Chapter 14
Risk and Managerial
Options in Capital
Budgeting
14-1
© 2001 Prentice-Hall, Inc.
Fundamentals of Financial Management, 11/e
Created by: Gregory A. Kuhlemeyer, Ph.D.
Carroll College, Waukesha, WI
Risk and Managerial
Options in Capital Budgeting
The
Problem of Project Risk
Total
Project Risk
Contribution
to Total Firm Risk:
Firm-Portfolio Approach
Managerial
14-2
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
14-3
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 ($)
14-4
13,000
Expected Value of Year 1
Cash Flows (Proposal A)
CF1
$ -3,000
1,000
5,000
9,000
13,000
14-5
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)
14-6
(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)
14-7
(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
14-8
An Illustration of Total Risk
(Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL B
State
Deep Recession
Mild Recession
Normal
Minor Boom
Major Boom
14-9
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 ($)
14-10
13,000
Expected Value of Year 1
Cash Flows (Proposal B)
CF1
$ -1,000
2,000
5,000
8,000
11,000
14-11
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
14-12
(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
14-13
(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
The standard deviation of
Proposal B < Proposal A.
( $2,846 < $3,795 )
14-14
Projects have risk
that may change
from period to
period.
Projects are more
likely to have
continuous, rather
than discrete
distributions.
Cash Flow ($)
Total Project Risk
1
14-15
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.
14-16
Probability Tree Approach
-$900
14-17
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
14-18
(.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
14-19
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
14-20
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.
14-21
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
14-22
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!
14-23
Actual NPV Solution Using
Your Financial Calculator
Solving for Branch #3:
14-24
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!
14-25
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
14-26
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
14-27
Summary of the
Decision Tree Analysis
The standard deviation =
SQRT ($1,031,800) = $1,015.78
The expected NPV
14-28
= -$
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.
14-29
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
14-30
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.
14-31
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:
14-32
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.
14-33
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.
14-34
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,
14-35
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.
14-36
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
14-37
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).
14-38
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
14-39
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
14-40
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
14-41
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
14-42
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
14-43
* For “True” Project considering abandonment option