Chapter 1 Making Economic Decisions by 7akgJz52

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									           Chapter 14

Risk and Managerial (Real) Options
       in Capital Budgeting
                     Learning Objectives

After studying Chapter 14, you should be able to:
•   Define the "riskiness" of a capital investment project.
•   Understand how cash-flow riskiness for a particular period
    is measured, including the concepts of expected value,
    standard deviation, and coefficient of variation.
•   Describe methods for assessing total project risk, including
    a probability approach and a simulation approach.
•   Judge projects with respect to their contribution to total firm
    risk (a firm-portfolio approach).
•   Understand how the presence of managerial (real) options
    enhances the worth of an investment project.
•   List, discuss, and value different types of managerial (real)
    options.
                     Topics

• The Problem of Project Risk
• Total Project Risk
• Contribution to Total Firm Risk: Firm-
  Portfolio Approach
• Managerial (Real) Options
           An Illustration of Total Risk
             (Discrete Distribution)
     ANNUAL CASH FLOWS: YEAR 1
            PROPOSAL A
   State          Probability   Cash Flow
Deep Recession       .10         $   3,000
Mild Recession       .20             3,500
Normal               .40             4,000
Minor Boom           .20             4,500
Major Boom           .10             5,000
                Probability Distribution of
              Year 1 Cash Flows (Proposal A)

              .40
Probability




              .20


              .10



                       3,000   4,000   5,000

                        Cash Flow ($)
            Expected Value of
     Year 1 Cash Flows (Proposal A)
    CF1       P1         (CF1)(P1)
$ -3,000     .10         $ 300
   1,000     .20           700
   5,000     .40          1,600
   9,000     .20            900
  13,000     .10            500
           S=1.00     CF1=$4,000
               Variance of
     Year 1 Cash Flows (Proposal A)

(CF1)(P1)        (CF1 - CF1)2(P1)
$ 300       ( 3,000 - 4,000)2 (.10)= 100,000
   700      ( 3,500 - 4,000)2 (.20)= 50,000
 1,600      ( 4,000 - 4,000)2 (.40)=     0
   900      ( 4,500 - 4,000)2 (.20)= 50,000
   500      ( 5,000 - 4,000)2 (.10)= 100,000
$4,000                               300,000
              Summary of Proposal A

Standard deviation = SQRT (300,000)= $548
Expected cash flow = $4,000
Coefficient of Variation (CV) = $548 / $4,000 = 0.14

CV is a measure of relative risk and is the ratio of standard
deviation to the mean of the distribution.
           An Illustration of Total Risk
             (Discrete Distribution)
     ANNUAL CASH FLOWS: YEAR 1
            PROPOSAL B
   State          Probability   Cash Flow
Deep Recession       .10         $   2,000
Mild Recession       .20             3,000
Normal               .40             4,000
Minor Boom           .20             5,000
Major Boom           .10             6,000
                Probability Distribution of
              Year 1 Cash Flows (Proposal B)
              .40
Probability




              .20



              .10



                    2,000    3,000   4,000   5,000   6,000

                            Cash Flow ($)
             Expected Value of
      Year 1 Cash Flows (Proposal B)

     CF1       P1      (CF1)(P1)
$   2,000     .10        $ 200
    3,000     .20           600
    4,000     .40         1,600
    5,000     .20         1,000
    6,000     .10           600
            S=1.00   CF1=$4,000
               Variance of
     Year 1 Cash Flows (Proposal B)

(CF1)(P1)            (CF1 - CF1)2(P1)
$ 200       (   2,000 - 4,000)2 (.10) =   400,000
   600      (   3,000 - 4,000)2 (.20) =   200,000
 1,600      (   4,000 - 4,000)2 (.40) =       0
 1,000      (   5,000 - 4,000)2 (.20) =   200,000
   600      (   6,000 - 4,000)2 (.10) =   400,000
$4,000                                    1,200,000
             Summary of Proposal B

Standard deviation = SQRT (1,200,000) = $1,095
Expected cash flow = $4,000
Coefficient of Variation (CV) = $1,095 / $4,000 = 0.27
        Comparison of Proposal A & B

                                  Proposal A      Proposal B
Standard deviation                   $548           $1,095
Expected cash flow                  $4,000          $4,000
Coefficient of Variation (CV)        0.14            0.27


The standard deviation of B > A ($1,095 > $548), so “B” is
more risky than “A”.
The coefficient of variation of B > A (0.27 < 0.14), so “B” has
higher relative risk than “A”.
                Total Project Risk

Projects have risk that
  may change from
   period to period.
  Projects are more


                          Cash Flow ($)
    likely to have
  continuous, rather
    than discrete
    distributions.

