Managing Strategic Investment in an Uncertain World: A Real Options Approach

1
Managing Strategic Investment in an Uncertain
WorldA Real Options Approach

• Roger A. Morin, PhD
• Georgia State University
• FI 8360 January 2003

2
3 Valuation Frameworks
Discounted Cash Flow (DCF)
Comparables
Option Value
3
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

4
Capital Investments as Options

• All kinds of business decisions are options!

5

• 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.

6
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?

7
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

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Investment Decisions

• 1. Irreversibility
• 2. Uncertainty
• 3. Flexibility
• Timing
• Scale
• Operations

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Investment Decisions

• 1 2 3 is valuable
• 1 2 3 Option (flexibility)
• valuation

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Option Value (a.k.a. flexibility)

• Can be large
• Sensitive to uncertainty
• Explains why firms appear to underinvest

11
Flexibility Investments have uncertainty and
decision-points

• Fund First Develop Test
  Product Sales Brand Retire
• Research Results More Market Launch
  Extension Product

New Information
Your decision
12
What types of investments does this describe?

• RD related businesses - biotech,
  pharmaceuticals, entertainment.
• Natural resource businesses - extractive
  industries.
• Consumer product companies
• High-tech companies

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Real Option Type
Real Option Category
Scale Up
Invest/ Grow
Switch Up
Scope Up
Defer/ Learn
Study/Start
Scale Down
Disinvest/ Shrink
Switch Down
Scope Down
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Current ApplicationsSome Frequently Encountered
Real Options

• Timing -- now or later
• Exit -- limiting possible future losses by
  exiting now
• Flexibility -- todays value of the future
  opportunity to switch
• Operating -- the value of temporary shutdown
• Learning -- value of reducing uncertainty to make
  better decision
• Growth -- todays value of possible future payoffs

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Future Growth Options

• Valuable new investment opportunities (follow-on
  projects) can be viewed as call options on
  assets
• Examples
• Exploration
• Capacity expansion projects
• New product introductions
• Acquisitions
• Advertising outlays
• RD outlays
• Commercial development

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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.

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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.

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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

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Which is a closer analogy to these types of
projects?
Bond
Option
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Standard NPV analysis treats projects like bonds

Average promised cash flow
up-front investment
21
NPV ignores valuable flexibility
Invest
Learn
Do not invest
Decide
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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

23
NPV
ROV
Certainty is a narrow path!
24

Flexibility
Active Management
25

NPV NPVpassive Option Value
26
Financial Options A Brief Review
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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).

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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 gt E
• Buyer makes the difference S E
• If the value of the underlying asset S lt 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

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Payoff on Call Option
Net payoff on call option
Exercise price
Price of underlying asset
If asset value lt exercise price, you lose what
you paid for call
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Payoff on IBM Call Option
Net payoff
E 100
IBM Stock price
Breakeven 105
Maximum loss 5
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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 lt E
• Buyer makes the difference E S
• If the value of the underlying asset S gt 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

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Payoff on Put Option
Net payoff on put
Exercise price
Price of underlying asset
If asset value gt exercise price, you lose what
you paid for put
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Determinants of Call Option Value

• Stock Price - the higher the price of the
  underlying stock, the greater the options
  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

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Effect of Volatility on Option Values
Call Option Payoff
Probability
10 Volatility
30 Volatility
Asset Price
Time to expiration is one year.
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Effect of Maturity on Option Value
Probability
1 Yr Expiration
Call Option Payoff
5 Yrs Expiration
Asset Price
Volatility is 20.
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Option Premium vs Intrinsic Value
C
Call option price
Time value
Intrinsic value
C
0
X
Stock Price
X Exercise Price CC Call option premium
as function of stock price
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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

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Summary of Determinants of Option Value
Factor Call Put
Increase in Stock Price
Increase in Exercise Price
Increase in risk
Increase in maturity
Increase in interest rates
Increase in dividends paid

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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

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Option Valuation

• Binomial Option Pricing Model
• Portfolio Replication Method
• Risk Neutral Method
• Black-Scholes Model
• Dividend adjustment
• Diffusion vs Jump process

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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

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Binomial Price Path
Su2
Su
Sud
S
Sd
Sd2
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Binomial Price Path
120
110
100
100
90
80
t 0
t 1
t 2
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Creating a replicating portfolio

• Objective use a combination of risk-free
  borrowing-lending and the underlying asset to
  create the same cash flows as the option being
  valued
• Call Borrowing Buying ? of Underlying Stock
• Put Selling short ? on Underlying Asset
  Lending
• The number of shares bought or sold is called the
  option delta
• The principles of arbitrage then apply, and the
  value of the option has to be equal to the value
  of the replicating portfolio

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Creating a Replicating Portfolio
Value of Position Value of Call
If S goes up to Su ?Su - B (1 r) Cu
If S goes down to Sd ?Sd - B (1 r) Cd
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Replicating Portfolio

• ? Su - B (1 r) Cu
• ? Sd - B (1 r) Cd
• ? No. of units of underlying asset bought
• Cu - Cd
• ?
• Su - Sd

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Replicating Portfolio Example 1

• 
  55
• Stock 50
• 
  45
• 1-yr Call, E 50 Rf 5
• ? C 3.57 all investors agree!

