Advanced Financial Statement Analysis by malj


									     Real Options

Advance Valuation Techniques
What is an Option?

n   An option gives the holder the right, but not
    the obligation to buy (call option) or sell (put
    option) a designated asset at a
    predetermined price (exercise price) on or
    before a fixed expiration date
n   Options have value because their terms allow
    the holder to profit from price moves in one
    direction without bearing (or, limiting) risk in
    the other direction.

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 Some Option Basics
         Call option                        As _____ increase   Option Value
                                                                Call     Put
                                            Asset price         Ý        ß
                                            Exercise price      ß        Ý
                                            Maturity            Ý         Ý
                                            Volatility          Ý        Ý
                                            Interest rate       Ý        ß

     Some Terms
    In -the-money
                          value                           Put option
    Intrinsic value
      Time value

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What is a Real Option?

n   An option on a non-traded asset, such as an
    investment project or a gold mine
n   Options in capital budgeting
    n   Delay a project (wait and learn)
    n   Expand a project (“follow-on” investments)
    n   Abandon a project
n   Real options allow managers to add value to
    their firms by acting to amplify good fortune
    or to mitigate loss.

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Managerial Decisions

n   Investment decision
    n   Invest now
                                                 Take into
    n   Wait
    n   Miss opportunity                         time and price
n   Operational decision
    n   Expand
    n   Status quo
    n   Close
    n   Abandon

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Discounted Cash Flow Analysis

n   DCF analysis approach
    n   Unknown risky future cash flows are summarized
        by their expected (mean) values
    n   Discounted to the present at a RADR
    n   Compared to current costs to yield NPV
n   Problem is sterilized of many problems
    n   Managerial options are ignored.

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Management’s Interest
n   Experts explain what option pricing captures
    what DCF and NPV don’t
    n   Often buried in complex mathematics
n   Managers want to know how to use option
    pricing on their projects
n   Thus, need a framework to bridge the gap
    between real-world capital projects and
    higher math associated with option pricing
    n   Show spreadsheet models with “good enough”
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Investment Opportunities
as Real Options
n   Executives readily see why investing today in
    R&D, a new marketing program, or certain
    capital expenditures can generate the
    possibility of new products or new markets
n   However, the journey from insight to action is
    often difficult.

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Corporate Investments
n   Corporate investment opportunity is like a call
    n   Corporation has the right but not the obligation to
        acquire something
n   If we can find a call option sufficiently similar
    to the investment opportunity, the value of
    the option would tell us something about the
    value of the opportunity
    n   However, most business opportunities are unique
    n   Thus, need to construct a similar option.

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Two Sides of Uncertainty
  Economic uncertainty                           Technical uncertainty
  - Correlated with economy                      - Not correlated with economy
  - Exogenous, so learn by waiting               - Endogenous, so learn by doing
  - Delays investment (NPV>0?)                   - Incentives for starting the
                                                           investment (NPV<0?)

                               Bad     Good
                               side    side

Investment: Governed quantitatively by the ‘bad news” principle (fear)
Abandon: Governed quantitatively by the “good news” principle (hope)

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Two Sides of Uncertainty

                                          Value of flexibility to
            Bad      Good                 alter decisions as info
            side     side                 becomes available

                                  Expected value
          Expected value          with flexibility

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Mapping a Project
onto an Option
n   Establish a correspondence between the
    project’s characteristics and 5 variables that
    determine value of a simple call option on a
    share of stock
    n   Slide 13 shows the variables
n   Use a European call
    n   Exercised on only one date, its expiration date
    n   Not a perfect substitute, but still informative.

