The Validity of Company Valuation Using Dis.docx

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
�� =
��∗ 1+� 1
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
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-M
a
i-
2
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8
USD LIBOR 3m vs US Treasury 3m …
FIN 430 — Finance Theory and PracticeStock Valuation project
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 methodsto 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 Calculationabout 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.
FIN 430 — Finance Theory and PracticeProject
AssignmentsYou have been assigned a company to research
(please check the excel list for the firm you are assigned to).
During this quarter you are expected to analyze a firm’s
financial statements, stock price, WACC, and valuation.
Project 1 focuses on the financial statement analysis.
Goals for this assignment:
· Gather financial statements
· Calculate financial ratios
· Financial performance analysisProject 1: Financial Statement
Analysis
a) Collect financial statements.
Financial 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 2014, 2015, and 2016 or 2015, 2016 and 2017.)

b) Calculate the financial ratio.
Calculate the ratios listed at the end of this document from the
financial statements of your company for the most recent 3
years. To do this, you will need to make a spreadsheet, (on
Excel or other), that essentially copies certain lines of your
various financial statements onto the spreadsheet. Then, make
spreadsheet formulas to calculate each financial ratio that is
required.
c) The DuPont decomposition Analysis.
Using the ratios you calculate above to conduct the DuPont
Decomposition analysis for each of the three years for your
company. The DuPont Decomposition is composed of
ROE = NI/Equity = NI/Sales *Sales/Assets * Assets/Equity
Therefore, you should include a total of twelve calculations
(four ratios for each of the three years). You can present the
ratios in the following format.
Year
ROE
Operation Management
Asset Management
Leverage Management
NI/Equity
NI/Sales
Sales/Assets
Assets/Equity
2012
2013

2014
d) Check information of M&A located in the company’s 10k
Once you have made these calculations, read the MA&D located
in the annual report, as well as the footnotes to the various
financial statements. These are the pieces of information that
management wants you to know, (or is required to tell you!), in
addition to “the numbers.”
e) Make observations.
Write a 2 page summary in which you describe what you
observe about the financial ratios for your company (double
spaced). And you can also discuss the most interesting and
relevant changes from one year to the next from your
calculations. After reading the MD&A and footnotes, you
should have a good idea of why certain ratios and figures
changed from one year to the next. If certain changes are not
explained, try to think of reasons why the figures might have
changed. For example, did one part of an equation change in
greater proportion than another part? (i.e. did a numerator grow
much faster than a denominator?) Why might that have
occurred?
These observations will vary greatly depending upon the
company you are analyzing. Some things you may want to
consider are:
Has the company drastically increased or decreased its use
of debt?
1. Has the company’s liquidity position changed over the three
years?
1. Has ROE been rising or falling? If so, what has contributed

to this change?
1. What trends do you see developing in the data?
1. Do you see any major changes in the financial status of the
company over the time period?
The goal with this project is to not only give you a chance to
calculate the ratios that accountants and analysts frequently use
when evaluating a company, but to also make you look for
reasons, (i.e. “drivers”), for those changes and to think of your
own reasons if none are given. If you only do the calculations
but do not discuss why certain changes took place, then you
haven’t achieved the goal of the assignment. Therefore, do
your best to go past the numbers!
f) Report Submit
In the end, you will hand in: (1) your page with cogs, assets,
sales etc.,. that you copied from your financial statements, (2) a
sheet of your calculations, labeled so that I know which
calculation is which, (3) a print out of your formulas, and (4)
your 2-3 page report on those calculations. (You can print out
your Excel formulas by choosing “Tools” then “Options” then
the “View” tab, then under “Windows options” check the
“formulas” box. This might mess up the layout of your page, so
don’t try to make it look pretty. Just print out the formulas,
then uncheck the box to make your spreadsheet go back to
normal).Keep it in mind that you are expected to be a business
person in the future and your report should look professional.
Required ratio calculations, (in their simplest form), are listed
below:
A. Profitability Ratios:
1. Return on Assets (net income/total assets)
2. Return on Sales, (aka profit margin percent) (net
income/sales)
3. Assets-to-Equity (total assets/stockholder’s equity)
4. Return on Equity (net income/stockholder’s equity)
B. Efficiency Ratios:

