C o l o r a d o S t a t e U n i v e r s i t y - P u e b l o .docx

C o l o r a d o S t a t e U n i v e r s i t y - P u e b l o
Division of Continuing Education Page 12
Independent Study and External Degree Completion Program
Lesson 3
Section 3: Once again there are questions listed for each of the
chapters in this section.
Respond to them fully after stating the questions.
Section 3: Chapter 7: Question 1
The five steps for classical decision making are found on
page 169, and the definition is on
page 171. In a risk environment or an uncertain environment, it
may be very difficult to follow
these steps. How can a risk environment or an uncertain
environment affect this process?
What is the difference between a risk environment and an
uncertain environment?
In the text, there is a discussion of framing errors,
confirmation errors, escalating
commitment, availability bias, representativeness bias,
anchoring bias, and adjustment bias.
Briefly define each of these errors and biases and provide an
example of each one (not the one

in the text). These are particularly important since they are
found in all levels of an
organization.
Managers are often confronted with structured problems
which require programmed
decisions, and unstructured problems which require non-
programmed decisions. Serious
problems may require a crisis decision which is the most serious
type of non-programmed
decision.
Provide an example of a programmed and non-programmed
decision which you have
encountered in your own experience. How do you determine
whether a decision is really a
programmed decision, or whether it actually requires a unique
solution? When should senior
management become involved?
(Many programmed decisions are just that today. In retail they
may be built into the computer
system, and made at the cash register – such as returns, returns
with or without receipts, or
information available regarding a customer’s past transactions!)
Organizations should have a mission statement, a strategic
plan, organizational plans,
tactical plans, goals and objectives. Which of these should
primarily be developed by directors
and senior management, middle management, and supervisors
and other first level
management personnel? How can these plans be best aligned in

order to clearly involve all
levels of management in these goals?
C o l o r a d o S t a t e U n i v e r s i t y - P u e b l o
Division of Continuing Education Page 13
Independent Study and External Degree Completion Program
Benchmarking is often used as a way to improve an
organization. What is organizational
benchmarking and how is it developed?
Planners often use forecasting, contingency planning, and
scenario planning. Define and
provide an example of each. The example should differ from
the one found in the text. It may
be either from additional reading or the student’s own
experience.
See if you can solve Puzzle Number One and Puzzle Number
2 on page 207. How did you do
it? Did you use math, special reasoning – or ask a friend?
(Five extra credit points)
Actual Question – Different companies have different basic
strategies. Michael Porter’s
model includes competitive, differentiation, cost leadership and
focus differentiation

strategies. Briefly define each one and provide an example
which is not found in the text.
Why did you choose this example?
Almost every class in management uses a SWOT analysis to
identify analyze organizational
strengths and weaknesses. Choose an organization and develop
a brief SWOT analysis for that
organization. It can be an organization that you work with
either for pay or on a volunteer
basis or a company in which you are interested.
Marketers often refer to products based on their position and
potential. They call these
products Stars, Question Marks, Cash Cows and Dogs. Define
each and identify a product
which meets the description in the text. Why did you choose
this product?
Once again select one of these questions and develop it into a
two to three page single
spaced essay.

The Validity of Company Valuation
Using Discounted Cash Flow Methods
Florian Steiger
1
Seminar Paper
Fall 2008
Abstract
This paper closely examines theoretical and practical aspects of
the widely used discounted
cash flows (DCF) valuation method. It assesses its potentials as
well as several weaknesses. A
special emphasize is being put on the valuation of companies
using the DCF method. The
paper finds that the discounted cash flow method is a powerful
tool to analyze even complex
situations. However, the DCF method is subject to massive
assumption bias and even slight
changes in the underlying assumptions of an analysis can
drastically alter the valuation

results. A practical example of these implications is given using
a scenario analysis.
____________
1
Author: Florian Steiger, European Business School, e-mail:
[email protected]
Table of Contents
List of abbreviations
...............................................................................................
............ i
List of figures and tables
...............................................................................................
.... ii
1 Introduction
...............................................................................................
................... 1
1.1 Problem Definition and Objective
...................................................................... 1
1.2 Course of the Investigation
................................................................................. 2
2 Company valuation
................................................................................ ...............
........ 2

2.1 General Goal and Use of Company Valuation
................................................... 2
2.2 Other Valuation Methods
................................................................................... 3
3 The Discounted Cash Flow Valuation Method
............................................................ 4
3.1 Approach of the Discounted Cash Flow Valuation
............................................ 4
3.2 Calculation of the Free Cash Flow
..................................................................... 5
3.2.1 Cash Flow to Firm and Cash Flow to
Equity.................................................. 5
3.2.2 Building Future Scenarios
.............................................................................. 6
3.3 The Weighted Average Cost of Capital
............................................................. 6
3.3.1 Cost of Equity
...............................................................................................
.. 7
3.3.2 Cost of Debt
...............................................................................................
..... 8
3.3.3 Summary
...............................................................................................
.......... 9

3.4 Calculation of the Terminal Value
................................................................... 10
3.5 Determination of Company Value
................................................................... 11
4 Validity of the Discounted Cash Flow Valuation Approach
...................................... 11
4.1 Case Study: BASF
............................................................................................
11
4.2 Sensitivity Analysis
.......................................................................................... 12
5 Conclusion
...............................................................................................
................... 14
Reference List
...............................................................................................
.................. 16
Appendix
...............................................................................................
.......................... 18
Discounted Cash Flow Valuation i

List of abbreviations
APV Adjusted Present Value
bp Base Point (equal to 0.01%)
Capex Capital Expenditure
CAGR Compounded Annual Growth Rate
CAPM Capital Asset Pricing Model
COD Cost of Debt
COE Cost of Equity
D&A Depreciation and Amortization
DCF Discounted Cash Flow
EBIT Earnings Before Interests and Taxes
EBITDA Earnings Before Interests, Taxes, Depreciation and
Amortization
EURm Millions of Euro
EV Enterprise Value
Eq. V. Equity Value
FCF Free Cash Flow
FCFE Free Cash Flow to Equity

FCFF Free Cash Flow to Firm
IPO Initial Public Offering
LBO Leveraged Buyout
LIBOR London Interbank Offer Rate
M&A Mergers and Acquisitions
NI Net Income
NOPAT Net Operating Profit After Taxes
NPV Net Present Value
P / E Price Earnings Ratio
r Discount Rate
ROA Return on Assets
ROE Return on Equity
SIC Standard Industry Classification
t or T Tax Rate
T-Bill US Treasury Bill
T-Bond US Treasury Bond
TV Terminal Value

Discounted Cash Flow Valuation ii
List of figures and tables
Table 1. Long term credit rating scales: Source: adapted from
HSBC handbook, 2008
Table 2. Trading comparables analysis
Table 3. Transaction multiple analysis
Table 4. Case Study: Calculation of the enterprise value
Table 5. Case Study: Sensitivity Analysis WACC, perpetual
growth rate
Table 6. Case Study: Sensitivity analysis perpetual growth rate,
sales CAGR
Table 7. Case Study: Income statement estimates
Table 8. Case Study: Liabilities structure
Table 9. Case Study: WACC calculation
Table 10. Case Study: Terminal Value calculation
Table 11. Case Study: DCF valuation
Figure 1. LIBOR credit spread (in bp): Source: Bloomberg
Professional Database, 2008

Discounted Cash Flow Valuation 1
1 Introduction
The goal of this paper is to introduce the reader to the method
of company valuation
using discounted cash flows, often referred to as “DCF”. The
DCF method is a standard
procedure in modern finance and it is therefore very important
to thoroughly understand
how the method works and what its limitations and their
implications are. Although this
paper is on a basic level, it requires some knowledge of
accounting and corporate
finance, as well as a good understanding of general economic
coherencies, since not
every topic can be explained in detail due to size limitations.
1.1 Problem Definition and Objective
Since the beginning of the year 2008, Goldman Sachs has
advised clients on merger and
acquisition (M&A) deals with aggregated enterprise values (EV)

of more than EURm
475,000 according to recent league tables (Thomson One
Banker, 2008). There are
“probably almost as many motives for M&As as there are bidder
and targets”
(Mukherjee, Kiymaz, & Bake, 2004, p. 8), but the transaction
volumes indicate the
importance that M&A activities have for the worldwide
economy and underline the
necessity for efficient methods to adequately value companies.
The DCF method is based upon forward looking data and
therefore requires a relatively
large amount of predictions for the future business situation of
the company and the
economy in general. Minor changes in the underlying
assumptions will result in large
differences in the company’s value. It is therefore very
important to know which
assumptions are used and how they influence the outcome of the
analysis. For this
reason, this paper will introduce the key input factors that are
needed for the DCF
analysis and examine the consequences that changes in the
assumptions have on the

