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Chapter 8, Real Options


... that contains gold. The costs per year for recovering the gold are $1 ... What if we could wait to build the mining equipment until the price of gold is known? ... – PowerPoint PPT presentation

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Title: Chapter 8, Real Options

Chapter 8, Real Options
  • Option to Expand, Option to Abandon, and Timing

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

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!

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
  • What if the opponent went all in with his 400
  • What if the opponent has 1000 more after his bet?

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.

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.

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

Final Decision Tree
  • What is the payoff if we decide to accept the
  • 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
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.

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

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.

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

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
  • Calculate the NPV of the project with the option
    (using the decision tree, and making optimal
  • Subtract the NPVs.

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.

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?
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.

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?

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
  • 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?