Risk Analysis in Capital Investment Decisions

8/9/2019 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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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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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



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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.



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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).



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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/


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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



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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



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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

Risk Analysis in Capital Investment Decisions

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