DQ/Assignment

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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.


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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.

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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,

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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)

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?

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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

just a percentage point or two, you’ll be bleeding money. Knowing

this, you might decide that your company can’t afford the risk.

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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

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.

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Essentially, a decision tree allows you to visually map the

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

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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

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,

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.

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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

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

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.  

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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 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.

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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

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.

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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.

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