14-1
Chapter 14
Risk and Managerial
Options in Capital
Budgeting
14-2
Risk and Managerial
Options in Capital
Budgeting
?The Problem of Project Risk
?Total Project Risk
?Contribution to Total Firm Risk,
Firm-Portfolio Approach
?Managerial Options
14-3
An Illustration of Total
Risk (Discrete Distribution)
ANNUAL CASH FLOWS,YEAR 1
PROPOSAL A
State Probability Cash Flow
Deep Recession,05 $ -3,000
Mild Recession,25 1,000
Normal,40 5,000
Minor Boom,25 9,000
Major Boom,05 13,000
14-4
Probability Distribution
of Year 1 Cash Flows
.40
.05
.25
Pr
ob
ab
ilit
y
-3,000 1,000 5,000 9,000 13,000
Cash Flow ($)
Proposal A
14-5
CF1 P1 (CF1)(P1)
$ -3,000,05 $ -150
1,000,25 250
5,000,40 2,000
9,000,25 2,250
13,000,05 650
?=1.00 CF1=$5,000
Expected Value of Year 1
Cash Flows (Proposal A)
14-6
(CF1)(P1) (CF1 - CF1)2(P1)
$ -150 ( -3,000 - 5,000)2 (.05)
250 ( 1,000 - 5,000)2 (.25)
2,000 ( 5,000 - 5,000)2 (.40)
2,250 ( 9,000 - 5,000)2 (.25)
650 (13,000 - 5,000)2 (.05)
$5,000
Variance of Year 1
Cash Flows (Proposal A)
14-7
Variance of Year 1
Cash Flows (Proposal A)
(CF1)(P1) (CF1 - CF1)2*(P1)
$ -150 3,200,000
250 4,000,000
2,000 0
2,250 4,000,000
650 3,200,000
$5,000 14,400,000
14-8
Summary of Proposal A
The standard deviation =
SQRT (14,400,000) = $3,795
The expected cash flow = $5,000
14-9
An Illustration of Total
Risk (Discrete Distribution)
ANNUAL CASH FLOWS,YEAR 1
PROPOSAL B
State Probability Cash Flow
Deep Recession,05 $ -1,000
Mild Recession,25 2,000
Normal,40 5,000
Minor Boom,25 8,000
Major Boom,05 11,000
14-10
Probability Distribution
of Year 1 Cash Flows
.40
.05
.25
Pr
ob
ab
ilit
y
-3,000 1,000 5,000 9,000 13,000
Cash Flow ($)
Proposal B
14-11
Expected Value of Year 1
Cash Flows (Proposal B)
CF1 P1 (CF1)(P1)
$ -1,000,05 $ -50
2,000,25 500
5,000,40 2,000
8,000,25 2,000
11,000,05 550
?=1.00 CF1=$5,000
14-12
(CF1)(P1) (CF1 - CF1)2(P1)
$ -50 ( -1,000 - 5,000)2 (.05)
500 ( 2,000 - 5,000)2 (.25)
2,000 ( 5,000 - 5,000)2 (.40)
2,000 ( 8,000 - 5,000)2 (.25)
550 (11,000 - 5,000)2 (.05)
$5,000
Variance of Year 1
Cash Flows (Proposal B)
14-13
Variance of Year 1
Cash Flows (Proposal B)
(CF1)(P1) (CF1 - CF1)2(P1)
$ -50 1,800,000
500 2,250,000
2,000 0
2,000 2,250,000
550 1,800,000
$5,000 8,100,000
14-14
Summary of Proposal B
The standard deviation of
Proposal B < Proposal A.
( $2,846 < $3,795 )
The standard deviation =
SQRT (8,100,000) = $2,846
The expected cash flow = $5,000
14-15
Total Project Risk
Projects have risk
that may change
from period to
period.
Projects are more
likely to have
continuous,rather
than discrete
distributions,
Ca
sh
Fl
ow
($
)
1 2 3
Year
14-16
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
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.
-$900
14-18
Probability Tree Approach
Node 1,20% chance of a
$1,200 cash-flow.
Node 2,60% chance of a
$450 cash-flow,
Node 3,20% chance of a
-$600 cash-flow.
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
14-19
Probability Tree Approach
Each node in
Year 2
represents a
branch of our
probability
tree.