company value.
The DCF analysis is a very powerful tool that is not only used
to value companies but
also to price initial public offerings (IPOs) and other financial
assets. It is such a
powerful tool in finance, that it is so widely used by
professionals in investment banks,
consultancies and managers around the world for a range of
tasks that it is even referred
to as “the heart of most corporate capital-budgeting systems”
(Luehrman, 1998, p. 51).
1.2 Course of the Investigation
This paper begins with a brief introduction to valuation
techniques in general and shows
how valuation techniques can be used to assess a company’s
value. Afterwards the basic
idea behind the DCF valuation technique will be introduced and
the key input factors

will be explained and discussed, since it is most important to
gain a deep understanding
on how the input is computed to state the company value. In the
next step a sensitivity
analysis will be conducted using BASF as an example to explain
how varying input will
lead to different results. In the end, a conclusion will be drawn
on the benefits and
shortfalls of the DCF valuation technique.
2 Company valuation
2.1 General Goal and Use of Company Valuation
The goal of company valuation is to give owners, potential
buyers and other interested
stakeholders an approximate value of what a company is worth.
There are different
approaches to determine this value but some general guidelines
apply to all of them.
In general there are two kind of possible takeover approaches.
An interested buyer could
either buy the assets of a company, known as asset deal, or the
buyer could take over a
majority of the company’s equity, known as share deal.
2
Since taking over the assets

will not transfer ownership of the legal entity known as “the
company”, share deals are
much more common in large transactions. Due to the financing
of a company by debt
and equity, valuation techniques that focus on share deals either
value the equity,
resulting in the equity value (Eq. V.) or the total liabilities,
stating the enterprise value
(EV) or firm value (FV). It is possible to derive the EV from the
Eq. V. and vice versa
(Bodie, Kane, & Marcus, 2008, pp. 630-631) by using the
following formula:
�� − �� − �� =
��. �.
Net debt and the corporate adjustments are derived with the
following definitions:
�� = �� + ��
�� + ��
+ �� −
��
____________
2
Actually there are more possibilities to gain ownership of a

company, like a debt-to-equity swap,
where debt holders offer the equity holders to swap their debt
into equity of the company and therewith
gain equity ownership. This usually happens with companies
that are in financial distress like insolvency
or bankruptcy.
��
= �� + ��
��
+ �� ±
��
2.2 Other Valuation Methods
There are many other valuation techniques besides the DCF
approach which are
commonly used. In fact, most of the time various techniques are
used and the results are
then compared to each other to increase the confidence that the
result is reasonable.
A widely used method is the so-called trading comparables
analysis. In this method a

peer group of listed companies is built, usually using firms with
similar standard
industry classification (SIC) and other similarities to the target
company like geographic
focus, financing structure, and client segments. If the company
is listed, the equity value
is simply the market capitalization
3
. The EV can be calculated based on this Eq. V. as
described above. Then some multiples are calculated to state
relationship between EV
and Eq. V. to a company’s fundamental data. Usually the
multiples are the following:
��
��
��
��
��
��
��. �.

��
4
The median and arithmetic average of these multiples is then
calculated for the peer
group.
5
These figures are a good approximation for a target’s EV and
Eq. V., but they
tend to be lower than actual transaction values, since trading
comparables do not include
majority premiums that have to be paid when acquiring a
majority stake in a company.
A similar approach to the trading comparables method is the
transaction comparables
valuation approach. It uses the same multiples, but the peer
group consists of previous
transactions and therefore includes all premiums that arise
during transactions. This
method is very reliable but since it is very difficult to find
previous transactions that are
similar, it is difficult to build peer groups that are statistically
significant
6
. These two
methods, in combination with the DCF are the most widely used

in modern finance.
____________
3
�� = �� ∗ ��
��
4
The
�� .�.
��
is the same as the trailing (historical)
�
�
ratio
5
Please see table 2 in the appendix for an exemplary trading
comparables analysis of the European car
rental market
6
Please see table 3 in the appendix for an example

3 The Discounted Cash Flow Valuation Method
3.1 Approach of the Discounted Cash Flow Valuation
The DCF method values the company on basis of the net present
value (NPV) of its
future free cash flows which are discounted by an appropriate
discount rate. The
formula for determining the NPV of numerous future cash flows
is shown below. It can
be found in various sources, e.g. in “Financial Management –
Theory and Practice”
(Brigham & Gapenski, 1997, p. 254).
�� =
��
(1 + �)�
�
�=0
The free cash flow is the amount of “cash not required for
operations or reinvestment”
(Brealey, Myers, & Allen, 2006, p. 998). Another possibility to

analyze a company’s
value using discounted cash flows is the adjusted present value
(APV). The APV is the
net present value of the company’s free cash flows assuming
pure equity financing and
adding the present value of any financing side effect, like tax
shield (Brealey, Myers, &
Allen, 2006, p. 993) In general you can say, that the APV is
based on the “principle of
value additivity” (Luehrmann, 1997, S. 135). However, APV
and NPV lead to the same
result.
Since the DCF method is a valuation technique that is based on
predictions, a scenario
analysis is usually conducted to examine the effects of changes
in the underlying
assumptions. Such a scenario analysis is usually based on three
scenarios, namely the
“base case” or “management scenario” that uses the
management’s estimations for the
relevant metrics, a “bull case” which uses very optimistic
assumptions and a “bear case”
that calculates the company’s value if it performs badly.

The process of valuing a company with the DCF method
contains different stages. In
the first stage scenarios are developed to predict future free
cash flows (FCF) for the
next five to ten years. Afterwards, an appropriate discount rate,
the weighted average
cost of capital (WACC) has to be determined to discount all
future FCFs to calculate
their NPVs. In the next step the terminal value (TV) has to be
identified. The TV is the
net present value of all future cash flows that accrue after the
time period that is covered
by the scenario analysis. In the last step the net present values
of the cash flows are
summed up with the terminal value.
7
�� =
��
(1 + �)�
�

�=0
+ ��
3.2 Calculation of the Free Cash Flow
3.2.1 Cash Flow to Firm and Cash Flow to Equity
There are two ways of using cash flows for the DCF valuation.
You can either use the
free cash flow to the firm (FCFF) which is the cash flow that is
available to debt- and
equity holders, or you can use the free cash flow to equity
(FCFE) which is the cash
flow that is available to the company’s equity holders only.
When using the FCFF, all inputs have to be based on accounting
figures that are
calculated before any interest payments are paid out to the debt
holders. The FCFE in
contrast uses figures from which interest payments have already
been deducted. Using
the FCFF as base for the analysis will result in the enterprise
value of the company,
using the FCFE will give the equity value. Since an acquirer
usually takes over all

liabilities, debt and equity, the FCFF is more relevant than the
equity approach.
The FCFF is calculated by deducting taxes from the company’s
earnings before interest
and taxes (EBIT), resulting in the net operating profit after tax
(NOPAT). All
calculatory costs (e.g. D&A) are then added back, since they do
not express any cash
flows. The capital expenditure (Capex) is deducted. It is a cash
outflow that is not
reflected in the income statement, because Capex is activated on
the asset side of the
balance sheet. The increase in net working capital (NWC) is
also deducted, because it is
does not represent any actual cash flows. The formula for
calculating the FCFF is
shown below. (Damodaran, 1996, p. 237)
�� = �� + �&� − �� − ��
��
There are more methods that can be used to calculate the FCFF,
but they will all result
in the same value.
____________

7
�� =
��
(1+�)�
∞
�=�+1
3.2.2 Building Future Scenarios
Deriving the NPV of the free cash flows that accrue in the
scenario period is very
complex, because all these cash flows are based on assumptions.
The method therefore
requires a detailed picture of the company’s future situation,
e.g. EBIT and Capex.
Predictions are usually made for the next five to fifteen years.
The NPV of the cash
flows accruing after this scenario period is included in the
terminal value, which is
derived using much less assumptions. These predictions are
usually based on historical
data, but may also reflect changes in the company’s business

plan, industry or in the
global economy.
To provide a detailed view on how the company’s value might
be affected by a change
in the underlying assumption, a scenario analysis is usually
conducted. In the bear case
scenario, low assumptions for rates of growth and margins are
used to build a very
pessimistic scenario. In the bull case the opposite is the case,
all assumptions are very
optimistic. These two cases mark the boundaries of where in
between the fair value of
the company should be with a high certainty. Of course,
additional scenario and risk
testing methods like value at risk using a Monte Carlo
Simulation can be used to further
evaluate any risks.
The most important scenario in the valuation of a company is
the base case. In this case
the management’s predictions and opinions regarding the future
development of the
company, its relevant markets and competitors are used to build
the scenario that is

most likely to happen. However, attention has to be paid to the
reliability of any
management provided figures, since managers often have a
personal incentive to
increase the takeover price and therefore might provide biased
estimates.
Another item that is usually included are potential synergies
between the target and the
acquirer. If the potential acquirer is a strategic acquirer who
runs a similar business,
many synergies can be realized. This will allow the strategic
bidder to offer a higher
price than a financial bidder, like a private equity funds for
example.
3.3 The Weighted Average Cost of Capital
Determining the discount rate requires extensive analysis of the
company’s financing
structure and the current market conditions. The rate that is
used to discount the FCFs is
called the weighted average cost of capital (WACC). The
WACC is one of the most
important input factors in the DCF model. Small changes in the
WACC will cause large

