Practical financial managment 7e LASHER chapter 12

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

3


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

4


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

5


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

7


Figure 12-3 Project NPVs Reflecting Risky Cash Flows

8

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

9


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

10


Concept Connection Example 12-1 Scenario Analysis

11

Concept Connection Example 12-1 Scenario Analysis

12


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

13


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

14

Figure 12-4 Results of Monte Carlo Simulation for NPV

15


Figure 12-5 A Simple Decision Tree

16


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.

17


Concept Connection Example 12-2 Decision Tree Analysis

A decision tree diagram and NPVs along each path are:

NPV

0

1
P = .6

2

3

$2.461M

$3M

$3M

$3M

$1.5M

$1.5M

$1.5M

($5M)
P = .4

$-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.

18


Figure 12-6 A More Complex
Decision Tree

19


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

20


Concept Connection Example 12-3 More Complex Decision Trees

The NPV for the new upper path is

21


Concept Connection Example 12-3 More Complex Decision Trees

22


Concept Connection Example 12-3 More Complex Decision Trees

23


Concept Connection Example 12-3 More Complex Decision Trees

The project’s probability distribution expected return are as follows.

24


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

25