The
probabilities
are said to be
conditional
probabilities.
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-20
Joint Probabilities [P(1,2)]
.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
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-21
Project NPV Based on
Probability Tree Usage
The probability
tree accounts for
the distribution
of cash-flows,
Therefore,
discount all
cash-flows at
only the risk-free
rate of return.
The NPV for branch i of
the probability tree for two
years of cash flows is
NPV = ? (NPVi)(Pi)
NPVi = CF1(1 + R
f )1 (1 + Rf )2
CF2
- ICO
+
i = 1
z
14-22
NPV for Each Cash-Flow
Stream at 5% Risk-Free Rate
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,017.91
-$ 1,562.13
-$ 2,106.35
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-23
Calculating the Expected
Net Present Value (NPV)
Branch NPVi
Branch 1 $ 2,238.32
Branch 2 $ 1,331.29
Branch 3 $ 1,059.18
Branch 4 $ 344.90
Branch 5 $ 72.79
Branch 6 -$ 199.32
Branch 7 -$ 1,017.91
Branch 8 -$ 1,562.13
Branch 9 -$ 2,106.35
P(1,2) NPVi * P(1,2)
.02 $ 44.77
.12 $159.75
.06 $ 63.55
.21 $ 72.43
.24 $ 17.47
.15 -$ 29.90
.02 -$ 20.36
.10 -$156.21
.08 -$168.51
Expected Net Present Value = -$ 17.01
14-24
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) (NPVi - NPV )2[P(1,2)]
.02 $ 101,730.27
.12 $ 218,149.55
.06 $ 69,491.09
.21 $ 27,505.56
.24 $ 1,935.37
.15 $ 4,985.54
.02 $ 20,036.02
.10 $ 238,739.58
.08 $ 349,227.33
Variance = $1,031,800.31
14-25
Summary of the
Decision Tree
Analysis
The standard deviation =
SQRT ($1,031,800) = $1,015.78
The expected NPV = -$ 17.01
14-26
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.
14-27
Simulation Approach
? 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
Factors we might consider in a model:
14-28
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 14-27.
14-29
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:
INTERNAL RATE OF RETURN (%)
PR
OB
AB
ILI
TY
OF
OC
CU
RR
EN
CE
14-30
Combining projects in this manner reduces
the firm risk due to diversification.
Contribution to Total Firm Risk,
Firm-Portfolio Approach
CA
SH
F
LO
W
TIME TIMETIME
Proposal A Proposal B Combination of Proposals A and B
14-31
NPVP = ? ( NPVj )
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 the Expected
NPV for a Portfolio of
Projects
m
j=1
14-32
?P = ?????jk
?jk is the covariance between possible
NPVs for projects j and k?
??jk = ??j ??k r?jk,
?j is the standard deviation of project j,
?k is the standard deviation of project k,
rjk is the correlation coefficient between
projects j and k.
Determining Portfolio
Standard Deviation
m
j=1
m
k=1
14-33
E,Existing Projects
8 Combinations
E E + 1 E + 1 + 2
E + 2 E + 1 + 3
E + 3 E + 2 + 3
E + 1 + 2 + 3
A,B,and C are
dominating combinations
from the eight possible.
Combinations of
Risky Investments
A
B
C
E
Standard Deviation
Ex
pe
ct
ed
Va
lu
e o
f N
PV
14-34
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
14-35
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).
14-36
Previous Example with
Project Abandonment
Assume that
this project
can be
abandoned at
the end of the
first year for
$200.
What is the
project
worth?
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-37
Project Abandonment
Node 3:
(500/1.05)(.1)+
(-100/1.05)(.5)+
(-700/1.05)(.4)=
($476.19)(.1)+
-($ 95.24)(.5)+
-($666.67)(.4)=
-($266.67)
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-38
Project Abandonment
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
The optimal
decision at the
end of Year 1
is to abandon
the project for
$200.
$200 >
-($266.67)
What is the
new project
value?
