Real Options
Mehmet Bozbay
Hoksung Yau
Laura Goadrich
Ping Fong Hsieh
Sirisha Sumanth
March 8, 2004
Chapter 4: Getting Real About
Real Options
Objectives
Overview
Terminology
Real options in the Real world
Overvaluing options (Agouron)
Exploring options (Cisco)
Case study (Nole)
Summary
Issues in Real Options
 Advantages:
Successfully explains valuation of multiple
companies believed to have substantial real options
Explain some of the difference in markets not
accounted by traditional techniques
 Disadvantage:
Real Options can be miscaluculated/misused and
misvalue a company
 Provides a method to exemplify market
outcomes using nontraditional techniques
Overview: Real Options
 Helps investors determine whether a
company’s stock is over- or undervalued
 Real options considers impact of:
Risk
New technology
New market
…
 Real-World Examples: Agouron
Pharmaceuticals, Cisco, Nole
Terminology
 Scope-up options
 Opportunities to increase variability in product lines
 Eg. IBM expanding to create graphic cards
 Scale-up options
 Opportunities to expand capacity
 Eg. Power Packaging took over one plant of General Mills
 Learning options
 Opportunities to acquire companies with the goal of entering
into new businesses
 Eg. GE taking over Datex-Ohmeda
 Equity Stakes
 Purchasing equity in start-up companies
Real-World Example:
Agouron Pharmaceuticals
 Kellogg & Charnes (2000) Financial Analysts
Journal
 Illustrates the problem of valuing a company with
real options and how that valuation can differ
from the market’s valuation
 Background: biotechnology companies known for
having high values when their products are in
development (no positive cash flow)
Real-World Example:
Agouron Pharmaceuticals
 Types of real options available
Growth option
 Expand production if favorable in the market
Abandonment option (why choose?)
 Viable reasons for abandonment
• inhibit share holder loss
• scrap failing projects
• …
Real-World Example:
Agouron Pharmaceuticals
Real World Example:
Agouron Pharmaceuticals
 Valuations of Agouron based on real options differed from
the actual market values of the company’s stock as a
particular drug progressed through the development
process






Discovery
Preclinical
Clinical trial- phase I
Clinical trial- phase II
Clinical trial- phase III
FDA filing and review
 Once the drug hit the market, the drug can vary in quality
from
Breakthrough - Above Average - Average - Below Average - Dog
Real World Example:
Agouron Pharmaceuticals
 Root cause of differences:
The abandonment of a drug is rarely announced
 Only one drug made it to phase II and III
 Potential projects were included in the valuation when
they were not part of the product pipeline
Investors were making different assumptions
 Political pressure for FDA to approve drugs for HIVpositive patients
 Assumed need less than eight years from phase II to
launch, but only took two years
Sales were four times expectations in the first year
 Lesson: real options were not overlooked by the
market, but may have been overvalued
Real-World Example:
Cisco Basics
 Sell: Networking supplies
 Scale-up options
Supply network equipment for Internet connectivity
 Scope-up options
 Supplies businesses and individuals
 Learning options
Integrating voice, video and data in their network
Real-World Example:
Cisco Example
 Traditional discounted cash flow example
 Market Value (FY 2000): $445.1 billion
 Assumptions:
Earnings will grow at a rate of 10% annually after 2005
The risk-free rate is 5%
The market risk premium is 6%
There is no adjustment for earnings after 5 years
Real-World Example:
Cisco Evaluation
CostOfCapital = riskFreeRateOfInterest + riskPremiumOfMarket * Volatility
= 5% + (6% * 1.45) = 13.7%
TermValue2005 
$15.093billion(1  0.10)
 448.800billion
(0.137  0.10)
Real-World Example:
Cisco Sensitivity Analysis
 DCF = $266.565billion vs. Market Value= $445.1billion
 Difference: $178.535billion
 Sensitivity Analysis
 Vary constant growth rate of 10% to 11%
 DCF – MarketValue = $91.061million
 Vary cost of capital from 13.7% to 16%
 Difference: $284.873million
 Lesson: Not considering options poorly represents the
actual market value.
Real-World Example:
Nole Background
 Example illustrating valuing an option.
 Initial start-up costs
capital expenditures $500million
investment in working capital $50million
 Depreciation & capital expenditures
$100million/year
 Option 1: Not expand
Revenues
Y1 $1billion
Y4 $1.526billion
Y2 $1.2billion
Y5 $1.617billion
Y3 $1.44billion
Y6 $1.715billion
Real-World Example:
Nole Choices
 Option 2: Expand in year 3 with $2billion
Annual depreciation $200million
Expenditures
Annual capital expenditures year 4, 5, 6 each
$100million
No additional capital expenditures
Revenues
Y1 $1billion
Y2 $1.2billion
Y4 $1.9billion Y5 $2.47billion
Y3 $1.44billion
Y6 $3.211billion
Real-World Example:
Nole Expanding in Y3, init Y0
Real-World Example:
Nole Without Expanding in Y3, init Y0
Real-World Example:
Nole Value of Expanding Option
Real-World Example:
Nole Strategic Value
Real-World Example:
Nole Expanding Black-Scholes
P   presentValueOfCashFlow  termValue
Value of option=
P x N(d1) –
X
x e –r x t x N(d2)
= $1,231 x 0.4678 – $2,300 x e-6% x 3 x 0.1718
= $245million
Value of Expansion Option using DCF = -$31million
Real-World Example:
Nole Volitility
Real-World Example:
Nole Variability of Volatility
Increasing volatility
increases cost of capital
decreases value of underlying
decreases value of option
Summary
 Agouron showed a large difference between real
world valuations and traditional methods.
 Cisco illustrated the positive impact of using
options.
 Nole compared the valuation traditional verses
options and clearly expressed the need for
options to describe the marketplace.
Chapter 5: Pitfalls and
Pratfalls in Real Option
Valuation
Complication from Internal and External
Interactions
Interaction between option holders and underlying
asset’s value can complicate the analysis of real option.
Inability to Explain Absurd Valuation
The options a company has are usually not independent
with each other. Their values are not additive. It’s
questionable whether the presence of real options can
explain the absurd price that were witnessed in recent
years for many Internet stock.
 Model Risk
The risk associated with the use of an incorrect model
or incorrect inputs
Example :





