatization Program

In the 90’s Brazil privatized state owned steel
mills, phone and public utility firms and part of
the federal and state highways.

The privatized highways were to be operated and
maintained through a concession contract

The President Dutra highway was the most
important one of the federal network, linking
Brazil’s two largest cities, Rio and Sao Paulo.

Highway was 400km (250 miles) long.
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Rio de Janeiro, Brazil
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Rio de Janeiro, Brazil
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Rio de Janeiro, Brazil
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Sao Paulo, Brazil
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The Project

Twenty five year concession

Obligation to invest over US$ 500 million in
repairs, upgrading and maintenance.

Bi-directional toll collection at four toll plazas

Bidders were the largest construction firms in
Brazil.

Very few roads in Brazil were toll roads at the
time.
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Via Dutra, Inauguration, 1948.
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Via Dutra, Inauguration, 1948.
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Via Dutra, 2003
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Via Dutra: Before and After
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Via Dutra: Before and After
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Via Dutra: Before and After
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Via Dutra: Before and After
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Project Risks and Options
Risks
Options

Traffic risk

Option to Abandon

Foreign exchange risk

Option to Expand

Political risk

Interest rate risk

Inflation risk

Implementation risk

Operational risk
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Correlation between Traffic and
GDP - USA
8%
Traffic
7%
GDP
6%
% de mudança
5%
4%
3%
2%
1%
0%
1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
-1%
-2%
Ano
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Real Options Model

Create DCF spreadsheet

Model the stochastic process of each uncertainty

Use Monte Carlo simulation to estimate the
project volatility

Model project GBM diffusion process with a
binomial lattice

Insert options as decision nodes in tree.

Solve using risk neutral probabilities.
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Binomial Approximation

A lognormal stochastic process can be modeled
with a binomial lattice.

This allows us to use a simpler, discrete model
V u3
V u2
Vu
V u2d
V ud
V
V ud2
Vd
Vd2
Vd3
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Binomial Model

The binomial parameters are:
 t
u e
 t
and d  e
Vu
p
V
1-p

(1   )  d
p
ud
e t  d
p
ud
Vd
Note that volatility is the annualized standard
deviation of the project returns. The Δt factor
adjusts for time intervals different than a year.
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Risk Neutral Probabilities

Risk Neutral Probabilities are the probabilities
that provide us the same PV as before, when we
discount at the risk free rate.

They can easily be derived from the relationship
that exists between the project cash flows, the
discount rate, the probabilities and the Present
Value.

This way we can discount the cash flows with the
risk free rate and arrive at the same PV, as long
as we use the risk neutral probabilities
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How can we adjust for risk?
Risk
[50]
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High
.500
[100]
100
Low
.500
[0]
0
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Discount the outcomes at the Risk
Adjusted Rate?
100
90.91 
(1  0.10)
Risk
[45.45]
High
.500
[90.91]
90.91
Low
.500
[0]
The discount rate is 10%
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Discount the outcomes at the Risk
Free Rate?
100
95.24 
(1  0.05)
Risk
[47.62]
High
.500
[95.24]
95.24
Low
.500
[0]
0
I f we discount the cash flows at the Risk
Free rate instead of the Risk Adjusted rate,
we arrive at an incorrect PV.
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Discount the outcomes at the risk
free rate and adjust the probabilities?
100
95.24 
(1  0.05)
Risk
[45.45]
High
.477
[95.24]
95.24
Low
.523
[0]
0
We can correct this by “adjusting” the
probability to 0.477
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Real Option Valuation
Class Website
www.mccombs.utexas.edu/faculty/luiz.brandao