                                          1   2          3
                                                  Year
        Probability Tree Approach

A graphic or tabular approach for
organizing the possible cash-flow
streams generated by an investment.
The presentation resembles the
branches of a tree. Each complete
branch represents one possible cash-
flow sequence.
        Probability Tree Approach

        Basket Wonders is examining
        a project that will have an
        initial cost today of $240.
-$240   Uncertainty surrounding the
        first year cash flows creates
        three possible cash-flow
        scenarios in Year 1.
             Probability Tree Approach

        (.25) $500
                      1   Node 1: 25% chance of a
                                   $500 cash-flow.

        (.50) $200
-$240                 2   Node 2: 50% chance of a
                                  $200 cash-flow.

        (.25) -$100
                      3   Node 3: 25% chance of a
                                  -$100 cash-flow.
          Year 1
                Probability Tree Approach
                            (.40) $800
                                           Each node in
        (.25) $500          (.40) $500
                        1                  Year 2
                            (.20) $200     represents a
                                           branch of our
                            (.20) $ 500
                                           probability tree.
        (.50) $200          (.60) $ 200
-$240                   2
                            (.20) -$ 100   The
                                           probabilities
                            (.20) $ 200
                                           are said to be
        (.25)   -$100       (.40) -$ 100   conditional
                        3
                            (.40) -$ 400   probabilities.
           Year 1             Year 2
            Joint Probabilities [P(1,2)]
                          (.40) $800
                                        .10 Branch 1
        (.25) $500        (.40) $500
                      1                 .10 Branch 2
                          (.20) $200
                                        .05 Branch 3
                          (.20) $500
        (.50) $200
                                        .10 Branch 4
                          (.60) $400
-$240                 2                 .30 Branch 5
                          (.20) -$100
                                        .10 Branch 6
                          (.20) $200
                                        .05 Branch 7
        (.25) -$100       (.40) -$100
                      3                 .10 Branch 8
                          (.40) -$400
                                        .10 Branch 9
          Year 1            Year 2
              Project NPV Based on
                 Probability Tree
                                  z
  The probability      NPV = iS1 (NPVi)(Pi)
                              =
tree accounts for
the distribution of   The NPV for branch i of the
     cash flows.      probability tree for two years
     Therefore,             of cash flows is
discount all cash
 flows at only the               CF1            CF2
  risk-free rate of   NPVi =              +
                               (1 + Rf   )1   (1 + Rf )2
       return.
                            - ICO
          NPV for Each Cash-Flow Stream
               at 8% Risk-Free Rate
                          (.40) $ 800
                                         $ 909
        (.25) $500        (.40) $ 500
                      1                  $ 652
                          (.20) $ 200
                                         $ 394
                          (.20) $ 500
        (.50) $200
                                          $ 374
                          (.60) $ 200
-$240                 2                   $ 117
                          (.20) -$ 100
                                         -$ 141
                          (.20) $ 200
                                         -$ 161
        (.25) -$100       (.40) -$ 100
                      3                  -$ 418
                          (.40) -$ 400
                                         -$ 676
          Year 1            Year 2
           Calculating the
   Expected Net Present Value (NPV)
 Branch        NPVi           P(1,2)   NPVi * P(1,2)
Branch 1    $ 909              .10        $ 91
Branch 2    $ 652              .10        $ 65
Branch 3    $ 394              .05        $ 20
Branch 4    $ 374              .10        $ 37
Branch 5    $ 117              .30        $ 35
Branch 6   -$ 141              .10       -$ 14
Branch 7   -$ 161              .05       -$ 8
Branch 8   -$ 418              .10       -$ 42
Branch 9   -$ 676              .10       -$ 68

       Expected Net Present Value = $116
      Calculating the Variance of the Net
                Present Value
   NPVi      P(1,2)    (NPVi - NPV )2[P(1,2)]
 $ 909        .10         $ 62,884.90
 $ 652        .10         $ 28,729.60
 $ 394        .05         $ 3,864.20
 $ 374        .10         $ 6,656.40
 $ 117        .30         $      0.30
-$ 141        .10         $ 6,604.90
-$ 161        .05         $ 3,836.45
-$ 418        .10         $ 28,515.60
-$ 676        .10         $ 62,726.40

