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14-1
Chapter 14Chapter 14
Risk and Managerial Risk and Managerial (Real) Options in (Real) Options in Capital BudgetingCapital Budgeting
Risk and Managerial Risk and Managerial (Real) Options in (Real) Options in Capital BudgetingCapital Budgeting
Created by: Gregory A. Kuhlemeyer, Ph.D.Carroll College, Waukesha, WI
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After studying Chapter 14, After studying Chapter 14, you should be able to: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.
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Risk and Managerial (Real)Risk and Managerial (Real)Options in Capital BudgetingOptions in Capital BudgetingRisk and Managerial (Real)Risk and Managerial (Real)Options in Capital BudgetingOptions in Capital Budgeting
The Problem of Project Risk
Total Project Risk
Contribution to Total Firm Risk: Firm-Portfolio Approach
Managerial (Real) Options
The Problem of Project Risk
Total Project Risk
Contribution to Total Firm Risk: Firm-Portfolio Approach
Managerial (Real) Options
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An Illustration of Total An Illustration of Total Risk (Discrete Distribution)Risk (Discrete Distribution)An Illustration of Total An Illustration of Total Risk (Discrete Distribution)Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1PROPOSAL 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 1PROPOSAL 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
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Probability Distribution Probability Distribution of Year 1 Cash Flowsof Year 1 Cash FlowsProbability Distribution Probability Distribution of Year 1 Cash Flowsof Year 1 Cash Flows
Expected Value of Year 1 Expected Value of Year 1 Cash Flows (Cash Flows (Proposal AProposal A))Expected Value of Year 1 Expected Value of Year 1 Cash Flows (Cash Flows (Proposal AProposal A))
Variance of Year 1 Variance of Year 1 Cash Flows (Cash Flows (Proposal AProposal A))Variance of Year 1 Variance of Year 1 Cash Flows (Cash Flows (Proposal AProposal A))
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Variance of Year 1 Variance of Year 1 Cash Flows (Cash Flows (Proposal AProposal A))Variance of Year 1 Variance of Year 1 Cash Flows (Cash Flows (Proposal AProposal A))
The standard deviation standard deviation = SQRT (14,400,000) = $3,795$3,795
The expected cash flow expected cash flow = $5,000$5,000
Coefficient of Variation (CV)Coefficient of Variation (CV) = $3,795 / $5,000 = $3,795 / $5,000 = = 0.7590.759
CV is a measure of CV is a measure of relativerelative risk and is the ratio of risk and is the ratio of standard deviation to the mean of the distribution.standard deviation to the mean of the distribution.
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An Illustration of Total An Illustration of Total Risk (Discrete Distribution)Risk (Discrete Distribution)An Illustration of Total An Illustration of Total Risk (Discrete Distribution)Risk (Discrete Distribution)
ANNUAL CASH FLOWS: YEAR 1PROPOSAL 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 1PROPOSAL 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
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Probability Distribution Probability Distribution of Year 1 Cash Flowsof Year 1 Cash FlowsProbability Distribution Probability Distribution of Year 1 Cash Flowsof Year 1 Cash Flows
.40
.05
.25
Pro
bab
ility
-3,000 1,000 5,000 9,000 13,000
Cash Flow ($)
Proposal BProposal B
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Expected Value of Year 1 Expected Value of Year 1 Cash Flows (Cash Flows (Proposal BProposal B))Expected Value of Year 1 Expected Value of Year 1 Cash Flows (Cash Flows (Proposal BProposal B))
Variance of Year 1 Variance of Year 1 Cash Flows (Cash Flows (Proposal BProposal B))Variance of Year 1 Variance of Year 1 Cash Flows (Cash Flows (Proposal BProposal B))
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Variance of Year 1 Variance of Year 1 Cash Flows (Cash Flows (Proposal BProposal B))Variance of Year 1 Variance of Year 1 Cash Flows (Cash Flows (Proposal BProposal B))
The standard deviation of B B < < AA ( ($2,846$2,846< < $3,795$3,795), so “), so “BB” ” is is lessless risky than “A”. risky than “A”.
The coefficient of variation of B < A (The coefficient of variation of B < A (0.5690.569<<0.7590.759), so “), so “BB” ” has has lessless relative risk than “ relative risk than “AA”.”.
The standard deviation standard deviation = SQRT (8,100,000)= $2,846$2,846
The expected cash flow expected cash flow = $5,000$5,000
Coefficient of Variation (CV)Coefficient of Variation (CV) = $2,846 / $5,000 = $2,846 / $5,000 = = 0.5690.569
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Total Project RiskTotal Project Risk
Projects have risk that may change
from period to period.
Projects are more likely to have
continuous, rather than discrete distributions.
Cas
h F
low
($)
11 22 33 Year
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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.
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Probability Tree ApproachProbability Tree Approach
Basket Wonders is examining a project that will have an initial cost initial cost today of
$900$900. Uncertainty surrounding the first year cash flows creates three
possible cash-flow scenarios in Year 1Year 1.
-$900-$900
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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
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Probability Tree ApproachProbability Tree Approach
Project NPV Based on Project 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 i NPV for branch i of the probability tree for two
years of cash flows is
NPV = (NPVNPVii)(PPii)
NPVNPVii = CFCF11
(1 + RRff )11 (1 + RRff )22
CFCF22
- ICOICO
+
i = 1
z
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NPV for Each Cash-Flow NPV 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
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NPV on the CalculatorNPV on the Calculator
Remember, we can use the cash flow registry
to solve these NPV problems quickly and
accurately!
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Actual NPV Solution Using Actual NPV Solution Using Your Financial CalculatorYour Financial CalculatorActual NPV Solution Using Actual 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
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Actual NPV Solution Using Actual NPV Solution Using Your Financial CalculatorYour Financial CalculatorActual NPV Solution Using Actual 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!
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Calculating the Expected Calculating the Expected Net Present Value (Net Present Value (NPVNPV))
The resulting proposal value is dependent on the distribution and interaction of EVERY variable listed on slide 14-30.
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Simulation ApproachSimulation Approach
Each proposal will generate an internal rate of internal 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 (%)
PR
OB
AB
ILIT
YO
F O
CC
UR
RE
NC
E
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Combining projects in this manner reduces the firm risk due to diversificationdiversification.
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 ApproachContribution to Total Firm Risk: Contribution to Total Firm Risk: Firm-Portfolio ApproachFirm-Portfolio Approach
CA
SH
FL
OW
TIME TIMETIME
Proposal AProposal A Proposal BProposal BCombination of Combination of
Proposals Proposals AA andand BB
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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.
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 Determining the Expected NPV for a Portfolio of ProjectsNPV for a Portfolio of ProjectsDetermining the Expected Determining the Expected NPV for a Portfolio of ProjectsNPV for a Portfolio of Projects
m
j=1
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PP = jk
jk is the covariance between possible
NPVs for projects j and k
jk = j k rrjk .
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.
PP = jk
jk is the covariance between possible
NPVs for projects j and k
jk = j k rrjk .
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 Determining Portfolio Standard DeviationStandard DeviationDetermining Portfolio Determining Portfolio Standard DeviationStandard Deviation
m
j=1
m
k=1
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E: Existing ProjectsE: Existing Projects
8 Combinations
EE EE + 1 EE + 1 + 2 EE + 2 EE + 1 + 3EE + 3 EE + 2 + 3
EE + 1 + 2 + 3
AA, BB, and CC are dominatingdominating combinations from the eight possible.
Combinations of Combinations of Risky InvestmentsRisky Investments