Financial Management 14 Edition

1. 4-1
Chapter 14Chapter 14
Risk and ManagerialRisk and Managerial
Options in CapitalOptions in Capital
BudgetingBudgeting
Instructor: Ajab Khan Burki

2. 4-2
Risk and ManagerialRisk and Managerial
Options in Capital BudgetingOptions in Capital Budgeting
The Problem of Project Risk
Total Project Risk
Contribution to Total Firm Risk:
Firm-Portfolio Approach
Managerial Options

3. 4-3
An Illustration of TotalAn Illustration of Total
Risk (Discrete Distribution)Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL APROPOSAL A
State ProbabilityProbability Cash FlowCash 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
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL APROPOSAL A
State ProbabilityProbability Cash FlowCash 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

4. 4-4
Probability DistributionProbability Distribution
of Year 1 Cash Flowsof Year 1 Cash Flows
.40
.05
.25
Probability
-3,000 1,000 5,000 9,000 13,000
Cash Flow ($)
Proposal AProposal A

5. 4-5
CFCF11 PP11 (CFCF11)()(PP11))
$ -3,000 .05 $ -150
1,000 .25 250
5,000 .40 2,000
9,000 .25 2,250
13,000 .05 650
ΣΣ=1.001.00 CFCF11=$5,000$5,000
CFCF11 PP11 (CFCF11)()(PP11))
$ -3,000 .05 $ -150
1,000 .25 250
5,000 .40 2,000
9,000 .25 2,250
13,000 .05 650
ΣΣ=1.001.00 CFCF11=$5,000$5,000
Expected Value of Year 1Expected Value of Year 1
Cash Flows (Cash Flows (Proposal AProposal A))

6. 4-6
(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22
((PP11))
$ -150 ( -3,000 - 5,000)22
((.05.05))
250 ( 1,000 - 5,000)22
((.25.25))
2,000 ( 5,000 - 5,000)22
((.40.40))
2,250 ( 9,000 - 5,000)22
((.25.25))
650 (13,000 - 5,000)22
((.05.05))
$5,000$5,000
(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22
((PP11))
$ -150 ( -3,000 - 5,000)22
((.05.05))
250 ( 1,000 - 5,000)22
((.25.25))
2,000 ( 5,000 - 5,000)22
((.40.40))
2,250 ( 9,000 - 5,000)22
((.25.25))
650 (13,000 - 5,000)22
((.05.05))
$5,000$5,000
Variance of Year 1Variance of Year 1
Cash Flows (Cash Flows (Proposal AProposal A))

7. 4-7
Variance of Year 1Variance of Year 1
Cash Flows (Cash Flows (Proposal AProposal A))
(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22
*(*(PP11))
$ -150 3,200,000
250 4,000,000
2,000 0
2,250 4,000,000
650 3,200,000
$5,000$5,000 14,400,00014,400,000
(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22
*(*(PP11))
$ -150 3,200,000
250 4,000,000
2,000 0
2,250 4,000,000
650 3,200,000
$5,000$5,000 14,400,00014,400,000

8. 4-8
Summary ofSummary of Proposal AProposal A
The standard deviationstandard deviation =
SQRT (14,400,000) = $3,795$3,795
The expected cash flowexpected cash flow = $5,000$5,000

9. 4-9
An Illustration of TotalAn Illustration of Total
Risk (Discrete Distribution)Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL BPROPOSAL B
State ProbabilityProbability Cash FlowCash 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
ANNUAL CASH FLOWS: YEAR 1
PROPOSAL BPROPOSAL B
State ProbabilityProbability Cash FlowCash 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

10. 4-10
Probability DistributionProbability Distribution
of Year 1 Cash Flowsof Year 1 Cash Flows
.40
.05
.25
Probability
-3,000 1,000 5,000 9,000 13,000
Cash Flow ($)
Proposal BProposal B

11. 4-11
Expected Value of Year 1Expected Value of Year 1
Cash Flows (Cash Flows (Proposal BProposal B))
CFCF11 PP11 (CFCF11)()(PP11))
$ -1,000 .05 $ -50
2,000 .25 500
5,000 .40 2,000
8,000 .25 2,000
11,000 .05 550
ΣΣ=1.001.00 CFCF11=$5,000$5,000
CFCF11 PP11 (CFCF11)()(PP11))
$ -1,000 .05 $ -50
2,000 .25 500
5,000 .40 2,000
8,000 .25 2,000
11,000 .05 550
ΣΣ=1.001.00 CFCF11=$5,000$5,000

