Introduction to Valuation and Discounted Cash Flow Methods
Keith Vorkink1 and Kristin Workman
Brigham Young University
This document provides an introduction into discounted cash flow valuation. Our first note
provides an introduction into valuation concepts and methods. The second note provides
detailed instructions of how to download financial statements from the SEC’s Edgar website into
Excel spreadsheets using web query functionality. In the third note, we provide instructions for
constructing pro forma forecasts of financial statements using sound economic reasoning and
accounting consistency. In the fourth and last note, we then provide instruction as to
constructing measures of intrinsic value based on free cash flow to equity methods. We motivate
free cash flow to equity valuation from simple dividend discount models.
1
Contact author. Address: 667 TNRB, Marriott School, Brigham Young University, Provo, UT 84602; email:
keith_vorkink@byu.edu; phone: 801.422.1765
Introduction to Valuation and Discounted Cash Flow Methods
Abstract:
This document provides an introduction into discounted cash flow valuation. Our first note
provides an introduction into valuation concepts and methods. The second note provides
detailed instructions of how to download financial statements from the SEC’s Edgar website into
Excel spreadsheets using web query functionality. In the third note, we provide instructions for
constructing pro forma forecasts of financial statements using sound economic reasoning and
accounting consistency. In the fourth and last note, we then provide instruction as to
constructing measures of intrinsic value based on free cash flow to equity methods. We motivate
free cash flow to equity valuation from simple dividend discount models.
Teaching Note One: An Introduction To Fundamental Analysis
The core of the efficient market hypothesis (EMH) is the notion that the value of
needed information about any publicly traded stock is reflected in the stock’s price. The point is
that the presence or lack there of, of information within a market will determine how efficient the
market is. According to this notion, as new information is released into the market either by
outside investors or by internal managers, all new information will be valued by market
participants and will be reflected in the security’s price. To illustrate this point, assume
information becomes available that indicates that Wal-Mart’s stock is actually worth $10 more
than the current selling price. Investors without holdings of Wal-Mart would be willing to pay
more than its current price for the stock—up to $10 more. However, investors with holdings of
Wal-Mart would be unwilling to sell at the current price. As a result the value of Wal-Mart
would be bid up to a price of $10. Economically speaking, we would see a transition from one
supply and demand equilibrium at the current price to the supply and demand equilibrium of the
new price.
Intro to Valuation: 1
Assuming the EMH holds true in all cases, is there any incentive that would encourage
analysts to gather information or to research the value of various stocks? Strictly speaking, there
would not be; however, evidence suggests that inefficiencies do exist within financial markets.
In direct evidence of this fact includes the point that there are so many money managers that still
exist—if they could not add value in some way (earning an extra return) they would have been
driven out of business long ago. Also, there is an investing paradox that leads some to believe
that inefficiencies do exist. The point here is that financial markets are only efficient if there are
people out there who are actively making them efficient. In essence, the markets become
efficient when people continue to dig up more information or more inefficiencies.
With these thoughts in mind, it is important to note that opinions of analysts and investors
concerning the EMH vary widely. In fact three versions of the EMH exist. The first, the weakform EMH, states that stock prices already reflect all information that can be derived by
examining market trading data such as the history of past prices, trading volume, or short
interest. In summary, the weak-form EMH price will reflect only information embedded in the
history of the stock prices and volume. The semistrong-form EMH asserts that all “publicly
available information”—i.e. information made available to the public through annual reports or
through general announcements made by the company through the media—regarding the
prospects of a firm must be already reflected in the stock price. This differs from the weak-form
EMH price in that future performance is considered when valuing the stock. Lastly, the strongform EMH stock price will reflect al information relevant o the firm, even including information
available only to company insiders. This form of EMH is quite extreme. It is also important to
note here that the information timing has an effect on what form the market takes. If information
is made available after an event has already occurred, that information will obviously add no
value and a weak-form EMH will exist. However, if information is released to the general public
Intro to Valuation: 2
that would lend light to any future performance or events, a market would display a semistrongform EMH.
One can see that true market form is still an active debate among analysts. Generally,
markets display some sort of weak-form of EMH rewarding those who widely invest time and
money to become profitable by digging up those small pockets of inefficiency. In summary, if
we assume markets are at least weak-form efficient investors have an incentive to spend time and
resources to analyze and uncover new information only if such activity is likely to generate
higher investment returns.
As the portfolio manager of a large fund or as the manager of your
own portfolio, you will want to develop some type of valuation skills because they may lead the
possibility of higher investment returns. Even if you can not trade any better, you will at least
understand markets better.
One valuation technique, fundamental analysis, uses earnings and dividends prospects
of the firm, expectations of future interest rates, and risk evaluation of the firm to determine
proper stock prices. Essentially, this method involves an investor’s attempt to determine the
present discounted value of all future payments that he or she may receive as holder of that stock.