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Investment opportunity                            Call option
PV of a project’s operating               S       Stock price
 assets to be acquired

Expenditure required to
acquire the project assets                X       Exercise price

Length of time the decision               t
may be deferred                                   Time to expiration

Time value of money                       rf
                                                  Risk-free rate of return
Riskiness of the project                 s2
 assets                                           Variance of returns on
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    NPV & Option Value Identical
n   Investment decision can no longer be
    Conventional NPV
     NPV = (value of project  assets)                  Option
    Value                                  When t = 0, s2 and
                  - (expenditure required) r do not affect call
                                                        option value. Only
                                                        S and X matter.
    This is S.       This is X.                         At expiration, call
                                                        option value is
                                                        greater of S - X or 0.
    So: NPV= S - X
          We decide to “go” or “no go”.                      Here it’s “exercise”
                                                                     or “not”.

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n   When do NPV & option pricing diverge?
    n   Investment decisions may be deferred
n   Deferral gives rise to two sources of value
    n   Better to pay later than sooner, all else equal
    n   Value of assets to be acquired can change
         n   If value increases, we haven’t missed out -- simply need
             to exercise the option
         n   If value decreases, we might decide not to acquire them
n   Traditional NPV misses the deferral
    n   It assumes the decision can’t be put off.
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1st Source:
Capture Time Value
n   Suppose you just put enough money in the
    bank now so that when it’s time to invest,
    that money plus interest it earned is sufficient
    to fund the required expenditure
n   How much money is it?

n   Extra value = rf * PV(X) compounded t
    periods or X - PV(X)
n   Conventional NPV misses the extra value.

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“Modified” NPV
n   NPV = S - X
n   Rewrite using PV(X) instead of X
       “Modified” NPV = S - PV(X)
         S is value; PV(X) is cost adjusted for TVM
n   “Modified” NPV ³ NPV
    n   Implicitly includes interest to be earned while
    n   Modified NPV can be positive, negative, or zero
    n   Express the relationship between cost and value
        so that the number > 0.
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NPV as a Quotient
n   Instead of expressing modified NPV as a
    difference, express it as a quotient
    n   Converts negative value to decimals between 0
        and 1
         NPVq = S ¸ PV(X)
n   NPV and NPVq are not equivalent
    n   S = 5, PV(X) = 7, NPV = -2 but NPVq = 0.714
    n   When modified NPV > 0, NPVq > 1
    n   When NPV < 0, NPVq < 1
    n   When modified NPV = 0, NPVq = 1.
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Relationships: NPV & NPVq

           NPV < 0                NPV = S - X                    NPV > 0
           NPVq < 1             NPVq = S / PV(X)                NPVq > 1

When time runs out, projects here              When time runs out, projects here
are rejected (option isn’t exercised).         are accepted (option is exercised).

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Interpretation of Real Options

n   NPVq > 1 Þ      Positive NPV & call options “in the money”
     n   NPVq = Asset value / PV(exercise price)
n   NPVq < 1 Þ Negative NPV & call options “out of the money”
n   Call option value increases as
     n   NPVq increases
     n   Cumulative variance increases
n   Traditional DCF treats management as passive
n   Real options treat management as active.

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2nd Source:
Cumulative Volatility
n   Asset value can change while you wait
    n   Affect investment decision
    n   Difficult to quantify since not sure asset values will
        change, or if they do, what the future value will be
n   Don’t measure change in value directly
    n   Measure uncertainty and let option-pricing model
        quantify the value
n   Two steps
    n   Identify a sensible way to measure uncertainty
    n   Express the metric in a mathematical form.

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Measure Uncertainty
n   Most common probability-weighted measure
    of dispersion is variance
    n   Summary measure of the likelihood of drawing a
        value far away from the average value
    n   The higher the variance, the more likely it is that
        the values drawn will be either much higher or
        much lower than average
         n   High-variance assets are riskier than low-variance assets
n   Variance is incomplete because need to
    consider time.
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Time Dimension
n   How much things can change while we wait
    depends on how long we can afford to wait
    n   For business projects, things can change a lot
        more if we wait 2 years than if we wait only 2
n   Must think in terms of variance per period
    n   Total uncertainty = s2 * t
         n   Called cumulative variance
              n   Option expiring in 2 periods has twice the cumulative
                  variance of an identical option expiring in one period, given
                  the same variance per period.
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Adjustments to
Cumulative Variance
n   Don’t use variance of project values
    n   Use variance of project returns
         n   Instead of working with actual dollar values of the project, we’ll
             work with percentage gain or loss per year

n   Express uncertainty in terms of standard deviation
    n   Denominated in same units as the thing being measured
n   Convert to cumulative volatility =

