Transcript Chapter 14 -- Risk and Managerial Options in Capital Budgeting

Chapter 14
Risk and Managerial
(Real) Options in
Capital Budgeting
14-1
© Pearson Education Limited 2004
Fundamentals of Financial Management, 12/e
Created by: Gregory A. Kuhlemeyer, Ph.D.
Carroll College, Waukesha, WI
After studying Chapter 14,
you should be able to:






14-2
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.
Risk and Managerial (Real)
Options in Capital Budgeting
The
Problem of Project Risk
Total
Project Risk
Contribution
to Total Firm Risk:
Firm-Portfolio Approach
Managerial
14-3
(Real) Options
An Illustration of Total Risk
(Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL A
State
Deep Recession
Mild Recession
Normal
Minor Boom
Major Boom
14-4
Probability
.05
.25
.40
.25
.05
Cash Flow
$ -3,000
1,000
5,000
9,000
13,000
Probability Distribution
of Year 1 Cash Flows
Proposal A
Probability
.40
.25
.05
-3,000
1,000
5,000
9,000
Cash Flow ($)
14-5
13,000
Expected Value of Year 1
Cash Flows (Proposal A)
CF1
$ -3,000
1,000
5,000
9,000
13,000
14-6
P1
.05
.25
.40
.25
.05
S=1.00
(CF1)(P1)
$ -150
250
2,000
2,250
650
CF1=$5,000
Variance of Year 1
Cash Flows (Proposal A)
14-7
(CF1)(P1)
(CF1 - CF1)2(P1)
$ -150
250
2,000
2,250
650
$5,000
( -3,000 - 5,000)2 (.05)
( 1,000 - 5,000)2 (.25)
( 5,000 - 5,000)2 (.40)
( 9,000 - 5,000)2 (.25)
(13,000 - 5,000)2 (.05)
Variance of Year 1
Cash Flows (Proposal A)
14-8
(CF1)(P1)
(CF1 - CF1)2*(P1)
$ -150
250
2,000
2,250
650
$5,000
3,200,000
4,000,000
0
4,000,000
3,200,000
14,400,000
Summary of Proposal A
The standard deviation = SQRT (14,400,000)
= $3,795
The expected cash flow
= $5,000
Coefficient of Variation (CV) = $3,795 / $5,000
= 0.759
CV is a measure of relative risk and is the ratio of
standard deviation to the mean of the distribution.
14-9
An Illustration of Total Risk
(Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL B
State
Deep Recession
Mild Recession
Normal
Minor Boom
Major Boom
14-10
Probability
.05
.25
.40
.25
.05
Cash Flow
$ -1,000
2,000
5,000
8,000
11,000
Probability Distribution
of Year 1 Cash Flows
Proposal B
Probability
.40
.25
.05
-3,000
1,000
5,000
9,000
Cash Flow ($)
14-11
13,000
Expected Value of Year 1
Cash Flows (Proposal B)
CF1
$ -1,000
2,000
5,000
8,000
11,000
14-12
P1
.05
.25
.40
.25
.05
S=1.00
(CF1)(P1)
$
-50
500
2,000
2,000
550
CF1=$5,000
Variance of Year 1
Cash Flows (Proposal B)
(CF1)(P1)
$
-50
500
2,000
2,000
550
$5,000
14-13
(CF1 - CF1)2(P1)
( -1,000 - 5,000)2 (.05)
( 2,000 - 5,000)2 (.25)
( 5,000 - 5,000)2 (.40)
( 8,000 - 5,000)2 (.25)
(11,000 - 5,000)2 (.05)
Variance of Year 1
Cash Flows (Proposal B)
(CF1)(P1)
$
-50
500
2,000
2,000
550
$5,000
14-14
(CF1 - CF1)2(P1)
1,800,000
2,250,000
0
2,250,000
1,800,000
8,100,000
Summary of Proposal B