changes in the firm value. The WACC is calculated by
weighting the sources of capital
according to the company’s financial structure and then
multiplying them with their
costs. Therefore the formula for the WACC calculation is:
8
�� =
��
�� + ��
∗ �� +
��
�� + ��
∗ ��
3.3.1 Cost of Equity
The cost of equity (COE) is calculated with the help of the
capital asset pricing model
(CAPM). The CAPM reveals the return that investors require for
bearing the risk of
holding a company’s share. This required return is the return on
equity (ROE) that

investors demand to bear the risk of holding the company’s
share, and is therefore
equivalent to the company’s cost of equity. According to the
CAPM, the required ROE,
or in this case the COE is derived with the following formula
(Ross, Westerfield, &
Jordan, 2008, p. 426):
�� = �� + � �� − ��
Although the risk-free interest rate is the yield on T-Bills or T-
Bonds, professionals use
the London Interbank Offer Rates (LIBOR) as an approximation
for the short-term risk-
free interest rates, since “. . . treasury rates are too low to be
used as risk-free rates . . . “
(Hull, 2008, p. 74) It is therefore common to use the LIBOR as
the risk-free rate for
valuation purposes.
The input factor β is the risk, that holding the stock will add to
the investor’s portfolio
9
(Rhaiem, Ben, & Mabrouk, 2007, p. 80). It is derived using
linear regression analysis,
where the excess return of the stock is the dependent variable

and the excess market
return is the independent variable. The beta is the slope of the
regression line. (Brealey,
Myers, & Allen, 2006, p. 220) Beta is an empirical determined
input factor that is also
based on the company’s historical level of leverage, because
higher leverage ratios
increase the shareholder’s risk. Since the company’s level of
leverage often changes
during a transaction, the beta has to be adjusted for this change
by unlevering and
relevering to the new capital structure. If the company is not
listed there is no data
____________
8
In case of any preferred share outstanding, the formula has to be
rearranged to include this source of
financing as well. The adjusted formula will be as following:
�� =
��
��
∗ �� +
��

��
∗ �� +
��
��
∗ ��
9
� =
�� (�� ,�� )
�� (�� )
available to compute a linear regression. As a consequence, a
peer group of similar
companies is set up and the median of their unlevered betas is
then relevered to fit the
target’s financing structure. Although the CAPM approach is
very useful to estimate the
cost of equity, some scientists argue that the CAPM was
developed for liquid assets
(Michailetz, Artemenkov, & Artemenkov, 2007, p. 44), and

therefore its significance
for the valuation of illiquid assets, like non-listed companies
should be subject to further
research.
3.3.2 Cost of Debt
The cost of debt (COD) is the interest rate that a company has
to pay on its outstanding
debt. The most influencing factor on the COD is a company’s
credit rating. A company
with an investment grade credit rating
10
(e.g.: S&P AAA) is able to borrow at
considerably lower interest rates than a company that is rated as
non-investment grade
(e.g.: S&P BB-). The difference between the risk-free interest
rate and the interest rate
that a company has to pay to borrow money is called the
company’s credit spread. The
credit spread does not only depend on a company’s credit
worthiness, but is also
determined by market conditions. An indicator for these
conditions is the spread of the
USD 3m LIBOR vs. the 3m T-Bills

11
depicted in figure 1 in the appendix (Bloomberg
Professional Database, 2008). The chart reflects a massive
widening in credit spreads
that occurred in August 2007 after numerous banks and hedge
funds announced a
massive exposure to the so-called subprime mortgage market.
The dependence of
overall market conditions should be kept in mind when
calculating the COD. Especially
when the company has a high leverage ratio, special attention
has to be paid to the credit
markets.
Interest rate costs are tax deductable in most economies, so that
the true COD is lower
than the interest rate a company pays out to its debt holders
12
. Due to the fact that
taxation laws are very different around the world, a very
thorough analysis is needed to
verify how much of the interest costs are deductable. The COD
after tax can be
calculated as following, where i is the interest rate on

outstanding debt and t is the
effective tax rate paid by the company:
____________
10
Please see table 1 for an overview of long term credit rating
scales of different rating agencies
11
Another widely used benchmark to assess the credit spread is
the iTraxx Europe index, a credit index
consisting of 125 investment grade companies in Europe
12
Assuming the fact that the company is paying taxes from which
the COD can be deducted
�� = � ∗ (1 − �)
If the company has different kinds of debt outstanding, the COD
is the weighted
average cost of debt of these different tranches, adjusted for

tax:
13
�� = 1 − � ∗ ��
�
�=1
3.3.3 Summary
By plugging in the formulas for the COE and COD, we get the
full formula for the
WACC including all factors that influence the discount rate:
�� =
�
� + �
∗ �� + � �� − �� +
�
� + �
∗ � ∗ (1 − �)
The WACC is therefore determined by the COE, which is
derived by applying the
CAPM with its underlying assumptions for beta. The COD is
derived from the interest
rate that the company has to pay to its debt holders and by the

tax rate that the
corporation has to pay on its profits. Changing the assumptions
for the cost of capital
will have large effects on the result of the overall valuation
process.
The WACC of a company is dependent on a variety of economic
factors. Especially the
company’s industry and the steadiness of its cash flows
influence it. Companies with
stable cash flows in mature industries with low growth rates
will typically have low
capital costs (Morningstar, 2007, pp. 1-2). For example, Bayer
will have a substantially
lower WACC than Conergy.
The WACC is used to discount the FCFs that we predicted in
our scenario analysis. The
result is the NPV of the company in the scenario period, to
which we will later add the
terminal value, which also makes uses of the WACC.
Using current figures for beta, risk-free rate, credit spread, and
interest costs will lead to
a fairly realistic approximation for the discount rate in most
cases. However, to get an

exact value, the company’s future WACC must be used.
Therefore, all input factors of
the WACC formula have to be predicted, resulting in leeway for
the outcome of the
DCF analysis.
____________
13
The weights are calculated by dividing the market value of a
tranche by the market value of total
debt outstanding: �� =
��
��
3.4 Calculation of the Terminal Value
The terminal value is the NPV of all future cash flows that
accrue after the time period
that is covered by the scenario analysis. Due to the fact that it is
very difficult to
estimate precise figures showing how a company will develop
over a long period of

time, the terminal value is based on average growth
expectations, which are easier to
predict.
The idea behind the terminal value is to assume constant growth
rates for the time
following the time period that was analyzed more extensively.
The constant perpetual
growth rate g, together with the WACC as the discount rate r
allows for the use of a
simple dividend discount model to determine the terminal value.
Therefore the TV can
be expresses as
14
(Beranek & Howe, 1990, p. 193), where the FCF is one period
before
the TV period:
�� =
�� ∗ (1 + �)
�
(1 + �)�
∞
�=1

=
�� (1 + �)
� − �
Since all these cash flows are discounted to a date in the future,
the TV has to be
discounted again to give us the NPV of all free cash flows that
occur after the scenario
predicted period.
The determination of the perpetual growth rate is one of the
most important and
complex tasks of the whole DCF analysis process, since minor
changes in this rate will
have major effects on the TV and therefore on the firm value in
total. The huge range of
values that result from a change in this growth rate will be
examined in a case study
later on in this chapter. In most cases a perpetual growth rate
should be between 0% and
5%. It has to be positive since in the long-term, the economy is
always growing.
However, according to economists, any growth rate above 5% is
not sustainable on the

long-term. The perpetual growth rate should be in line with the
nominal GDP growth.
(JP Morgan Chase, 2006).
Due to the fact, that the TV often accounts for more than half of
the total company
value, special attention has to be paid to its calculation and
input coefficients. As
discussed in the case study later in this paper, even very small
changes that might not
____________
14
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1+� 1
+
��∗ 1+� 2
1+� 2
+
��∗ 1+� 3
(1+�)3
…
��∗ 1+� �
(1+�)�

which can be mathematically
rearranged to equal the formula given in the text
even be significant from an economist’s perspective will result
in substantial changes in
the company value. Therefore it is very easy to move the TV
into the desired direction
without having to drastically change any underlying business
predictions, like EBIT
margin or capital expenses.
3.5 Determination of Company Value
After having determined the NPV of the cash flows accruing
within the scenario period
and the TV, the TV is discounted to its NPV. Both NPVs are
then added together to
give the enterprise value or the equity value, depending on
whether the valuation is
based on FCFFs or FCFEs:
�� =
��

(1 + �)�
+
��
(1 + �)�+1
�
�=0
Usually the company value is calculated using different levels
of leverage to find an
optimal financing structure. The determined company value can
then be used for further
analysis, e.g. the equity value could be divided by the number
of shares outstanding to
determine a fair share price for listed companies.
4 Validity of the Discounted Cash Flow Valuation Approach
4.1 Case Study: BASF
To demonstrate the wide range of possible results of the DCF
analysis, this paper will
now analyze the BASF stock and the DCF’s sensitivity to
changes in the WACC, the
perpetual growth rate, and sales growth. For this purpose, a base
scenario based on

broker estimates (Credit Suisse Equity Research, 2008) will be
built to obtain a fair
reference value for one BASF stock. Afterwards a sensitivity
analysis will be conducted
to examine the effects on this reference price that modifying
factors will have.
The base case scenario uses the estimates by Credit Suisse
analysts for the cash flow
forecasts for the years 2008 to 2013. The unlevered beta was
determined to be 0.9 using
a linear regression model leading to the cost of equity of 10.3%.
BASF’s current credit
rating results in a credit spread of 500bp according to analysts
(Credit Suisse Equity
Research, 2008). This leads to a WACC of 9.0%. Furthermore
we assume the perpetual
growth rate to be equal to 1.5%. Discounting the predicted free
cash flows to the firm
for the years 2008 to 2013 using the WACC of 9.0% and then
adding the discounted
terminal value results in an enterprise value of EURm 67,850.

