Transcript What types of investments does this describe?

Managing Strategic Investment in
an Uncertain World:
A Real Options Approach
Roger A. Morin, PhD
Georgia State University
FI 8360
January 2003
3 Valuation Frameworks
Discounted Cash Flow (DCF)
Comparables
Option Value
Agenda
 The
value of flexibility
 Real options as a way to capture flexibility
 Real options and financial options
 So what? The importance of real options
 Implementing real option valuation
 Next steps
Capital Investments as Options
All kinds of business decisions
are options!
Virtually every corporate finance decision
involving the issuance of securities or the
commitment of capital to a project involves
options in one way or another.
Real Options Defined

Nobel Prize-winning work
of Black-Merton-Scholes


Applications for real
(nonfinancial) assets


Extensions for how real
assets are managed

What is the value of a contract that
gives you the right, but not the
obligation to purchase a share of
IBM at $100 six months from now?
What is the value of starting a
project that gives you the right, but
not the obligation, to launch a sales
program at a cost of $7M six months
from now?
We operate in a fast changing and
uncertain market. How can we
better make strategic decisions,
manage our investments, and
communicate our strategy to Wall
St?
Why An Options Perspective?
 Some
shortcomings in the use of ordinary NPV
analysis can be overcome
 Common ground for uniting capital budgeting
and strategic planning can be established
 Risk-adjusted discounted rates problem
Investment Decisions
1. Irreversibility
2. Uncertainty
3. Flexibility
– Timing
– Scale
– Operations
Investment Decisions
1&2
1&2&3
3 is valuable
Option (flexibility)
valuation
Option Value (a.k.a. flexibility)
Can
be large
Sensitive to uncertainty
Explains why firms appear to
underinvest
Flexibility: Investments have
uncertainty and decision-points
Fund
First Develop Test
Product
Research Results More
Market Launch
Your decision
Sales Brand
Retire
Extension Product
New Information
What types of investments does this
describe?
 R&D
related businesses - biotech,
pharmaceuticals, entertainment.
 Natural resource businesses - extractive
industries.
 Consumer product companies
 High-tech companies
Real Option
Category
Real Option
Type
Scale Up
Invest/
Grow
Switch Up
Scope Up
Defer/
Learn
Study/Start
Scale Down
Disinvest/
Shrink
Switch Down
Scope Down
Current Applications:
Some Frequently Encountered Real Options
 Timing
 Exit
-- now or later
-- limiting possible future losses by exiting now
 Flexibility -- today’s value of the future opportunity to switch
 Operating -- the value of temporary shutdown
 Learning -- value of reducing uncertainty to make better decision
 Growth -- today’s value of possible future payoffs
Future Growth Options
 Valuable
new investment opportunities (“followon projects”) can be viewed as call options on
assets
 Examples:
–
–
–
–
–
–
–
Exploration
Capacity expansion projects
New product introductions
Acquisitions
Advertising outlays
R&D outlays
Commercial development
Investment Project Options: Examples

Growth Option (“Follow-On Projects”)
– Nortel commits to production of digital switching equipment specially
designed for the European market. The project has a negative NPV, but is
justified by the need for a strong market position in this rapidly growing,
and potentially very profitable, market.

Switching Option
– Atlanta Airways buys a jumbo jet with special equipment that allows the
plane to be switched quickly from freight to passenger use or vice versa.
Investment Project Options: Examples
 Timing
Option
– Dow Chemical postpones a major plant expansion. The expansion has
positive NPV, but top management wants to get a better fix on product
demand before proceeding.
 Flexible
Production Facilities
– Lucent Technologies vetoes a fully-integrated, automated production line
for the new digital switches. It relies on standard, less-expensive
equipment. The automated production line is more efficient overall,
according to a NPV calculation.
Investment Project Options: Examples

Fuel Switching
– A power plant has the capacity of burning oil or gas. Mgrs can decide
which fuel to burn in light of fuel prices prevailing in the future

Shut-Down Option
– A power plant can be shut down temporarily. Mgt. can decide whether or
not to operate the plant in light of the avoided cost of power prevailing in
the future

