Chapter 8, Real Options

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Chapter 8, Real Options

• Option to Expand, Option to Abandon, and Timing
  Options

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Initial Comments

• Even though this is still listed under topic
  three on our syllabus, we will start to consider
  risk in valuing projects. The risk we will
  (mostly) consider will have binary outcomes,
  which simplify the analysis greatly.
• This chapter will mostly be explained through
  examples. There are general guidelines that will
  be explained, but these problems will be solved
  in a way that hopefully your intuition would
  suggest.

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Poker example

• Suppose in Texas Holdem (No Limit) you have
• And the flop and turn come
• And your opponent bets 400 into a 600 pot?
  Should you call?
• Answer it depends!

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Example Continued

• Assumptions you need one of the eight remaining
  5s and 10s in the deck to win (your opponent
  has two pair, or three of a kind)
• If you hit, youll get the rest of the opponents
  money.
• What if the opponent went all in with his 400
  bet?
• What if the opponent has 1000 more after his bet?

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Decision Trees

• Previously there was only one decision, whether
  to undertake the project or not. Now, our project
  under consideration will have multiple decisions,
  and information revealed during the course of the
  project will affect those decisions.
• A decision tree is simply a graphical
  representation of the decisions facing the
  project and the information obtained about that
  project in chronological order.

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Example from RWJ, pg. 211

• SEC is considering a project for solar powered
  jet engines. It must first undertake research to
  develop a prototype and test the prototypes. This
  phase of the project will take one year and cost
  100 million. There is a 75 chance of success.
  If the research is successful, a further
  investment can be made of 1,500 million and will
  result in cash flows of 900 million for the next
  five years. Under failure, undertaking the second
  investment will result in a negative NPV.
• We will assume the relevant interest rate for
  this project is 15.

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The decision tree
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Working backwards

• The payoffs of the decisions that should be made
  replace everything after the decision.

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Final Decision Tree

• What is the payoff if we decide to accept the
  project?
• It will be
• Average NPV 0.751,517 0.250 1,138

Remembering the initial 100 investment, the NPV
of the project can be calculated NPV
-1001,138/1.15 890
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A Digression into Sensitivity Analysis and Risk

• What about other sources of uncertainty? For the
  solar jet engine company we could decompose the
  earnings and costs with the following equations
• Revenue Market Share Market Size Price
• Cost Var. Cost / Unit Units sold FC
• It is easier to estimate a Pessimistic, Expected
  and Optimistic forecast of the factors rather
  than the revenue or cost.

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Single variable variation

• The table below is calculated using the expected
  value of everything except the variable singled
  out.
• It gives a good idea of what variables affect the
  NPV of the project significantly.

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Other Analysis of Risk ideas Cottage Hospital

• Population was modelledUsed estimates for high,
  low and expected migration (as above)
• Other statistical tools were used when we have
  (relatively) known probabilities
• Births and Deaths were determined many times
  using a Monte Carlo simulation (computer flips a
  coin many times).
• Hospital visits were likewise determined using
  Monte Carlo simulation.
• The multiple simulations were then used to
  determine percentiles and spreads for the various
  service lines.

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Real Options

• Real Options can help increase the NPV of a
  project, and thus can move a project from having
  a negative NPV to a positive NPV.
• Option to Expand--learning takes place, and
  similar ventures are possible
• Option to Abandon--Projects can be liquidated or
  simply stopped
• Timing Options--Decisions can be postponed

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Valuing these options

• The value of any of these real options can be
  calculated using the following steps
• Calculate the NPV of the project without the
  option.
• Calculate the NPV of the project with the option
  (using the decision tree, and making optimal
  decisions)
• Subtract the NPVs.

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Option to Expand

• A single ice hotel can be built for 12
  million. Its estimated cash flows are 2 million
  in perpetuity. At a 20 interest rate (high, to
  compensate for the risk) the NPV of this project
  is -2 million.
• Sadly, no ice hotels then would seem to be built.
  

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Add in information

• First, the hotel could be a hit and generate 3
  million per year, or it could flop and generate
  1 million. Second our hotelier has scouted out 9
  additional sites for hotels and knows the revenue
  would be the same at each location.

So the Project now has a positive NPV. The value
of the option to expand is 9.25M. Why?
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Option to Abandon Example

• Consider starting a mine the company has already
  performed a survey (sunk cost--not a cash flow
  remember!) and found a site that contains gold.
• The costs per year for recovering the gold are 1
  million. The amount of gold is unknown. It is
  equally likely that revenues from the sale of the
  gold will be 0.25, 1.0 or 1.5 million.

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Cash Flows from Mine

• At an interest rate of 25, this is 0.1333.
• What is the value of the option to abandon?
• Suppose the revenues were equally likely to be
  0.5, 1.25 or 2.0 million. What would change?

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Timing Option Example

• Thinking about the mine example above, suppose we
  had to buy the land now, and knew exactly how
  much gold per year could be extracted. However,
  the price of gold is variable.
• The land will cost 1 million but we will have to
  invest 2 million to start mining. It will cost
  1 million per year to extract and the revenue
  from the gold will be either 2 million or 1
  million, based upon the price gold will be in the
  future.
• What is the NPV of the project (at r20)?
• What if we could wait to build the mining
  equipment until the price of gold is known?