The standard deviation = SQRT (8,100,000)
= $2,846
The expected cash flow = $5,000
Coefficient of Variation (CV) = $2,846 / $5,000
= 0.569
The standard deviation of B < A ($2,846< $3,795), so “B”
is less risky than “A”.
The coefficient of variation of B < A (0.569<0.759), so “B”
has less relative risk than “A”.
14-15
Projects have risk
that may change
from period to
period.
Projects are more
likely to have
continuous, rather
than discrete
distributions.
Cash Flow ($)
Total Project Risk
1
14-16
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.
14-17
Probability Tree Approach
-$900
14-18
Basket Wonders is
examining a project that will
have an initial cost today of
$900. Uncertainty
surrounding the first year
cash flows creates three
possible cash-flow
scenarios in Year 1.
Probability Tree Approach
-$900
14-19
(.20) $1,200 1
Node 1: 20% chance of a
$1,200 cash-flow.
(.60)
$450
2
Node 2: 60% chance of a
$450 cash-flow.
(.20)
-$600 3
Node 3: 20% chance of a
-$600 cash-flow.
Year 1
Probability Tree Approach
(.20) $1,200 1
-$900
(.60)
$450
2
(.10) $2,200
(.60) $1,200
(.30) $ 900
(.35) $ 900
(.40) $ 600
Each node in
Year 2
represents a
branch of our
probability
tree.
(.25) $ 300
(.10) $ 500
(.20)
-$600 3
(.50) -$ 100
(.40) -$ 700
14-20
Year 1
Year 2
The
probabilities
are said to be
conditional
probabilities.
Joint Probabilities [P(1,2)]
(.20) $1,200 1
-$900
(.60)
$450
2
(.10) $2,200
(.60) $1,200
(.30) $ 900
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.20)
-$600 3
(.50) -$ 100
(.40) -$ 700
14-21
Year 1
Year 2
.02 Branch 1
.12 Branch 2
.06 Branch 3
.21 Branch 4
.24 Branch 5
.15 Branch 6
.02 Branch 7
.10 Branch 8
.08 Branch 9
Project NPV Based on
Probability Tree Usage
z
The probability
tree accounts for
the distribution
of cash flows.
Therefore,
discount all cash
flows at only the
risk-free rate of
return.
14-22
NPV = iS= 1 (NPVi)(Pi)
The NPV for branch i of
the probability tree for two
years of cash flows is
NPVi =
CF1
(1 + Rf
- ICO
+
)1
CF2
(1 + Rf )2
NPV for Each Cash-Flow
Stream at 5% Risk-Free Rate
(.20) $1,200 1
-$900
(.60)
$450
2
(.10) $2,200
(.60) $1,200
(.30) $ 900
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.20)
-$600 3
(.50) -$ 100
(.40) -$ 700
14-23
Year 1
Year 2
$ 2,238.32
$ 1,331.29
$ 1,059.18
$
$
344.90
72.79
-$
199.32
-$ 1,017.91
-$ 1,562.13
-$ 2,106.35
NPV on the Calculator
Remember, we can
use the cash flow
registry to solve
these NPV problems
quickly and
accurately!
14-24
Actual NPV Solution Using
Your Financial Calculator
Solving for Branch #3:
14-25
Step 1:
Press
Step 2:
Press
Step 3: For CF0 Press
CF
2nd
CLR Work
-900
Enter
Step 4:
Step 5:
Step 6:
Step 7:
1200
1
900
1
For C01 Press
For F01 Press
For C02 Press
For F02 Press
Enter
Enter
Enter
Enter
key
keys

