! JWI 531 Financial Management II Week Four | Lecture Two ! ! Please note that this basic version of the lecture is provided as a convenience for the student, and may be missing interactive materials throughout. Students are still responsible for reviewing the missing materials - including audio, video, and interactive widgets - that are found in the full lecture.
 - Page -1 ADDITIONAL VALUATION TECHNIQUES: SENSITIVITY ANALYSIS AND DECISION TREES ! In the digital age, businesses are deluged with data. Sophisticated tools are abundant. Until recently, however, the financial world’s wizardry seemed invincible.   Recent events have significantly changed that perception. But a few complex techniques still remain unblemished. Sensitivity analysis and decision trees, in particular, can help you manage uncertainty about the future. And businesses today have learned to live with a high degree of uncertainty. The assets companies own will eventually reveal their full, productive capacity. The key word is eventually. You won’t know just how valuable an entity or a project is until that time comes. Since you know you’re going to be wrong at some point, what can you do about it? Not much, except to minimize the damage and incorporate uncertainty into your decision-making processes. - Page -2 HOW TO BE GOOD AT BEING WRONG The greatest value of sensitivity analysis is that it quickly shows you just how wrong your valuation estimate can be and still be OK. When you’re investing precious resources into a project or a business, you’ll definitely want to know what will happen should things turn out worse or better than expected. Simply stated, sensitivity analysis studies multiple scenarios. You create a range of excessively negative and positive situations (including the most likely scenario in between) and adjust a limited number of key variables like discount and growth rates. You then compare all these scenarios. The purpose is to reveal how sensitive a model is to fluctuations in one direction or another. Because valuation is an imperfect science, financial decision-makers desperately want to know the margin of error they have if something goes wrong. The most basic approach in the sensitivity-analysis tool kit is simple data entry—substituting different figures into your formulas and models and seeing what you get. When doing your analysis of discounted cash flow, net present value, or internal rate of return, the easiest way to incorporate sensitivity analysis is to make a table with long-term growth figures as column values and various discount rates as row values. (You can select other relevant inputs, - Page -3 but whichever you choose, make sure you’re focusing on those that have the most influence over the outcome.) Changing these variables can show you how a small movement can vastly alter the expected intrinsic value of an investment. L ...

1. !
JWI 531
Financial Management II
Week Four | Lecture Two
!
!
Please note that this basic version of the lecture is provided as a
convenience for the student, and may be
missing interactive materials throughout. Students are still
responsible for reviewing the missing
materials - including audio, video, and interactive widgets - that
are found in the full lecture.
- Page
-1
ADDITIONAL VALUATION
TECHNIQUES: SENSITIVITY ANALYSIS
AND DECISION TREES
!
In the digital age, businesses are deluged with data.
Sophisticated
tools are abundant. Until recently, however, the financial
world’s

2. wizardry seemed invincible. Recent events have significantly
changed that perception.
But a few complex techniques still remain unblemished.
Sensitivity
analysis and decision trees, in particular, can help you manage
uncertainty about the future. And businesses today have learned
to
live with a high degree of uncertainty.
The assets companies own will eventually reveal their full,
productive capacity. The key word is eventually. You won’t
know just
how valuable an entity or a project is until that time comes.
Since you know you’re going to be wrong at some point, what
can
you do about it? Not much, except to minimize the damage and
incorporate uncertainty into your decision-making processes.
- Page
-2
HOW TO BE GOOD AT BEING WRONG
The greatest value of sensitivity analysis is that it quickly
shows you

3. just how wrong your valuation estimate can be and still be OK.
When you’re investing precious resources into a project or a
business, you’ll definitely want to know what will happen
should
things turn out worse or better than expected.
Simply stated, sensitivity analysis studies multiple scenarios.
You
create a range of excessively negative and positive situations
(including the most likely scenario in between) and adjust a
limited
number of key variables like discount and growth rates. You
then
compare all these scenarios. The purpose is to reveal
how sensitive a
model is to fluctuations in one direction or another. Because
valuation is an imperfect science, financial decision-makers
desperately want to know the margin of error they have if
something goes wrong.
The most basic approach in the sensitivity-analysis tool kit is
simple
data entry—substituting different figures into your formulas and

4. models and seeing what you get. When doing your analysis of
discounted cash flow, net present value, or internal rate of
return,
the easiest way to incorporate sensitivity analysis is to make a
table
with long-term growth figures as column values and various
discount rates as row values. (You can select other relevant
inputs,
- Page
-3
but whichever you choose, make sure you’re focusing on those
that
have the most influence over the outcome.) Changing these
variables can show you how a small movement can vastly alter
the
expected intrinsic value of an investment.
Let’s take a look at a real scenario, using the stock of
consumer-
goods giant Procter & Gamble.
Pretend that you’ve just completed a discounted cash flow
(DCF)