We define this as the intrinsic value as it is the value of the stock to the one doing the valuation,
which may or may not be the same for all investors. If this value exceeds the current stock price,
the user of fundamental analysis would recommend purchasing the stock. Remember that
because of the EMH, fundamental analysis may or may not add value to a portfolio. Also, there
are some underlying assumptions which play a part in this type of analysis. These assumptions
are as follows: 1) the relationship between value and the underlying financial factors can be
measured, 2) the relationship is stable over time, and 3) deviations from the relationship are
corrected in a reasonable time period. The trick to fundamental analysis is to identify firms that
are better than the rest of the market believes.
Intro to Valuation: 3
Fundamental analysis usually begins with a review of the stock’s past earnings and an
examination of the company’s historical financial statements. For an example, review the
historical financial statements for Wal-Mart Inc. listed in exhibits 1 through 3 of the appendix to
this teaching note. This initial step is important in forecasting future cash flows that may come
to the investor if he or she chooses to hold the stock. Forecasting of future payments is the basis
of one’s own intrinsic value. As an analyst, one must obtain the financial statements of the
company being evaluated from a reputable source and must be able to manipulate the
information using a variety of fundamental analysis models. This generally requires some excel
and internet skills. These skills will be developed later in this note.
Following this objective but historical review, an analyst will supplement his or her
findings with a somewhat more subjective review of other economic factors such as the quality
of the firm’s management, the firm’s standing within its industry, and the prospects of the
industry as a whole. These factors can be determined through review of the notes to the financial
statements in the company’s annual reports. A firm will often state up-and-coming projects, new
investments, and changes to future firm structure in an attempt to attract new investors. All of
these factors will have an effect on future cash inflows and outflows, which will affect the value
of the firm. As an analyst, you will want to point out these special circumstances as supporting
arguments for your calculation of intrinsic value. However, you must also remember that
management is more willing to discuss potential successful activities, rather than potential
problems for the company. In this case, a successful analyst will only value these prospects as
compared to the prospects of other competitors. This leads to the value of an industry report as
part of an overall fundamental analysis. Although no standard for this report exists, one simple
way in which to complete it is to compare the strengths and weaknesses that the industry faces as
a whole. Also, opportunities and threats that may impact the future would be important to note.
Intro to Valuation: 4
In summary, “the basic premise surrounding fundamental analysis, “is that the true value
of the firm can be related to its financial characteristics—its growth prospects, risk profile, and
cash flows” (Damadoran, 2002). Generally if the current stock price of the firm differs from that
of its “true value,” one would assume that the stock is either under or overvalued. Types of
fundamental analysis include discounted cash flows models, or some sort of earnings ratios, such
as price-earnings and price-book value ratios.
Intro to Valuation: 5
Teaching Note Two: Downloading the Data
This teaching note will suggest steps for obtaining and converting financial statements to
a specific user-friendly format. As many company websites’ provide simplified, or scaled down,
financial statements designed to appeal to their respective investing audiences, it is suggested
that more detailed financial statements be downloaded from the SEC’s website. Downloading
data from the SEC website can be complicated, so specific steps are provided below to facilitate
the gathering of data for your fundamental analysis project:
1. Go to www.sec.gov.
2. Under the fillings and forms section, click on the “Search for Company Fillings” link.
3. This will take you to the EDGAR database. Click on the “Companies and Other Filers”
link.
4. On the next page, type in the name of the company exactly as it is registered with the
SEC. For example, if your company is SanDisk Corporation but you are unsure of
whether the name is spelled “SanDisk,” or “San Disk” you could try both spellings or
simply search under “san” and browse through the hundreds of results shown in
alphabetical order that start with “san” to find the SanDisk entry. For this example enter
“Wal Mart”.
5. From the search results page click on the link to the left of company name you want to
analyze. For this example click on the link to the left of Wal Mart Stores Inc. If you
typed the name of the company exactly then you can skip step five.
6. After clicking on the company’s link you will see a list of fillings that the company has
made with the SEC. In order to refine your search to just the annual reports, type 10-K
into the search box entitled “Form Type” at the upper right-hand corner of the page, and
then click on the “Retrieve Fillings” button.
7. A list of 10-K, 10-K/A, or 10-K405 fillings should be shown as displayed in the figure
below. Select the report for the period you are evaluating. If your company’s fiscal year
ends in December then the fillings you want will be dated somewhere around February to
May of the year following the reported date (companies are given approximately 3
months after the close of their fiscal year to report information to the SEC). If multiple
Intro to Valuation: 6
reports are listed for that period, select the one that is dated the latest—this report will
usually be labeled as a 10-K/A, as it is an amendment to the original annual report.
