14b.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson...

14b.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson Education Limited 2009. Created by Gregory Kuhlemeyer.

Chapter 14 – Chapter 14 – SupportSupport

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


Remember?Remember? An Illustration of An Illustration of Total Risk (Discrete Distribution)Total Risk (Discrete Distribution)Remember?Remember? An Illustration of An Illustration of Total Risk (Discrete Distribution)Total Risk (Discrete Distribution)

ANNUAL CASH FLOWS: YEAR 1PROPOSAL APROPOSAL A

State ProbabilityProbability Cash FlowCash Flow

Deep Recession 0.05 $ –3,000

Mild Recession 0.25 1,000

Normal 0.40 5,000

Minor Boom 0.25 9,000

Major Boom 0.05 13,000

ANNUAL CASH FLOWS: YEAR 1PROPOSAL APROPOSAL A




Normal 0.40 5,000




Summary of Summary of 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.


What if we used Excel?What if we used Excel?Summary of Summary of Proposal AProposal A

State Probability (P) Cash Flow (CF) P x CF P x (CF - CF-bar)Deep Recession 0.05 ($3,000) ($150) $3,200,000Mild Recession 0.25 1,000 $250 $4,000,000

Normal 0.4 5,000 $2,000 $0Minor Boom 0.25 9,000 $2,250 $4,000,000Major Boom 0.05 13,000 $650 $3,200,000

$5,000 $14,400,000 $3,794.73 0.7589CF-bar (wtd avg) Variance Standard Dev Coef of Variation

We end up with the exact same answers, except it allows us to do some other types of scenario analysis.

• What if the probabilities are different?

• What if the cash flows are different?

Refer to VW13E-14b.xlsx on tab ‘Probability Dist’


Remember? Remember? An Illustration of An Illustration of Total Risk (Discrete Distribution)Total Risk (Discrete Distribution)Remember? Remember? An Illustration of An Illustration of Total Risk (Discrete Distribution)Total Risk (Discrete Distribution)

ANNUAL CASH FLOWS: YEAR 1PROPOSAL BPROPOSAL B




Normal 0.40 5,000



ANNUAL CASH FLOWS: YEAR 1PROPOSAL BPROPOSAL B




Normal 0.40 5,000




What if we used Excel?What if we used Excel?Summary of Summary of Proposal BProposal B

We end up with the exact same answers, except it allows us to do some other types of scenario analysis.

• What if the probabilities are different?

• What if the cash flows are different? State Probability (P) Cash Flow (CF) P x CF P x (CF - CF-bar)

Deep Recession 0.05 ($1,000) ($50) $1,800,000Mild Recession 0.25 2,000 $500 $2,250,000

Normal 0.40 5,000 $2,000 $0Minor Boom 0.25 8,000 $2,000 $2,250,000Major Boom 0.05 11,000 $550 $1,800,000

$5,000 $8,100,000 $2,846.05 0.5692CF-bar (wtd avg) Variance Standard Dev Coef of Variation

Refer to VW13E-14b.xlsx on tab ‘Probability Dist’


Remember?Remember? Probability Probability Tree ApproachTree Approach

It is a graphic or tabular approach for organizing the possible cash-

flow streams ...

Let us replicate the work in Excel! It can be faster and afford us the opportunity to run many different

analyses quickly.


Summary of the Decision Summary of the Decision Tree AnalysisTree Analysis

(P) (NPV)Joint Probability Formula Branch NPV of each branch (P) x (NPV)

Risk-free 22005.00% 0.10 0.02 =$D$11*G9 1 $2,238.32 $44.77

1200 12000.20 0.60 0.12 =$D$11*G11 2 $1,331.29 $159.76

9000.30 0.06 =$D$11*G13 3 $1,059.18 $63.55

9000.35 0.21 =$D$18*G16 4 $344.90 $72.43

-900 450 6000.60 0.40 0.24 =$D$18*G18 5 $72.79 $17.47

3000.25 0.15 =$D$18*G20 6 ($199.32) ($29.90)

5000.10 0.02 =$D$25*G23 7 ($1,017.91) ($20.36)

-600 -1000.20 0.50 0.1 =$D$25*G25 8 ($1,562.13) ($156.21)

-7000.40 0.08 =$D$25*G27 9 ($2,106.35) ($168.51)

1.00 =SUM(I9:I27) -17.01Expected NPV

'NPV-bar'

Decision Tree Analysis(P) x [(NPV - NPV-bar)^2]

$101,730.16

$218,149.33

$69,491.16

$27,504.76

$1,935.19

$4,985.70

$20,036.30

$238,741.04

$349,228.13

1015.78Standard Deviation

Refer to “VW13E-13b.xlsx” on tab ‘Decision Tree’


Remember? Remember? Simulation ApproachSimulation Approach

An approach that allows us to test the possible results of an investment

proposal before it is accepted. Testing is based on a model coupled with

probabilistic information.

