Risk Analysis in Capital Investment Decisions
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Risk Analysis in Capital
Investment Decisions Measurement of Risk Method of Incorporating Risk into
Capital Budgeting
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Measures of Risk
Range
Mean absolute Deviation
Semi-Variance Coefficient of Variation
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example
NPV Probability
200 0.3
600 0.5
900 0.2
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For your Project
Assign uneven probability for your cashflow and calculate , variance and semi-variance and coefficient of variation
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Method of Incorporating Risk intoCapital Budgeting
Certainty Equivalent Method
Risk adjusted Discount Rate Method
-Perfectly Correlated cashflows
-Uncorrelated cash flows
-Moderately correlated cashflows
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Certainty Equivalent Method
Utility of Decision Maker for the returnobtained by taking each additional unit ofrisk
Useful when the Decision makers risk-return perception vary from one year toanother
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Certainty Equivalent Method
Outcome probability
1000 0.30
5000 0.70
Expected Value=
Which alternative uwill take?
Find out Certainty
Equivalent Coefficient
Sure cash flow Rs 3000
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Certainty Equivalent Coefficient
=Sure Cash flow/Exp cash flow
=3000/3800
=0.79 Shows the level of confidence of the top
mgt about the receipt of the cash flow from
the project.
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Example (00 000)
Year Cash flow CEC
1 10 0.9
2 15 0.85
3 20 0.82
4 25 0.72
Find out CEC? And Comment on your findings, if
Initial investment is 45 lakhs; Rf=5%pa
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Use formula for CEC in aboveproblem
Ii
ANPV
n
t
t
tt +
==1 )1(
=CEC for the cash flow
A= the expected relevant cash flow
i=risk free rate
I=initial investment
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CEC
Varies between 0-1
Higher the CEC, higher the confidence ofthe decision maker
CEC=1 for T-bills & Risk free instruments
If cash flows are highly correlated CEC will
be same in all the years
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Cash Flows as RandomVariables
Risk is chance that a random variable will takeon a value significantly different from theexpected value In capital budgeting the estimate of each future
period's cash flow is a random variable
The NPV and IRR of any project are random variableswith expected values and variances that reflect risk
Thus, the actual value is likely to be different than the mean
The amount the actual value is likely to differ from theexpected is related to the variance or standard deviation
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The Probability Distribution of a FutureCash Flow as a Random Variable
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Risk in Estimated Cash Flows
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Risk Adjusted Discount Rate Method
Category of Investment Discount Rate
Replacement ofInvestments
Cost of capital +2%
New Projects Cost of capital +4%
R&D Investments Cost of capital +5%
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Calculation of SD of NPV
Un-correlated cash flows-use Rf as discounting rate
expected NPV
Expected cash flowfor year t
i = Rf
I=Initial outlay
VPN
Ii
AVPN
n
t
t
t +
==1 )1(
A2/1
1
2
2
)1(
)(
+
= =
n
t
t
t
i
NPV
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Example
Year 1 Year 2 Year 3
3000 0.3 2000 0.2 3000 0.3
5000 0.4 4000 0.6 5000 0.4
7000 0.3 6000 0.2 7000 0.3
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Perfectly correlated cash flows
Ii
AVPN
n
tt
t +
==1 )1(
+=
=
n
t
t
t
iNPV
1 )1()(
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Example
Work out previousone
Next, see table; given
I=10,000
Year Aver.CF
Std DevCF
1 5000 1500
2 3000 1000
3 4000 20004 3000 1200
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Moderately correlated cash flow
Page 212
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Using probability table
Given average NPV=96,000
Dtd devn NPV = 60,000
What is the probability that NPV will beless than 0?
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Advanced Techniques in RA
Sensitivity Analysis
Scenario Analysis
Simulation approach Decision Tree Analysis
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Sensitivity Analysis I
Method Sensitivity analysis is a risk analysis technique that tells how
much NPV will change in response to given changes in one cashflow factor with other factors held constant.
-5% 20%15%10%5%-10%-15%-20%
Deviation from Base-Case Value (%)
NPV ($)
$ 0
0%
Unit sales price
NPV based on the originallyestimated unit sales price
NPV when unit sales pricegoes up by 15%
NPV when unit sales pricegoes down by 20%
Based on: Financial Management, Eugene F. Brigham and Michael C. Ehrhardt, 2008
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Sensitivity Analysis II
The slopes of the lines indicate how sensitive NPV is to changes ineach individual cash flow.
Relatively small error in estimating individual cash flow with steeperslope leads to a large error in estimating projects NPV.