12. 4-12
(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22
((PP11))
$ -50 ( -1,000 - 5,000)22
((.05.05))
500 ( 2,000 - 5,000)22
((.25.25))
2,000 ( 5,000 - 5,000)22
((.40.40))
2,000 ( 8,000 - 5,000)22
((.25.25))
550 (11,000 - 5,000)22
((.05.05))
$5,000$5,000
(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22
((PP11))
$ -50 ( -1,000 - 5,000)22
((.05.05))
500 ( 2,000 - 5,000)22
((.25.25))
2,000 ( 5,000 - 5,000)22
((.40.40))
2,000 ( 8,000 - 5,000)22
((.25.25))
550 (11,000 - 5,000)22
((.05.05))
$5,000$5,000
Variance of Year 1Variance of Year 1
Cash Flows (Cash Flows (Proposal BProposal B))

13. 4-13
Variance of Year 1Variance of Year 1
Cash Flows (Cash Flows (Proposal BProposal B))
(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22
((PP11))
$ -50 1,800,000
500 2,250,000
2,000 0
2,000 2,250,000
550 1,800,000
$5,000$5,000 8,100,0008,100,000
(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22
((PP11))
$ -50 1,800,000
500 2,250,000
2,000 0
2,000 2,250,000
550 1,800,000
$5,000$5,000 8,100,0008,100,000

14. 4-14
Summary ofSummary of Proposal BProposal B
The standard deviation of
Proposal BProposal B << Proposal AProposal A..
(( $2,846$2,846 << $3,795$3,795 ))
The standard deviationstandard deviation =
SQRT (8,100,000) = $2,846$2,846
The expected cash flowexpected cash flow = $5,000$5,000

15. 4-15
Total Project RiskTotal Project Risk
Projects have risk
that may change
from period to
period.
Projects are more
likely to have
continuous, rather
than discrete
distributions.
CashFlow($)
11 22 33
Year

16. 4-16
Probability Tree ApproachProbability 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.

17. 4-17
Probability Tree ApproachProbability Tree Approach
Basket Wonders is
examining a project that will
have an initial costinitial cost today of
$900$900. Uncertainty
surrounding the first year
cash flows creates three
possible cash-flow
scenarios in Year 1Year 1.
-$900-$900

18. 4-18
Probability Tree ApproachProbability Tree Approach
Node 1: 20% chance of a
$1,200$1,200 cash-flow.
Node 2: 60% chance of a
$450$450 cash-flow.
Node 3: 20% chance of a
-$600-$600 cash-flow.
-$900-$900
(.20) $1,200$1,200
(.20) -$600-$600
(.60) $450$450
Year 1Year 1
11
22
33

19. 4-19
Probability Tree ApproachProbability Tree Approach
Each node in
Year 2Year 2
represents a
branchbranch of our
probability
tree.
The
probabilities
are said to be
conditionalconditional
probabilitiesprobabilities.
-$900-$900
(.20.20) $1,200$1,200
(.20.20) -$600-$600
(.6060) $450$450
Year 1Year 1
11
22
33
(.60) $1,200$1,200
(.30) $ 900$ 900
(.10) $2,200$2,200
(.35) $ 900$ 900
(.40) $ 600$ 600
(.25) $ 300$ 300
(.10) $ 500$ 500
(.50) -$ 100-$ 100
(.40) -$ 700-$ 700
Year 2Year 2

20. 4-20
Joint Probabilities [P(1,2)]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-$900
(.20.20) $1,200$1,200
(.20.20) -$600-$600
(.6060) $450$450
Year 1Year 1
11
22
33
(.60) $1,200$1,200
(.30) $ 900$ 900
(.10) $2,200$2,200
(.35) $ 900$ 900
(.40) $ 600$ 600
(.25) $ 300$ 300
(.10) $ 500$ 500
(.50) -$ 100-$ 100
(.40) -$ 700-$ 700
Year 2Year 2

21. 4-21
Project NPV Based onProject NPV Based on
Probability Tree UsageProbability Tree Usage
The probability
tree accounts for
the distribution
of cash flows.
Therefore,
discount all cash
flows at only the
risk-freerisk-free rate of
return.
The NPV for branch iNPV for branch i of
the probability tree for two
years of cash flows is
NPV = Σ (NPVNPVii)(PPii)
NPVNPVii =
CFCF11
(1 + RRff )11
(1 + RRff )22
CFCF22
- ICOICO
+
i = 1
z