Amended 10-K filing
Normal 10-K filing
8. Once you have selected a time period, you will be see a page in text form which contains
links to different forms filed with the SEC. See the 2004 example below for Wal Mart:
Example First and Second
Link
Example 10-K document html text page
Click on the first link and then use the find function (ctrl F) to search for ”consolidated
Intro to Valuation: 7
balance sheet” to see if the financial statements are contained on that page. (The financial
statement information is normally found under the Item 8 heading after clicking on the first
link.) If not, go back to the text page and try this step with the next link. An example
consolidated financial statement is shown in the following figure for Wal Mart 2004 10-K/A,
which is found in the seventh link, entitled “Document 7 - file: dex13.htm”.2
Wal Mart’s Example Consolidated Financial Statement
9. Once you have found the appropriate link and within that document the consolidated
balance sheet highlight the URL and place it in your clipboard by clicking Ctrl-C. You
will paste this URL into the WebQuery in Excel in step 13.
10. The next step involves downloading the financial information into an Excel file. This
step may vary depending on how current your filing is. Recent reports will copy easily
into an Excel format—this is a result of the SEC’s efforts to make companies easier to
compare one with another. Older reports may have been constructed as a text-only
document. In Wal Mart’s case the files are available in non-text versions. The following
steps won’t work with the older text-only format.
11. Open a new Excel workbook. On Sheet 1 type “Consolidated Balance Sheet” in row 1 as
indicated in the figure below.
2
Note that some companies only reference their annual reports (available via their website) for Item 8 rather than
provide the consolidated financial information.
Intro to Valuation: 8
12. In Excel place your cursor in the cell A3 of worksheet 1 (the “Consolidated Balance
Sheet” title should be somewhere in row 1 above this cell). Then click on the Data pulldown menu and select “Import External Data” and then select “New Web Query”.
13. A New Web Query window should open with your default home page shown. Click in
the URL Address line of this new window and delete the reference to your homepage.
Then click Ctrl-V to paste the URL from step 9 into this box. Click the Go button to the
right of the address line. You can expand the window size by clicking in the bottom right
corner of the new window and dragging the window down and to the right.
14. Navigate within the New Web Query window to the place where you can see the
consolidated balance sheet numbers (same place you saw in your browser for step 9).
You should see a little yellow arrow to the upper left side of the balance sheet. Click the
yellow arrow and it will turn green (you have selected this table to import). Then click
the “Options” button in the upper right corner of the new window and make sure that the
Intro to Valuation: 9
Full Html Formatting box is checked (leave the other boxes as they are.) A Wal Mart
example is shown below:
15. Click the Import button. Cell A3 should be preselected in the Import Data dialog box
that appears after you click the Import button. Click OK. The table of data should now
appear in your excel spreadsheet. The Wal Mart example is shown below.
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16. Place your cursor in the next unchanged column on row 3. In the example above this
would be I3. Then repeat steps 7-15 for different 10-K years to obtain consolidated
balance sheet information for earlier years (note that each time you should select an older
10-K document to provide earlier years’ information). You will have duplicated
columns but in the end you should have information that spans 5 years.
17. Delete the duplicated columns and clean up the spreadsheet until you are left with only
one set of row names on the left and each year’s information appears in only one column.
This may require the adding of rows to the most recent reporting of the balance sheet
(column A in Figure below) to accommodate entries in previous balance sheets that do
not show up on the most recent version. The figure below shows how the Excel
spreadsheet will look before deleting duplicate columns after downloading the
consolidated balance sheets for Wal Mart from the 2004 10-K/A and 2003 10-K filings.
You may notice that the formatting of the balance sheet may change from year to year as
note in the figure below.
In addition, you should look for differences in the entries of a given year’s
balance sheet across the different year’s reports. For example, Wal Mart reports 2003
balance sheet items in both the 2004 10-K/A and 2003 10-K filings as noted below in
columns G and K of the Figure respectively. The most recent production of these items
is generally assumed to be the most correct; noting any discrepancies can help inform you
as to any restatements or changes that could potentially influence a valuation or
investment decision. Repeat these steps for to obtain a sequence of five years of balance
sheets or the desired history.
Intro to Valuation: 11
Check for compatibility
Compare
18. After finishing with the balance sheets you will repeat the above steps to obtain five years
worth of income statements. Be sure to place the income statement information on
Sheet2. (IE be sure to type “Consolidate Income Statements” in row one of Sheet2 and
place your cursor in A3 of Sheet2 when doing the first web query for income statements.
19. Do the same steps in Sheet3 to obtain five years of the “statement of cash flows” .
20. When you are done should have a five year comparative balance sheet on worksheet one,
a five year comparative income statement on worksheet two, and a five year comparative
statement of cash flows on worksheet three.
21. The last step in this process is to continue cleaning up in order to make the report look
professional. Fix column widths in order to fit information. Bold or capitalize titles in
order to make them stand out. Insert “0” into categories for which no data exists.