Investment Timing
– Mgt. can invest in new capacity now or defer when more information on
demand growth and fuel prices is available
Which is a closer analogy to these
types of projects?
Bond
Option
Standard NPV analysis treats
projects like bonds
Average promised cash flow
up-front investment
NPV ignores valuable flexibility
Invest
Learn
Do not invest
Decide
Shortcomings of NPV Analysis
– Passive, assumes business as usual with no
management intervention
– Strategic factors ignored
– NPV understates value
 Operating
flexibility ignored
 Valuable follow-on investment projects ignored
– Many investments have uncertain payoffs that are
best valued with an Options approach
– Risk-adjusted discounted rates problem
NPV
ROV
Certainty is a narrow path!
Flexibility
Active Management
NPV’ = NPVpassive + Option Value
Financial Options
A Brief Review
What is an option?
An option provides the holder with the right to buy or
sell a specified quantity of an underlying asset at a fixed
price (exercise price) at or before the expiration date of
the option.
 Since it is a right and not an obligation, the holder can
choose not to exercise the right and allow the option to
expire.
 Two types – call options (right to buy) and put options
(right to sell).

Call Options


A call option gives the buyer of the option the right to buy the
underlying asset at a fixed price (E) at any time prior to the
expiration date. The buyer pays a price for this right (premium)
At expiration,
– If the value of the underlying asset S > E

Buyer makes the difference: S – E
– If the value of the underlying asset S < E


Buyer does not exercise
More generally,
– Value of a call increases as the value of the underlying asset increases
– Value of a call decreases as the value of the underlying asset decreases
Payoff on Call Option
Net payoff on
call option
Exercise price
Price of underlying asset
If asset value < exercise price, you
lose what you paid for call
Payoff on IBM Call Option
Net payoff
E = $100
IBM Stock price
Breakeven = $105
Maximum loss = $5
Put Options


A put option gives the buyer of the option the right to sell the
underlying asset at a fixed price (E) at any time prior to the
expiration date. The buyer pays a price for this right (premium)
At expiration,
– If the value of the underlying asset S < E

Buyer makes the difference: E – S
– If the value of the underlying asset S > E


Buyer does not exercise
More generally,
– Value of a put decreases as the value of the underlying asset increases
– Value of a put increases as the value of the underlying asset decreases
Payoff on Put Option
Net payoff on put
Exercise price
Price of underlying asset
If asset value > exercise price, you
lose what you paid for put
Determinants of Call Option Value





Stock Price - the higher the price of the underlying stock, the
greater the option’s intrinsic value
Exercise Price - the higher the exercise price, the lower the
intrinsic value
Interest Rates - the higher interest rates, the more valuable the
call option
Volatility of the Stock Price - the more volatile the stock
price, the more valuable the option
Time to Maturity - call options increase in value the more time
there is remaining to maturity
Probability
Effect of Volatility on Option Values
Call Option Payoff
10% Volatility
30% Volatility
Asset Price
Time to expiration is one year.
Probability
Effect of Maturity on Option Value
1 Yr Expiration
5 Yrs Expiration
Call Option Payoff
Asset Price
Volatility is 20%.
Option Premium vs Intrinsic Value
Call option price
C
Time value
Intrinsic value
C
0
X
X = Exercise Price
CC = Call option premium
as function of stock price
Stock Price
Determinants of option value
 Variables
Relating to Underlying Asset
 Value
of Underlying Asset
 Variance in that value
 Expected dividends on the asset
 Variables
Relating to Option
 Exercise
Price
 Life of the Option
 Level
of Interest Rates
Summary of Determinants of Option
Value
Factor
Increase in Stock Price
Increase in Exercise Price
Increase in risk
Increase in maturity
Increase in interest rates
Increase in dividends paid
Call
Put
American vs European Options



American: exercise at any time
European: exercise at maturity
American options more valuable


Time premium makes early exercise sub-optimal
Exception:

Asset pays large dividends
Option Valuation

Binomial Option Pricing Model
– Portfolio Replication Method
– Risk Neutral Method

Black-Scholes Model
– Dividend adjustment
– Diffusion vs Jump process
Binomial Option Pricing Model
The Binomial Option Pricing Model assumes that there
are two possible outcomes for the price of the
underlying asset in each period.
 Although this assumption is artificial, realism can be
achieved by partitioning the time horizon into many
short time intervals, so the number of possible outcomes
is large
 Useful first approximation