22. 4-22
NPV for Each Cash-FlowNPV for Each Cash-Flow
Stream at 5% Risk-Free RateStream 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-$900
(.20.20) $1,200$1,200
(.20.20) -$600-$600
(.6060) $450$450
Year 1Year 1
11
22
33
(.60) $1,200$1,200
(.30) $ 900$ 900
(.10) $2,200$2,200
(.35) $ 900$ 900
(.40) $ 600$ 600
(.25) $ 300$ 300
(.10) $ 500$ 500
(.50) -$ 100-$ 100
(.40) -$ 700-$ 700
Year 2Year 2

23. 4-23
NPV on the CalculatorNPV on the Calculator
Remember, we can
use the cash flow
registry to solve
these NPV problems
quickly and
accurately!

24. 4-24
Actual NPV Solution UsingActual NPV Solution Using
Your Financial CalculatorYour Financial Calculator
Solving for Branch #3:
Step 1: Press CF key
Step 2: Press 2nd
CLR Work keys
Step 3: For CF0 Press -900 Enter ↓ keys
Step 4: For C01 Press 1200 Enter ↓ keys
Step 5: For F01 Press 1 Enter ↓ keys
Step 6: For C02 Press 900 Enter ↓ keys
Step 7: For F02 Press 1 Enter ↓ keys

25. 4-25
Actual NPV Solution UsingActual NPV Solution Using
Your Financial CalculatorYour Financial Calculator
Solving for Branch #3:
Step 8: Press ↓ ↓ keys
Step 9: Press NPV key
Step 10: For I=, Enter 5 Enter ↓ keys
Step 11: Press CPT key
Result: Net Present Value = $1,059.18
You would complete this for EACH branch!

26. 4-26
Calculating the ExpectedCalculating the Expected
Net Present Value (Net Present Value (NPVNPV))
Branch NPVNPVii
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)P(1,2) NPVNPVii * P(1,2)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 -$168.51
Expected Net Present ValueExpected Net Present Value = -$ 17.01-$ 17.01

27. 4-27
Calculating the VarianceCalculating the Variance
of the Net Present Valueof the Net Present Value
NPVNPVii
$ 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)P(1,2) ((NPVNPVii - NPVNPV )2
[P(1,2)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
VarianceVariance = $1,031,800.31$1,031,800.31

28. 4-28
Summary of theSummary of the
Decision Tree AnalysisDecision Tree Analysis
The standard deviationstandard deviation =
SQRT ($1,031,800) = $1,015.78$1,015.78
The expected NPVexpected NPV = -$ 17.01-$ 17.01

29. 4-29
Simulation ApproachSimulation 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.

30. 4-30
Simulation ApproachSimulation Approach
Market analysisMarket analysis
Market size, selling price, market
growth rate,
and market share
Investment cost analysisInvestment cost analysis
Investment required, useful life of
facilities, and residual value
Operating and fixed costsOperating and fixed costs
Operating costs and fixed costs
Factors we might consider in a model:

31. 4-31
Simulation ApproachSimulation 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.

32. 4-32
Simulation ApproachSimulation Approach
Each proposal will generate an internal rate ofinternal rate of
returnreturn. The process of generating many, many
simulations results in a large set of internal
rates of return. The distributiondistribution might look like
the following:
INTERNAL RATE OF RETURN (%)
PROBABILITY
OFOCCURRENCE

33. 4-33
Combining projects in this manner reduces
the firm risk due to diversificationdiversification.
Contribution to Total Firm Risk:Contribution to Total Firm Risk:
Firm-Portfolio ApproachFirm-Portfolio Approach
CASHFLOW
TIME TIMETIME
Proposal AProposal A Proposal BProposal B
Combination ofCombination of
ProposalsProposals AA andand BB

34. 4-34
NPVP = Σ ( 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 ExpectedDetermining the Expected
NPV for a Portfolio of ProjectsNPV for a Portfolio of Projects
m
j=1

35. 4-35
σσPP = Σ Σ σjk
σjk is the covariance between possible
NPVs for projects j and k,
σσ jk = σ j σ k rr jk .
σj is the standard deviation of project j,
σkis the standard deviation of project k,
rjk is the correlation coefficient between
Determining PortfolioDetermining Portfolio
Standard DeviationStandard Deviation
m
j=1
m
k=1