Please see tables 3 - 7 for
the exact calculations.
Period 2008E 2009E 2010E 2011E 2012E 2013E TV
FCFF 4,284 4,405 4,866 5,409 6,148 6,212 -
NPV 3,930 3,708 3,758 3,832 3,996 3,704 44,923
EV 67,850
Table 4: Case Study: Calculation of the enterprise
value
It is remarkable that the terminal value accounts for EURm
44,923 of the total EV. This
makes obvious, that the outcome of the DCF analysis is highly
sensitive to changes in
the perpetual growth rate, since it has a major effect on the TV.
Having determined the
EV, net debt and corporate adjustments are deducted from the
EV to calculate the equity
value of EURm 55,332. The equity value is then divided by the
number of shares
outstanding. The result of EUR 58.49 is the fair price for one
BASF share given the
underlying assumptions. Knowing the fact that the current share

price equals only EUR
39.41 (Thomson Reuters, 2008), this would make the BASF
share a great investment if
you believe that the underlying assumptions are valid. This
share price will serve as the
reference value for the sensitivity analysis, since it lies in
between of most research
analyst’s target price for BASF.
4.2 Sensitivity Analysis
To investigate the sensitivity of the DCF method, the BASF
case study developed above
will be used. The changes that occur in the share price will be
stated as percentage
offset from the base case share price of EUR 58.49.
The WACC and the perpetual growth rate are two main input
factors that have large
effect on the outcome of the analysis. Therefore the table below
shows the result of the
sensitivity analysis regarding those two factors. The base case
assumptions of 9.0% for
the WACC and 1.5% for the perpetual growth rate are
highlighted in dark blue.

WACC (%)
0.00 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0%
P
e
r
p
e
tu
a
l
g
r
o
w
th
r
a
te
(

%
)
0.0% 19.2% 9.0% 0.2% -7.6% -14.5% -20.7% -26.2% -31.2% -
31.2%
0.5% 27.2% 15.8% 5.9% -2.7% -10.3% -17.0% -23.0% -28.3% -
28.3%
1.0% 36.6% 23.6% 12.5% 2.9% -5.4% -12.8% -19.3% -25.1% -
25.1%
1.5% 47.6% 32.7% 20.1% 9.3% 0.0% -8.1% -15.3% -21.6% -
21.6%
2.0% 60.9% 43.5% 29.0% 16.7% 6.2% -2.8% -10.7% -17.7% -
17.7%
2.5% 77.2% 56.4% 39.4% 25.3% 13.4% 3.2% -5.6% -13.3% -
13.3%
3.0% 97.5% 72.2% 52.0% 35.5% 21.8% 10.2% 0.3% -8.2% -
8.2%
Table 5: Case Study: Sensitivity Analysis WACC, Perpetual
growth rate
The table clearly shows that even slight changes in the WACC
or in the perpetual
growth rate, which might not even be significant from an
economist’s perspective, will
largely offset the determined fair share price from the base case

scenario. For example
increasing the WACC by 100bp and simultaneously decreasing
the perpetual growth
rate by 50bp will shrink the calculated fair stock price by more
than 19%. Since it is
very difficult to estimate the perpetual growth rate or the cost
of capital with an
exactness of just a few base points, the determined fair share
price can only be seen as
guidance, but not as an absolutely exact value.
The sensitivity to changes in the WACC can be expressed as the
first derivative of the
company value in respect to the discount rate, similar to the
concept of bond duration.
The formula below shows the approximate change in the
company value when
modifying the WACC.
15
��
��
=
1

1 + �
−� ∗ ��
(1 + �)�
�
�=0
The next step in the sensitivity analysis is to assess whether
changes in the perpetual
growth rate or in the growth rate for the predicted period (Sales
CAGR) have a higher
impact on the share price. Since both growth rates affect the
nominal value free cash
flow, the result of the analysis should be helpful to understand
the importance that the
terminal value has on the DCF analysis since all other factors
are kept fixated. If
modifying the perpetual growth rate leads to larger changes than
modifying the sales
CAGR for the scenario period, the terminal value would be of
significantly higher
importance than the scenario predictions for the first years.
____________
15

Due to convexity however, this approximation should only be
used in the case of small changes
in the discount rate.
Perpetual growth rate (%)
0.00 0.50% 0.75% 1.00% 1.25% 1.50% 1.75% 2.00% 2.25%
2.50%
S
a
le
s
C
A
G
R
(
%
) 6.75% -14.0% -11.8% -9.4% -6.9% -4.3% -1.4% 1.6% 4.9%
8.5%
7.00% -12.8% -10.5% -8.1% -5.6% -2.9% 0.0% 3.2% 6.5%
10.1%

7.25% -11.5% -9.2% -6.8% -4.2% -1.4% 1.5% 4.7% 8.1% 11.8%
7.50% -10.3% -7.9% -5.5% -2.8% 0.0% 3.0% 6.2% 9.7% 13.4%
7.75% -9.0% -6.6% -4.1% -1.4% 1.5% 4.5% 7.8% 11.3% 15.1%
8.00% -7.7% -5.3% -2.7% 0.0% 2.9% 6.1% 9.4% 13.0% 16.9%
8.25% -6.4% -3.9% -1.3% 1.5% 4.5% 7.6% 11.0% 14.7% 18.6%
Table 6: Case Study: Sensitivity analysis perpetual growth
rate, sales CAGR
As expected, changes in the perpetual growth rate have a higher
impact than changes in
the sales CAGR have. For example an increase in the perpetual
growth rate by 25bp
result in a 3% higher share price, whereas a change by the same
amount in the sales
CAGR will only drive the fair share price up by 1.5%. Looking
at this result, the
importance of the terminal value becomes evident again. It
underlines the fact that the
TV includes all cash flows from the end of the scenario period
up to infinity compared
to just a few years in the scenario period. Therefore the TV,
together with its underlying

assumptions, is the most important and influential part of the
whole discounted cash
flow analysis. As mentioned before it is very easy to slightly
adjust the assumptions that
influence the TV, without having to justify these changes since
they are very small.
However, these small adjustments will significantly change the
TV and therefore the
value of the whole company.
5 Conclusion
The sensitivity analysis has shown that the DCF method is very
vulnerable to changes
in the underlying assumptions. Only marginally changes in the
perpetual growth rate
will lead to huge variances in the terminal value. Since the
terminal value accounts for a
large portion of the company’s value, this is of big significance
for the validity of the
DCF method.
It is very easy to manipulate the DCF analysis to result in the
value that you want it to
result in by adjusting the inputs. This is even possible without
making changes that

would be significant from an economist’s point of perspective,
e.g. a change in the
perpetual growth rate or in the WACC by just a few base points.
Analysts or business
professionals have no tools to estimate the input factors with
that kind of exactness.
However, the DCF analysis is a great tool to analyze what
assumptions and conditions
have to be fulfilled in order to reach a certain company value.
This is especially helpful
in the case of capital budgeting and in the creation of feasibility
plans.
The company valuation using discounted cash flows is a valid
method to assess the
company’s value if special precaution is put on the validity of
the underlying
assumptions. As with all other financial models, the validity of
the DCF method almost
completely depends on the quality and validity of the data that
is used as input. If used
wisely, the discounted cash flow valuation is a powerful tool to

evaluate the values of a
variety of assets and also to analyze the effects that different
economic scenarios have
on a company’s value.
The range of reasonable rates for discount factor and perpetual
growth rate depends on
each specific firm, its business situation and many more
variables. In general you can
say that the more risky a firm is, the higher its capital costs
(WACC) are. The perpetual
growth rate should be the same for all industries, since
according to the arbitrage theory
in the long run all companies and industries will grow by the
same rate.
I conclude that using the DCF method in combination with other
methods, like the
trading comparables or precedent transaction analysis, is an
effective approach to obtain
a realistic range of appropriate company values. This
combination technique is indeed
the method that most companies and investment banks use
today. When using several
valuation techniques, their individual shortfalls are eliminated
and the ultimate goal in

the field of company valuation can be reached: determining a
fair and valid company
value.
Reference List
Beranek, W., & Howe, K. M. (1990). The Regulated Firm and
the DCF Model: Some
Lessons From Financial Theory. Joumal of Regulatory
Economics , 193.
Bloomberg Professional Database. (2008, August 09). Credit
Derivates and Interest
Rates. New York, New York, United States of America.
Retrieved August 09,
2008
Bodie, Kane, & Marcus. (2008). Investments (7th Edition ed.).
McGraw Hill.
Brealey, R. A., Myers, S. C., & Allen, F. (2006). Principles of
Corporate Finance (8th
Edition ed.). McGraw-Hill.
Brigham, E. F., & Gapenski, L. C. (1997). Financial