1. Asset Turnover (sales/total assets)
2. A/R Turnover Rate (sales/accounts receivable)
3. Inventory Turnover Rate (COGS/average inventory)
4. Fixed Asset Turnover (sales/average fixed assets)
C. Leverage Ratios:
1. Debt Ratio (total liabilities/total assets)
2. Debt-to-Equity Ratio (total liabilities/stockholder’s equity)
3. Times Interest Earned (earnings before interest and
taxes/interest expense)
D. Liquidity Ratios:
1. Current Ratio (current assets/current liabilities)
2. Working Capital (current assets – current liabilities)
These ratios are explained in your textbook, so if you don’t
understand why a particular calculation is important or relevant,
you can look up more information there.
3
Updated 08/01/2007
Discounted Cash Flow
Analysis
By Ben McClure
http://www.investopedia.com/university/dcf/
Thanks very much for downloading the printable version of this
tutorial.

As always, we welcome any feedback or suggestions.
http://www.investopedia.com/contact.aspx
Table of Contents
1) DCF Analysis: Introduction
2) DCF Analysis: The Forecast Period & Forecasting Revenue
Growth
3) DCF Analysis: Forecasting Free Cash Flows
4) DCF Analysis: Calculating The Discount Rate
5) DCF Analysis: Coming Up With A Fair Value
6) DCF Analysis: Pros & Cons Of DCF
7) DCF Analysis: Conclusion
Introduction
It can be hard to understand how stock analysts come up with
"fair value" for
companies, or why their target price estimates vary so wildly.
The answer often
lies in how they use the valuation method known as discounted
cash flow (DCF).
However, you don't have to rely on the word of analysts. With
some preparation
and the right tools, you can value a company's stock yourself
using this method.
This tutorial will show you how, taking you step-by-step
through a discounted
cash flow analysis of a fictional company.
In simple terms, discounted cash flow tries to work out the
value of a company
today, based on projections of how much money it's going to

make in the future.
DCF analysis says that a company is worth all of the cash that it
could make
available to investors in the future. It is described as
"discounted" cash flow
because cash in the future is worth less than cash today. (To
learn more,
see The Essentials Of Cash Flow and Taking Stock Of
Discounted Cash Flow.)
For example, let's say someone asked you to choose between
receiving $100
today and receiving $100 in a year. Chances are you would take
the money
today, knowing that you could invest that $100 now and have
more than $100 in
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Investopedia.com – Your Source For Investing Education.

a year's time. If you turn that thinking on its head, you are
saying that the amount
that you'd have in one year is worth $100 dollars today - or the
discounted value
is $100. Make the same calculation for all the cash you expect a
company to
produce in the future and you have a good measure of the
company's value.
There are several tried and true approaches to discounted cash
flow analysis,
including the dividend discount model (DDM) approach and the
cash flow to firm
approach. In this tutorial, we will use the free cash flow to
equity approach
commonly used by Wall Street analysts to determine the "fair
value" of
companies.
As an investor, you have a lot to gain from mastering DCF
analysis. For starters,
it can serve as a reality check to the fair value prices found in
brokers' reports.
DCF analysis requires you to think through the factors that
affect a company,
such as future sales growth and profit margins. It also makes
you consider the
discount rate, which depends on a risk-free interest rate, the
company's costs of
capital and the risk its stock faces. All of this will give you an
appreciation for
what drives share value, and that means you can put a more
realistic price tag on
the company's stock.