5. analysis. You are inclined to believe that the company will grow
its
cash flows by 2% per year and that the most appropriate
discount
rate to apply is 10%.
Without sensitivity testing, this is what you would see
(Adapting the
formula for the present value of a growing dividend and using
2008
data):
• Share valuation = (Operating Cash Flows per Share) /
(Discount Rate – Growth Rate)
• Share valuation = ($5.276) / (0.10 – 0.02)
• Share valuation = $65.95
Simple enough. You’ve done your homework and you’re
confident
that a share today is worth $65.95. But what if you’ve erred on
one
of these inputs in either direction?
!
- Page
-4

6. Here’s what we can quickly see with sensitivity testing:
The sensitivity table shows, for example, that choosing between
a
1% growth rate and a 3% growth rate, when discounted at 10%,
can change your intrinsic value estimate for P&G from $61.82
to
$71.26-or a whopping 15% difference in the company’s value.
In
our example, that’s a difference of about $25 billion. The
lesson
here is that when you’re examining a sensitivity table for an
investment or for a project, you’re able to visually capture what
being wrong might mean for your business.
Let’s say this isn’t P&G’s stock. Instead, the numbers might
describe
a company’s investment in a new product website, with both
positive and negative values. If you hit certain sections of the
chart,
your company will be fine. But if your growth estimates are off
by

7. just a percentage point or two, you’ll be bleeding money.
Knowing
this, you might decide that your company can’t afford the risk.
- Page
-5
This exercise shows the imprecision of an individual valuation
analysis. That’s why you should steer clear of trying to hit a
single,
precise number and think instead in terms of ranges of
acceptable
values. Mistakes will be made. The question is, how will you
fare
when those modeling errors happen?
While you might not be able to determine the to-the-penny price
of
a stock or project, realistic scenarios can give you confidence
that
you’ve got a good chance of landing somewhere in a given
range of
values. The trick is to establish a wide enough band of possible
scenarios to ensure that 99% of what actually happens falls
within

8. your sensitivity analysis. Chapter 11 of Financial
Management can
help you delve into this subject further.
Reams of calculations are not a replacement for good old-
fashioned
business sense, of course. But with some thoughtfully
considered
estimates in hand, you can make a much more informed
decision.
HOW TO USE PROBABILITY
TO HELP YOU DECIDE
Sensitivity tables are great for when you want to present a wide
array of possible conclusions, each with an equal probability of
coming true. But often you have a strong sense that some
scenarios
are more probable than others. This is where decision trees
come
into play.
- Page
-6
Essentially, a decision tree allows you to visually map the

9. progression of various scenarios for a project or investment.
The
tree starts with an initial decision (either do X or do Y). From
this
base sprout additional decisions. The basis for each additional
scenario is a simple statement: “If we decide to do X, either Y
or Z
will happen.” The tree keeps growing branches until the list of
possible scenarios has been exhausted. Here’s what one might
look
like:
A Sample Decision Tree
!
- Page
-7
You don’t have to add probabilistic expectations to each branch
on
the tree, but it certainly adds value to the exercise. You’re now
incorporating a relative level of confidence that a given
outcome
will happen. As you progress through the twists and turns of a

10. possible situation, it is much easier to see the likelihood that
you’ll
wind up in a certain place.
For a given project or investment, the value of creating such a
chart
is threefold. First, a visual display allows you to quickly and
easily
absorb a wide range of outcomes. Second, decision trees offer a
tremendous amount of flexibility, which comes in handy when
you
face many possible outcomes. Finally, a well-formulated chart
will
help you determine a more accurate intrinsic value of an asset
(as
we’ll explain in the next section).
To explain how to better use decision trees, let’s go back to
Procter
& Gamble. We’ll create two hypothetical scenarios for the
current
price of P&G’s stock to demonstrate how to build the
foundation of
a decision tree. One we’ll call the “reversion to the mean”
scenario,

11. in which P&G’s long-term growth rate resumes its typical 2% to
3%
increase per year. The other we’ll call the “new normal,” a term
we’ve borrowed from legendary bond investor Bill Gross, the
head
of PIMCO. In this scenario, we’ll assume that the economy goes
to
hell and P&G’s long-term growth rate flatlines at 0% per year.
This
is obviously a highly pessimistic scenario.
- Page
-8
So after constructing a DCF model, you plug in these two
growth
rates and find out that the “reversion to the mean” scenario
reveals
a stock price of $90. Meanwhile, the “new normal” spits out a
stock
price of $45. This is all well and good, but now what?
You can use these outcomes to create the first two branches of
your