Management - Theory and
Practice (8th Edition ed.). Orlando: The Dryden Press.
Credit Suisse Equity Research. (2008). BASF's balancing act.
Frankfurt: Credit Suisse.
Damodaran, A. (1996). Investment Valuation. New York: John
Wiley & Sons, Inc.
Hull, J. C. (2008). Options, Futures and Other Derivatives (7th
Edition ed.). Upper
Saddle River: Pearson Prentince Hall.
JP Morgan Chase. (2006). JP Morgan M&A EBS lecture
presentation. Frankfurt.
Luehrman, T. A. (1998, July). Investment Opportunities as Real
Options. Harvard
Business Review , 51-67.
Luehrmann, T. A. (1997). What's it worth? Harvard Business
Review , 135.
Michailetz, V. B., Artemenkov, A. I., & Artemenkov, I. L.
(2007). Income Approach
and Discount Rates for Valuing Income-Producing Illiquid
Assets. The Icfai
Journal of Applied Finance , 43-80.
Morningstar. (2007). Morningstar's Approach to Rating Stocks.

Mukherjee, T. K., Kiymaz, H., & Bake, H. K. (2004,
Fall/Winter). Merger Motives and
Targets: A Survey of Evidence from CFOs. Journal of Applied
Finance , 7-24.
Rhaiem, N., Ben, S., & Mabrouk, A. B. (2007). Estimation of
Capital Asset Pricing
Model at Different Time Scales. The International Journal of
Applied
Economics and Finance , 80.
Ross, Westerfield, & Jordan. (2008). Corporate Finance
Fundamentals. New York:
McGraw-Hill Irwin.
Thomson One Banker. (2008, August 14). M&A League Tables.
Retrieved August 14,
2008, from Thomson One Banker:
http://banker.thomsonib.com/ta
Thomson Reuters. (2008, August 26). Worldscope Database.
New York.

Appendix
Table 1: Long term credit rating scales
Rating Agency Moody's
Standard & Poor's
(S&P)
Fitch
Investment
grade debt
Aaa AAA AAA
Aa1 AA+ AA+
Aa2 AA AA
Aa3 AA- AA-
A1 A+ A+
A2 A A
A3 A- A-
Baa1 BBB+ BBB+
Baa2 BBB BBB

Baa3 BBB- BBB-
Non-investment
grade debt
Ba1 BB+ BB+
Ba2 BB BB
Ba3 BB- BB-
B1 B+ B+
B2 B B
B3 B- B-
Caa1 CCC+ CCC+
Caa2 CCC CCC
Caa3 CCC- CCC-
Ca CC CC
C C C
Default grade
debt C D D

Table 2: Trading comparables analysis
2008e 2009e 2010e 2008e 2009e 2010e 2008e 2009e 2010e
2008e 2009e 2010e
Sixt 1.0x 1.0x 1.0x 3.2x 3.1x 2.9x 9.2x 8.9x 8.4x 7.3x 7.1x 6.7x
Avis Europe 0.8x 0.8x 0.8x 2.4x 2.3x 2.1x 9.9x 8.9x 8.2x 6.6x
5.3x 4.6x
D'ieteren 0.5x 0.5x 0.4x 4.0x 3.7x 3.5x 8.2x 7.6x 6.8x 6.9x 5.9x
5.0x
Hertz 1.7x 1.6x 1.6x 9.5x 8.7x 8.2x 10.9x 10.3x 9.9x 8.4x 7.0x
6.0x
Dollar Thrifty 1.5x 1.4x 1.4x 29.5x 26.0x 28.3x 12.3x 8.0x 8.4x
Penske 0.3x 0.3x 0.2x 10.2x 9.3x 8.0x 14.4x 12.4x 10.7x 9.6x
9.3x
Amerco
Mean 1.0x 0.9x 0.9x 9.8x 8.8x 8.8x 10.5x 9.6x 8.3x 8.7x 7.2x
6.7x
Median 0.9x 0.9x 0.9x 6.7x 6.2x 5.8x 9.9x 8.9x 8.3x 7.8x 7.1x
6.3x
EV/Sales EV / EBITDA EV / EBIT Eq. V. / Net income

Company
Table 3: Transaction multiple analysis
Table 4: Case Study: Calculation of the enterprise value
Period 2008E 2009E 2010E 2011E 2012E 2013E TV
FCFF 4,284 4,405 4,866 5,409 6,148 6,212 -
NPV 3,930 3,708 3,758 3,832 3,996 3,704 44,923
EV 67,850
Table 5: Case Study: Sensitivity Analysis WACC,
perpetual growth rate
WACC (%)
0.00 7.0% 7.5% 8.0% 8.5% 9.0% 9.5% 10.0% 10.5% 11.0%
P
e
r
p
e
tu

a
l
g
r
o
w
th
r
a
te
(
%
)
0.0% 19.2% 9.0% 0.2% -7.6% -14.5% -20.7% -26.2% -31.2% -
31.2%
0.5% 27.2% 15.8% 5.9% -2.7% -10.3% -17.0% -23.0% -28.3% -
28.3%
1.0% 36.6% 23.6% 12.5% 2.9% -5.4% -12.8% -19.3% -25.1% -
25.1%
1.5% 47.6% 32.7% 20.1% 9.3% 0.0% -8.1% -15.3% -21.6% -
21.6%
2.0% 60.9% 43.5% 29.0% 16.7% 6.2% -2.8% -10.7% -17.7% -
17.7%
2.5% 77.2% 56.4% 39.4% 25.3% 13.4% 3.2% -5.6% -13.3% -

13.3%
3.0% 97.5% 72.2% 52.0% 35.5% 21.8% 10.2% 0.3% -8.2% -
8.2%
Table 6: Case Study: Sensitivity analysis perpetual growth rate,
sales CAGR
Perpetual growth rate (%)
0.00 0.50% 0.75% 1.00% 1.25% 1.50% 1.75% 2.00% 2.25%
2.50%
S
a
le
s
C
A
G
R
(
%
) 6.75% -14.0% -11.8% -9.4% -6.9% -4.3% -1.4% 1.6% 4.9%
8.5%
7.00% -12.8% -10.5% -8.1% -5.6% -2.9% 0.0% 3.2% 6.5%
10.1%
7.25% -11.5% -9.2% -6.8% -4.2% -1.4% 1.5% 4.7% 8.1% 11.8%

7.50% -10.3% -7.9% -5.5% -2.8% 0.0% 3.0% 6.2% 9.7% 13.4%
7.75% -9.0% -6.6% -4.1% -1.4% 1.5% 4.5% 7.8% 11.3% 15.1%
8.00% -7.7% -5.3% -2.7% 0.0% 2.9% 6.1% 9.4% 13.0% 16.9%
8.25% -6.4% -3.9% -1.3% 1.5% 4.5% 7.6% 11.0% 14.7% 18.6%
Table 7: Case Study: Income statement estimates
Target Acquirer Date EV (€m) EV / SALES EV / EBITDA EV /
EBIT EqV / Net Income
Vanguard Car Rental EMEA Europcar International 13/11/2006
670.00 1.70x 6.34x 23.92x n.m.
Keddy Car Europcar International 30/06/2006 0.00
Europcar International Eurazeo SA 03.09.2006 3083.00 2.41x
Hertz Group (Canada) FirstGroup plc 20/12/2000 18.07 1.22x
Laidlaw International FirstGroup plc 02.09.2007 2701.76 1.11x
7.43x 13.84x 22.10x
Cognisa Transportation First Transit, Inc 01.05.2007 11.87
SKE Support Services FirstGroup plc 13/09/2004 22.85 0.38x
Aircoach FirstGroup plc 11.01.2003 16.99
GB Railways Group FirstGroup plc 16/07/2003 44.51 0.34x
29.67x 55.64x 88.99x

Coach USA Kohlberg & Company LLC 06.06.2003 130.99
0.72x
Verona Bus Service FirstGroup plc 08.01.2001 6.51 1.00x 3.81x
7.15x
Avis Greece Piraeus Bank SA 05.02.2007 215.50 2.65x
Avis French Avis Europe plc 02.03.2003 8.50 0.43x
Budget International Avis Europe plc 23/01/2003 37.28
SAISC Avis Europe plc 31/01/2002 25.58
3 Arrows Avis Europe plc 12.10.1998 57.09
Fraikin SA CVC Capital 12.08.2006 1350.00 2.21x 18.10x
Average 1.29x 11.81x 23.73x 55.54x
Median 1.11x 6.89x 18.10x 55.54x
Period 2008E 2009E 2010E 2011E 2012E 2013E 2014E
Sales 64,702.10 65,388.80 67,645.50 71,390.10 74,631.10
76,870.00 86,517.90
EBIT Margin 12.2% 11.2% 11.9% 13.2% 14.0% 13.0% 11.0%