Remember that your report will tell a lot about you and your professionalism. A great
report can be used in job interviews or in other professional settings as an example of
your analytical skills.
Intro to Valuation: 12
Teaching Note Three: Forecasting Financial Statements
Because fundamental analysis is based on expectations of future cash flows, it is
important to develop a good set of forecasting skills. Successful pro forma analysis requires
both objective and subjective forecasting skills. Forecasting techniques will range from basic
methods such as percent of sales to more complex methods such as sensitivity analysis,
regression, and simulation techniques. Some forecasting techniques will rely more on current
trends rather than the methods above, which primarily rely on historical data. To illustrate this
point, assume Wal Mart doubled sales two years ago and tripled sales last year. However, Wal
Mart’s long-run sales’ growth trend averages about a 12 percent each year. Given these two sets
of information, which method would be most acceptable to forecast next year’s sales? Would
that same method accurately represent a sales forecast for five years into the future? Hence, the
most suitable forecasting method will be influenced not only by past events, but also present
circumstances, future plans, and the horizon over which we are forecasting. In addition, sales
trends of competitors, macroeconomic conditions, and a host of other circumstances can have an
impact on future sales growth.
One must be open to a number of different forecasting techniques and one must apply
these techniques as circumstances dictate. While there is no single correct method, we propose
the following steps to follow when constructing a forecast: Step 1: Construct historical averages,
Step 2: Adjust for macroeconomic factors, Step 3: Adjust for industry factors, and Step 4: Adjust
for company specific factors. As one makes adjustments to their historical averages (Steps 2 –
4), we suggest two tenets to guide these adjustments to your financial projections: economic
plausibility—the projected statements must reflect how the firm might realistically be expected
to operate in the future given current information about the firm, its industry, and the economy as
a whole—and accounting consistency—projections must satisfy basic accounting rules i.e., the
Intro to Valuation: 13
balance sheet must balance (Daves, Ernhardt, Shrieves, 2004). With this in mind, this note will
discuss financial statement forecasting with an emphasis on valuation.
Forecasting Sales Growth
The first and possibly most important step in preparing pro forma financial statements is
to accurately project future sales growth as it will have a direct impact on the forecasts of most
other balance sheet and income statement accounts. This principle is demonstrated in Figure
One—the sales forecast will drive forecasted figures for capital expenditures, working capital
needs, and net income. Figure One indicates that with a forecast for sales in hand, various
methods can be used to forecast other items including: percent of sales, ratio analysis, and
regression. The following quote from Daves, Ehrhardt, Shrieves, (2004), indicates that Step 1
must be followed with Steps 2 – 4 to create informative sales forecasts, “As an analyst, you
should use the recent historical sales growth rates, your knowledge about the company and its
industry, and expectations about inflation to guide you.”
Figure One: Pro Forma Map of Activities
Intro to Valuation: 14
Step 1: Historical Average
In most cases, sales growth can be reasonably forecasted using an average growth rate for
the company over the last 3 to 5 years. For example, Wal Mart grew 15.95 percent in 2001, and
then dropped to 6.63 percent in 2002. The following years Wal Mart grew at 12.55 percent in
2003 and 11.63 percent in 2004 (see appendix Table 1: Wal Mart corporation Financial
Statements). From a historical average, 11.69 percent is a reasonable starting point estimate for
the company’s sales growth for 2005. Implicit in our forecast is the assumption that the last 3 to
5 years sales growth reflects potential or future economic conditions. In turn, this growth rate
could be used to forecast sales growth for 3 to 5 years in the future as long as the same
assumption is made and defendable; however, this assumption must also reflect all available
knowledge about future conditions.
One should be wary of outliers in the historical data; if the historical information contains
a year in which sales seemed to be inconsistent with past and/or future performance, then this
particular year should be disregarded when calculating a historical growth rate. In the end, you
should feel comfortable defending whatever spans of history you use to construct your forecast.
Again, an average sales growth rate can be used as a starting point, but other information is
likely to drive a final estimate to vary from this starting point.
Step 2: Macroeconomic Adjustments
With a historical sales growth estimate in hand, we now move to the more difficult, and
relevant, steps. A number of macroeconomic issues can have an impact on the prospects of sales
for a company going forward. For example, one question to ask in evaluating future forecasts
would be will inflation affect sales growth? Modifications can be made to the forecasted sales
growth figure (in our ABC example, the average growth rate) if information exists that suggests,
Intro to Valuation: 15
for example, that inflation will decrease (a drop in estimated sales growth). Sales forecasters
also need to identify important macroeconomic trends and quantify their impact on the
company’s current and future business. Macroeconomic activity—expansion or recession—can
have a positive or negative impact on sales depending on the capital structure of the company. In
addition, if the sales of a company you are analyzing historically shows a positive (or negative)
relationship with the state of the business cycle, you may want to increase (or decrease) your
forecasted growth rate by a few (some personal judgment used here) percentage points if you
believe the economy is expanding. For example, From Table 1 in the appendix, we see that the
sales growth for Wal Mart was 6.63% in 2002, much lower that the other years listed. Further
analysis would show that the US economy was in a contraction during much of 2002, in fact
GDP growth rates were negative during the final two quarters of 2002. Retailers, including Wal
Mart, suffered due to the slowing economy and sales growth lagged. One might conclude that, if
the current state of the economy is more robust that the recent history used to construct our
average, we should adjust Wal Mart’s sales growth upwards to reflect our positive
macroeconomic perspectives.