              Variance = $203,818.75
               Calculating the Variance of the Net
                         Present Value
Prob             Prob             Joint
(CF1)    CF1     (CF2)    CF2     Prob.     NPV         EV(NPV)      Var(NPV)
  0.25     500      0.4     800       0.1    $908.83       $90.88       62755.08
  0.25     500      0.4     500       0.1    $651.63       $65.16       28620.30
  0.25     500      0.2     200     0.05     $394.43       $19.72        3858.02
   0.5     200      0.2     500       0.1    $373.85       $37.39        6615.27
   0.5     200      0.6     200       0.3    $116.65       $35.00               0.00
   0.5     200      0.2    -100       0.1   ($140.55)     ($14.05)       6615.27
  0.25    -100      0.2     200     0.05    ($161.12)      ($8.06)       3858.02
  0.25    -100      0.4    -100       0.1   ($418.33)     ($41.83)      28620.30
  0.25    -100      0.4    -400       0.1   ($675.53)     ($67.55)      62755.08
                                                          $116.65    $203,697.35
     Summary of the Decision Tree
              Analysis

Standard deviation = SQRT ($203,697) =
$451.33

Expected NPV = $116.65
          Simulation Approach

An approach that allows us to test the
possible results of an investment
proposal before it is accepted.
Testing is based on a model coupled
with probabilistic information.
            Simulation Approach

Factors we might consider in a model:
  – Market analysis
     • Market size, selling price, market
       growth rate, and market share
  – Investment cost analysis
     • Investment required, useful life of
       facilities, and residual value
  – Operating and fixed costs
     • Operating costs and fixed costs
               Simulation Approach

Each variable is assigned an appropriate
probability distribution. The distribution for the
selling price of baskets created by Basket
Wonders might look like:
   $20 $25 $30 $35 $40 $45 $50
    .02 .08 .22 .36 .22 .08 .02
The resulting proposal value is dependent on
the distribution and interaction of EVERY
variable.
                      Simulation Approach

Each proposal will generate an internal rate of
return. The process of generating many, many
simulations results in a large set of internal rates of
return. The distribution might look like the following:
   OF OCCURRENCE
     PROBABILITY




                   INTERNAL RATE OF RETURN (%)
              Contribution to Total Firm Risk:
                 Firm-Portfolio Approach
                                        Combination of
            Proposal A    Proposal B   Proposals A and B
CASH FLOW




               TIME           TIME            TIME

Combining projects in this manner reduces the
       firm risk due to diversification.
         Determining the Expected
        NPV for a Portfolio of Projects
                       m
            NPVP   NPV j
                       j 1

NPVP is the expected portfolio NPV,
NPVj is the expected NPV of the jth NPV that
  the firm undertakes,
m is the total number of projects in the firm
  portfolio.
          Determining Portfolio Standard
                    Deviation
                             m    m
                    sp      s
                             j 1 k 1
                                         jk


sjk is the covariance between possible NPVs for
projects j and k,
                    s jk = s j s k r jk .
sj is the standard deviation of project j,
sk is the standard deviation of project k,
rjk is the correlation coefficient between projects j & k.
                   Combinations of
                  Risky Investments

  E: Existing Projects                                                C

    8 Combinations
                                                            B




                              Expected Value of NPV
E     E+1      E+1+2
      E+2      E+1+3                                              E
      E+3      E+2+3
       E+1+2+3                                          A
A, B, and C are dominating
combinations from the eight
         possible.                                    Standard Deviation
         Managerial (Real) Options

Management flexibility to make future
decisions that affect a project’s expected
cash flows, life, or future acceptance.


 Project Worth = NPV +
                   Option(s) Value
           Managerial (Real) Options

Expand (or contract)
  – Allows the firm to expand (contract) production if
    conditions become favorable (unfavorable).
Abandon
  – Allows the project to be terminated early.
Postpone
  – Allows the firm to delay undertaking a project
    (reduces uncertainty via new information).
            Probability Tree Approach

       (.25) $1M
                   1   Node 1: 25% chance of a
                                $1M cash-flow.

       (.50) $2M
-$3M               2   Node 2: 50% chance of a
                                $2M cash-flow.

       (.25) $3M
                   3   Node 3: 25% chance of a
                                $3M cash-flow.
         Year 1
              Example without Project
                  Abandonment
                        (.25) $ 0
                                       Assume that
        (.25) $1M       (.50) $ 1M
                    1                  this project can
                        (.25) $ 2M     be abandoned
                                       at the end of
                        (.25) $ 1M
                                       the first year
        (.50) $2M       (.50) $ 2M
-$900               2                  for $1.5M.
                        (.25) $ 3M
                                       What is the
                        (.25) $ 2M
                                       project worth?
        (.25) $3M       (.50) $ 3M
                    3
                        (.25) $ 3.5M

