risk and capital budgeting.ppt

8/10/2019 Risk and Capital Budgeting.ppt

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7-1

Capital Budgeting and Risk


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7-2

Risk Adjustment

Techniques Two opportunities to adjust the present

value of cash inflows for risk

The cash inflows can be adjusted

The discount rate can be adjusted


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7-3

Cash inf low adjus tment process

us ing certainty Equ ivalent

Most direct and theoretically preferred

approach

Represent the percent of estimated cashinflow that investor would be satisfied to

receive for certain

certainty equivalent method adjusts theestimated value of the uncertain cash flows.


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7-4

The certainty equivalent method uses the rationale that given a risky

cash flow, the decision maker will evaluate this cash flow according to

an expected utility, the utility estimate being hypothesized to be equal

to utility derived from some certain cash flow amount. The decision

maker performs this process for each cash flow. The valuation model isas follows:

where Ct= certainty equivalent cash flow at period t,

i = riskless interest rate.

1 (1 )

Nt

tt

CV

i

Cash inf low adjustment p rocess us ing

certain ty Equ ivalent


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7-5

Ctcan be expressed as a fraction of the expected value of the cashflow as follows:

where some fractional value.

The valuation formula becomes

The certainty equivalent method (CE) adjusts for risk directly through

the expected value of the cash flow in each period and then discounts

these risk adjusted cash flows by the risk free rate of interest, Rf. The

formula for this method is given as follows:

t t tC X

t

1 (1 )

Nt t

tt

XV

i

01(1 )

Nt t

tt

f

XNPV I

R

Cash in f low adjustment process

us ing certainty Equ ivalent


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7-6

Risk Adjusted Discoun t Rates

More practical approach for risk adjustment (RADRs)

The risk adjusted discount rate method (RADR) is similar to the

NPV. It is defined as the present value of the expected or mean

value of future cash flow distributions discounted at a discountrate, k, which includes a risk premium for the riskiness of the

cashflows from the project. It is defined by the following

equation:

RADR is the rate of return that must be earned on a given

project to compensate the firms owners adequately, thereby

resulting in maintenance or improvement in share price

Logic underlying the use of RADR is closely linked to CAPM

0

1(1 )

Nt

tt

XNPV I

k


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7-7

CE VS. RADR in Practice

CE theoretically preferred approach for risk adjustment.They separately adjust for risk and time; they first eliminaterisk from cash flows and then discount the certain cash

flows as risk free rate The RADR have major theoretical problem; it combine risk

and time adjustment in a single discount rate adjustment.

However due to complexity of developing Ces, RADR aremost often in practice. Two reasons:

Consistent with general disposition of decision makertowards rate of return

Easily estimated and applied


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7-8

Annualized NPV Approach

Useful where the projects have unequal lives andare mutually exclusive projects.

This approach converts the NPV of unequal-livedproejcts into equivalent(in NPV terms) annualamount that can be used to select project.

STEPS

Calculate NPV of each project over its life using Cost of Capital Divide the NPV of each project having a positive NPV by the

present value interest factor for an annuity at the given cost of

capital and the projectslife to get annualized NPV of each project

Rank order and select the best project. The project having highest

ANPV would be the best


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7-9

Annualized NPV Approach

Example

Step-I

NPV of project X with 3 years life and 10% discount rateis Rs. 11,248

NPV of project Y with 6 years life and 10% discount rateis Rs. 18,985

Step-II

By dividing NPV of each project by present valu interestfactor annuity at K and project life

ANPVx= 11248/PVIFA10%, 3Y = 4523

ANPVy= 18985/PVIFA10%, 6Y = 4359


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7-10

What is Mean by Risk iness of

ProjectRiskiness of an investment project

means the variability of its cash

flows from those that are expected.

