Transcript Real Options Valuation - IAG PUC-Rio

Real Options
Introduction to Real Options
Prof. Luiz Brandão
[email protected]
2009
Managerial Flexibility

Managerial flexibility is present in many projects

Mining firms may choose to increase rate of extraction when
prices rise, and reduce production when they fall.

Auto firms can adjust production levels to market demand

Hollywood movie studios have the flexibility to release a
sequel to a blockbuster movie (Zorro I, II, Spiderman I, II, III,
etc, Star Wars, Back to the Future, etc.)

Drug firms can abandon new drug development if the trial
tests show that the drug will not work as expected.

These flexibilities are options that the firm has to change the
original development strategy of the product.

These options add value to the firm, but this value cannot be
captured by traditional DCF analysis.
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An Investment Decision

Suppose a firm is analyzing the following investment project:

Investment = $3.000

Project value in one year:



$5.500 with 50% probability

$2.200 with 50% probability
Cost of capital is 10% per year.
Decision
Value
High
5.500
Invest
-3.000
Low
2.200
What is the value of this project?
Do not Invest
NPV 10%   3.000  (0.5)
5.500
2.200
 (0.5)
1.10
1.10
NPV 10%  3.000  2.500  1.000  $500
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Project with Flexibility



Note we implicitly are adopting
the assumption that the project
will be implemented now or
never.
Invest
-3.000 + 5.500/1.1
High
No
But what if the project can be
delayed for one year?
In this case, we can wait for the
uncertainty over the cash flows
be resolved before committing to
the project.
Invest
-3.000 + 2.200/1.1
Low
No
 3.000 5.500 
 3.000 2.200 
VPL  0.5 


0.5

2 

1.10 
1.102 
 1.10
 1.10
VPL  0.5  2.272  4.545  0.5  2.727  1.818
VPL  909   456   909
zero
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Evolution of Evaluation Methods
1930-1950
DCF
NPV
IRR
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Sensitivity
Analysis
Impact of
Variables
Brandão
1960
Decision
Trees
Simulation
Models
1970
Financial
Options
Risk Analysis Risk
Management
CAPM
1980
Real Options
Value of the
Information
Strategic
Considerations
5
DCF Method

Steps
 Project the expected future cash flow of the project
 Determine the appropriate discount rate that takes into
consideration the risk of the project and the time value of money
 Determine the Present Value of the Project
 Deduct the implementation cost of the project to determine the
NPV
 If the NPV > 0 invest on the project.

Assumptions
 The project will be executed now or never
 Once initiated, the project is not affected by future managerial
decision.
 The expected future cash flows will happen with certainty
 The project’s risk does not change throughout its life
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DCF Method

Problems

Ignores the value of the option to invest

Ignores the project’s uncertainties

Ignores the value of managerial flexibility

Generally underestimates the value of projects that possess
real options

Can lead to sub optimal investment decisions
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The Investment Decision

Traditional Methods of Investment Evaluation involve the use of
discounted cash flows (DCF) (NPV and IRR)

DCF was originally developed to value financial investments like
stocks and company’s obligations.

These financial securities are passive in nature, since the investor
has no influence over the return.

Real securities present important differences in relation to
financial assets.

The statistical and mathematical modeling of real assets is more
complex than the one for financial assets.

Many of the assumptions used for financial assets do no apply to
real assets.
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Financial Securities and Real Securities
Financial Securities
Real Securities
Comments
Divisibility
Indivisibility
Projects are not divisible,
value of control
High Liquidity
Low Liquidity
Implies greater risk
Low Transaction Cost
High Transaction
Cost
Violates CAPM
Disseminated
Information
Asymmetry of
Information
Allows arbitrage profits
Markets
No Market
No Market Value
Market Risk
Market Risk and
Private Risk
Private Risk is not correlated
to Market
Short Term
Long Term
Expiration Time
Passive Management
Active Management
Value of Flexibility
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Investment Decision

Characteristics of Investment Decision

The Investment is generally Irreversible.


The Future Cash Flows are Uncertain.