Binomial Price Path
Su2
Su
Sud
S
Sd
Sd2
Binomial Price Path
$120
$110
$100
$100
$90
t=0
t=1
$80
t=2
Creating a replicating portfolio
 Objective:
use a combination of risk-free borrowinglending and the underlying asset to create the same
cash flows as the option being valued
 Call
= Borrowing + Buying Δ of Underlying Stock
= Selling short Δ on Underlying Asset + Lending
 The number of shares bought or sold is called the option delta
 Put
 The
principles of arbitrage then apply, and the value
of the option has to be equal to the value of the
replicating portfolio
Creating a Replicating Portfolio
Value of Position
Value of Call
If S goes up to Su
ΔSu - $B (1 + r)
Cu
If S goes down to Sd
ΔSd - $B (1 + r)
Cd
Replicating Portfolio
Δ Su - $B (1 + r) = Cu
Δ Sd - $B (1 + r) = Cd
Δ = No. of units of underlying asset bought
Cu - Cd
Δ
=
Su - Sd
Replicating Portfolio: Example 1
$55
Stock:
$50
$45
1-yr Call, E = $50

Rf = 5%
C = $3.57 all investors agree!
Replicating Portfolio: Example 1
Call - Stock Payoffs:
(55, 5)
(50, ?)
(45, 0)
We can duplicate the above payoffs with a position in common
stock and borrowing, that is, by “portfolio replication”.
Replicating Portfolio
Δ Su - $B (1 + r) = Cu
Δ Sd - $B (1 + r) = Cd
Cu - Cd
Δ =
$5 - $0
=
Su - Sd
Δ = 50 shares !
= 0.50
$55 - $45
B = $2,142 !
50 shares of stock
+
1-year loan of $2,142.86
Portfolio is now worth: 50 x $50 - $2,142.86 = $357.14
Portfolio payoffs:
50 x $55 - 2,250 = 500
(50, ?)
50 x $45 - 2,250 = 0
SAME AS CALL OPTION PAYOFFS!
FAIR VALUE OF 100 CALLS = $357.14
No Free Lunch!
Absence of Riskless Arbitrage Profits
If C > $357.14, sell overpriced call
buy duplicating portfolio
KEY: can construct a levered position in
underlying stock that gives the same payoffs
as the call option.
Binomial Valuation: Example 2
Call
$100
$50
$50
$0
$25
t=2
$0
E = $50
Rf = 11%
$70
$50
$35
t=0
t=1
Binomial Valuation: Example 2
Call
$100
$50
$50
$0
$25
t=2
$0
E = $50
Rf = 11%
$70
$50
$35
t=0
t=1
Replicating Portfolio When S = $70
E = $50
Call
Replicating Portfolio
$100 $50
100 Δ - 1.11B = 50
$50
50 Δ - 1.11B = 0
Rf = 11%
$70
t=1
t=2
$0
Solving: Δ = 1 B = 45
Buy 1 share, borrow $45
Value of Call at t = 1
70 Δ - B = 70 - 45 = $25
Binomial Valuation: Example 2
Call
$100
$50
$50
$0
$25
t=2
$0
E = $50
Rf = 11%
$70
$50
$35
t=0
t=1
Replicating Portfolio When S = $35
E = $50
Call
Replicating Portfolio
$50
$0
50 Δ - 1.11B = 0
$25
$0
25 Δ - 1.11B = 0
Rf = 11%
$35
Solving: Δ = 0 B = 0
t=1
t=2
Binomial Valuation: Example 2
Call
$100
$50
$50
$0
$25
t=2
$0
E = $50
Rf = 11%
$70
$50
$35
t=0
t=1
Replicating Portfolios for Call Value
E = $50
Replicating Portfolio
Call
Rf = 11%
$70 $25 from Step 1
70 Δ - 1.11B = 25
$35 $0 from Step 1
35 Δ - 1.11B = 0
$50
Solving: Δ = 5/7 B = 22.5
Buy 5/7 share, borrow $22.5
t=0
t=1
Value of Call at t = 0
Cost of replicating portfolio = value of call
50 Δ - B = 50 x 5/7 - 22.5 = $13.20
Binomial Pricing
Risk-Neutral Method
$55
Stock:
$50
$45
1-year Call, E = $50, Rf = 5%
Binomial Pricing: Risk-Neutral Method
Step 1
Step 2
Step 3
Solve for probability of rise
0.05 = 0.10 p + (-0.10) (1 - p)
p = 0.75
Solve for expected future value of option
C1 = 0.75 x $5 + 0.25 x $0
= $3.75
Solve for current value of option
C0 = $3.75/1.05 = $3.57
Note: This is an extremely powerful and useful result from the perspective of
devising numerical procedures for computing option values.
The Limiting Distributions……..