American put option on a stock priced $100
The exercise price is $100
Risk-free is 5 %
One year to expiration
Volatility is 32 %
The correct model (binomial model) gives the price value $16.41
Incorrect model ( Black-Scholes) gives the price value
$15.48
Error 5.7%
Failure to meet Assumption
Major Assumptions
Lognormality
Randomness
Known and constant volatility
Minor Assumptions
Known and constant risk-free rate
No taxes and transaction costs
American-style option
Major Assumptions
Lognormality
The rate of return on the underlying asset is lognormally distribution.
Example:
A non-dividend –paying stock sells for $100 and moves up to $110 after one
year. The logarithmic return is ln(1.10) = 9.53%
The model typically assume the logarithmic return follows a normal distribution,
which means the return itself follows a lognormality distribution
Randomness
Prices are randomness to assure that markets are competitiveness that allows
pricing models to work. No one participant can dominate all the others.
Known and constant volatility
The volatility in standard option-pricing models is not directly observe and easy
to obtain.
Also, the models are sensitive to the volatility.
Minor Assumptions
1. Known and constant risk-free rate
Option-pricing models generally assume a known and
constant risk-free rate.
2. No taxes and transaction costs
It facilitates the capture of most essential elements of
the economic process being modeled.
3. American-style option
The option is the one that can be exercised before
expiration. It offers more flexibility.
Difficulty of Estimating Inputs
1. Market Value of the Underlying Asset
Sometimes, the estimating for appropriate discount rate, the life of a
project may be difficult.
2. Exercise Price
The amount of money can be received or paid in the future are difficult
to determine.
3. Time to Expiration
A company can’t know how long it can keep a project before
abandoning it to claim a salvage value.
4. Volatility
The option prices are very sensitive to the estimate of volatility. But it is
very difficult to observe in financial option-pricing application.
5. Risk-Free Rate
The value of an option is not so sensitive to estimate of the risk-free
rate.
It is acceptable to obtain an estimate of the risk-free rate by
estimating the rate on a default-free zero-coupon security.
Example
A real option expires in 275 days
Let the bid and ask discount rates on US government zero-coupon
bonds (Treasury Bills) for maturity be 4.52% and 4.54%
We spilt the difference and assume a rate of 4.53%
Example
The price of one year bill
 Days to maturity 
Price  Face value  Discount Rate