14-39
Project Abandonment
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,280.95
-$900
(.20) $1,200
(.20) -$400
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(1.0) $ 0
Year 2
14-40
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
Abandonment Option = $ 88.89
Chapter 14
Risk and Managerial
Options in Capital
Budgeting
14-2
Risk and Managerial
Options in Capital
Budgeting
?The Problem of Project Risk
?Total Project Risk
?Contribution to Total Firm Risk,
Firm-Portfolio Approach
?Managerial Options
14-3
An Illustration of Total
Risk (Discrete Distribution)
ANNUAL CASH FLOWS,YEAR 1
PROPOSAL A
State Probability Cash Flow
Deep Recession,05 $ -3,000
Mild Recession,25 1,000
Normal,40 5,000
Minor Boom,25 9,000
Major Boom,05 13,000
14-4
Probability Distribution
of Year 1 Cash Flows
.40
.05
.25
Pr
ob
ab
ilit
y
-3,000 1,000 5,000 9,000 13,000
Cash Flow ($)
Proposal A
14-5
CF1 P1 (CF1)(P1)
$ -3,000,05 $ -150
1,000,25 250
5,000,40 2,000
9,000,25 2,250
13,000,05 650
?=1.00 CF1=$5,000
Expected Value of Year 1
Cash Flows (Proposal A)
14-6
(CF1)(P1) (CF1 - CF1)2(P1)
$ -150 ( -3,000 - 5,000)2 (.05)
250 ( 1,000 - 5,000)2 (.25)
2,000 ( 5,000 - 5,000)2 (.40)
2,250 ( 9,000 - 5,000)2 (.25)
650 (13,000 - 5,000)2 (.05)
$5,000
Variance of Year 1
Cash Flows (Proposal A)
14-7
Variance of Year 1
Cash Flows (Proposal A)
(CF1)(P1) (CF1 - CF1)2*(P1)
$ -150 3,200,000
250 4,000,000
2,000 0
2,250 4,000,000
650 3,200,000
$5,000 14,400,000
14-8
Summary of Proposal A
The standard deviation =
SQRT (14,400,000) = $3,795
The expected cash flow = $5,000
14-9
An Illustration of Total
Risk (Discrete Distribution)
ANNUAL CASH FLOWS,YEAR 1
PROPOSAL B
State Probability Cash Flow
Deep Recession,05 $ -1,000
Mild Recession,25 2,000
Normal,40 5,000
Minor Boom,25 8,000
Major Boom,05 11,000
14-10
Probability Distribution
of Year 1 Cash Flows
.40
.05
.25
Pr
ob
ab
ilit
y
-3,000 1,000 5,000 9,000 13,000
Cash Flow ($)
Proposal B
14-11
Expected Value of Year 1
Cash Flows (Proposal B)
CF1 P1 (CF1)(P1)
$ -1,000,05 $ -50
2,000,25 500
5,000,40 2,000
8,000,25 2,000
11,000,05 550
?=1.00 CF1=$5,000
14-12
(CF1)(P1) (CF1 - CF1)2(P1)
$ -50 ( -1,000 - 5,000)2 (.05)
500 ( 2,000 - 5,000)2 (.25)
2,000 ( 5,000 - 5,000)2 (.40)
2,000 ( 8,000 - 5,000)2 (.25)
550 (11,000 - 5,000)2 (.05)
$5,000
Variance of Year 1
Cash Flows (Proposal B)
14-13
Variance of Year 1
Cash Flows (Proposal B)
(CF1)(P1) (CF1 - CF1)2(P1)
$ -50 1,800,000
500 2,250,000
2,000 0
2,000 2,250,000
550 1,800,000
$5,000 8,100,000
14-14
Summary of Proposal B
The standard deviation of
Proposal B < Proposal A.
( $2,846 < $3,795 )
The standard deviation =
SQRT (8,100,000) = $2,846
The expected cash flow = $5,000
14-15
Total Project Risk
Projects have risk
that may change
from period to
period.
Projects are more
likely to have
continuous,rather
than discrete
distributions,
Ca
sh
Fl
ow
($
)
1 2 3
Year
14-16
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
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.
-$900
14-18
Probability Tree Approach
Node 1,20% chance of a
$1,200 cash-flow.
Node 2,60% chance of a
$450 cash-flow,
Node 3,20% chance of a
-$600 cash-flow.
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
14-19
Probability Tree Approach
Each node in
Year 2
represents a
branch of our
probability
tree.
The
probabilities
are said to be
conditional
probabilities.