Independent of the result of the project, the capital invested, or
the major part of it, cannot be recuperated
The uncertainties can be originated from many distinct sources.
The uncertainties are a source of risk for the project.
Many times there is a degree of Managerial Flexibility in the
project

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The cash flows of the project can be affected by managerial
decisions taken after the project is initiated and the uncertainties
are resolved.
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What is the Real Options Method?

It is project evaluation technique that uses option pricing methods
to value projects with managerial flexibility.

Real Options value the existing managerial flexibilities on the
projects that are not captured by traditional methods such as
DCF.

Real Options complements, but does not substitute for the DCF
method.

The degree of managerial flexibility and the level of uncertainty
increases the value of a real options project.

Offers a valuation more consistent with the true value of the
project.

Offers more specific and detailed decision rule for investment.
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Identifying Real Options
A) This is not an option

Traditional DCF treats the
project as shown in Fig A

For some types of
projects this can be an
inadequate
representation

This decision tree
assumes that the
manager won’t interfere
in the operation of the
project throughout its
useful life
Good News + $$$
Invest
Bad News
- $$$
Good News
0
Bad News
0
Don’t Invest
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Identifying Real Options
B) This is an option
Invest

Many times managers
have the option to
postpone an investment
decision while they wait
for better information.

The possibility to make
decisions after receiving
new information about the
project can avoid negative
results.

Intuitively , which of the
two project (A or B) has a
greater value?
+ $$$
Good News
Don’t Invest
Invest
0
X
- $$$
Bad News
Don’t Invest
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Identifying Options
Hollywood


Microsoft



The value of a film may include the value of the option to
make sequels.
Windows is a basic platform that gives Microsoft the option to
commercialize other compatible products.
Natural Resources

Mining: Exploration decreases uncertainty and orients the
investment decision.

Oil: A lease concession is an option of exploration.
Energy

Biofuels: Producers have option to choose inputs and even
outputs.
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Example: Option to Abandon




Biodata S.A. hopes to
introduce a new product to
the market, which will have
a life of two years.
The investment is $100
millions and the cash flow
of the project are highly
uncertain.
Biodata competitors are
also actively working to
develop a similar product.
t=0
t=1
t=2
0.50
150
0.50
88.0
0.50
70
-100
0.50
-30
0.50
66.0
0.50
-60
The project’s cash flow will be affected by the uncertainty of the
market as well as by whether competitors will enter the market.
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Biodata: Cash Flow
t=0
t=1
t=2
0.50
150
0.50
70
0.50
-30
0.50
-60
0.50
88.0
-100
0.50
66.0
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Example: Abandonment Option

What is the NPV of this project?
 88 + 66 
 150  70 
 30  60 
VPL  -100  0.5 

0.25

0.25




  3.14
2
2
1.10
1.10
1.10







The negative NPV indicates that the company shouldn’t invest in
this project.

Does the flexibility of being able to abandon the project at any
moment have any impact on the decision?

How can we determine this?
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Example: Abandonment Option
t=0
t=1
t=2
0.50
150
0.50
70
0.50
-30
0.50
--60
0.50
88.0
-100
0.50
66.0
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Exemplo: Opção de Abandono

What is the NPV with the option to abandon?
 88 +66 
 150  70 
 30  60 
VPL  -100  0.5 

0.25

0.25
3.14




  15.45
2
2
 1.10 
 1.10 
 1.10 

What is the value of the abandonment option?


It is approximately the difference between the value of
the project with and without the option.
What effect does this option have on the risk of the
project?

The existence of the option reduces the risk of the project
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Level of Flexibility
Capacity to react to new
information
Effect of flexibility and uncertainty
Option Value
Moderate
High
Low
Moderate
Level of Uncertainty
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How real options affect risk


StereoGram is analyzing an
opportunity to invest in a
government concession.
The investment cost is $115M,
and the cash flows of the
project will be $160 if the
project does well or $80
otherwise.
t=1
t=0
0.50
$180M
- $115M

The project’s risk is 20%, the
probability of success is 50%
and the risk free discount rate
is 8%.