-5% 20%15%10%5%-10%-15%-20%
Deviation from Base-Case Value (%)
NPV ($)
$ 0
0%
Unit sales price
Estimated values of cashflow factors
Price growth rate
Sales quantity
Asset beta
Utility price
Input price
Input price growth
Operating costs
Construction costsNPV breakevenanalysis
Original NPVvalue
Based on: Financial Management, Eugene F. Brigham and Michael C. Ehrhardt, 2008
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Sensitivity Analysis III
Implication Sensitivity analysis is a powerful technique to understand which factors
need to be more accurately examined to reduce the entire credit risk.
Weak Points
Sensitivity analysis does not incorporate a concept of probability
It can deal with only one cash flow for each analysis NPV Breakeven Analysis
NPV breakeven analysis examines a value of each factor which makesNPV exactly zero.
Based on: Financial Management, Eugene F. Brigham and Michael C. Ehrhardt, 2008
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Sensitivity Analysis for your project
Find what happens to your projects NPV ifthe cash flow affected by:
Increase/decrease in Initial Outlay
fall / rise in Saleshike / dip in Variable Costs
up / down in Fixed Costs
Only one variable is varied at a time
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Sensitivity Analysis for Your Project
Key variable Range
Pessimistic Expected Optimistic
Investment -20% Normal +20%
Sales Rs m -16% Normal +16%
Variablecost as % ofsales
+10% Normal -5%
Fixed costs +30% Normal -20%
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Advantages Vs Disadvantages
How robust orvulnerable to changesin underlying
variables Help explore where
the vulnerability ismore
Intuitively appealing
Nothing about thelikelihood of thesechanges
Specified variablebased
Inherently subjective
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Scenario Analysis I
Method Scenario analysis examines a set of scenarios under tha
assamption that each scenario occurs with a certain probability
Example 1: sales price would drop by 6% with 25% probability forworst case scenario.
Example 2: operating cost would be reduced by 2% with 25%probability for best case scenario.
Then obtain base-case, best-case, and worst-case NPV andcalculate mean NPV and standard deviation to (roughly)estimate the magnitude of the risk inherent to the project.
Implication Scenario analysis is very useful technique to grasp the worst
case situation of the project (by assuming 1.0 correlation).
Based on: Financial Management, Eugene F. Brigham and Michael C. Ehrhardt, 2008
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Scenario Analysis II
Simplified illustration of scenario analysis process
Standard Deviation
of NPV
Expected NPV(mean value)
Base-, best-, and worst-case scenarios of each cashflow
Slot in all base-, best-,and worst-case scenariosof each cash
Excel
Sheet
NPV ($)$0
50%
40%
30%
Probability (%)
FCF from best-
case scenario
FCF from base-
case scenario
FCF from worst-
case scenario
Mean value
20%
10%
Projected NPVs on the basis of the three scenarios
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Your Projects Scenario Analysis
Considerworst, normal, best scenario foryour project & work out scenario analysis
All items in P&L undergo changes
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Monte Carlo Simulation
Technique for evaluation of
capital investments underconditions of risk
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An Imitation of a real worldsystem, using a mathematical
model that captures thecharacteristic features of thesystem as it encounters random
events in time.
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Monte Carlo Simulation
Simplified illustration of monte-carlo simulation process
Probability distribution of each cashflow and correlations between them
Randomly picking upscenarios
NPV ($)$0
10%
8%
6%
4%
2%
Probability (%)
Simplified illustration of probability distribution of NPVs
NPVs probabilityDistribution
Standard Deviationof NPV
Expected NPV(mean value)
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6 step process
Define the problem
Identify the fixed & variable factors
Identify the alternatives available Construct a mathematical model
Run the model & get results
Decide best of the alternatives
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For Your Project
Assign same probabilities as in the bookwith respect to the three variables Cost ofthe Project, Life of the project and annual
cash flows Your mathematical model could be NPV,
IRR
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example
Annual Cash Flow ################################
################################
####################
Project life
Value Probability 3 0.05
1000 0.02 4 0.10
1500 0.03 5 0.302000 0.15 6 0.25
2500 0.15 7 0.15
3000 0.30 8 0.103500 0.20 9 0.03
4000 0.15 10 0.02
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Initial Decisions
1. You want to set 10 runs of simulations
2. Exogenous variables identified areAnnual cash flows and Life of project
3. You want to use two-digit randomnumbers only
4. Model applied is NPV
( )estmentInitialInv
teRiskfreera
FlowAnnualCashNPV
n
t
+
==1 1
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Steps
1. assign two-digit random numbers rangefrom 0-99
2. Assign probabilities
Set up correspondence between
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Set up correspondence betweenValues of Exogenous variables & 2
digit random numbersAnnual cash flow
alue
Rs.