EBIT 7,893.66 7,323.55 8,049.81 9,423.49 10,448.35 9,993.10
9,516.97
Taxes (2,368.10) (2,197.06) (2,414.94) (2,827.05) (3,134.51)
(2,997.93) (2,855.09)
NOPLAT 5,525.56 5,126.48 5,634.87 6,596.45 7,313.85
6,995.17 6,661.88
D&A 2,700.90 2,740.90 2,779.20 2,829.50 2,902.30 2,989.40
3,431.80
Increase in
NWC (1,031.20) (519.80) (503.60) (804.20) (709.70) (783.60)
(593.80)
Capex (2,911.60) (2,942.50) (3,044.00) (3,212.60) (3,358.40)
(2,989.40) (3,431.80)
FCFF 4,283.66 4,405.08 4,866.47 5,409.15 6,148.05 6,211.57
6,068.08
Table 8: Case Study: Liabilities structure
Shareholders
Equity 20,097.90
Financial Debt 10,100.70
Long Term 6,953.00

Short Term 3,147.70
Leverage 0.33
Table 9: Case Study: WACC calculation
Cost of Equity (%)
Risk free rate (%) 4.3%
Unlevered Beta 0.9
Levered Beta 1.2
Market return (%) 9.3%
CAPM required RoE 10.3%
Cost of Debt (%)
Average Credit Spread (%) 5.0%
Cost of Debt before taxes 9.3%
CoD adjusted for tax 6.5%
WACC 9.0%
Table 10: Case Study: Terminal Value calculation

FCFF in terminal period 6,068.08
Perpetual growth rate (%) 1.5%
WACC (%) 9.0%
Terminal Value 81,731.65
NPV of TV 44,607.47
Table 11: Case Study: DCF valuation
Period 2008E 2009E 2010E 2011E 2012E 2013E TV
FCFF (EURm) 4,283.66 4,405.08 4,866.47 5,409.15 6,148.05
6,211.57 -
NPV (EURm) 3,929.96 3,707.67 3,757.81 3,831.97 3,995.81
3,703.76 44,923.18
EV (EURm) 67,850.16
Net debt (EURm) (11,547.00)
Minorities
(EURm) (971.20)
Eq.V. (EURm) 55,331.96

No. Of shares (m) 946
Fair share price 58.49
Figure 1: LIBOR credit spread (in bp)
0.0
50.0
100.0
150.0
200.0
250.0
1
5
-A
u
g
-2
0
0
3

1
5
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o
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2
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0
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4
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5
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a
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0
0
4
1
5
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g
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0
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4
1
5
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0
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0
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8

1
5
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a
i-
2
0
0
8
USD LIBOR 3m vs US Treasury 3m …
Project4Income StatementAll numbers in thousandsRevenue
12/30/1712/31/1612/26/15Total
Revenue63,525,00062,799,00063,056,000Cost of
Revenue28,785,00028,209,00028,731,000Gross
Profit34,740,00034,590,00034,325,000Cash FlowOperating
ExpensesAll numbers in thousandsResearch Development---
Period Ending12/31/1712/31/1612/31/15Selling General and
Administrative24,231,00024,805,00024,613,000Net
Income1,248,0006,527,0007,351,000Non Recurring--
1,359,000Operating Activities, Cash Flows Provided By or Used
InOthers---Depreciation1,260,0001,787,0001,970,000Total
Operating Expenses---Adjustments To Net
Income923,000680,0001,349,000Operating Income or
Loss10,509,0009,785,0008,353,000Changes In Accounts
Receivables---Income from Continuing OperationsChanges In
Liabilities---Total Other Income/Expenses
Net244,000110,00059,000Changes In Inventories---Earnings
Before Interest and
Taxes10,753,0009,895,0008,412,000Changes In Other

Operating Activities3,537,000-221,000-157,000Interest
Expense1,151,0001,342,000970,000Total Cash Flow From
Operating Activities6,995,0008,796,00010,528,000Income
Before Tax9,602,0008,553,0007,442,000Investing Activities,
Cash Flows Provided By or Used InIncome Tax
Expense4,694,0002,174,0001,941,000Capital Expenditures-
1,675,000-2,262,000-2,553,000Minority
Interest92,000104,000107,000Investments-609,0001,125,000-
1,752,000Net Income From Continuing
Ops4,857,0006,329,0005,452,000Other Cash flows from
Investing Activities-101,000138,000-1,881,000Non-recurring
EventsTotal Cash Flows From Investing Activities-2,385,000-
999,000-6,186,000Discontinued Operations---Financing
Activities, Cash Flows Provided By or Used InExtraordinary
Items---Dividends Paid-6,320,000-6,043,000-5,741,000Effect
Of Accounting Changes---Sale Purchase of Stock-2,087,000-
2,247,000-2,319,000Other Items---Net
Borrowings1,089,0001,666,0002,696,000Net IncomeOther Cash
Flows from Financing Activities-91,00079,000251,000Net
Income4,857,0006,329,0005,452,000Total Cash Flows From
Financing Activities-7,409,000-6,545,000-5,113,000Preferred
Stock And Other Adjustments---Effect Of Exchange Rate
Changes242,000-6,000-878,000Net Income Applicable To
Common Shares4,857,0006,329,0005,452,000Change In Cash
and Cash Equivalents-2,549,0001,246,000-1,649,000Balance
SheetAll numbers in thousandsPeriod
Ending12/26/1512/31/1612/30/17Current AssetsCash And Cash
Equivalents9,096,0009,158,00010,610,000Short Term
Investments2,913,0006,967,0008,900,000Net
Receivables6,437,0006,694,0007,024,000Inventory2,720,0002,7
23,0002,947,000Other Current
Assets1,865,000908,0001,546,000Total Current
Assets23,031,00026,450,00031,027,000Long Term
Investments2,311,0001,950,0002,042,000Property Plant and
Equipment16,317,00016,591,00017,240,000Goodwill14,177,000
14,430,00014,744,000Intangible

Assets13,081,00013,433,00013,838,000Accumulated
Amortization---Other Assets750,000636,000913,000Deferred
Long Term Asset Charges---Total
Assets69,667,00073,490,00079,804,000Current
LiabilitiesAccounts
Payable13,507,00014,243,00015,017,000Short/Current Long
Term Debt4,071,0006,892,0005,485,000Other Current
Liabilities---Total Current
Liabilities17,578,00021,135,00020,502,000Long Term
Debt29,213,00030,053,00033,796,000Other
Liabilities5,887,0006,669,00011,283,000Deferred Long Term
Liability Charges4,959,0004,434,0003,242,000Minority
Interest107,000104,00092,000Negative Goodwill---Total
Liabilities57,744,00062,395,00068,915,000Stockholders'
EquityMisc. Stocks Options Warrants-145,000-151,000-
156,000Redeemable Preferred Stock---Preferred Stock---
Common Stock24,00024,00024,000Retained
Earnings50,472,00052,518,00052,839,000Treasury Stock-
29,185,000-31,468,000-32,757,000Capital
Surplus4,076,0004,091,0003,996,000Other Stockholder Equity-
13,319,000-13,919,000-13,057,000Total Stockholder
Equity12,068,00011,246,00011,045,000Net Tangible Assets-
15,190,000-16,617,000-17,537,000Cash FlowAll numbers in
thousandsPeriod Ending12/30/1712/31/1612/26/15Net
Income4,857,0006,329,0005,452,000Operating Activities, Cash
Flows Provided By or Used
InDepreciation2,369,0002,368,0002,416,000Adjustments To Net
Income3,545,000950,0002,089,000Changes In Accounts
Receivables-202,000-349,000-461,000Changes In Liabilities-
137,0001,326,0001,747,000Changes In Inventories-168,000-
75,000-244,000Changes In Other Operating Activities-
321,00074,000-184,000Total Cash Flow From Operating
Activities9,994,00010,673,00010,864,000Investing Activities,
Cash Flows Provided By or Used InCapital Expenditures-
2,969,000-3,040,000-2,758,000Investments-1,910,000-
4,301,000-400,000Other Cash flows from Investing