For $20M, the company has the option to buy an insurance that
would pay $120M if the project fails.
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0.50
$60M
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Ex: StereoGram Ltd.

StereoGram

The expected value of the project
without the insurance is:
PV 

0.5(180)  0.5(60)
 $100
1.2
Given that the investment cost is
$115, the project is not appealing
to the company because its NPV
will be negative.
t=1
t=0
0.50
$180M
- $115M
0.50
$60M
NPV  115  100  $15
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Ex: StereoGram Ltd.

StereoGram

With the insurance, the company has the option to receive
$120M if the project fails, and the cash flow of the project will
therefore be:
t=1
t=0
0.50
180M + 0 = $180M
- $115M
0.50


60M+120M = $180M
In this case, the value of the project will be
0.5(180)  0.5(180)
PV 
 $150
1.2
The NPV increases to
NPV  115  150  $35
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Ex: StereoGram Ltd.

StereoGram

However, the previous analysis is incorrect, since purchasing
the insurance gives the company the option to recoup the
investments made on the project and guarantees its cash flow
independent of the project.

This way, the buying of the insurance actually eliminates any
risk in this project, which makes the 20% rate of risk used
previously no longer appropriate.

The appropriate rate in this case is the risk free rate, and the
real value of the project and its NPV are, respectively:
PV 

0.5(180)  0.5(180)
 $166.7
1.08
NPV  115  166.7  $51.67
Even buying the insurance for $20M, the company still
increases its value by 51.67 – 20 = $31.67
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Graham & Harvey (2001)

Survey done with 392 US and Canada CFOs indicates that 26.6% use real
options “always or almost always”
Journal of Financial
Economics, vol.60,
2001, pp.187-243
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ROV Practice in Brazil



Mining (Vale)

Value of investing in a coal mine in Australia

Decision to shut down aluminum smelter
Oil and Gas (Petrobrás)

Value of the exploration concession period

Biodiesel option analysis.
Public Utilities (Endesa)


Treasury Department (Federal Government)


Value of the flexibility of a small Hydroelectric Power Plant
Value of government guarantees for infra-structure projects
Renewable Fuels:

Value of flex fuel automobiles

Value of flexibility in sugar cane conversion, Biodiesel plants
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The Challenge of Real Options

Since the work of Black, Scholes and Merton in 1973, the use
of Financial Options grew rapidly in the following years.

The same growth was not observed with Real Options even two
decades later.

The principal reason is the fact that Real Options are much
more complex than Financial Options.

Some recent advancements allows us now to resolve some of
these limitations and obtain practical results.

The Monte Carlo simulation and the decision trees are some of
the tools that allows us to make stochastic simulations and
model the flexibilities of a project.

These tools require the extensive use of computers to resolve
automatically the mathematical models.
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Real Option Valuation Timeline
1973
1979
1980
1990
2001
2004
-
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Black-Scholes-Merton equations for European Options
 Exercised only at expiration
 Basic security doesn’t pay dividends
 Constant volatility
 Simple Options
 Only one source of uncertainty
Cox, Ross and Rubinstein Binomial Model
Electronic forms for use in the PC
Efficient programs for tha analysis of Monte Carlo, Decision Trees
Copeland and Antikarov proposes discrete models
Practical modeling for real problems with: (BDH)
 American Options
 Basic security with dividends
 Variable volatility
 Composed options
 Multiple sources of uncertainty
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Options
What is an option?


An opportunity or a contract that gives you a right but not an
obligation...

Asymmetry of returns

Exercise only if advantageous

Cost to acquire
… of doing something…


… now or in the future…


Usually buying or selling some security
Usually there is a time limit after which the option will expire
… for a pre-determined price.

The price of the security is distinct from the price of the option
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The value of a project depends on:


Value of its assets

Current production capacity

Expected cash flows

Generally evaluated by the DCF method
Value of the Option

Option to postpone

Option to abandon

Option of growth and expansion: investment opportunities

Option to suspend, resume or substitute input or outputs of
production

Cannot be evaluated with the DCF method, it is necessary to
use option evaluation methods
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Options: Basic Concepts

Basic Security(S)





It s an option where the basic
security is a real security.