While these examples are by no means comprehensive, they help to build intuition as to
the importance macroeconomic factors can have on sales forecasts. We reiterate the need to bind
ourselves to the forecasting tenets; all adjustments pass both the economic plausibility and
accounting consistency tests.
Step 3: Industry Adjustments
As important as macroeconomics are factors that are specific to a company’s industry and
their information about futures sales. Examples of industry motivated adjustments are also
abundant. For example, you may ask yourself, will the industry grow into new markets?
Intro to Valuation: 16
Another example of industry factors follows from economists’ well-established
understanding of industry life cycles; most companies grow very rapidly during the first couple
years after establishment only to slow down to a more stable growth rate in subsequent years. If
the company resides in an industry that is maturing, historical growth rates are likely to be
greater than sales growth rates moving forward. Another factor analyzes the dynamics of the
industry. For example, an industry that is restructuring may dramatically shift market share
among its participants and historical growth rates may not be good estimates for forward-looking
growth rates. Coming back to our example of Wal Mart, much uncertainty still remains
surrounding the impact of online retail sales versus brick-and-mortal retail venues. Other
industry dynamics including recent merger between Kmart and Sears, expansion of retail into
new economies such as China, all can have a profound impact on our sales forecasts. These
examples only skim the surface of industry issues to analyze when constructing sales growth
forecasts; good understanding of industrial economics and adherence to our two forecasting
tenets will allow one to make valuable and necessary adjustments to a historical forecasts based
on industry factors.
Step 4: Company Specific Adjustments
This step may be the most ambiguous of all post Step 1 adjustments to sales forecasts. In
this step, you look for any factors not covered above that may have information about the future
sales prospects of the company and quantify how these factors may impact our estimates of sales
growth.
For example, seasonality tends to distort balance sheet numbers and can impact
forecasting sales growth forecasts over partial years; necessary for analyzing a company at any
time of the year except recently after a company’s financial year end (Clarke and McQueen,
2001). November and December are the most important months of the year for retailers,
Intro to Valuation: 17
including our example firm of Wal Mart, many of whom harvest 25% to 40% of their annual
sales during that period. If we were to use recent quarter sales number as our guide for
forecasting future cash flows, we would need to account for the particular quarter’s historical
contribution to annual sales (e.g. first-third quarters sales are low, fourth quarter sales quite
high).
As an analyst, how would one project sales for a company that is experiencing a “growth
spurt” as seen recently in the tech industry? How would the forecast change for a company that
has very volatile earnings? One could take an average sales growth rate over the last few
quarters or even the last few months if they seem to be more representative of future conditions.
Investigation of financial statement notes, analyst comments, and other public
information sources will help to provide you with a sense of the company’s prospects moving
forward. While the notes to the financial statement may appear daunting, regularly numbering in
the hundreds of pages, often times they include statements by the company that can help you
make more informed decisions about growth rates that are more solidly based on stated future
policies or strategies. Good economic intuition and experience will help to quantify these effects
and make appropriate adjustments to your sales forecasts to reflect this information. Operating
from the perspective that capital markets (picking stocks) is an extremely competitive
environment, rewards will come to those who carefully and logically assimilate and process the
pertinent information in constructing sales forecasts. While little disagreement among analysts is
likely to occur surrounding the state of the macroeconomy or inflation in the coming year, much
dispersion may be associated with company specific factors. The implication that follows is that
your ability to add value will likely come (or not) in your ability to correctly incorporate
Intro to Valuation: 18
company specific factors, or that developing a competitive advantage in this step of the valuation
process may be more possible than in other more competitive steps.
For example, in Appendix A, we have provided a few examples of information that can
be found in the notes to the financial statements. One paragraph discusses a strategic move by
Wal Mart to open 40 – 45 new discount stores, 230-240 new Supercenters, and 30 – 35 new
Sam’s Clubs. One can use this information relative to prior year’s expansions and sales growths
to help refine the important sales growth figures that play such a key role in financial statements
forecasting.