Activities476,000193,000-411,000Total Cash Flows From
Investing Activities-4,403,000-7,148,000-3,569,000Financing
Activities, Cash Flows Provided By or Used InDividends Paid-
4,472,000-4,227,000-4,040,000Sale Purchase of Stock-
1,543,000-2,542,000-4,501,000Net
Borrowings2,050,0003,746,0004,632,000Other Cash Flows from
Financing Activities-221,000-188,000-203,000Total Cash Flows
From Financing Activities-4,186,000-3,211,000-4,112,000Effect
Of Exchange Rate Changes47,000-252,000-221,000Change In
Cash and Cash Equivalents1,452,00062,0002,962,000Figure 1
Liabilities and equity20162017MicroDrive’s Most Recent
Financial Statements (Thousand, Except for Per Share
Data)Accounts Payable$ 14,243,000$ 15,017,000INCOME
STATEMENTSBALANCE SHEETSShort/Current Long Term
Debt6,892,0005,485,00020162017Assets20162017Other Current
Liabilities--Net sales$ 62,799,000$ 63,525,000Cash And
Cash Equivalents$ 9,158,000$ 10,610,000Total Current
Liabilities21,135,00020,502,000COGS (excl.
depr.)28,209,00028,785,000Short Term
Investments6,967,0008,900,000Long Term
Debt30,053,00033,796,000Depreciation2,368,0002,369,000Net
Receivables6,694,0007,024,000Other
Liabilities6,669,00011,283,000Other operating expenses--
Inventory2,723,0002,947,000Deferred Long Term Liability
Charges4,434,0003,242,000EBIT$ 32,222,000$
32,371,000Other Current Assets908,0001,546,000Minority
Interest104,00092,000Interest expense1,342,0001,151,000Total
Current Assets26,450,00031,027,000Negative Goodwill--Pre-
tax earnings$ 30,880,000$ 31,220,000Long Term
Investments1,950,0002,042,000Total
Liabilities62,395,00068,915,000Taxes
(7,849,073)15,262,100Property Plant and
Equipment16,591,00017,240,000Stockholders' EquityNI before
pref. div.$ 38,729,073$
15,957,900Goodwill14,430,00014,744,000Misc. Stocks Options
Warrants(151,000)(156,000)Preferred div.--Intangible

Assets13,433,00013,838,000Redeemable Preferred Stock--Net
income$ 38,729,073$ 15,957,900Accumulated Amortization--
Preferred Stock--Other Assets636,000913,000Common
Stock24,00024,000Other DataDeferred Long Term Asset
Charges--Retained Earnings52,518,00052,839,000Common
dividends$0$0Total Assets73,490,00079,804,000Treasury
Stock(31,468,000)(32,757,000)Addition to
RE$52,518,000$50,472,000Capital
Surplus4,091,0003,996,000Tax rate-25%49%Other Stockholder
Equity(13,919,000)(13,057,000)Shares of common
stock4,000,0004,000,000Total Stockholder
Equity11,246,00011,045,000Earnings per share$9.68$3.99Net
Tangible Assets(16,617,000)(17,537,000)Dividends per
share$0.00$0.00Price per share$5.67$6.89Figure 2Pepsi's
Forecast: Inputs for the Selected ScenarioStatus QuoKOPepsi
ActualPepsiInputsActualActualForecast1. Operating
Ratios20172016201720182019202020212022Sales growth
rate5%-1%1%8%6%7%5%5%COGS (excl. depr.) /
Sales76%223%221%200%178%178%178%178%Depreciation /
Net PP&E9%14%14%35%35%35%35%35%Other op. exp. /
Sales10%0%0%18%18%18%19%20%Cash /
Sales1%15%17%6%6%7%7%7%Actual Historical
FinancingAcc. rec. /
Sales8%11%11%10%8%8%8%8%20162017Inventory /
Sales15%4%5%20%5%4%4%4%Long-term
debt$30,053,000$33,796,000Net PP&E /
Sales33%26%27%40%55%60%60%60%Short-term
debt$6,892,000$5,485,000Acc. pay. /
Sales4%23%24%20%20%23%23%23%Preferred
stock$0$0Accruals / Sales7%6%6%6%6%6%6%5%Market value
of equity = (Price x # shares)$0$0Tax rate40%-
25%49%9%12%13%13%13%Total$36,945,000$39,281,0002.
Capital StructureActual Market WeightsTarget Market
Weights% Long-term
debt22%48%49%50%50%44%55%57%See the box to the right
for calculations of the actual capital structures, based on market

values, for the past two years.Percent long-term debt49%54%%
Short-term debt3%11%8%8%8%6%7%9%Percent short-term
debt8%8%% Preferred stock0%0%0%0%0%0%2%3%Percent
preferred stock0%0%% Common
stock75%100%100%80%80%80%5%5%Percent market value of
equity0%0%3. Costs of CapitalForecastTotal57%62%Rate on
LT debt9.0%9%9%9%9%Rate on ST
debt10.0%10%10%10%10%Rate on preferred stock (ignoring
flotation costs)8.0%8%8%8%8%Cost of
equity13.58%14%14%14%14%4. Target Dividend
PolicyActualGrowth rate of
dividends0%0.0%0%0%0%0%0%Figure 3Pepsi's Forecast of
Operations for the Selected Scenario (Thousands of Dollars,
Except for Per Share Data)INCOME
STATEMENTSKOPepsiPepsiPanel A:
InputsActualActualForecastA1. Operating
Ratios20172016201720182019202020212022Sales growth
rate5%-7%7%8%6%7%5%5%COGS (excl. depr.) /
Sales76%211%182%200%178%178%178%178%Depreciation /
Net PP&E9%33%41%35%35%35%35%35%Other op. exp. /
Sales10%22%15%18%18%18%19%19%Cash /
Sales1%8%8%6%6%7%7%7%Acc. rec. /
Sales8%3%12%10%8%8%8%8%Inventory /
Sales15%4%3%20%5%4%4%4%Net PP&E /
Sales33%63%56%40%55%60%60%60%Acc. pay. /
Sales4%23%21%20%20%23%23%23%Accruals /
Sales7%6%6%6%6%6%6%6%Tax
rate40%8%15%9%12%13%13%13%Panel B:
ResultsActualForecastB1. Sales
Revenues201720182019202020210Net
sales$63,525,000$68,607,000$72,723,420$77,814,059$81,704,7
62$81,704,762B2. Operating Assets and Operating
LiabilitiesCash$10,610,000$4,116,420$4,363,405$5,446,984$5,
719,333$0Accounts
receivable$7,024,000$7,726,400$8,344,512$9,012,073$9,733,03
9$0Inventories$2,947,00013721400363617131125623268190$0

Net
PP&E$17,240,000$27,442,800$39,997,881$46,688,436$49,022,
857$0Accounts
payable$15,017,000$13,721,400$14,544,684$17,897,234$18,79
2,095$0Accruals$2,319,863$2,282,244$2,339,425$2,474,740$2,
647,971$0B3. Operating IncomeCOGS (excl.
depr.)$18,969,000$137,214,000$129,447,688$138,509,026$145,
434,477$0Depreciation$7,848,000$24,012,450$25,453,197$27,2
34,921$28,596,667$0Other operating
expenses$5,349,000$12,349,260$13,090,216$14,006,531$15,52
3,905$0EBIT$2,366,000$2,507,960$2,658,438$2,844,528$3,043
,645$81,704,762Net operating profit after
taxes−$12,896,100$2,282,244$2,339,425$2,474,740$2,647,971$
81,704,762B4. Free Cash FlowsNet operating working
capital$3,244,137$9,560,576−$540,021−$2,800,354−$2,719,504
$0Total operating
capital$20,484,137$37,003,376$39,457,860$43,888,082$46,303
,353$0FCF = NOPAT – Δ op
capital−$33,380,236−$14,236,996−$115,059−$1,955,482$232,7
00$128,008,116B5. Estimated Intrinsic ValueTarget
WACC15.7%15.7%15.7%15.7%0.0%Return on invested capital-
63.0%11.7%11.7%11.7%11.7%ERROR:#DIV/0!Growth in FCF-
99%1599.6%-111.9%54910.0%Horizon Value:Value of
operations 101745634.55$101,745,635+ ST
investments8900000.00$0=−$128,241,239Estimated total
intrinsic value110645634.55$101,745,635− All
debt45079000.00$0Value of Operations:− Preferred
stock0.00$0Present value of HV$53,495,882Estimated intrinsic
value of equity65566634.55$101,745,635+ Present value of
FCF$48,249,753÷ Number of shares4000000.00$0Value of
operations =$101,745,635Estimated intrinsic stock price
=16.39ERROR:#DIV/0!
All four projects are due by 1:50pm on Mar 18 th,2019
(Monday)FIN 430 — Finance Theory and PracticeStock
Valuation project