The right to buy the basic
security.
Option to Sell - Put

The right to sell the basic
security.
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The date the rights guaranteed by
the option cease.
Premium

Is the price paid to acquire an option.

Equals the value of the option.
Volatility


The pre-determined price for which
the holder of the option can buy or
sell the security.
Expiration Date (T)

Option to Buy - Call


Its an option where the basic
security is a title negociated in
the financial market or a
comodity.
Exercise Price (X)

Real Option


The security that will be received
or given if the option is
exercised.
Financial Option


Represents the degree of uncertainty
on the future price of a basic security
Types of Options

European and American
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The return of a Call is asymmetrical
S<X
S>X
Region of
Exercise
Call Value at
Expiration
Region of no
Exercise
Distribution of
S at time T
0
X

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Value of Basic Security S
The value of the option will never be negative
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The return of a Call is asymmetrical
S<X
S>X
Region of
Exercise
Call Value at
Expiration
Region of no
Exercise
Distribution of
S at time T
0
X

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Value of Basic Security S
The value of the option will never be negative
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Expected Return increases with
uncertainty
S<X
S>X
Region of
Exercise
Call Value at
Expiration
Region of no
Exercise
Distribution of
S at time T
0
X

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Value of Basic Security S
Probability of S > X increases with the volatility of S
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Call: Value before Expirations
S<X
S>X
Inside the
Money
Call Value at
Expiration
Outside the
Money
0
X

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S
Before the expiration the option can have value even if
S < X. This occurs due to the uncertainty in the value of
S at expiration.
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Put Option: Value at Expiration
S<X
S>X
Region of no
Exercise
Call Value at
Expiration
Region of
Exercise
0

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X
Value of Basic Security S
Value at Expiration is F = max (0, X - S)
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Put Option: Value before Expiration
S<X
S>X
Outside the
Money
Call Value at
Expiration
Inside the
Money
0


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X
S
Before the expiration the option can have a value even if
S>X.
This occurs due to the uncertainty in the value of S at
expiration.
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Factors that affect the value of the
Option
Factor
Effect on
Call
Effect on
Put
Increase in price of the basic security(S)
Increases
Decreases
Increase in Exercise Price (X)
Decreases
Increases
Increase in Volatility ( σ)
Increases
Increases
Increase in the expiration term (T)
Increases
Increases
Increase in Interest rates (r)
Increases
Decreases
Increase in Dividends paid (δ)
Decreases
Increases
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Black and Scholes Formula
c 1  2c 2 2
c
rc 

 S r S
2
S 2 S
S
c  SN(d1 )  X ert N (d2 )
S
2
ln  (r  )  t
2
d1  X
 t
where
d2  d1   t
and N(.) is the cumulative normal distribution function

Assumptions:

The value of the basic security grows exponentially and its distribution
is lognormal

The basic security does not pay dividends

Applicable only to European options
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Example

Ex: A European option to buy stock has exercise price of $120 and
expires in a year. The actual value of the stock is $100, the
volatility is 35% and the risk free discount rate is 10%. What is
the value of the option today?

Using the B&S formula: (Hull)
S = $100
X = $120
σ = 35%
C = 10.59
r = 10%
T=1
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Example

Use the Derivagem Software to determine the value of the
following option:
S = $50
X = $50
σ = 20%
r = 6%
T=4

Analytic European

Binomial European 4 steps

Binomial European 20 steps
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Analogy between Financial Optiona
dand Real Options
Financial Options
Real Options
Option to buy (Call)
Option to Invest
Value of the option
PV of the project
Exercise Price
PV of the investment
Time till Expiration
Expiration time
Risk free discount rate
Risk free discount rate
Volatility of the Stock
Volatility of the Project
Dividends
Project Cash Flows
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Real Options
Introduction to Real Options
Prof. Luiz Brandão
[email protected]
2009