Forecasting Other Accounts
Once a sales forecast has been made, the next step would be to forecast the rest of the
income statement and balance sheet accounts. Figure Two below explains traditional methods
for forecasting other items in these statements. Remember, as the analyst you must make the
decisions as to which are the most appropriate forecasting methods in your circumstances. This
may prove to be the toughest part of the task. You may find direction by delving into the notes
to the financial statements to see if the company gives any indication regarding its future plans.
If not, Figure Two should start you in the right direction.
Figure Two: Forecasting Financial Statements
Income Statement
Forecast Method
Sales
Forecasted by choice
Cost of Sales (GOGS)
Calculated: Sales – Gross Profit
Gross Profit
Percent of Sales (“Gross Margin”)
Selling, General, and Admin. Expense (SG&A)
Percent of Sales
Income before Depreciation and Amortization (EBITDA)
Calculated: Gross Profit – SG&A
Depreciation and Amortization Expense (Dep. and Amort.)
Percent of Net PP&E
Income after Dep. and Amort. (EBIT)
Calculated: EBITDA – Dep. and Amort.
Non-Operating Income (Expense)
Pretax Income
Forecast driven by expected company policy
Percent of Prior Year Net Debt (ST Borrowing + LT Debt –
Excess Cash)
Calculated: EBIT + Non-Operating Income – Interest Expense
Income Taxes
Percent of Pretax Income (“Tax Rate”)
Initial Interest Expense
Intro to Valuation: 19
Net Income
Calculated: Pretax Income – Income Taxes
Dividends
Percent of Net Income (“Payout Ratio”)
Addition to Retained Earnings
Calculated: Net Income – Dividends
Balance Sheet
Forecast Method
Assets
Current Assets
Zero if operating assets are greater than sources of funds;
otherwise, the amount required to make the sheet balance
Percent of Sales
Net Property, Plant, & Equipment
Percent of Sales (“Fixed Asset Turnover”)
Intangibles
Forecast driven by expected company policy
Other Long Term Assets
Percent of Sales
Total Assets
Calculated: sum of all asset accounts
Excess Cash (Plug item)
Liabilities & Owners’ Equity
Current Liabilities
Long Term Debt
Percent of Sales
Zero if sources of funds are greater than operating assets;
otherwise, the amount required to make the sheet balance
Forecast driven by expected company policy
Other Liabilities & Preferred
Percent of Sales
Shareholders’ Equity
Constant based on most recent year’s data
New Retained Earnings
Sum of forecasted Additions to Retained Earnings
Total Liabilities & Shareholders’ Equity
Calculated: sum of all liability and equity accounts
Short Term Borrowing (Plug item)
Discussion of Figure Two:
Because in the end, the balance sheet must balance, any shortfall will need to be financed
through additional external financing. These additional financing requirements in Figure Two
are referred to as “Plug items”. A positive plug item for Excess Cash is used when excess
funding is forecasted; if additional funding is needed, the excess cash is set to zero and Shortterm borrowing is used as the second plug item. The importance and order of the forecasted Plug
item is also illustrated in Figure One.
Although we include our suggested method to forecast other accounts in Figure Two,
these suggestions should not be interpreted as being the only or necessarily best forecasting
method. Other methods include regression, where historical values of some account variable is
regressed on historical sales levels to develop a historical relationship which can be used to
Intro to Valuation: 20
construct forecasts of other accounts. We do not discuss specifically regression analysis, given
the introductory nature of this note, but refer the interested reader to Clarke and McQueen
(2001). Some accounts may be more amenable to forecasts using ratio analysis. Fore example,
net income may be forecast using historical profit margin ratios or accounts receivable may be
forecast using historic collection ratios in connection with forecasted sales.
The method we suggest to forecast three accounts in Figure Two requires more
discussion. In particular, we suggest that Non-Operating Income, Intangibles, and Long-Term
Debt are all forecasted based on our expectations of company policy. In particular, these
accounts may be lumpy over time, do not necessarily follow a sustained pattern that can be
extracted from historical data, and whose changes may be driven by changes in company policy
or strategy. For example, found in the notes to financial statements in Wal Mart’s most recent
10-K filings is a section titled future expansion, as summarized in Appendix A. In this section,
Wal Mart states that they plan to increase stores by over 50 million square feet and that a portion
of this expansion is expected to be funded with long-term debt. If we were using historical data
to forecast the Long-Term Debt account we might construct a flawed forecast ignoring the
information about the monetary need for store expansion. As analysts, generally we behave as
outsiders and hence can only speculate as to how these accounts may be expected to move in the
future, however, notes in financial statements along with company announcements can help
provide some information about company plans which may help to construct reasonable
forecasts for these three accounts. We provide a number of statements found in the notes to the
financial statements in Appendix A that potentially would help in the forecasting of various
accounts.
