Real Options Valuation

Document Sample
Real Options Valuation Powered By Docstoc
					   Real Options:
 The Via Dutra Case
               Luiz Brandao
        The University of Texas at Austin
     luiz.brandao@mccombs.utexas.edu
              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.

MSIS 383N                       3
University of Texas at Austin
Federal Highway Network of Brazil




MSIS 383N                           4
University of Texas at Austin
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.


MSIS 383N                                                5
University of Texas at Austin
Rio de Janeiro, Brazil




MSIS 383N                       6
University of Texas at Austin
Rio de Janeiro, Brazil




MSIS 383N                       7
University of Texas at Austin
Rio de Janeiro, Brazil




MSIS 383N                       8
University of Texas at Austin
Sao Paulo, Brazil




MSIS 383N                       9
University of Texas at Austin
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.



MSIS 383N                                                 10
University of Texas at Austin
           Via Dutra, Inauguration, 1948.




MSIS 383N                                   11
University of Texas at Austin
Via Dutra, Inauguration, 1948.




MSIS 383N                        12
University of Texas at Austin
Via Dutra, 2003




MSIS 383N                       13
University of Texas at Austin
Via Dutra: Before and After




MSIS 383N                       14
University of Texas at Austin
Via Dutra: Before and After




MSIS 383N                       15
University of Texas at Austin
Via Dutra: Before and After




MSIS 383N                       16
University of Texas at Austin
Via Dutra: Before and After




MSIS 383N                       17
University of Texas at Austin
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

MSIS 383N                                               18
University of Texas at Austin
        Correlation between Traffic and
                  GDP - USA
                          8%
                                                                                       Traffic
                          7%
                                                                                       GDP
                          6%

                          5%
           % de mudança




                          4%

                          3%

                          2%

                          1%

                           0%
                            1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997
                          -1%

                          -2%
                                                             Ano

MSIS 383N                                                                                           19
University of Texas at Austin
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.



MSIS 383N                                               20
University of Texas at Austin
Binomial Approximation
    A lognormal stochastic process can be modeled
     with a binomial lattice.
    This allows us to use a simpler, discrete model
                                           Vu3

                                     Vu2

                                Vu
                                           Vu2d

                                     Vud
                V

                                           Vud2
                                Vd


                                     Vd2

                                           Vd3
MSIS 383N                                              21
University of Texas at Austin
Binomial Model
     The binomial parameters are:
                          t            t
              u e              and d  e
                                 Vu                (1   )  d
                          p                     p
                                                      ud
            V                                       e t  d
                                                 p
                      1-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.
MSIS 383N                                                         22
University of Texas at Austin
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


MSIS 383N                                               23
University of Texas at Austin
How can we adjust for risk?


        Risk                    High   [100]
       [50]                     .500     100
                                Low      [0]
                                .500       0



MSIS 383N                                      24
University of Texas at Austin
Discount the outcomes at the Risk
Adjusted Rate?
                                                                      100
                                                           90.91 
                                                                   (1  0.10)

    Risk                        High                  [90.91]
[45.45]                         .500                    90.91
                                Low                          [0]
                                .500

                                The discount rate is 10%

MSIS 383N                                                                 25
University of Texas at Austin
Discount the outcomes at the Risk
Free Rate?
                                                             100
                                                  95.24 
                                                          (1  0.05)

    Risk                        High             [95.24]
[47.62]                         .500               95.24
                                Low                  [0]
                                .500                   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.
MSIS 383N                                                        26
University of Texas at Austin
Discount the outcomes at the risk
free rate and adjust the probabilities?
                                                               100
                                                    95.24 
                                                            (1  0.05)

    Risk                        High             [95.24]
[45.45]                         .477               95.24
                                Low                   [0]
                                .523                    0

                   We can correct this by “adjusting” the
                   probability to 0.477

MSIS 383N                                                          27
University of Texas at Austin
  Real Option Valuation

            Class Website
www.mccombs.utexas.edu/faculty/luiz.brandao

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:2
posted:9/16/2012
language:English
pages:28