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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.

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Replicating Portfolio

• ? Su - B (1 r) Cu
• ? Sd - B (1 r) Cd
• Cu - Cd 5 -
  0
• ?
  0.50
• Su - Sd 55 -
  45
• ? 50 shares ! B 2,142 !

50

• 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

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No Free Lunch!

• Absence of Riskless Arbitrage Profits
• If C gt 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.

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Binomial Valuation Example 2
Call
100
50
E 50 Rf 11
70
50
0
50
35
25
0
t 0
t 1
t 2
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Binomial Valuation Example 2
Call
100
50
E 50 Rf 11
70
50
0
50
35
25
0
t 0
t 1
t 2
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Replicating Portfolio When S 70
E 50 Rf 11
Call
Replicating Portfolio
100
50
100 ? - 1.11B 50
70
50
0
50 ? - 1.11B 0
Solving ? 1 B 45 Buy 1 share, borrow 45
t 1
t 2
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Value of Call at t 1

• 70 ? - B 70 - 45 25

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Binomial Valuation Example 2
Call
100
50
E 50 Rf 11
70
50
0
50
35
25
0
t 0
t 1
t 2
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Replicating Portfolio When S 35
E 50 Rf 11
Call
Replicating Portfolio
50
0
50 ? - 1.11B 0
35
25
0
25 ? - 1.11B 0
Solving ? 0 B 0
t 1
t 2
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Binomial Valuation Example 2
Call
100
50
E 50 Rf 11
70
50
0
50
35
25
0
t 0
t 1
t 2
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Replicating Portfolios for Call Value
E 50 Rf 11
Call
Replicating Portfolio
70
25 from Step 1
70 ? - 1.11B 25
50
35
0 from Step 1
35 ? - 1.11B 0
Solving ? 5/7 B 22.5 Buy 5/7 share,
borrow 22.5
t 0
t 1
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Value of Call at t 0

• Cost of replicating portfolio value of call
• 50 ? - B 50 x 5/7 - 22.5 13.20

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Binomial PricingRisk-Neutral Method

• 55
• Stock 50
• 
  45
• 1-year Call, E 50, Rf 5

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Binomial Pricing Risk-Neutral Method

• Step 1 Solve for probability of rise
• 0.05 0.10 p
  (-0.10) (1 - p)
• p 0.75
• Step 2 Solve for expected future value of
  option
• C1 0.75 x 5 0.25 x 0
• 3.75
• Step 3 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.

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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

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Black-Scholes Model

• C S N(d1) - K e-iT N(d2)
• Where
• C value of the call option
• S current stock price
• N(d1) cumulative normal density function of
  d1
• K the exercise price of the option
• i the risk-free rate of interest
• T expiration date of the option
  (fraction of a year)
• N(d2) cumulative density function of d2
• s standard deviation of the annual
  rate of return

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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
  Black-Scholes 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)

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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

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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)

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Jumping from financial options to real options
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Real Options Link betweenInvestments and
Black-Scholes Inputs
PV of project Free Cash Flow
Stock price
S
Outlay to acquire project assets
Exercise price
X
Time the decision can be deferred
Time to expiration
T
Time value of money
Risk-free rate
i
Risk of project assets
Variance of returns
s2
70

S - X Conditional NPV of project
NPV
NPV

Savg
S Value of Developed Project
X Investment
71

Option Value dead and live
S - X Intrinsic Value of Option
NPV

Live Option Value
Dead Option Value
Savg
S Value of Developed Project
X Investment
72

When options really matter
S - X

In the Money
S
At the Money
Out of the Money
73

When options really matter
S - X

In the Money
S
At the Money
Out of the Money
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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

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Im sold, but what do I do?

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Technique

• First step is framing the question
• Next, there are a variety of techniques
• Force-fit problem into stylized model, like
  Black-Scholes.
• Create customized model to recognize the
  complicated set of managerial choices
• Finally, you have to work through some important
  nuances.

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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?