Binnenlandse Francqui Leerstoel VUB 2004-2005 Real Options

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Binnenlandse Francqui Leerstoel VUB
2004-2005Real Options

• André Farber
• Solvay Business School
• University of Brussels

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Valuation the traditional approach

• Standard approach V PV(Expected Free Cash
  Flows)
• Free Cash Flow CF from operation CF from
  investment
• Valuation technique discounting using a
  risk-adjusted discount rate
• Setting the discount rate Capital Asset Pricing
  Model

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Making Investment Decisions NPV rule

• NPV a measure of value creation
• NPV V-I with VPV(Additional free cash
  flows)
• NPV rule invest whenever NPVgt0
• Underlying assumptions
• one time choice that cannot be delayed
• single roll of the dices on cash flows
• But
• delaying the investment might be an option
• what about flexibility ?

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Capital Budgeting What techniques are used?
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A simple example the widget factory

• Cost of factory I 4,000
• Produces one widget per year forever with zero
  operating cost
• Price of widget uncertain

t 0
t 1
t 2
P1 300
P2 300
Proba 0.50
P0 200
Proba 0.50
P1 100
P2 100
Risk-free interest rate 5 ß 0
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Traditional NPV calculation

• Expected price 0.5 300 0.5 100 200
• Expected cash flows

t 0 t 1 t 2 t 3
Operating CF 200 200 200 200
Investment CF -4,000
What would you decide?
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What if we wait one year?
P1 300 ? NPV -4,000 300 300/0.05
2,300 DECISION INVEST
Invest ?NPV 200 Wait ? DECISION WAIT
P1 100 ? NPV -4,000 100 100/0.05
-1,900 DECISIONDO NOT INVEST
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Real options take a number of forms

• If an initial investment works out well, then
  management can exercise the option to expand its
  commitment to the strategy.
• For example, a company that enters a new
  geographic market may build a distribution center
  that it can expand easily if market demand
  materializes.
• An initial investment can serve as a platform to
  extend a company's scope into related market
  opportunities.
• For example, Amazon.com's substantial investment
  to develop its customer base, brand name and
  information infrastructure for its core book
  business created a portfolio of real options to
  extend its operations into a variety of new
  businesses.
• Management may begin with a relatively small
  trial investment and create an option to abandon
  the project if results are unsatisfactory.
• Research and development spending is a good
  example. A company's future investment in product
  development often depends on specific performance
  targets achieved in the lab. The option to
  abandon research projects is valuable because the
  company can make investments in stages rather
  than all up-front.

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Portlandia Ale an example

• (based on Amram Kulatilaka Chap 10 Valuing a
  Start-up)
• New microbrewery
• Business plan
• 4 million needed for product development
  (0.5/quarter for 2 years)
• 12 million to launch the product 2 years later
• Expected sales 6 million per year
• Value of established firm 22 million
• (based on market value-to-sales ratio of 3.66)

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DCF value calculation
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But there no obligation to launch the product..

• The decision to launch the product is like a call
  option
• By spending on product development, Portlandia
  Ale acquires
• a right (not an obligation)
• to launch the product in 2 years
• They will launch if, in 2 years, the value of the
  company is greater than the amount to spend to
  launch the product (12 m)
• They have some flexibility.
• How much is it worth?

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Valuing the option to launch

• Let use the Black-Scholes formula (for European
  options)
• At this stage, view it as a black box (sorry..)
• 5 inputs needed
• Call option on a stock Option to launch
• Stock price Current value of established firm
• Exercise price Cost of launch
• Exercise date Launch date
• Risk-free interest rate Risk-free interest rate
• Standard deviation of Volatility of value
• return on the stock

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Volatility

• Volatility of value means that the value of the
  established firm in 2 years might be very
  different from the expected value

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Using Black Scholes

• Current value of established firm 14.46
• Cost of launch 12.00
• Launch date 2 years
• Risk-free interest rate 5
• Volatility of value 40 ??
• andmagic, magic..value of option 4.96

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The value of Portlandia Ale

• (all numbers in millions)
• Traditional NPV calculation
• PV(Investment before launch) - 3.83
• PV(Launch) - 10.86
• PV(Terminal value) 14.46
• Traditional NPV - 0.23
• Real option calculation
• PV(Investment before launch) - 3.83
• Value of option to launch 4.96
• Real option NPV 1.13

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Let us add an additional option

• Each quarter, Portlandia can abandon the project
• This is an American option (can be exercised at
  any time..)
• Valuation using numerical methods (more on this
  later..)
• Traditional NPV calculation
• Traditional NPV - 0.23
• Real option calculation
• PV(Investment before launch) - 3.83
• Value of options to launch and
• to abandon 5.57
• Real option NPV 1.74

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Real option vs DCF NPV

• Where does the additional value come from?
• Flexibility
• changes of the investment schedule in response to
  market uncertainty
• option to launch
• option to continue development

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Back to Portlandia Ale

• Portlandia Ale had 2 different options
• the option to launch (a 2-year European call
  option)
• value can be calculated with BS
• the option to abandon (a 2-year American option)
• How to value this American option?
• No closed form solution
• Numerical method use recursive model based on
  binomial evolution of value
• At each node, check whether to exercice or not.
• Option value Max(Option exercised, option alive)

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Binomial option pricing model review

• Used to value derivative securities PVf(S)
• Evolution of underlying asset binomial model
• u and d capture the volatility of the underlying
  asset
• Replicating portfolio Delta S M
• Law of one price f Delta S M

uS
fu
S
dS
fd
?t
M is the cash positionMgt0 for investmentMlt0 for
borrowing
r is the risk-free interest rate with continuous
compounding
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Risk neutral pricing