36. 4-36
E: Existing ProjectsE: Existing Projects
8 Combinations
EE EE + 1 EE + 1 + 2
EE + 2 EE + 1 + 3
EE + 3 EE + 2 + 3
EE + 1 + 2 + 3
AA, BB, and CC are
dominatingdominating combinations
from the eight possible.
Combinations ofCombinations of
Risky InvestmentsRisky Investments
A
B
C
E
Standard Deviation
ExpectedValueofNPV

37. 4-37
Managerial (Real) OptionsManagerial (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

38. 4-38
Managerial (Real) OptionsManagerial (Real) Options
Expand (or contract)Expand (or contract)
Allows the firm to expand (contract) production
if conditions become favorable (unfavorable).
AbandonAbandon
Allows the project to be terminated early.
PostponePostpone
Allows the firm to delay undertaking a project
(reduces uncertainty via new information).

39. 4-39
Previous Example withPrevious Example with
Project AbandonmentProject Abandonment
Assume that
this project
can be
abandoned at
the end of the
first year for
$200$200.
What is the
projectproject
worthworth?
-$900-$900
(.20.20) $1,200$1,200
(.20.20) -$600-$600
(.6060) $450$450
Year 1Year 1
11
22
33
(.60) $1,200$1,200
(.30) $ 900$ 900
(.10) $2,200$2,200
(.35) $ 900$ 900
(.40) $ 600$ 600
(.25) $ 300$ 300
(.10) $ 500$ 500
(.50) -$ 100-$ 100
(.40) -$ 700-$ 700
Year 2Year 2

40. 4-40
Project AbandonmentProject Abandonment
Node 3Node 3:
(500500/1.05)(.1)+
(-100-100/1.05)(.5)+
(-700-700/1.05)(.4)=
($476.19)(.1)+
-($ 95.24)(.5)+
-($666.67)(.4)=
-($266.67)-($266.67)
-$900-$900
(.20.20) $1,200$1,200
(.20.20) -$600-$600
(.6060) $450$450
Year 1Year 1
11
22
33
(.60) $1,200$1,200
(.30) $ 900$ 900
(.10) $2,200$2,200
(.35) $ 900$ 900
(.40) $ 600$ 600
(.25) $ 300$ 300
(.10) $ 500$ 500
(.50) -$ 100-$ 100
(.40) --$ 700$ 700
Year 2Year 2

41. 4-41
Project AbandonmentProject Abandonment
-$900-$900
(.20.20) $1,200$1,200
(.20.20) -$600-$600
(.6060) $450$450
Year 1Year 1
11
22
33
(.60) $1,200$1,200
(.30) $ 900$ 900
(.10) $2,200$2,200
(.35) $ 900$ 900
(.40) $ 600$ 600
(.25) $ 300$ 300
(.10) $ 500$ 500
(.50) -$ 100-$ 100
(.40) -$ 700-$ 700
Year 2Year 2
The optimal
decision at the
end of Year 1Year 1
is to abandon
the project for
$200$200.
$200$200 >
-($266.67)-($266.67)
What is the
“new”“new” project
value?

42. 4-42
Project AbandonmentProject Abandonment
$ 2,238.32
$ 1,331.29
$ 1,059.18
$ 344.90
$ 72.79
-$ 199.32
-$ 1,280.95
-$900-$900
(.20.20) $1,200$1,200
(.20.20) -$400*-$400*
(.6060) $450$450
Year 1Year 1
11
22
33
(.60) $1,200$1,200
(.30) $ 900$ 900
(.10) $2,200$2,200
(.35) $ 900$ 900
(.40) $ 600$ 600
(.25) $ 300$ 300
(1.0) $ 0$ 0
Year 2Year 2
*-$600 + $200 abandonment

43. 4-43
Summary of the AdditionSummary of the Addition
of the Abandonment Optionof the Abandonment Option
* For “True” Project considering abandonment option
The standard deviation*standard deviation* =
SQRT (740,326) = $857.56$857.56
The expectedexpected NPV*NPV* = $$ 71.8871.88
NPV*NPV* = Original NPV +
Abandonment OptionAbandonment Option
Thus,Thus, $71.88$71.88 = -$17.01 + OptionOption
Abandonment OptionAbandonment Option = $ 88.89$ 88.89