PROB CUMPROB
2 DIGIT
R N
1000 0.02 0.02 00-01
1500 0.03 0.05 02-04
2000 0.15 0.20 05-19
2500 0.15 0.35 20-34
3000 0.30 0.65 35-64
3500 0.20 0.85 65-84
4000 0.15 1.00 86-99
Project LifeValue Yrs Prob Cum Prob 2 Digi
R N
3 0.05 0.05 00-04
4 0.10 0.15 05-14
5 0.30 0.45 15-44
6 0.25 0.70 45-69
7 0.15 0.85 70-84
8 0.10 0.95 85-94
9 0.03 0.98 95-97
10 0.02 1.00 98-99
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Choosing the Probabilitydistribution for basic variables
Portrait Approach - like police
Building Block approach expert dividethe data according to pattern & arrive at
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Uniform DistTrapezoidal Distribution
Normal
Step Rectangular
Distbn
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What to use when
Uniform Distribution : safe limits
Trapezoidal : data in a small range around itsbest estimate large class of subjective
judgments satisfactorily Step Rectangular : divides data into ranges &assign different probability to each
Normal where no statistical errors or random
disturbances affect the data
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Simulation resultsRun RN Rs CF
1 53 3000
2 66 3500
3 30 2500
4 19 2000
5 31 2500
6 81 3500
7 38 3000
8 48 3000
9 90 4000
10 58 3000
R N Yrs NPV
97 9 4277
99 10 8506
81 7 (829)
09 4 (7660)
67 6 (2112)
70 7 4039
75 7 1605
83 7 1605
33 5 2163
52 6 66
http://random%20numbers.xls/http://random%20numbers.xls/8/9/2019 Risk Analysis in Capital Investment Decisions
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World Bank
Powerful technique
Efficient medium of communication
Not replacing skilled judgment; morejudgment than traditional analysis
Treatment of correlations betweenvariables can be completely misleading ifcorrelations are not handled properly
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Decision Tree Analysis
Decision Tree analysis lets us approximate the NPVdistribution if we can estimate the probability of certainevents within the project
A decision tree is an expanded time line which branches
into alternate paths whenever an event can turn outmore than one way The place at which branches separate is called a node
Any number of branches can emanate from a node but theprobabilities must sum to 1.0 (or 100%)
A path represents following the tree along a branch Evaluating a project involves calculating NPVs along all possible
paths and developing a probability distribution
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Decision tree analysis
Identify the problem
Delineate the decision tree
Specify probability & monetary outcomes Evaluate the decision alternatives
Decision Tree Analysis
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Q: The Wing Foot Shoe Company is considering a three-year projectto market a running shoe based on new technology. Successdepends on how well consumers accept the new idea and demandthe product. Demand can vary from great to terrible, but forplanning purposes management has collapsed that variation into
just two possibilities, good and poor. A market study indicates a60% probability that demand will be good and a 40% chance that itwill be poor.
It will cost Rs5M to bring the new shoe to market. Cash flowestimates indicate inflows of Rs3M per year for three years at full
manufacturing capacity if demand is good, but just Rs1.5M per yearif its poor. Wing Foots cost of capital is 10%. Analyze the projectand develop a rough probability distribution for NPV.
Example
Decision Tree AnalysisExample 1
Decision Tree Analysis
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Decision Tree AnalysisExample
A: First, draw a decision tree diagram for the project. Then calculatethe NPV along each path.
Examp
leRs1.5MRs1.5MRs1.5M
(Rs5M)
Rs3MRs3MRs3M
3210
P = .6
P = .4
NPV
Rs2.461M
Rs-
1.270M
Then calculate the weighted NPV for the tree.
Rs1.077MExpectedNPV =
Rs-.508M40%-1.270MPoor
Rs1.585M60%2.641MGood
ProductProbabilityNPVDemand
The decisiontree explicitly
calls out the fact
that a big loss isquite possible,although the
expected NPVis positive.
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Example 2
The scientists at Spectrum have come upwith an electric moped. The firm is readyfor pilot production and test marketing .
This will cost Rs. 20 million and take 6months. Mgt believes that there is 70%chance that the pilot production and test
marketing will be successful. In the caseof success , they can build the plantcosting Rs 150m.
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- contd
The plant will generate an annual cashinflow of Rs.30m for 20 yrs if the demandis high or an annual cash inflow of Rs.20m
if the demand is low. High demand has aprobability 0.6; low demand 0.4; pl advisethe co using decision tree analysis
E l 3 E t d V l &
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Example 3- Expected Value &Decision Tree
Decision
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Expected Value
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Decision Tree
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