360


 275 
 $100  4.53

 360 
 $96.54
If the T-bill price is $96.54 per $100 par, the annual rate is
 Face value 
Rate  

Price


 100 


 96.54 
 0.0478
( Days to maturity/ 365)
1
( 365/ 275)
1
The continuous compounded rate is (in order to use in Black-Schole Model)
ln( 1.0478)  0.0467  4.67%
Nontradability of the Underlying Asset
 Assumption in the area of real options analysis:
underlying asset can be bought and sold in a
liquid market.
 When using binomial approach, the ability to
trade the asset and the option in such a manner
that no arbitrage opportunity exists is the glue
that binds the models together.
Assumptions of Hedging, Tradability, and
Risk Neutral Valuation
1 r  d
1.05  0.50
p

 0.55
ud
1.5  0.5
 r: Risk-free rate (5%)
 u: Holding period return on the stock if it goes
up ($150)
 d: Holding period return on the stock if it goes
down ($50)
 Stock price: $100
Option price calculation
0.55($50)  0.45($0)
c
 $26.19
1.05
Risk-adjusted discount rate and
probability of outcomes
q ($150)  (1  q )($ 50)
$100 
1 k
If the probability of up move is 0.6, then
Risk-adjusted discount rate k = 0.1.
If k = 0.12, then q=0.62.
Risk-adjusted discount rate and
probability of outcomes (cont.)
 If k is risk-free rate, then
q ($150)  (1  q )($ 50)
$100 
1.05
q  0.55
q p
 q plays the same role as p in the optionvaluation problem. Option-pricing models are
often said to use risk neutral valuation.
Consistency of All Approaches
 No one assume investors are risk neutral.
Rather, risk neutral valuation is simple and
imposes only light demands.
 Risk neutral valuation is not a different approach
that obtains different numbers from a standard
risk-adjusted approach.(Feinstein 1999)
Example
 Invest $9 in a project
 If the outcome is good, invest $18 and begin to
generate $10 a year forever.
 If the outcome is bad, invest $18 and begin to
generate $3 a year forever.
 Probability of good outcome is 0.6 and bad
outcome is 0.4
 Discount rate is 25%
Example (cont.)
 The market value of the project is:
G
1
V
V1B
$10

 $40 or
0.25
$3

 $12
0.25
 The market value of the project at time 1 is:
X 1G  $40  $18  $22 or
X 1B  $12  $18  $6
Example (cont.)
 The value of the project at time 0 is:
V 
0
 NPV is
[0.6($22)  0.4( $0.6)]
 $8.64
1.25
$8.64$9$0.36
$22
 Up factor: u 
 2.5463
8.64
$6
 Down factor: d 
 0.6944
$8.64
 The risk neutral probability is
1.05( 0.6944)
p 
 0.5383
( 2.5463( 0.6944)
Example (cont.)
 Option value  0.5383($22)  0.4617($0)  $11.28
1.05
 According to Feinstein’s approach, the overall discount rate
is a blend of 25% and 5%. So the weighted discounted rate
is:
G
B
kw 
[qX 1  (1  q ) X 1 ](1  r )
-1
G
B
pX 1  (1  p ) X 1
[0.6($22)  0.4($0)](1.05)
1
0.5383($22)  0.4617($0)
 0.1704