Greater the variability, The riskier theproject said to be


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7-11

Prob lem o f Project Risk

Assumption of single requiredrate of return for selection ofproject

Different Projects have different

RiskRisk Return and Firm Value


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7-12

Mean & Standard Dev iat ion

Mean Value

For Frequency dataWeighted mean

For Probability DistributionStandard Deviation


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7-13

An Il lus trat ion o f To tal

Risk (Disc rete Dis tr ibu t ion )

ANNUAL CASH FLOWS: YEAR 1PROPOSAL 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


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7-14

Probab i li ty Distr ibu t ion

o f Year 1 Cash Flows

.40

.05

.25

P

robability

-3,000 1,000 5,000 9,000 13,000

Cash Flow ($)

Proposal A


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7-15



ANNUAL CASH FLOWS: YEAR 1PROPOSAL B




Normal .40 5,000




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7-16



.40

.05

.25

P

robabili

ty

-3,000 1,000 5,000 9,000 13,000

Cash Flow ($)

Proposal B


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7-17

Expectation and Measurement of

Dispersion - A Cash Flow ExampleExpected Value: The weighted average of

possible outcomes, with the weights being theprobabilities of occurrence

Standard Deviation: A statistical Measureof the variability of a distribution around its mean.It is the square root of the Variance

Coefficient of Variation: The ratio of thestandard deviation of a distribution to the meanof that distribution. It is a measure of relative risk


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7-18

CF1 P1 (CF1)(P1)

$ -3,000 .05 $ -1501,000 .25 250

5,000 .40 2,000

9,000 .25 2,25013,000 .05 650

S=1.00 CF1=$5,000

Expec ted Value of Year 1

Cash Flows (Proposal A)


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7-19

(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



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7-20

Variance of Year 1


(CF1)(P1) (CF1- CF1)2*(P1)

$ -150 3,200,000250 4,000,000

2,000 0

2,250 4,000,000650 3,200,000

$5,000 14,400,000


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7-21

Summary of Proposal A

The standard deviation = SQRT (14,400,000)= $3,795

The expected cash flow= $5,000

Coefficient of Variation (CV)= $3,795 / $5,000

= 0.759

CV is a measure of relativerisk and is the ratio ofstandard deviation to the mean of the distribution.


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7-22



ANNUAL CASH FLOWS: YEAR 1PROPOSAL B




Normal .40 5,000




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7-23



.40

.05

.25

P

robabili

ty

-3,000 1,000 5,000 9,000 13,000

Cash Flow ($)

Proposal B


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7-24

Expec ted Value of Year 1

Cash Flows (Proposal B)

CF1 P1 (CF1)(P1)

$ -1,000 .05 $ -502,000 .25 500

5,000 .40 2,000

8,000 .25 2,00011,000 .05 550

S=1.00 CF1=$5,000


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7-25

(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



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7-26

Variance of Year 1


(CF1)(P1) (CF1- CF1)2(P1)

$ -50 1,800,000500 2,250,000

2,000 0

2,000 2,250,000550 1,800,000

$5,000 8,100,000


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7-27

Summary of Proposal B

The standard deviation of B < A($2,846< $3,795), so Bis less risky than A.

The coefficient of variation of B < A (0.569


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7-28

Total Pro jec t Risk

Projects have riskthat may change

from period toperiod.

Projects are morelikely to have

cont inuous, ratherthan discretedistributions.

CashFlow(

$)

1 2 3

Year


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7-29

Assumption of Independence

Cash Flow in Period t does notdepend on what happened in period

t-1

There is no causative relationshipbetween cash flows from period to

period.

Risk Free rate for Discounting


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7-30

Steps to Follow When Cash

Flows are IndependentMean Expected Value of Cash Flows

for period t

Standard Deviation of Possible cashFlows for Period t

Calculate NPV for Proposal

Calculate Standard Deviation forProposal

Standardizing the Dispersion


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7-31

An Example

EXPECTED CASH FLOWS: YEAR 1

Prob Cash Flow

.10 $ 3,000

.25 4,000

.30 5,000

.25 6,000

.10 7,000


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7-32

An Example


Prob Cash Flow

.10 $ 2,000

.25 3,000

.30 4,000

.25 5,000

.10 6,000


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7-33

An Example


Prob Cash Flow

.10 $ 2,000

.25 3,000

.30 4,000.25 5,000

.10 6,000


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7-34

Standardizing the Dispersion

The above information help us to evaluatethe risk of investment

If Prob. Distribution is approx. normal(bellshaped), we are able to calculate the prob.Of proposal providing a NPV of less thanor more than an amount.