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Valuing the Option
n   Call-option metrics NPVq and        contain all
    the info needed to value a project as a
    European call option
    n   Capture the extra sources of value associated with
    n   Composed of the 5 fundamental option-pricing
        variables onto which we map our business
         n   NPVq: S, X, rf, and t
         n   Cumulative volatility combines s with t.

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Digress: Black-Scholes Model
    Call = S N(d1) - E e   -rt
                                 N(d2)                  S = stock price
                                                        N(d) = cumulative normal
    d1 = [ln(S/E) + (r + s2/2)t] / sÖt                              distribution
                                                        E = exercise price
    d2 = d1 - sÖt                                       r = continuous risk-free rate
                                                        t = time to maturity
    Put = E e -rt + C - S                               s = std deviation in returns

     n Known as put-call parity

n   No early exercise or payment of dividends
n   Inputs are consistent on time measurement
    n   All weekly, quarterly, etc…

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Interpretation of N(d)

n   Think of N(d) as risk-adjusted probabilities that the
    option will expire in-the-money
n   Example:
    n   S/E >> 1.0 Þ Stock price is high relative to exercise price,
        suggesting a virtual certainty that the call option will expire
         n   Thus, N(d) terms will be close to 1.0 and call option formula
             will collapse to S - E e-rt Þ Intrinsic value of option
    n   S/E << 1.0 Þ Both N(d) terms close to zero and option
        value close to zero as it is deep out-of-the-money.

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N(d): Risk-Adjusted
n   ln(S/E) = % amount the option is in or out of the
       S = 105 and E = 100, the option is 5% in the money
        n ln(S/E) = 4.9%

       S = 95 and E = 100, the option is 5% out of the money
        n ln(S/E) = -5.1%

n   sÖt adjusts the amount by which the option is in or
    out of the money for the volatility of the stock price
    over the remaining life of the option.

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  Linking Black-Scholes
  to Real Options
                                                          Combining values allows
Investment opportunity                                     us to work in 2-space
PV of a project’s operating               S
 assets to be acquired
Expenditure required to
acquire the project assets                X

Length of time the decision               t
may be deferred

Time value of money                       rf

Riskiness of the project                 s2

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Locating the Option Value
         lower values                 1.0                  higher values          NPVq:
                                                                                lower X;
                                                                                higher S,
values                                                                            rf or t
              Call option value
              increases in these

                                                                           various projects
                                                                             reveals their
higher                                                                      relative value
values                                                                         to each
            Higher s and t increase
               the option value

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“Pricing the Space”
 Black-Scholes value expressed as % of underlying

  Suppose S = $100, X = $105, t = 1 year, rf = 5%, s = 50% per year
                 Then NPVq = 1.0 and sÖt = 0.50
                   Table gives a value of 19.7%
         Viewed as a call option, the project has a value of:
                Call value = 0.197 * $100 = $19.70
              Conventional NPV = $100 - $105 = -$5.

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Interpret the Option Value
n   Why is the option value of $19.70 less than the asset
    value (S) of $100?
    n   We’ve been analyzing sources of extra value associated with
        being able to defer an investment
n   Don’t expect the option value > S = $100; rather
    expect it to be greater than NPV = S - PV(X)
    n   For NPVq = 1, then S / PV(X) = 100 / ($105 / 1.05)
n   Thus, conventional NPV = S - X = $100 - $105
                                   = -$5.