          Year 1           Year 2
                        Example without Project
                            Abandonment
Prob           Prob              Joint
(CF1)     CF1 (CF2)     CF2      Prob.       NPV          EV(NPV)        Var(NPV)
 0.25   1000000 0.25         0   0.0625 ($2,090,909.09) ($130,681.82) 402005778400.55
 0.25   1000000 0.5    1000000    0.125 ($1,264,462.81) ($158,057.85) 365388853433.85
 0.25   1000000 0.25   2000000   0.0625 ($438,016.53) ($27,376.03)      48759756953.93
  0.5   2000000 0.25   1000000    0.125 ($355,371.90) ($44,421.49)      80124014966.53
  0.5   2000000 0.5    2000000      0.25   $471,074.38 $117,768.60        166751331.88
  0.5   2000000 0.25   3000000    0.125 $1,297,520.66 $162,190.08       90796100206.61
 0.25   3000000 0.25   2000000   0.0625 $1,380,165.29      $86,260.33   54629403835.97
 0.25   3000000 0.5    3000000    0.125 $2,206,611.57 $275,826.45 387800232438.02
 0.25   3000000 0.25   3500000   0.0625 $2,619,834.71 $163,739.67 295551728130.76
                                                          $445,247.93 1725222619698.11

                                                                         $1,313,477.30
                    Decision Trees

• Decision tree graphically displays all decisions in
  a complex project and all the possible outcomes
  with their probabilities.
                                D1
   Decision Node                D2   Outcome Node
                                DX

                      p1        C1
                           p2
   Chance Node                  C2   Pruned Branch
                      py        CY
                               Decision Tree (14.3)
                 (New Product Development – with Abandonment)

                                                                 7. CF1=$1.5M
                                                     Terminate
                                                                    8.CF2=$0 (.25)
                         Low Volume 4. CF1=$1M
                           P=0.25                                   9.CF2=$1M (.5)
                                                 Continue
                                                                   10.CF2=$2M (.25)
                          Med. Vol.
                           P=0.5                                   11.CF2=$1 (.25)
            2. Volume for
                                 5. CF1=$2M                        12.CF2=$2M (.5)
               New Product
                                                  Continue
                                                                   13.CF2=$3M (.25)
       Yes                                                         14.CF2=$2 (.25)
                            High Volume
       First cost=$3M                            Continue
                              P=0.25                               15.CF2=$3M (.5)
1. Build New                        6. CF1=$3M                     16.CF2=$3.5M (.25)
   Product
                                                     Expand
            No
                 3. $0
      t=0                              t=1                          t=2, …,
                               Decision Tree (14.4)
                 (New Product Development – with Abandonment)

                                                                 7. CF1=$1.5M
                                                     Terminate
                                                                    8.CF2=$0 (.25)
                         Low Volume 4. CF1=$1M
                           P=0.25                                   9.CF2=$1M (.5)
                                                 Continue
                                                                   10.CF2=$2M (.25)
                          Med. Vol.              EV(CF1)=.909M
                           P=0.5                                    EV(CF2)=1M
            2. Volume for
               New Product                                         11.CF2=$1 (.25)
                                 5. CF1=$2M                        12.CF2=$2M (.5)
                                                  Continue
       Yes                                                         13.CF2=$3M (.25)
       First cost=$3M
                            High Volume                            14.CF2=$2 (.25)
1. Build New                  P=0.25             Continue          15.CF2=$3M (.5)
   Product
                                    6. CF1=$3M                     16.CF2=$3.5M (.25)
            No
                 3. $0                               Expand
      t=0                                 t=1                       t=2, …,
                              Example with Project
                                 Abandonment
Prob            Prob              Joint
(CF1)   CF1     (CF2)   CF2       Prob.     NPV         EV(NPV)             Var(NPV)
 0.25 2500000       1         0    0.25 ($727,272.73) ($181,818.18)         426943440082.65
  0.5 2000000 0.25 1000000 0.125 ($355,371.90)          ($44,421.49)        109258807671.95
  0.5 2000000     0.5 2000000      0.25   $471,074.38   $117,768.60           2941493494.30
  0.5 2000000 0.25 3000000 0.125 $1,297,520.66          $162,190.08          64436049663.62
 0.25 3000000 0.25 2000000 0.0625 $1,380,165.29          $86,260.33          40062007483.27
 0.25 3000000     0.5 3000000 0.125 $2,206,611.57       $275,826.45         330918018108.39
 0.25 3000000 0.25 3500000 0.0625 $2,619,834.71         $163,739.67         260173765559.90
                                                        $579,545.45        1234733582064.07
                                                                       $       1,111,185.66

								
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