# 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

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
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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