keys




keys
keys
keys
keys
Actual NPV Solution Using
Your Financial Calculator
Solving for Branch #3:
Step 8:
Step 9:
Press
Press
Step 10: For I=, Enter


keys
key
NPV
5
CPT
Enter

keys
Step 11:
Press
key
Result:
Net Present Value = $1,059.18
You would complete this for EACH branch!
14-26
Calculating the Expected
Net Present Value (NPV)
Branch
Branch 1
Branch 2
Branch 3
Branch 4
Branch 5
Branch 6
Branch 7
Branch 8
Branch 9
NPVi
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$
72.79
-$ 199.32
-$ 1,017.91
-$ 1,562.13
-$ 2,106.35
P(1,2)
.02
.12
.06
.21
.24
.15
.02
.10
.08
NPVi * P(1,2)
$ 44.77
$159.75
$ 63.55
$ 72.43
$ 17.47
-$ 29.90
-$ 20.36
-$156.21
-$168.51
Expected Net Present Value = -$ 17.01
14-27
Calculating the Variance
of the Net Present Value
NPVi
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$
72.79
-$ 199.32
-$ 1,017.91
-$ 1,562.13
-$ 2,106.35
P(1,2)
.02
.12
.06
.21
.24
.15
.02
.10
.08
(NPVi - NPV )2[P(1,2)]
$ 101,730.27
$ 218,149.55
$ 69,491.09
$ 27,505.56
$ 1,935.37
$ 4,985.54
$ 20,036.02
$ 238,739.58
$ 349,227.33
Variance = $1,031,800.31
14-28
Summary of the
Decision Tree Analysis
The standard deviation =
SQRT ($1,031,800) = $1,015.78
The expected NPV
14-29
= -$
17.01
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.
14-30
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
14-31
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 listed on slide 14-30.
14-32
Simulation Approach
PROBABILITY
OF OCCURRENCE
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:
14-33
INTERNAL RATE OF RETURN (%)
Contribution to Total Firm Risk:
Firm-Portfolio Approach
Proposal B
CASH FLOW
Proposal A
Combination of
Proposals A and B
TIME
TIME
TIME
Combining projects in this manner reduces
the firm risk due to diversification.
14-34
Determining the Expected
NPV for a Portfolio of Projects
m
NPVP = S ( NPVj )
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.
14-35
Determining Portfolio
Standard Deviation
sP =
m
m
S k=1
S sjk
j=1
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,
14-36
rjk is the correlation coefficient between
projects j and k.
E: Existing Projects
8 Combinations
E
E+1
E+2
E+3
E+1+2
E+1+3
E+2+3
E+1+2+3
A, B, and C are
dominating combinations
from the eight possible.
14-37
Expected Value of NPV
Combinations of
Risky Investments
C
B
E
A
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
14-38
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).
14-39
Previous Example with
Project Abandonment
(.20) $1,200 1
-$900
(.60)
$450
2
(.10) $2,200
(.60) $1,200
(.30) $ 900
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.20)
-$600 3
(.50) -$ 100
(.40) -$ 700
14-40
Year 1
Year 2
Assume that
this project
can be
abandoned at
the end of the
first year for
$200.
What is the
project
worth?
Project Abandonment
(.20) $1,200 1
-$900
(.60)
$450
2
(.10) $2,200
(.60) $1,200
(.30) $ 900
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.20)
-$600 3
Year 1
(500/1.05)(.1)+
(-100/1.05)(.5)+
(-700/1.05)(.4)=
($476.19)(.1)+
-($ 95.24)(.5)+
-($666.67)(.4)=
(.50) -$ 100
(.40) -$ 700
14-41
Node 3:
Year 2
-($266.67)
Project Abandonment
(.20) $1,200 1
-$900
(.60)
(.20)
$450
2
-$600 3
(.10) $2,200
(.60) $1,200
(.30) $ 900
(.35) $ 900
(.40) $ 600
The optimal
decision at the
end of Year 1 is
to abandon the
project for
$200.
(.25) $ 300
$200 >
(.10) $ 500
-($266.67)
(.50) -$ 100
What is the
“new” project
value?
(.40) -$ 700
14-42
Year 1
Year 2
Project Abandonment
(.20) $1,200 1
-$900
(.60)
$450
2
(.10) $2,200
(.60) $1,200
(.30) $ 900
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.20)
-$400* 3
(1.0) $
0
*-$600 + $200 abandonment
14-43
Year 1
Year 2
$ 2,238.32
$ 1,331.29
$ 1,059.18
$
$
344.90
72.79
-$
199.32
-$ 1,280.95
Summary of the Addition
of the Abandonment Option
The standard deviation* =
SQRT (740,326)
= $857.56
The expected NPV*
= $ 71.88
NPV* = Original NPV +
Abandonment Option
Thus, $71.88 = -$17.01 + Option
Abandonment Option
= $ 88.89
14-44
* For “True” Project considering abandonment option