Let us look at an example related to prices similar to the example in the ppts.


Simulation Exercise!Simulation Exercise!

Here we have assumed a mean price of $35 per unit and a standard deviation of $5. In step 2 we have pulled a price of $37.14 from the distribution which is 0.43 standard

deviations to the right of the mean.

Let us create a simple simulation exercise using price:

Step 1: Describe the distribution. We will assume a standard normal for pricesExpected Price 35.00$ Variation (stand dev) 5.00$

Step 2: We will now grab a price for our product from a continuous distribution that has a mean value of $35 and a standard deviation of $5.

Value: 37.14$ Note how far away this value is from 500.

Step 3: We can calculate a z-score and determine the probability under the curvez-score 0.43 <--- (C11-C4)/C5


Simulation Exercise!Simulation Exercise!Now let us use more than one observation and ‘simulate’ the distribution. Let us use 500

data observation points and look at the frequency distribution.

Step 4: What if we wanted to expand this to a LARGER sample size to generatea better distribution than a sample size of 1? Why don't we createlots of observations for our data - say 500 points.[ See cells F2:O51 ]

Step 5: Use FREQUENCY to create a frequency distribution for our 500 data pts.Bin Frequency15 0 =FREQUENCY(F2:O51,B22:B30)20 025 1130 7535 15740 18145 6650 955 1

>55 0Observations: 500

Mean: 34.95Standard Dev: 5.02

Create the beginning of the table that is yellow. In the cell that is purple enter the formula. The portion that is F2:O51

is the 500 randomly generated data points to the right. Theportion of the formula that is B22:B30 represents the

"bins" that we want to use to determine our distribution. After entering the formula, press the 'F2' button and then press "CNTRL-SHIFT-ENTER" all at the same time. This will

automatically fill your bins!


Simulation Exercise!Simulation Exercise!We can graph the distribution and we notice how the graph is beginning to look like a standard normal continuous graph. If we were to add more bins and additional data

observations are graph would approximate the standard normal distribution.


Remember?Remember?Managerial (Real) OptionsManagerial (Real) Options

Management flexibility to make future decisions that affect a project’s expected cash flows, life,

or future acceptance.

Project Worth = NPV + Option(s) Value

What if we could abandon a project for $200 at the end of the first period (year)?


Summary of the Decision Summary of the Decision Tree AnalysisTree Analysis

Refer to “VW13E-13b.xlsx” on tab ‘Decision Tree 2’

(P) (NPV)Joint Probability Formula Branch NPV of each branch (P) x (NPV)

Risk-free 22005.00% 0.10 0.02 =$D$11*G9 1 $2,238.32 $44.77

1200 12000.20 0.60 0.12 =$D$11*G11 2 $1,331.29 $159.76

9000.30 0.06 =$D$11*G13 3 $1,059.18 $63.55

9000.35 0.21 =$D$18*G16 4 $344.90 $72.43

-900 450 6000.60 0.40 0.24 =$D$18*G18 5 $72.79 $17.47

3000.25 0.15 =$D$18*G20 6 ($199.32) ($29.90)

5000.10

-600 -1000.20 0.50 0.20 =D25 7 ($1,280.95) ($256.19)

-700Sell for $200 as 200.00$ 0.40Worth more than -> ($266.67)

Value at the "yellow" node if 1.00 =SUM(I9:I27) 71.88we were to "abandon" the project Expected NPV

'NPV-bar' Option Value is then $71.88 - (-$17.01) = $88.89

Decision Tree Analysis

14b.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson...

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Transcript of 14b.1 Van Horne and Wachowicz, Fundamentals of Financial Management, 13th edition. © Pearson...