As the time interval is shortened, the limiting
distribution, as t
0, can take one of two forms:
– as t
0, price changes become smaller, the limiting
distribution is the normal distribution and the price process is
a continuous one.
– as t
0, price changes remain large, the limiting
distribution is the Poisson distribution, i.e. a distribution that
allows for price jumps

The Black-Scholes model applies when the limiting
distribution is the normal distribution, and assumes that
the price process is continuous and that there are no
jumps in asset prices
Black-Scholes Model

C = S N(d1) - K e-iT N(d2)

Where:
–
–
–
–
–
–
–
–
C
S
N(d1)
K
i
T
N(d2)
s
= value of the call option
= current stock price
= cumulative normal density function of d1
= the exercise price of the option
= the risk-free rate of interest
= expiration date of the option (fraction of a year)
= cumulative density function of d2
= standard deviation of the annual rate of return
Black-Scholes Model
C
= S N(d1) - K e-iT N(d2)
Where:
d1 = [ln(S/K) + (i + 0.5s2)T] / sT1/2
d2 = d1 - sT1/2

The replicating portfolio is embedded in the BlackScholes model. To replicate this call, you need to:
–
–
Buy N(d1) shares of stock; N(d1) is the option delta
Borrow K e-iT N(d2)
Adjusting for Dividends

If the dividend yield (y) of the underlying asset is
expected to remain unchanged during the life of the
option, the Black-Scholes can be modified:
C
= S e-yT N(d1) - K e-iT N(d2)
Where:
d1 = [ln(S/K) + (i – y + 0.5s2)T] / sT1/2
d2 = d1 - sT1/2
Application Problems
1. Underlying asset may not be traded; difficult to
estimate value and variance of underlying asset
2. Price of the asset may not follow a continuous process
3. Variance may not be known and may change over the
life of the option
4. Exercise may not be instantaneous
5. Some real options are complex and their exercise
creates other options (compound) or involve learning
(learning options)
6. More than one source of variability (rainbow options)
Jumping from financial options to real options
FINANCIAL OPTION
REAL OPTION
Underlying asset
Stock price
Value of developed
project
Volatility of project
returns
Value of investment
Volatility
Exercise price
Volatility of stock price
returns
Exercise price
Time to maturity
Contract’s maturity
Ownership rights
Interest rates
Dividends paid prior to
exercise
Interest rate
Contract terms
American or European Early exercise permitted?
License period or
rights period
Cash flow foregone
by waiting
Interest rate
Real Options: Link between
Investments and Black-Scholes Inputs
PV of project
Free Cash Flow
Outlay to acquire
project assets
Time the decision
can be deferred
Time value of
money
Risk of project assets
S
Stock price
X
Exercise price
T
Time to expiration
i
Risk-free rate
s2
Variance of returns
“S - X”
Conditional
NPV of project
NPV
NPV
“X”
Investment
Savg
“S”
Value of
Developed
Project
Option Value: dead and live
“S - X”
Intrinsic Value
of Option
NPV
Live
Option
Value
Dead
Option
Value
“X”
Investment
Savg
“S”
Value of
Developed
Project
When options really matter
“S - X”
In the
Money
At the
Out of the
Money
Money
“S”
When options really matter
“S - X”
In the
Money
At the
Money
Out of the
Money
“S”
Characteristics of Projects Where
Optionality is Important
 “Long-shot”
projects (out of the $)
 Substantial flexibility ignored in project
 Examples: Valuing investments in oil fields
– Where you are valuing the rights to an “expensive” field
– Where you are valuing the rights to produce in a very cheap
field
“ I’m sold, but what do I do?”
Technique
 First
step is framing the question
 Next, there are a variety of techniques
– Force-fit problem into stylized model, like BlackScholes.
– Create customized model to recognize the
complicated set of managerial choices
 Finally,
you have to work through some
important nuances.
Framing the question is critical
 Identifying
the optionality
– What is the flexibility?
– Is it like a call? A put? A more complicated
structure?
 Scope
out the importance
 Is this flexibility that is likely to be important to
you? Is the project “marginal” under NPV, but
there is phased investment and learning?