Intro to Valuation: 21
Application to Wal Mart
For instructional purposes, we have constructed a pro forma for Wal Mart using past
financial statement data and using the guidelines discussed in this note and formalized in Figure
Two. Our pro forma spreadsheet is found in the sheet title “Combined Pro Forma” in the Excel
file “Walmart.xls”. This spread sheet can be subdivided in to three main sections: first, income
statement accounts; second, balance sheet accounts; and third, forecasting ratios.
Income Statement Accounts:
This section includes both historical levels of key income statement accounts as well as five-year
forecasts for these accounts. You will notice that many accounts found in the income statements
spreadsheet that you downloaded and organized in note two are missing from Figure Two and
hence the Combined Pro Forma sheet. At this point of the valuation exercise, we concentrate
solely on the accounts that will help us to calculate free-cash flows to Wal Mart over the past
five years which, in turn, help us to forecast free-cash flows for valuation purposes as indicated
in Figure One. You will note that the columns under Minority Interest are not listed in Figure
Two and hence merit some discussion. Financial Statements require flexibility for company
specific cases and these Extraordinary Items often times show up in this section of the income
statement. In our example, Wal Mart lists a Minority Interest expense after taxes. To find out
the source of this expense requires you to: 1) understand accounting definitions as they pertain to
use of Minority interest expenses and 2) read the notes to Financial Statements to see Wal Mart’s
application of Minority interest. If you read the notes to the financial statements you will find
that Wal Mart owns a 37.8% minority interest in The Seiyu, Ltd. (“Seiyu”), a retailer in Japan
and this requires that Wal Mart adjust for any cash flows that come from this partial ownership
given the consolidated accounting treatment on the financial statements that is required for this
Intro to Valuation: 22
holding. Other business activities could lead to a Minority Interest account, including trading
profits for example; emphasizing the importance of reading the notes to get accurate information
about the financial statements as well as information that may prove useful for forecasting.
Reading the notes would also inform you as to the 2004 cash flow from discontinued operations
came from the sale of McLane Company, Inc.
Balance Sheet Accounts:
The accounts under balance sheet, similar to Income Statements, are a subset of the full number
of accounts that are represented in Wal Mart’s consolidated balance sheets; we include on the
accounts that are necessary for free-cash flow calculation and forecasting. The most interesting
accounts are our two plug accounts (excess cash and short-term borrowing) that are created to
ensure that the balance sheet will balance and to provide the picture, given our assumptions, of
the forecasted short-term liquidity needs. By clicking on the cells of the forecasted plug figures
and analyzing the formulas in these cells, you will see that the accounts do ensure the balancing
of the balance sheet by setting excess cash (short-term borrowing) to zero if other forecasted
asset (liabilities) totals exceed forecasted liabilities (assets).
Forecasting Ratios:
We also include on the Combined Sheet Pro Forma spreadsheet all of the ratios used in
constructing forecasts as referred to in Figure Two. These ratios are well-known and should be
familiar to 410 students, for those interested in a refresher we refer to Higgins (2004). We
suggest that you take time to look in the cells of the forecasted Income Statement and Balance
sheet accounts to see where each ratio is used; you will want to look in the cells under the 2005
column where the forecast formulas are found. While Figure Two and the Combined Sheet Pro
Forma spreadsheet follow a common method for forecasting free-cash flows there is always
Intro to Valuation: 23
room for your own judgment. If, following sound economic reasoning, you feel the forecasting
methods should be altered/changed, by all means do not be tied to this method and express your
individual opinions through some deviation to our proposed forecasting method.
Intro to Valuation: 24
Appendix A: Financial Notes Excerpts
Below we have provided some selected sections from the most recent 10-K filings from Wal
Mart Inc. The filing itself is more than 60 printed pages, so there is an abundance of information
provided, only some of which than may prove valuable when constructing forecasted financial
statements. We have selected examples of notes provided in the financial statements that
provide important information about Wal Mart and their business going forward. Other relevant
and valuable information was excluded for brevity’s sake.
Management’s Discussion and Analysis of Results and Financial Condition
Overview: Wal-Mart is a global retailer committed to growing by improving the standard of
living for our customers throughout the world. “Every day low prices” is our pricing philosophy.
Sam’s Club is in business for small businesses. Internationally, we operate with similar
philosophies.
Operations: Our operations are comprised of three business segments. Our Wal-Mart stores
segment accounts for 68% of our fiscal 2004 sales. This segment consists of three different retail
formats: discounts stores which have a variety of general merchandise and limited variety of
food products, Supercenters which offer a wide variety of general merchandise and a full-line
supermarket, and neighborhood markets, which offer a full-line supermarket and a limited
variety of general merchandise.
Our Sam’s Club segment consists of membership warehouse clubs and account for 13.5% of our
fiscal 2004 sales.
Our International segment consists of operations in eight countries and Puerto Rico. This
segment accounted for 18.5% of our fiscal 2004 sales.
The Retail Industry: We operate in the highly competitive retail industry. We face strong
competition from other general merchandise, food and specialty retailers. Additionally, we
compete for prime retail site locations, as well as for attracting and retaining quality employees.