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Estimate Cumulative Variance
n   Most difficult variable to estimate is s
n   For a real option, s can’t be found in a
    newspaper and most people don’t have a
    highly developed intuition about uncertainty
n   Approaches:
    n   A(n educated) guess
    n   Gather some data
    n   Simulate s.

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A(n Educated) Guess
n   s for returns on broad-based U.S. stock
    indexes = 20% per year for most of the past
    15 years
    n   Higher for individual stocks
    n   GM’s s = 25% per year
n   s of individual projects within companies >
n   Range within a company for manufacturing
    assets is probably 30% to 60% per year.
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Gather Some Data
n   Estimate volatility using historical data
    on investment returns in the same or
    related industries
n   Computed implied volatility using
    current prices of stock options traded
    on organized exchanges
    n   Use Black-Scholes model to figure out what
        s must be.
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n   Spreadsheet-based projections of a project’s
    future cash flows, together with Monte Carlo
    simulation techniques, can be used to
    synthesize a probability distribution for
    project returns
    n   Requires educated guesses about outcomes and
        distributions for input variables
n   Calculate s for the distribution.

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Capital Budgeting Example

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Capital Budgeting Example

       Discount at 5.5%
                                                             X = -382
                                                              rf = 5.5
                                                             S = 256.1
                                                          Assume s = 40%


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Valuing the Option
n   Combine the option-pricing variables into our
    two option-value metrics:

n   Look up call value as a % of asset value in table

          About 19% of underlying asset (S) or $48.6 million.

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Value of Project
Project value = NPV(phase 1) + call value
  (phase 2)
Project value = $16.3 + $48.6 = $64.9
n Original estimate = $0.2

n A marginal DCF analysis project is in fact very
n What to do next?
  n   Check and update assumptions
  n   Check for disadvantages to deferring investment
  n   Simulate, ...
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Another Example Using NPVq:
“Follow-on” Investment Option

 NPV at 20% = -$46.45 million. Project fails to meet hurdle rate.
 If the company doesn’t make the investment now, it will
 probably be too cost prohibitive later. By investing now, the
 opportunity exists for later “follow-on” investments. The project
 gives its own cash flows & the call option to go to the next step.

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    Valuing the
    “Follow-on” Option...
n   “Follow-on” investment must be made in 3 years
n   New investment = 2 * initial investment ($900 M)
n   Forecast cash inflows = 2 * initial inflows
     n   PV = $800 M in 3-years; $463 M today @ 20%
n   Future cash flows highly uncertain
     n   Standard deviation = 35% per year
n   Annual risk-free rate = 10%
n   Interpretation:
     n   The opportunity to invest is a 3-year call option on an asset
         worth $463 M with a $900 M exercise price.

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 Valuing the
 “Follow-on” Option
NPVq = Underlying asset value / PV (exercise price)
       = $463 / [$900 / (1.1)3 ] = .68
Cumulative variance = s Ötime = .35 Ö3 = .61
Call value = Asset value * BS value as % of asset
            = $463 * 11.9% = $55 M
n Value of project = -$46 M + $55 M = $9 M

n Interpretation:

   n   “Follow-on” has a NPV = -$100, 3 years from now. The
       project may be very profitable because of its high variance.
   n   The call option allows you to cash in on the opportunity.

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NPV Rules vs. Real Options

             NPV                                Real Options
n   Invest in all projects            n    Invest when the project
    with NPV > 0                           is “deep in the money”
n   Reject all projects with          n    Can recommend to start
    NPV < 0                                “strategic projects”
n   Among mutually                    n    Frequently chooses
    exclusive projects,                    smaller projects
    choose the higher NPV                  sufficiently deep in the

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    Practical Considerations
n   Difficult to estimate project’s value and variance
n   Behavior of prices over time may not conform to the
    price path assumed by option pricing models
n   How long can the investment be deferred?
n   Need to know the probability distribution for X and
    joint probability distribution of S and X
n   Does uncertainty change over time?
n   Is the option an American type as opposed to
n   Do the Black-Scholes assumptions hold?

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The End

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