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-20
Joint Probabilities [P(1,2)]
.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
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-21
Project NPV Based on
Probability Tree Usage
The probability
tree accounts for
the distribution
of cash-flows,
Therefore,
discount all
cash-flows at
only the risk-free
rate of return.
The NPV for branch i of
the probability tree for two
years of cash flows is
NPV = ? (NPVi)(Pi)
NPVi = CF1(1 + R
f )1 (1 + Rf )2
CF2
- ICO
+
i = 1
z
14-22
NPV for Each Cash-Flow
Stream at 5% Risk-Free Rate
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,017.91
-$ 1,562.13
-$ 2,106.35
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-23
Calculating the Expected
Net Present Value (NPV)
Branch NPVi
Branch 1 $ 2,238.32
Branch 2 $ 1,331.29
Branch 3 $ 1,059.18
Branch 4 $ 344.90
Branch 5 $ 72.79
Branch 6 -$ 199.32
Branch 7 -$ 1,017.91
Branch 8 -$ 1,562.13
Branch 9 -$ 2,106.35
P(1,2) NPVi * P(1,2)
.02 $ 44.77
.12 $159.75
.06 $ 63.55
.21 $ 72.43
.24 $ 17.47
.15 -$ 29.90
.02 -$ 20.36
.10 -$156.21
.08 -$168.51
Expected Net Present Value = -$ 17.01
14-24
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) (NPVi - NPV )2[P(1,2)]
.02 $ 101,730.27
.12 $ 218,149.55
.06 $ 69,491.09
.21 $ 27,505.56
.24 $ 1,935.37
.15 $ 4,985.54
.02 $ 20,036.02
.10 $ 238,739.58
.08 $ 349,227.33
Variance = $1,031,800.31
14-25
Summary of the
Decision Tree
Analysis
The standard deviation =
SQRT ($1,031,800) = $1,015.78
The expected NPV = -$ 17.01
14-26
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.
14-27
Simulation Approach
? 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
Factors we might consider in a model:
14-28
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 14-27.
14-29
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:
INTERNAL RATE OF RETURN (%)
PR
OB
AB
ILI
TY
OF
OC
CU
RR
EN
CE
14-30
Combining projects in this manner reduces
the firm risk due to diversification.
Contribution to Total Firm Risk,
Firm-Portfolio Approach
CA
SH
F
LO
W
TIME TIMETIME
Proposal A Proposal B Combination of Proposals A and B
14-31
NPVP = ? ( NPVj )
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 the Expected
NPV for a Portfolio of
Projects
m
j=1
14-32
?P = ?????jk
?jk is the covariance between possible
NPVs for projects j and k?
??jk = ??j ??k r?jk,
?j is the standard deviation of project j,
?k is the standard deviation of project k,
rjk is the correlation coefficient between
projects j and k.
Determining Portfolio
Standard Deviation
m
j=1
m
k=1
14-33
E,Existing Projects
8 Combinations
E E + 1 E + 1 + 2
E + 2 E + 1 + 3
E + 3 E + 2 + 3
E + 1 + 2 + 3
A,B,and C are
dominating combinations
from the eight possible.
Combinations of
Risky Investments
A
B
C
E
Standard Deviation
Ex
pe
ct
ed
Va
lu
e o
f N
PV
14-34
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
14-35
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).
14-36
Previous Example with
Project Abandonment
Assume that
this project
can be
abandoned at
the end of the
first year for
$200.
What is the
project
worth?
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-37
Project Abandonment
Node 3:
(500/1.05)(.1)+
(-100/1.05)(.5)+
(-700/1.05)(.4)=
($476.19)(.1)+
-($ 95.24)(.5)+
-($666.67)(.4)=
-($266.67)
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
14-38
Project Abandonment
-$900
(.20) $1,200
(.20) -$600
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(.10) $ 500
(.50)-$ 100
(.40)-$ 700
Year 2
The optimal
decision at the
end of Year 1
is to abandon
the project for
$200.
$200 >
-($266.67)
What is the
new project
value?
14-39
Project Abandonment
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,280.95
-$900
(.20) $1,200
(.20) -$400
(.60) $450
Year 1
1
2
3
(.60) $1,200
(.30) $ 900
(.10) $2,200
(.35) $ 900
(.40) $ 600
(.25) $ 300
(1.0) $ 0
Year 2
14-40
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
Abandonment Option = $ 88.89