12. tree. Going forward, you can add an infinite array of additional
scenarios, such as a loss of market share, inflation, changes in
the
costs of capital, unexpected growth opportunities, and so on.
Then
plug in the effects on the stock price. The options are endless,
and
each one has the potential to form the next branch of the tree.
In addition to mapping out individual options, you’re also
attaching
your relative confidence that an event will take place. In the
example above, if you’re 80% confident that the “reversion to
the
mean” scenario is going to happen, that means you have a 20%
confidence level in the other option. As a result, you might
spend a
lot more time evaluating the much more likely scenario and not
as
much on the other (while not ignoring the possibility, of
course).
There’s a lot more to learn about creating useful decision trees.
Chapter 11 of Financial Management explores them in greater

13. detail. For the time being, just know that a carefully constructed
decision tree essentially creates a map of possible events for the
financial decision-maker.
- Page
-9
HOW TO USE THE RESULTS OF A
DECISION TREE
Now that you’ve completed a decision tree, you have two
incredibly
disparate values ($45 and $90) with two unequally probable
outcomes. This is interesting, but what if you’re looking for a
single
actionable take-away? Can you just use the average of the two
numbers above (or the average of all possible outcomes in a
given
scenario) to make a decision? Not quite.
You need an average of some kind, but rather than a simple
average
you should use an expectations-weighted average, or in other
words,
the expected value. You want a number that has been adjusted

14. to
incorporate the relative likelihood that an event will occur.
If you strongly believe that the “reversion to the mean” scenario
is
going to play out (since you think there’s an 80% chance it will
happen), but you also want to incorporate the less rosy 20%
probability of a “new normal,” then your expected value is
going to
be the outcome of the first scenario times the probability you
believe it will occur, plus the outcome of the second scenario
times
the probability you fear it might occur.
!
- Page
-10
That $81 is your expected value once you’ve accounted for the
relative likelihood of the two events occurring. This is an
incredibly
useful number. Once you’ve done a lot of thinking about the

15. possible outcomes your project might face, the resulting
expected
value takes the outcomes of all those scenarios (plus the relative
likelihood that they’ll happen) and offers a single convenient
output. It’s not literally what will happen, but rather represents
the
long-run average outcome to keep in mind when making a
decision.
And when making decisions based on that number, you
generally
want the expected value, as with estimates like net present
value, to
be as high as possible.
Of course, this example only considers two scenarios. The
potential
for decision-tree analysis extends well beyond that. The
technique
allows you to consider many possible futures and how they can
be
reflected in prices today.
- Page
-11

16. LOOKING INTO THE CRYSTAL BALL
As powerful as these techniques are, the most important one is
your
brain. Remember that with valuation, you are predicting the
innately unpredictable. A pinch of humility and a dash of
mental
flexibility allow you to deal with the future in a rational and
realistic
way.
Given that you probably won’t be figuring out how to travel
through
time anytime soon, you won’t ever truly know what the future
holds
until you get there. But techniques like sensitivity analysis and
decision trees can help you make sense of the inherent
uncertainty
that comes with life. They most certainly can help you make
informed decisions about tomorrow, today.
- Page
-12
Assignment 1: What’s It Worth?
Due Week 4, (Weight: 16%)

17. The following are specific course learning outcomes associated
with this assignment:
arch issues
in advanced financial management.
management using proper writing mechanics.
Introduction
offered you an assortment of tools designed to enhance your
ability to value a business. You’ve learned how to assess a
business through the lens of several competitive-advantage
frameworks, you’ve learned numerous ways to quantify the
value of a stock, and you’ve become familiar with the thinking
behind valuing a company’s fixed income. Now, as you might
have suspected, it’s time to implement some of this new-found
knowledge.
your choosing. It should be one you’re familiar with, one that
sells a product that you’ve used or seen, and one you would like
to understand better. Then, we’re going to ask you to evaluate
the company closely. You should go about doing this using any
materials you can get your hands on, including the following:
o Financial Statements
o Investor Presentations
o Industry Reports

18. o Newspaper/Magazine Articles
o Consumer Reviews
o Etc.
standing, and its competitive positioning, we want you to use
the tools we introduced in the first four lectures to evaluate the
company from a variety of different angles. The successful
assignment will include all of the following:
Write a 3-4 page paper in which you do the following:
1. Analyze the company’s competition advantages, including the
Sellers framework.
2. Analyze the company’s stock value. This will include
analysis of a company’s present P/E, PEG, P/B, and P/S
multiples versus competitors in the industry and versus historic
multiples going over the past 1-, 3-, and 5-year periods. You are
expected to offer an opinion as to the current pricing of the
company’s stock. You are also welcome to perform a DCF
analysis utilizing appropriate growth rates and discount rate,
but this is not required.
DQ
What are the major limitations of the two tools described in this
lecture? What other information would you need to know to
make informed financial decisions?