To demonstrate how this valuation method works, this tutorial
will take you step-
by-step through a DCF analysis of a fictional company called
The Widget
Company. Let's begin by looking at how to determine the
forecast period for your
analysis and how to forecast revenue growth.
The Forecast Period & Forecasting Revenue Growth
The Forecast Period
The first order of business when doing discounted cash flow
(DCF) analysis is to
determine how far out into the future we should project cash
flows.
For the purposes of our example, we'll assume that The Widget
Company is
growing faster than the gross domestic product (GDP)
expansion of the
economy. During this "excessive return" period, The Widget
Company will be
able to earn returns on new investments that are greater than its
cost of capital.
So, our discounted cash flow needs to forecast the amount of
free cash flow that
the company will produce for this period.
The excess return period tells us how far into the future we
should forecast the
company's cash flows. Alas, it's impossible to say exactly how
long this period of
excess returns will last. The best we can do is make an educated
guess based

on the company's competitive and market position. Sooner or
later, all companies
settle into maturity and slower growth. (The common practice
with DCF analysis
is to make the excess return period the forecast period. But it is
important to note
This tutorial can be found at:
http://www.investopedia.com/university/dcf/default.asp
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that this valuation method does not restrict your analysis to only
excess return
periods - you could estimate the value of a company growing
slower than the
economy using DCF analysis too.)
The table below shows good guidelines to use when determining
a company's

excess return period/forecast period:
Company Competitive
Position
Excess
Return/Forecast
Period
Slow-growing company;
operates in highly
competitive, low margin
industry
1 year
Solid company; operates with
advantage such as strong
marketing channels,
recognizable brand name, or
regulatory advantage
5 years
Outstanding growth
company; operates with very
high barriers to entry,
dominant market position or
prospects
10 years
Figure 1
How far in the future should we forecast The Widget Company's
cash flows?

Let's assume that the company is keeping itself busy meeting
the demand for its
widgets. Thanks to strong marketing channels and upgraded,
efficient factories,
the company has a reasonable competitive position. There is
enough demand for
widgets to maintain five years of strong growth, but after that
the market will be
saturated as new competitors enter the market. So, we will
project cash flows for
the next five years of business.
Revenue Growth Rate
We have decided that we want to estimate the free cash flow
that The Widget
Company will produce over the next five years. To arrive at this
figure, the
standard procedure is to forecast revenue growth over that time
period. Then (as
we will see in later chapters), by breaking down after-tax
operating profits,
estimated capital expenditure and working capital needs, we can
estimate the
cash flow the company will produce.
Let's start with top line growth. Forecasting a company's
revenues is arguably the
most important assumption one can make about its future cash
flows. It can also
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be the most difficult assumption to make. (For more on
forecasting sales, see
Great Expectations: Forecasting Sales Growth.)
We need to think carefully about what the industry and the
company could look
like as they evolve in the future. When forecasting revenue
growth, we need to
consider a wide variety of factors. These include whether the
company's market
is expanding or contracting, and how its market share is
performing. We also
need to consider whether there are any new products driving
sales or whether
pricing changes are imminent. But because that future can never
be certain, it is
valuable to consider more than one possible outcome for the
company.
First, the upbeat revenue growth scenario: The Widget Company
has grown
revenues at 20% for the past two years, and your careful market
research

suggests that demand for widgets will not let up any time soon.
Management -
always optimistic - argues that the company will keep growing
at 20%.
That being said, there may be reasons to downplay revenue
growth
expectations. While the company's revenue growth will stay
strong in the first few
years, it could slow to a lower rate by Year 5 as a result of
increasing
international competition and industry commoditization. We
should err on the
side of caution and conservatism and assume that The Widget
Company's top
line growth rate profile will commence at 20% for the first two
years, then drop to
15% for the next two years and finally drop to 10% in Year 5.
Posting $100
million of revenue in its latest annual report, the company is
projected to grow its
revenues to $209.5 million at the end of five years (based on
realistic, rather than
optimistic, growth expectations).
Forecast Revenue Growth Profiles
Current Year Year 1 Year 2 Year 3 Year 4 Year 5
Optimistic:
Growth Rate
Revenue
-

