Practical financial management lasher 7th ed chapter 012

Chapter 12 Risk Topics and Real Options in
Capital Budgeting and Cash Flow Estimation


Cash Flows as Random Variables
“Risk” in every day usage: the probability
that something bad will happen
“Risk” in financial theory: Associated
with random variables and their
probability distributions


Cash Flows as Random Variables
Risk – the chance that a random variable
will take on a value significantly different
from the expected value
– In capital budgeting the future period's cash
flow estimate is a random variable

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Figure 12-1 The Probability Distribution of a Future Cash
Flow as a Random Variable

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Cash Flows as Random Variables
The NPV and IRR are random variables
with their own probability distributions

– Actual value may be different than the mean
– The amount the actual value is different
from expected is related to the variance or
standard deviation

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Figure 12-2 Risk in Estimated
Cash Flows


The Importance of Risk in
Capital Budgeting
Until now we have viewed cash flows as point
estimates – a single number rather than a range of
possibilities
Actual cash flows are estimates, a wrong decision
could be made using point estimates for NPV and
IRR
The riskiness of a project's cash flows must be
considered
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Figure 12-3 Project NPVs Reflecting
Risky Cash Flows

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The Importance of Risk in Capital
Budgeting
Risk Aversion
Changing the Nature of a Company
– A company is a portfolio of projects
– Ignoring risk when undertaking new projects
can change the firm’s overall risk
characteristics

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Scenario/Sensitivity Analysis
Select a worst, most likely, and best case for each cash
flow

Recalculate the project's NPV (or IRR) under several scenarios
– Gives an intuitive sense of the variability of NPV
– Also called sensitivity analysis

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Concept Connection Example 12-1
Scenario Analysis

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Concept Connection Example 12-1
Scenario Analysis

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Decision Tree Analysis

Decision Tree: A graphic representation of a
project in which certain events have multiple
outcomes
Decision Tree Analysis – Develops a
probability distribution of NPV given the
probabilities of certain events within the project

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Computer (Monte Carlo) Simulation
Assume separate probability distribution for each cash flow
Computer draws observation from each and calculates NPV
Sort outcomes into histogram of probability distribution of
NPV (next slide)
Drawbacks
– Probability distributions are difficult to estimate
– Cash flows tend to be correlated
– Interpretation of results is subjective

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Figure 12-4 Results of Monte Carlo
Simulation for NPV

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Figure 12-5 A Simple Decision Tree

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Concept Connection Example 12-2
Decision Tree Analysis
The Wing Foot Shoe Company is considering a
new running shoe. A market study indicates a 60%
probability that demand will be good and a 40%
chance that it will be poor.
C0 is $5M. Cash inflows are estimated at $3M
per year for three years at full manufacturing capacity
if demand is good, but just $1.5M per year if it’s poor.
Wing Foot’s cost of capital is 10%.
Develop a rough probability distribution for NPV.

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Concept Connection Example 12-2
Decision Tree Analysis
A decision tree diagram and NPVs along each path are:

0

1

2

NPV

3

P = .6

$3M

$3M

$3M

P = .4

$1.5M

$1.5M

$1.5M

$2.461M

($5M)

$-1.270M

The expected NPV is:
The decision tree
explicitly calls
out the fact that
a big loss is quite
possible,
although the
expected NPV is
positive.

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Figure 12-6 A More Complex
Decision Tree

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Concept Connection Example 12-3 More
Complex Decision Trees
Wing Foot now feels there are two possibilities along the
upper branch.
If first year demand is good, there’s a 30% chance it will
be excellent in the second and third years, and a $1 million
factory expansion will generate cash inflows of $5 million in
years 2 and 3.
That means net cash inflows will be $4 million in year 2

and $5 million in year 3.
A decision tree for the project with this additional
possibility is on the next slide
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Concept Connection Example 12-3 More
Complex Decision Trees
The NPV for the new upper path is

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Concept Connection Example 12-3 More
Complex Decision Trees

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Concept Connection Example 12-3 More
Complex Decision Trees

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Concept Connection Example 12-3 More
Complex Decision Trees
The project’s probability distribution expected return are
as follows.

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Real Options
An option is the right or ability to
take a certain course of action
A real option is a course of action that usually
– Improves financial results under certain
conditions
– Exists in a real, physical business sense
– Frequently occurs in capital budgeting
– Generally increases a project's expected NPV
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