For example we want to determine theprob. That NPV will be zero or less thanzero.


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7-35

Assumption of dependence

Cash Flow in Period t depend onwhat happened in period t-1

There is causative relationshipbetween cash flows from period toperiod.

Risk Free rate for Discounting


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7-36

Steps to Follow When Cash

Flows are dependentAll steps are same as they were

for the independent projects

except the step 4 whichestimates the standard deviationfor the whole proposal. Different

formula is used for this purpose


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7-37

Moderate Correlat ion

Where the cash flows of the firm are neitherapproximately independent nor perfectly correlated

over time, the classification of the cash flow streamas one or the other is not appropriate

One method for dealing with the moderate correlationis with a series of conditional probability

distributions.


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7-38

Probab i li ty Tree Approach

A graphic or tabular approach fororganizing the possible cash-flow

streams generated by aninvestment. The presentation

resembles the branches of a tree.

Each complete branch representsone possible cash-flow sequence.


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7-39


Basket Wonders isexamining a project that will

have an initial cost today of$900. Uncertainty

surrounding the first year

cash flows creates threepossible cash-flowscenarios inYear 1.

-$900


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7-40


Node 1: 20% chance of a$1,200cash-flow.

Node 2: 60% chance of a$450cash-flow.

Node 3: 20% chance of a-$600cash-flow.

-$900

(.20) $1,200

(.20) -$600

(.60) $450

Year 1

1

2

3


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7-41


Each node inYear 2

represents a

branchof ourprobability

tree.

Theprobabilitiesare said to beconditional

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


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7-42

Jo in t Probabil i t ies [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


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7-43

Project NPV Based on

Probab i l i ty Tree Usage

The probabilitytree accounts for

the distributionof cash flows.

Therefore,discount all cashflows at onlytherisk-freerate of

return.

The NPV for branch i ofthe probability tree for two

years of cash flows is

NPV =S

(NPVi)(Pi)

NPVi=CF1

(1+ Rf)1 (1 + Rf)

2

CF2

- ICO

+

i = 1

z


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7-44

NPV fo r 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


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7-45

Calcu lat ing the Expec ted

Net Presen t Value (NPV)

Branch NPVi

Branch 1 $ 2,238.32Branch 2 $ 1,331.29

Branch 3 $ 1,059.18Branch 4 $ 344.90Branch 5 $ 72.79Branch 6 -$ 199.32

Branch 7 -$ 1,017.91Branch 8 -$ 1,562.13Branch 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


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7-46

Calcu lat ing the Variance

o f the Net Presen t 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


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7-47

Summary of the

Decis ion Tree Analys is

The standard deviation =SQRT ($1,031,800) = $1,015.78

The expected NPV = -$ 17.01


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7-48

NPVP= S( NPVj)

NPVPis the expected portfolio NPV,

NPVjis the expected NPV of the jthNPV that the firm undertakes,

mis the total number of projects inthe firm portfolio.

Determ ining the Expected

NPV for a Por t fo l io o f Projects

m

j=1

D t i i P t f l i


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7-49

sP= S S sjk

s

jkis the covariance between possibleNPVs for projectsjand k

s

jk= sj sk rjk.

sj is the standard deviation of projectj,

skis the standard deviation of project k,

rjkis the correlation coefficient between

projectsjand k.

Determ ining Port fo l io

Standard Dev iat ion

m

j=1

m

k=1


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7-50

Managerial (Real) Options

Management flexibility to makefuture decisions that affect a

projects expected cash flows, life,or future acceptance.

Project Worth = NPV +Option(s) Value


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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).

risk and capital budgeting.ppt

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