$100 M
20%
$120 M
20%
$144 M
20%
$172.8 M
20%
$207.4 M
20%
$248.9 M
Realistic:
Growth Rate
Revenue
-
$100 M

20%
$120 M
20%
$144 M
15%
$165.6 M
15%
$190.4 M
10%
$209.5 M
Figure 2
Now that we've determined our forecast period and our revenue
growth for that
period, we can move on to the next step in our analysis, where
we will estimate
the free cash flow produced over the forecast period.

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Forecasting Free Cash Flows
Now that we have determined revenue growth for our forecast
period of five
years, we want to estimate the free cash flow produced over the
forecast period.
Free cash flow is the cash that flows through a company in the
course of a
quarter or a year once all cash expenses have been taken out.
Free cash flow
represents the actual amount of cash that a company has left
from its operations
that could be used to pursue opportunities that enhance
shareholder value - for
example, developing new products, paying dividends to
investors or doing share
buybacks. (To learn more, see Free Cash Flow: Free, But Not
Always Easy.)

Calculating Free Cash Flow
We work out free cash flow by looking at what's left over from
revenues after
deducting operating costs, taxes, net investment and the
working capital
requirements (see Figure 1). Depreciation and amortization are
not included
since they are non-cash charges. (For more information, see
Understanding The
Income Statement.)
Figure 1 - How free cash flow is calculated
In the previous chapter, we forecasted The Widget Company's
revenues over the
next five years. Here we show you how to project the other
items in our
calculation over that period.
Future Operating Costs
When doing business, a company incurs expenses - such as
salaries, cost of
goods sold (CoGS), selling and general administrative expenses
(SGA), and
research and development (R&D). These are the company's
operating costs. If
current operating costs are not explicitly stated on a company's
income
statement, you can calculate them by subtracting net operating
profits -
or earnings before interest and taxation (EBIT) - from total
revenues.

A good place to start when forecasting operating costs is to look
at the
company's historic operating cost margins. The operating
margin is operating
costs expressed as a proportion of revenues.
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For three years running, The Widget Company has generated an
average
operating cost margin of 70%. In other words, for every $1 of
revenue, the
company incurs $0.70 in operating costs. Management says that
its cost cutting
program will push those margins down to 60% of revenues over
the next five
years.
However, as analysts and investors, we should be concerned
that competing
widget factories might be built, thus squeezing The Widget
Company's
profitability. Therefore, as we did when forecasting revenues,
we will err on the
side of conservatism and assume that operating costs will show
an increase as a
percentage of revenues as the company is forced to lower its
prices to stay
competitive over time. Let's say operating costs will hold at
65% of revenues over
the first three projected years, but will increase to 70% in Year
4 and Year 5 (see
Figure 2).
Taxation
Many companies do not actually pay the official corporate tax
rate on their
operating profits. For instance, companies with high capital
expenditures receive
tax breaks. So, it makes sense to calculate the tax rate by taking
the average
annual income tax paid over the past few years divided by
profits before income

tax. This information is available on the company's historic
income statements.
Let's assume that for each of the past three years, The Widget
Company paid
30% income tax. We will project that the company will continue
to pay that 30%
tax rate over the next five years (see Figure 2).
Net Investment
To underpin growth, companies need to keep investing in
capital items such as
property, plants and equipment. You can calculate net
investment by taking
capital expenditure, disclosed in a company's statement of cash
flows, and
subtracting non-cash depreciation charges, found on the income
statement.
Let's say The Widget Company spent $10 million last year on
capital
expenditures, with depreciation of $3 million, giving net
investment of $7 million,
or 7% of total revenues (see Figure 2). But in the two prior
years, the company's
net investment was much higher: 10% of revenues.
If competition does intensify in the widget industry, The Widget
Company will
almost certainly have to boost capital investment to stay ahead.
So, we will
assume that net investment will steadily return to its normal
level of 10% of sales
over the next five years, as seen in Figure 2: 7.6% of sales in
Year 1, 8.2% in
Year 2, 8.8% in Year 3, 9.4% in Year 4 and 10% in Year 5.