• The value of a derivative security is equal to
  risk-neutral expected value discounted at the
  risk-free interest rate
• p is the risk-neutral probability of an up
  movement

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Valuing a compound option (step 1)

• Each quaterly payment ( 0.5 m) is a call option
  on the option to launch the product. This is a
  compound option.
• To value this compound option
• 1. Build the binomial tree for the value of the
  company
• 0 1 2 3 4 5 6 7 8
• 14.46 17.66 21.56 26.34 32.17 39.29 47.99 58.62
  71.60
• 11.83 14.46 17.66 21.56 26.34 32.17 39.29
  47.99 9.69 11.83 14.46 17.66 21.56 26.34
  32.17 7.93 9.69 11.83 14.46 17.66
  21.56 6.50 7.93 9.69 11.83
  14.46 5.32 6.50 7.93
  9.69 4.35 5.32 6.50 3.56
  4.35 2.92

u1.22, d0.25
up
down
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Valuing a compound option (step 2)

• 2. Value the option to launch at maturity
• 3. Move back in the tree. Option value at a node
  is
• Max0,pVu (1-p)Vd/(1r?t)-0.5
• 0 1 2 3 4 5 6 7 8
• 1.74 4.24 7.88 12.71 18.79 26.25 35.29 46.27 59.60
  
• 0.42 1.95 4.57 8.35 13.30 19.47 26.94 35.99
• 0.00 0.53 2.16 4.93 8.87 13.99 20.17
• 0.00 0.00 0.62 2.36 5.30 9.56
• 0.00 0.00 0.00 0.67 2.46
• 0.00 0.00 0.00 0.00
• 0.00 0.00 0.00
• 0.00 0.00
• 0.00

p 0.481/(1r?t)0.9876
(0.48?2.460.52?0.00) ? 0.9876-0.5
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When to invest?

• Traditional NPV rule invest if NPVgt0. Is
  it always valid?
• Suppose that you have the following project
• Cost I 100
• Present value of future cash flows V 120
• Volatility of V 69.31
• Possibility to mothball the project
• Should you start the project?
• If you choose to invest, the value of the project
  is
• Traditional NPV 120 - 100 20 gt0
• What if you wait?

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To mothball or not to mothball

• Let analyze this using a binomial tree with 1
  step per year.
• As volatility .6931, u2, d0.5. Also, suppose
  r .10 gt p0.40
• Consider waiting one year..
• V240 gtinvest NPV140
• V120
• V 60 gtdo not invest NPV0
• Value of project if started in 1 year 0.40 x
  140 / 1.10 51
• This is greater than the value of the project if
  done now (20)
• Wait..
• NB you now have an American option

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Waiting how long to invest?

• What if opportunity to mothball the project for 2
  years?
• V 480 C 380
• V240 C 180
• V120 C 85 V 120 C 20
• V 60 C 9
• V 30 C 0
• This leads us to a general result it is never
  optimal to exercise an American call option on a
  non dividend paying stock before maturity.
• Why? 2 reasons
• better paying later than now
• keep the insurance value implicit in the put
  alive (avoid regrets)

85gt51 gt wait 2 years
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Why invest then?

• Up to know, we have ignored the fact that by
  delaying the investment, we do not receive the
  cash flows that the project might generate.
• In options parlance, we have a call option on a
  dividend paying stock.
• Suppose cash flow is a constant percentage per
  annum ? of the value of the underlying asset.
• We can still use the binomial tree recursive
  valuation with
• p (1r?t)/(1??t)-d/(u-d)
• A (very) brief explanation In a risk neutral
  world, the expected return r (say 6) is sum of
  capital gains cash payments
• So1r ?t pu(1 ??t) (1-p)d(1 ??t)

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American option an example

• Cost of investment I 100
• Present value of future cash flows V 120
• Cash flow yield ? 6 per year
• Interest rate r 4 per year
• Volatility of V 30
• Options maturity 10 years ??
• Binomial model with 1 step per year
• Immediate investment NPV 20
• Value of option to invest 35 WAIT

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Optimal investment policy

• Value of future cash flows
• (partial binomial tree)
• 0 1 2 3 4
  5
• 120.0 162.0 218.7 295.2 398.4 537.8
• 88.9 120.0 162.0 218.7 295.2
  65.9 88.9 120.0 162.0
  48.8 65.9 88.9
  
• 36.1 48.8 26.8

• Investment will be delayed.
• It takes place in year 2 if no down
• in year 4 if 1 down
• Early investment is due to the loss of cash flows
  if investment delayed.
• Notice the large NPV required in order to invest

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A more general model

• In previous example, investment opportunity
  limited to 10 years.
• What happened if their no time frame for the
  investment?
• McDonald and Siegel 1986 (see Dixit Pindyck 1994
  Chap 5)
• Value of project follows a geometric Brownian
  motion in risk neutral world
• dV (r- ? ) V dt ? V dz
• dz Wiener process random variable i.i.d.
  N(0,?dt)
• Investment opportunity PERPETUAL AMERICAN CALL
  OPTION

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Optimal investment rule

• Rule Invest when present value reaches a
  critical value V
• If VltV wait
• Value of project f(V)
• aV? if VltV
• V-I if V? V

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Optimal investment rule numerical example

• Cost of investment I 100
• Cash flow yield ? 6
• Risk-free interest rate r 4
• Volatility 30
• Critical value V 210
• For V 120, value of investment opportunity f(V)
  27

Sensitivity analysis ?
V 2 341 4 200 6 158
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Value of investment opportunity for different
volatilities
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Some Applications of Real Options

• Valuing a Start-Up
• Exploring for Oil
• Developing a Drug
• Investing in Infrastructure
• Valuing Vacant Land
• Buying Flexibility