 The correct project value is
0.6($22)  0.4($0)
 $11.28
1  0.1704
Summary
 One source of difficulty in applying real options
valuation is the assumption may or may not be
appropriate in the case of real options (lognormality
distribution of the value of the underlying asset,
randomness of prices)
 The estimation of inputs, such as the volatility of the
value of the underlying asset, the exercise price, the
time to expiration, is more challenging for real
options than for fincial options.
Chapter 6: Empirical Evidence
on the Use and Accuracy of
Real Options Valuation
Paddock, Siegel, and Smith (1988) – Option
Valuation of Claims on Real Assets: The Case of
Offshore Petroleum Leases
 Real options model for valuing offshore oil and gas
leases in a federal sale of 21 tracts in the Gulf of
Mexico.
 Real options were not able to explain the bids as
well as one might have hoped.
Real options theory was not very well-known in 1988.
Data provided by the government were not too good to
carry out analysis.
 Winner’s curse – tendency for the highest bidder
to pay more than fair
Quigg (1993) – Empirical Testing of Real Option-Pricing
Models
 Market prices of 2,700 land transactions in
Seattle during 1976-1979.
Market prices reflect a premium for the option to wait
to invest (optimal development) that has a mean
value of 6% of the land value.
Supports the belief that investors either use real
options models or trade in such a manner that their
valuations are consistent with those of real options
models.
Berger, Ofek, and Swary (1996) – Investor
Valuation of the Abandonment Option
 Whether investors price the option to abandon a firm
at its exit value.
 This option is priced as an American put, whose
value increases with exit value.
Significant relationship between a company’s market
value and its estimated exit value, suggesting that
investors take the option to exit into account when
valuing companies.
The more likely the option will be exercised, the more
valuable is the option.
Hayn (1995) – The Information Content of Losses
 Hypothesizes that because shareholders have a
liquidation option, losses are not expected to
perpetuate. They are thus less informative than
profits about the firm’s future prospects.
The results are consistent with the hypothesis.
Investors do not respond to losses to the same
magnitude that they do to profits.
Option to liquidate is valued by investors.
Moel and Tufano (2002) – When Are Real Options
Exercised? An Empirical Study of Mine Closings
 The flexibility that mining firms have to open and close
mines.
The overall pattern of closures is well predicted by real
option theory.
Closures are influenced by the price and volatility of gold,
firm’s operating costs, proxies for closing costs, and the
size of reserves.
Fail to capture aspects of firm-level decision making.
 Divisions within a firm share a common destiny and
decision about particular units are influenced by the
performance of the other parts of the firm.
Clayton and Yermack (1999) – Major League Baseball
Player Contracts: An Investigation of the Empirical
Properties of Real Options
 Contracts negotiated between professional baseball
players and teams to investigate the use of real
options in a commercial setting.
 Baseball contracts feature options in diverse forms,
and they found that these options have significant
effects on player compensation.
 As predicted by theory, players receive higher guaranteed
compensation when they allow teams to take options on
their future services, and lower salaries when they bargain
for options to extend their own contracts.
 The apparent value of options decreases as a function of the
"spread" between option exercise price and annual salary
and increases as a function of the time until exercise.
Howell and Jagle (1997) – Laboratory Evidence on How
Managers Intuitively Value Real Growth Options
 Asked managers series of questions on growth options from
some investment case studies, asked other questions related to
their personal situations and the kinds of investment decisions
they make in their work.
 Skilled managerial decision makers agree only approximately with
real option theory.
 They tend on average to value growth options in an erratic way.
 Overvaluation seems to be a function of “Industry”, being lowest in
the oil industry, and it is also a function of (Business) “Experience”
and “Position” being highest for more senior people.
 The result can be interpreted in two ways:
 This limited sample of managers is not sufficiently knowledgeable
about real options models.
 Real options models are simply not used in practice.
 Small sample size is a major limitation of this study (82 managers)
Busby and Pitts (1997) - Real options in practice: an
exploratory survey of how finance officers deal with
flexibility in capital appraisal
 Dissatisfaction with discounted cash flow techniques has lead to a
growing literature focusing on the value of managerial flexibility in
handling real asset investments, a subject area known as real options.
 An exploratory survey of senior finance officers in industrial firms,
examining the significance that real options assumed in their
investment decisions, whether their firms had established procedures
for assessing real options, and whether their intuitions were consistent
with what theory prescribes.
 There was wide variation between individual decision-makers in their
perception of real options.
 Few firms have procedures to assess options in advance.
 Very few decision-makers seemed to be aware of real option research but,
mostly, their intuitions agreed with the qualitative prescriptions of such work.
Chapter 7: Summary and
Conclusions
 Companies are often highly misvalued in the market
 Corporate investment decisions are typically made
using standard discounted cash flow (DCF)
techniques, which are not equipped to accommodate
real options
 Discounted cash flow techniques that attempt to
capture flexibility are not adequate
 The valuation of financial options has benefited from
years of study, evolving from the binomial and Black–
Scholes models.
 A number of limitations and difficulties arise in
applying real options
 Real options models oftentimes do not meet the
assumptions inherent in the models
 The estimation of inputs in real options models is
particularly challenging
 The models are based on the idea that one can trade
the underlying asset and the option to form a risk-free
hedge or trade a combination of the underlying asset
and risk free bonds to replicate the payoffs of the
option
 Empirical research has provided some, but very
limited, support for the real-world applicability of real
options models
Thank you