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Figure 2 - Forecasting The Widget Company's operating costs,
taxes,
net investment and change in working capital over the five-year
forecast
period
Change in Working Capital
Working capital refers to the cash a business requires for day-
to-day operations,
or, more specifically, short-term financing to maintain current
assets such as
inventory. The faster a business expands, the more cash it will
need for working
capital and investment.
Working capital is calculated as current assets minus current

liabilities. These
items are found on the company's balance sheet, published in its
quarterly and
annual financial statements. At year end, The Widget
Company's balance sheet
showed current assets of $25 million and current liabilities of
$16 million, giving
net working capital of $9 million.
Net change in working capital is the difference in working
capital levels from one
year to the next. When more cash is tied up in working capital
than the previous
year, the increase in working capital is treated as a cost against
free cash flow.
Working capital typically increases as sales revenues grow, so a
bigger
investment of inventory and receivables will be needed to match
The Widget
Company's revenue growth. In our forecast, we will assume that
changes in
working capital are proportional to revenue growth. In other
words, if revenues
grow by 20% in the first year, working capital requirements will
grow by 20% in
the first year, from $9 million to $10.8 million (see Figure 2).
Meanwhile, we will
keep a close watch for any signs of a changing trend.
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Figure 3 - Free cash flow forecast calculation for The Widget
Company
As you can see in Figure 3, we've determined our estimated free
cash flow for
our forecast period. Now we are one step closer to finding a
value for the
company. In the next section of the tutorial, we will estimate
the value at which
we will discount the free cash flows.
Calculating The Discount Rate
Having projected the company's free cash flow for the next five
years, we want to
figure out what these cash flows are worth today. That means
coming up with an
appropriate discount rate which we can use to calculate the net
present value
(NPV) of the cash flows.
So, how do we figure out the company's discount rate? That's a

crucial question,
because a difference of just one or two percentage points in the
cost of capital
can make a big difference in a company's fair value.
A wide variety of methods can be used to determine discount
rates, but in most
cases, these calculations resemble art more than science. Still, it
is better to be
generally correct than precisely incorrect, so it is worth your
while to use a
rigorous method to estimate the discount rate.
A good strategy is to apply the concepts of the weighted
average cost of capital
(WACC). The WACC is essentially a blend of the cost of equity
and the after-tax
cost of debt. (For more information, see Investors Need A Good
WACC.)
Therefore, we need to look at how cost of equity and cost of
debt are calculated.
Cost of Equity
Unlike debt, which the company must pay at a set rate of
interest, equity does
not have a concrete price that the company must pay. But that
doesn't mean that
there is no cost of equity. Equity shareholders expect to obtain a
certain return on
their equity investment in a company. From the company's
perspective, the
equity holders' required rate of return is a cost, because if the
company does not
deliver this expected return, shareholders will simply sell their
shares, causing
the price to drop.

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Therefore, the cost of equity is basically what it costs the
company to maintain a
share price that is satisfactory (at least in theory) to investors.
The most
commonly accepted method for calculating cost of equity comes
from the Nobel
Prize-winning capital asset pricing model (CAPM), where: Cost
of Equity (Re) =
Rf + Beta (Rm-Rf).