You have been assigned a company to research (please check
the excel list for the firm you are assigned to). statements are
available on the internet through at the http://finance.yahoo.com
website. At this website you will put the ticker symbol for your
company in the symbol box and press “go”. At this point you
will see a page that has financial information about your
company. On the left-hand side of the screen there will be a
series of options that you can choose to get more information
about your company. Under the heading “financial statements”
you will see an option for “income statement” and “balance
sheet.” You want annual statements. The financial statements
for the past 3 years should be available. (Depending on the
fiscal year for your company, these might be 2015, 2016, and
2017 or 2016, 2017 and 2018.).
The purpose of the project is to estimate and justify: (1) an
intrinsic (fundamental) value for the company of your choice
and (2) the fundamental price/share of equity in the firm. You
should attempt to justify that you have calculated your best
estimate of the firm’s stock price. You may compare your
values (ratios/prices/calculations, etc.) to those you find on the
internet, but your work should be your own and your job is to
calculate these figures. All calculations/ratios/values are
assumed to have been calculated by you own. You should not
substitute those figures for yours and using such figures from
other sources is plagiarism. All of your reports (including table,
graph, figures, reference, etc) should not be longer than 25
pages.
You may use up to three different methods to calculate firm
stock value (the FCF method is most important and you have to
include this analysis in your project). The three methods that
we study for valuing corporations include:
1. Free Cash Flow Method (or discounted cash flow
method). This method requires you to produce pro forma
financial statements as based upon the additional funds needed,
percentage of sales and constant ratio methods (see “Financial

forecasting” in the index). The pro forma statements are then
used to calculate the free cash flow as based upon the
formulas/examples in the: "Financial Statements, Cash Flow
and Taxes," "Financial Planning and Forecasting Financial
Statements," and the "Corporate Valuation," chapters in the
text. The FCF is discounted back to the present by the WACC,
which leads to the firm value as follows. Note that the present
value of the FCFs = the Value of Operations (see the CH 7 and
the formula runs as followings).
Value of Operations (Enterprise Value )
+ Value of non-operating assets (one example would be
marketable securities)
= Total Firm value
- Value of Debt [we use the book value of ST and LT debt;
though theory suggests that the market value
- Value of Preferred Shares [if any]
= Value of Equity
÷ Number of Shares of Common Stock outstanding
Price per share
This price per share is your estimate of the fundamental value
of the firm stock, which you would then use to argue that the
firm is either currently over/under/fairly valued according to the
market, i.e., by comparing your price/share to
the current market price/share. Warren Buffet calls this
estimate the "intrinsic value" of the firm. Remember that you
may consider the efficient market hypothesis in relation to your
price estimate.
2. Dividend Growth Model (Multi-stage growth model)
3. Comparables (Stock Price Multiples Model): This method is
relatively easy and provides some useful valuations that often
set the ranges for the stock price. The course packet lecture
entitled “Using Stock Price Multiples to Estimate Stock Price”
describes this method. You may use either a direct competitor

or industry averages. For example, if you are analyzing Ford
Motor Corp. it would be appropriate to use GM as a comparable
firm (and/or the auto industry). Note that sector/industry ratios
can be obtained on Yahoo.finance [look under profiles, then on
the left hand side under Financial Links you should
see competitors]. Many different financial ratios can be used,
although the P/E and Price/CF ratios are common. Another
alternative is to create your own "industry" averages from a
diverse group of firms within the industry. You are limited
only by your creativity; and a great deal of information is
available on the Internet. The goal should be to calculate
fundamental values by yourself.
General Guidelines (Mandatory)
The major focus of the project is to calculate and justify your
estimate of the price/share of equity using the FCF
Method. Many other elements of the project are necessary in
order to complete a satisfactory project. Minimally, these
include:
An example is given on CH12 (page 489- 495).
Completing 5-year pro-formas for your firm. The pro formas
serve as the central element of your project. Many steps lead up
to the pro formas, and many important steps follow from the pro
forma. All of your estimates should include
appropriate justification/ support/ explanation. Many of the
estimates of growth rates and ratios needed below should be
calculated using regression analysis.
Growth. You will need to calculate the historical growth
in dividends or in revenue for your firm (in order to obtain an
estimate of future growth). The method for estimating growth
is illustrated by an example of dividend growth for Firm XXX.
– the related file is provided on Blackboard (BB) by the name
of “Growth estimate sheet”.

Data Needed to Construct the Pro Formas
* Dividend data: You can attain the historical data from
https://www.dividata.com/
* An Excel spreadsheet that you use to construct your pro
formas. An excel file is provided on BB and here under the
name: CH12 (Figure 1-3) . This file “automatically” completes
the 5 years of pro formas for you; given that you have input the
data and assumptions correctly.
* 2 years of the firm’s historical financial statements,
including annual balance sheets, income and cash flow
statements (these form the basis of your pro formas). You may
also want to download 5-10 year historical data to do a better
estimate. This data may be downloaded at Mergent-
Online (available through the university library) or through the
SEC official site:
http://www.sec.gov/edgar/searchedgar/companysearch.html
NOTE: While you may want to read or skim the 10Ks for your
company, you need not construct the 10 years of financial data
from the 10Ks. Rather, using either SEC site or MergentOnline,
you are able to download the 5-10 years of financial statements
directly as a file which can be read by Excel. Should you have
difficulty, please contact me.
* Estimates of the company’s current and future (long-term
normal – gn ) sales growth (this should be completed in the
same manner that you calculate dividend growth for a company)
– you may use the Growth estimate sheet available on
Blackboard as a guide. Use the 10 years of financial
statements for the historical sales figures.
* A justification of your choice of constant or non-constant
ratios when completing the pro-formas (the base case should
usually be the constant ratio approach as discussed in the text).
* An estimate of the firm’s target capital structure (see the

guideline below about Calculating a Firm’s WACC) – note that
you need these weights both for the WACC.
* An estimate of the firm’s dividend payout policy.
* The firm’s tax rate.
Steps to Take after Completing the Pro Formas
* As mentioned above, the goal is to calculate the firm’s
value (in the end, your estimate of the stock price/share). This
requires that you calculate the firm’s FCFs (free cash flows) as
discussed in the relevant chapters in your text (CH2 and
CH12). This should be a relatively easy procedure, and should
be done on the same Excel spreadsheet as your pro-formas (see
CH12 (Figure 1-3)).
* You also need to calculate the Continuing Value (or
terminal or horizon values) as discussed in CH6 - see the related
equation (it is analogous to the constant growth part of the
supernormal growth model)! This is a crucial part of the
project, because the continuing value of the firm will typically
be the largest proportion of any firm’s current value.
* To discount the FCFs back to the “present” (to the date
of your last historical financial statements) you need to have
an estimate of the firm’s WACC(note that this includes the
weights of debt and equity, the costs of debt and equity, the
latter of which is calculated by using the CAPM, with your
estimate of the firm’s beta). Again, see the guidelines of
WACC Calculation about Calculating a Firm’s WACC, and also
review the “Four Mistakes to Avoid” (see the index to your
text).
* Once you have completed these steps, you are then ready
to follow the general steps described above to calculate your
estimate of the stock price/share.
Improving the Quality of your Project (Optional)
Other elements are left up to you, in terms of how complete
and/or creative you want your project to be. Some of these

elements must be completed in order to earn a higher than
average or satisfactory evaluation for the project. You
may/should include these other elements if you believe that they
will improve your “case” for your estimate of the price/share
for your firm. For example, a SWOT analysis is often used in
business. For this project, it may be useful, but only if you can
connect the main conclusions of the SWOT analysis to your
evaluation of the firm.
The most important extensions include:
* Using ratios that are not a constant percentage of sales
when constructing the pro formas (the basic percent of sales
method is described in the Financial Planning and Forecasting
Financial Statements chapter of the text). The relevant
procedures are either discussed in the text or are available on
spreadsheets that come with the text and/or are on the text's
homepage (listed in the syllabus). The firm’s profit margin has
a very important impact on firm value. If you use the most
recent profit margin in the pro formas, you may not be
providing an accurate longer-term picture of the firm’s
operations. As a result, it may be useful or even crucial to
analyze this ratio and/or others when constructing the pro
formas.
* Sensitivity analysis. How does your estimate of the
price/share change with changes in the firm’s WACC, the firm’s
short or long-term growth rates, changes in the firm’s profit
margin(s) and so on. The amount of work that could be done
here is almost limitless, so good projects would demonstrate
good judgment in which sensitivity analyses they conduct.
* Scenario analysis. This is similar to sensitivity analysis,
but discrete scenarios (e.g., a recession or a boom) are analyzed
instead.
* Ratio analysis. Ratios can be used as diagnostic tools in

evaluating the “health” of a firm. Note that such analysis would
typically include comparisons of your firm’s financial ratios to
the industry standards (or averages). These averages are
available on the Yahoo.finance site
under: Profile/Competitors (Sector or Industry). Ratio analysis
by itself is not very useful in terms of valuation. It provides a
diagnostic view of the company which may be helpful in terms
of analyzing the better and poorer practices of a company. In
order to make ratio analysis relevant for this project, it must be
tied directly to the firm's valuation. For example, if a
company's current Inventory Turnover is very poor, the group
can suggest that it should get better into the future, and then
make the necessary adjustments (which may require changes in
the formulas) in the pro forma sheets, to see how improving the
inventory turnover would increase the firm's value.
Advanced Elements of the Firm Valuation Project If you
attempt any of the following, you should connect the additional
analysis directly to the base case for your firm valuation
project.
* Managerial/Strategy Analysis. You may view your job of
this project as the managers of the firm. In completing the
project, you may recognize that the company is either
performing some function very well or very poorly. It is
perfectly appropriate to make suggestions for improving or
maintaining the operation of the firm.
* Marketing Analysis. Future sales typically depend upon
marketing. Projects which focus on companies for which this
may be particularly important may consider analyzing the
marketing policies of the company in order to determine how
those policies affect firm value.

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