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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    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

    An Il lus trat ion o f To tal

    Risk (Disc rete Dis tr ibu t ion )

    ANNUAL CASH FLOWS: YEAR 1PROPOSAL B

    State Probability Cash 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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    7-16

    Probab i li ty Distr ibu t ion

    o f Year 1 Cash Flows

    .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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    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

    Cash Flows (Proposal A)

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    7-20

    Variance of Year 1

    Cash Flows (Proposal A)

    (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

    An Il lus trat ion o f To tal

    Risk (Disc rete Dis tr ibu t ion )

    ANNUAL CASH FLOWS: YEAR 1PROPOSAL B

    State Probability Cash 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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    7-23

    Probab i li ty Distr ibu t ion

    o f Year 1 Cash Flows

    .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

    Cash Flows (Proposal B)

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    7-26

    Variance of Year 1

    Cash Flows (Proposal B)

    (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

    EXPECTED CASH FLOWS: YEAR 2

    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

    EXPECTED CASH FLOWS: YEAR 3

    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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    Probab i li ty Tree Approach

    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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    Probab i li ty Tree Approach

    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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    Probab i li ty Tree Approach

    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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    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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    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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    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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    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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    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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    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).