Let's explain what the elements of this formula are:
Rf - Risk-Free Rate - This is the amount obtained from
investing in securities
considered free from credit risk, such as government bonds from
developed
countries. The interest rate of U.S. Treasury bills or the long-
term bond rate is
frequently used as a proxy for the risk-free rate.
ß - Beta - This measures how much a company's share price
moves against the
market as a whole. A beta of one, for instance, indicates that the
company
moves in line with the market. If the beta is in excess of one,
the share is
exaggerating the market's movements; less than one means the
share is more
stable. Occasionally, a company may have a negative beta (e.g.
a gold mining
company), which means the share price moves in the opposite
direction to the
broader market. (To learn more, see Beta: Know The Risk.)
(Rm – Rf) = Equity Market Risk Premium - The equity market
risk premium
(EMRP) represents the returns investors expect, over and above
the risk-free
rate, to compensate them for taking extra risk by investing in
the stock market. In
other words, it is the difference between the risk-free rate and
the market rate. It
is a highly contentious figure. Many commentators argue that it
has gone up due
to the notion that holding shares has become riskier.

Barra and Ibbotson are valuable subscription services that offer
up-to-date equity
market risk premium rates and betas for public companies.
Once the cost of equity is calculated, adjustments can be made
to take account
of risk factors specific to the company, which may increase or
decrease the risk
profile of the company. Such factors include the size of the
company, pending
lawsuits, concentration of customer base and dependence on key
employees.
Adjustments are entirely a matter of investor judgment and they
vary from
company to company.
Cost of Debt
Compared to cost of equity, cost of debt is fairly
straightforward to calculate. The
rate applied to determine the cost of debt (Rd) should be the
current market rate
the company is paying on its debt. If the company is not paying
market rates, an
appropriate market rate payable by the company should be
estimated.
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As companies benefit from the tax deductions available on
interest paid, the net
cost of the debt is actually the interest paid less the tax savings
resulting from the
tax-deductible interest payment. Therefore, the after-tax cost of
debt is Rd (1 -
corporate tax rate).
Finally, Capital Structure
The WACC is the weighted average of the cost of equity and the
cost of debt
based on the proportion of debt and equity in the company's
capital structure.
The proportion of debt is represented by D/V, a ratio comparing
the company's
debt to the company's total value (equity + debt). The
proportion of equity is
represented by E/V, a ratio comparing the company's equity to
the company's
total value (equity + debt). The WACC is represented by the

following formula:
WACC = Re x E/V + Rd x (1 - corporate tax rate) x D/V.
A company's WACC is a function of the mix between debt and
equity and the
cost of that debt and equity. On the one hand, in the past few
years, falling
interest rates have reduced the WACC of companies. On the
other hand,
corporate disasters like those at Enron and WorldCom have
increased the
perceived risk of equity investments.
Be warned: the WACC formula seems easier to calculate than it
really is. Rarely
will two people derive the same WACC, and even if two people
do reach the
same WACC, all the other applied judgments and valuation
methods will likely
ensure that each has a different opinion regarding the
components that comprise
the company's value.
Widget Company WACC
Returning to our example, let's suppose The Widget Company
has a capital
structure of 40% debt and 60% equity, with a tax rate of 30%.
The risk-free rate
(RF) is 5%, the beta is 1.3 and the risk premium (RP) is 8%.
The WACC comes
to 10.64%. So, rounded up to the nearest percentage, the
discount rate for The
Widget Company would be 11% (see Figure 1).
WACC for The Widget Company

Cost of Debt Cost of Equity
0.40 [Rd x (1-.30)] +
0.40 [5.0 x 0.7)] +
0.40 [3.5] +
1.40 +
0.60 [RF + b(RP)]
0.60 [5.0 + 1.3(8)]
0.60 [15.4]
9.24
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WACC
Rounded WACC
10.64%
11%
Figure 1
In the next section of the tutorial, we'll do the final calculations
to generate a fair
value for The Widget Company.
Coming Up With A Fair Value
Now that we have calculated the discount rate for the Widget
Company, it's time
to do the final calculations to generate a fair value for the
company's equity.
Calculate the Terminal Value
Having estimated the free cash flow produced over the forecast
period, we need
to come up with a reasonable idea of the value of the company's
cash flows after
that period - when the company has settled into middle-age and
maturity.
Remember, if we didn't include the value of long-term future
cash flows, we
would have to assume that the company stopped operating at the

