real options introduction to real options prof. luiz brandão [email protected] 2009
TRANSCRIPT
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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.
What is the value of this project?
5.500 2.20010% 3.000 (0.5) (0.5)
1.10 1.10NPV
10% 3.000 2.500 1.000 $500NPV
High
5.500
Low
2.200
Invest
-3.000
Value
Do not Invest
Decision
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Project with Flexibility Note we implicitly are adopting
the assumption that the project will be implemented now or never.
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.
2 2
3.000 5.500 3.000 2.2000.5 0.5
1.10 1.10 1.10 1.10
0.5 2.272 4.545 0.5 2.727 1.818
VPL
VPL
909 456 909zero
VPL
Invest
-3.000 + 5.500/1.1
No
High
Invest
-3.000 + 2.200/1.1
No
Low
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Evolution of Evaluation Methods
DCF Sensitivity Analysis
Decision Trees
SimulationModels
Financial Options
Real Options
NPVIRR
Value of the Information
Strategic Considerations
Impact of Variables
Risk Management
Risk Analysis
CAPM
1930-1950 1950 1960 1970 1980
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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.
Independent of the result of the project, the capital invested, or the major part of it, cannot be recuperated
The Future Cash Flows are Uncertain.
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
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 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
Invest
Don’t Invest
Good News
Bad News
Good News
Bad News
A) This is not an option
+ $$$
0
0
- $$$
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Identifying Real Options 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?
Invest
Don’t Invest
Good News
Bad News
Don’t Invest
Invest
B) This is an option
0
0
+ $$$
- $$$X
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Identifying OptionsHollywood
The value of a film may include the value of the option to make sequels.
Microsoft 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.
The project’s cash flow will be affected by the uncertainty of the market as well as by whether competitors will enter the market.
88.0
66.0
0.50
0.50
150
70
0.50
0.50
-30
-60
0.50
0.50
-100
t = 1 t = 2t = 0
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Biodata: Cash Flow
88.0
66.0
0.50
0.50
150
70
0.50
0.50
-30
-60
0.50
0.50
-100
t = 1 t = 2t = 0
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Example: Abandonment Option What is the NPV of this project?
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?
2 2
88 + 66 150 70 30 60 -100 0.5 0.25 0.25 3.14
1.10 1.10 1.10VPL
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88.0
66.0
0.50
0.50
150
70
0.50
0.50
-30
--60
0.50
0.50
-100
t = 1 t = 2t = 0
Example: Abandonment Option
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Exemplo: Opção de Abandono
2 2
88 +66 150 70 30 60 -100 0.5 0.25 0.25
1.10 1.10 1.10VPL
15.453.14
What is the NPV with the option to abandon?
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 Uncertainty
Level of
Fle
xib
ilit
yC
ap
aci
ty t
o r
eact
to n
ew
in
form
ati
on Moderate High
Low Moderate
Option Value
Effect of flexibility and uncertainty
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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.
The project’s risk is 20%, the probability of success is 50% and the risk free discount rate is 8%.
How real options affect risk
$60M
t = 0
$180M
- $115M
0.50
0.50
t = 1
For $20M, the company has the option to buy an insurance that would pay $120M if the project fails.
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StereoGram The expected value of the project
without the insurance is:
Given that the investment cost is $115, the project is not appealing to the company because its NPV will be negative.
Ex: StereoGram Ltd.
$60M
t = 0
$180M
- $115M
0.50
0.50
t = 1
0.5(180) 0.5(60)$100
1.2PV
115 100 $15NPV
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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:
In this case, the value of the project will be
The NPV increases to
Ex: StereoGram Ltd.
60M+120M = $180M
t = 0
180M + 0 = $180M
- $115M
0.50
0.50
t = 1
0.5(180) 0.5(180)$150
1.2PV
115 150 $35NPV
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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:
Even buying the insurance for $20M, the company still increases its value by 51.67 – 20 = $31.67
Ex: StereoGram Ltd.
0.5(180) 0.5(180)$166.7
1.08PV
115 166.7 $51.67NPV
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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)
Value of the flexibility of a small Hydroelectric Power Plant
Treasury Department (Federal Government)
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 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
1979 Cox, Ross and Rubinstein Binomial Model
1980 - Electronic forms for use in the PC
1990 - Efficient programs for tha analysis of Monte Carlo, Decision Trees
2001 - Copeland and Antikarov proposes discrete models
2004 - Practical modeling for real problems with: (BDH) American Options Basic security with dividends Variable volatility Composed options Multiple sources of uncertainty
Options
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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… Usually buying or selling some security
… now or in the future… 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)
The security that will be received or given if the option is exercised.
Financial Option Its an option where the basic
security is a title negociated in the financial market or a comodity.
Real Option It s an option where the basic
security is a real security.
Option to Buy - Call The right to buy the basic security.
Option to Sell - Put The right to sell the basic security.
Exercise Price (X) The pre-determined price for which
the holder of the option can buy or sell the security.
Expiration Date (T) 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 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
Value of Basic Security SX
Call
Valu
e a
t
Expir
ati
on
S < X
Region of no Exercise
S > X
Region of Exercise
0
Distribution of S at time T
The value of the option will never be negative
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The return of a Call is asymmetrical
Value of Basic Security SX
Call
Valu
e a
t
Expir
ati
on
S < X
Region of no Exercise
S > X
Region of Exercise
0
The value of the option will never be negative
Distribution of S at time T
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Expected Return increases with uncertainty
X
S < X S > X
0
Probability of S > X increases with the volatility of S
Value of Basic Security S
Call
Valu
e a
t
Expir
ati
on
Region of no Exercise
Region of Exercise
Distribution of S at time T
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Call: Value before Expirations
SX
S < X S > X
Outside the Money
Inside the Money
0
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.
Call
Valu
e a
t Expir
ati
on
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X
S < X S > X
0
Value at Expiration is F = max (0, X - S)
Put Option: Value at Expiration
Value of Basic Security S
Call
Valu
e a
t Expir
ati
on
Region of Exercise
Region of no Exercise
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SX
S < X S > X
Outside the Money
Inside the Money
0
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.
Call
Valu
e a
t Expir
ati
on
Put Option: Value before 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
where
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
)()( 21 dNeXdSNc rt
t
trXS
d
)2
(ln2
1tdd 12
22 2
2
1
2
c c crc S r S
S S S
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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%
r = 10%
T = 1
C = 10.59
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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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Financial Options
Option to buy (Call)
Value of the option
Exercise Price
Time till Expiration
Risk free discount rate
Volatility of the Stock
Dividends
Analogy between Financial Optiona dand Real Options
Real Options
Option to Invest
PV of the project
PV of the investment
Expiration time
Risk free discount rate
Volatility of the Project
Project Cash Flows