end of the five-
year projection period.
The trouble is that it gets more difficult to forecast cash flows
over time. It's hard
enough to forecast cash flows over just five years, never mind
over the entire
future life of a company. To make the task a little easier, we use
a "terminal
value" approach that involves making some assumptions about
long-term cash
flow growth.
Gordon Growth Model
There are several ways to estimate a terminal value of cash
flows, but one well-
worn method is to value the company as a perpetuity using the
Gordon Growth
Model. The model uses this formula:
Terminal Value = Final Projected Year Cash Flow X (1+Long-
Term Cash Flow Growth Rate)
(Discount Rate – Long-Term Cash
Flow Growth Rate)
The formula simplifies the practical problem of projecting cash
flows far into the
future. But keep in mind that the formula rests on the big
assumption that the
cash flow of the last projected year will stabilize and continue
at the same rate
forever. This is an average of the growth rates, not one expected
to occur every
year into perpetuity. Some growth will be higher or lower, but

the expectation is
that future growth will average the long-term growth
assumption.
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Returning to the Widget Company, let's assume that the
company's cash flows
will grow in perpetuity by 4% per year. At first glance, 4%
growth rate may seem
low. But seen another way, 4% growth represents roughly
double the 2% long-
term rate of the U.S. economy into eternity.

In the section on "Forecasting Free Cash Flows", we forecast
free cash flow of
$21.3 million for Year 5, the final or "terminal" year in our
Widget Company
projections. You will also recall that we calculated The Widget
Company's
discount rate as 11% (see "Calculating The Discount Rate"). We
can now
calculate the terminal value of the company using the Gordon
Growth Model:
Widget Company Terminal Value = $21.3M X 1.04/ (11% - 4%)
=
$316.9M
Exit Multiple Model
Another way to determine a terminal value of cash flows is to
use a multiplier of
some income or cash flow measure, such as net income, net
operating profit,
EBITDA (earnings before interest, taxes, depreciation, and
amortization),
operating cash flow or free cash flow. The multiple is generally
determined by
looking at how comparable companies are valued by the market.
Was there a
recent sale of stock of a similar company? What is the standard
industry
valuation for a company at the same stage of maturity?
In Year 5, the Widget Company is expected to produce free cash
flow of $21.3M.
Multiplying this by a projected price-to-free cash flow of 15
gives us a terminal
value of $319.9M.

Widget Company Terminal Value = $21.3M X 15 =
$319.9M
You will see that the terminal value can contribute a great deal
to total value, so it
is important to use an exit multiple that can be justified. One
way to make the
multiple more believable is to give estimates on the
conservative side. Justifying
a multiple of 15 with your figures would certainly be easier to
justify than one at
20 or 25. Because it can be tricky to justify the multiple, this
method isn't used as
much as the Gordon Growth Model.
Calculating Total Enterprise Value
Now you have the following free cash flow projection for the
Widget Company.
Forecast
Period Year 1 Year 2 Year 3 Year 4 Year 5
Terminal Value (Gordon
Growth Model)
Free Cash $18.5M $21.3M $24.1M $19.9M $21.3M $316.9M
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Flow
Figure 1
To arrive at a total company value, or enterprise value (EV), we
simply have to
take the present value of the cash flows, divide them by the
Widget Company's
11% discount rate and, finally, add up the results.
EV = ($18.5M/1.11) + ($21.3M/(1.11)2) + ($24.1M/(1.11)3) +
($19.9M/(1.11)4) + ($21.3M/(1.11)5) +
($316.9M/(1.11)5)
EV = $265.3M
Therefore, the total enterprise value for The Widget Company is
$265.3 million.
Calculating the Fair Value of Equity
But we are not finished yet - we cannot forget about debt. The
Widget Company's
$265.3M enterprise value includes the company's debt. As

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