We, along with other retail companies, are influenced by a number of factors including, but not
limited to: cost of goods, consumer debt levels, economic conditions, customer preferences,
employment, inflation, currency exchange fluctuations, fuel prices and weather patterns.
Company Performance Measure: Comparative store sales is a measure which indicates whether
our existing stores continue to gain market share. Operating profit growth greater than sales
growth has long been a measure of success for us. Inventory growth at a rate less than half of
sales growth is a key measure of our efficiency. It is important for us to sustain our return on
assets at its current level.
Intro to Valuation: 25
Operating Results:
Net Sales: Our total net sales increased by 12% in fiscal 2004 when compared with fiscal 2003.
That increase resulted from our domestic and international expansion programs along with
comparative store sales increases.
As we continue to add new stores domestically, we do so with an understanding that additional
stores may take sales away from existing units. We estimate that comparative store sales in
fiscal 2004, 2003 and 2002 were negatively impacted by the opening of new stores by
approximately 1%. We expect that this effect will continue during fiscal 2005 at a similar rate.
Costs and Expenses: For fiscal 2004, our cost of sales decreased as a percentage of total net sales
when compared to fiscal 2003, resulting in an overall increase of 0.2% in the company’s gross
profit as a percentage of sales.
Due to the company’s program to convert many of our discount stores to Supercenters, which
have full-line supermarkets, and the opening of additional Supercenters and Neighborhood
Markets, we expect that food sales will increase as a percentage of our total net sales. Because
food items generally carry a lower gross margin than our other merchandise, increasing food
sales tends to have an unfavorable impact on our total gross margin. However, we feel that we
can more than compensate for the effect on gross margin by increased food sales in the near term
through reduced markdowns compared to fiscal 2004 and in the foreseeable future by continuing
to leverage our global sourcing programs and continuing to challenge our internal and external
cost structures.
Our operating, selling, general and administrative expenses increased 0.1% in fiscal 2004 when
compared to fiscal 2003. Most of this increase resulted from an increase in insurance costs. The
remainder of the increase is primarily attributable to the adoption of the Emerging Issues Task
Force Issue No. 02-16, “Accounting by a Reseller for Cash Consideration Received from a
Vendor.” The adoption of EITF 02-16 resulted in an after-tax reduction in net income of
approximately $140 million of $0.03 per share.
Interest Costs: For fiscal 2004, interest costs on debt and capital leases, net of interest income,
as a percentage of net sales decreased 0.1%.
Net Income: Our income from continuing operations for fiscal 2004 increased at a faster rate
than net sales (11.6%) largely as a result of the increase in our gross margin and a reduction in
net interest expense. Partially offsetting gross margin and net interest expense improvements
were increased SG&A expenses in fiscal 2004.
Wal-Mart Stores Segment: Comparative store sales in 2004 increased at a slower rate than 2003
due to a softer economy and softer apparel sales. During fiscal 2004, our total expansion
program added approximately 34 million of store square footage.
Intro to Valuation: 26
Sam’s Club Segment: Comparative store sales in 2004 increased at a higher rate than in 2003
primarily as the result of our renewed focus on the business member. Total expansion program
added approximately 2 million store square footage in 2004.
International Segment: The fiscal 2004 increase in International net sales primarily resulted
from both improved operating results and our international expansion program. In fiscal 2004,
the International segment added 9 million of additional square footage. Additionally, the impact
of changes in foreign currency exchange rates favorably affected the translation of International
segment sales into U.S. dollars by an aggregate of $2 billion in fiscal 2004.
Liquidity and Capital Resources:
Overview: Operating cash flows from continuing operations increased during fiscal 2004
compared with fiscal 2003 primarily due to an increase in net income, improved inventory
management, accounts payable growing at a faster rate than inventories, and a decrease in
accounts receivable of $373 million compared to an increase in fiscal 2003 of $159 million due
to the collection of foreign taxes receivable.
Company Stock Repurchase Program and Common Stock Dividends: In January 2004, our
Board of Directors authorized a new $7 billion share repurchase program. During fiscal 2004,
we repurchased 91.9 million shares of our common stock for approximately $5 billion.
We paid dividends totaling approximately $0.36 per share in fiscal 2004. In March 2004, our
Board of Directors authorized a 44% increase in our dividend to $0.52 per share for fiscal 2005.
The company has increased its dividend every year since its first declared dividend in March
1974.
Contractual Obligations and Other Commercial Commitments:
(in millions)
Recorded Contractual Obligations:
Payments Due During Fiscal Years Ending January 31
Total
2005
2006-2007
2008-2009
$ 20,006
3,267
5,086
$
2,904
3,267
430
Unrecorded Contractual Obligations:
Non-cancelable
operating
leases
Undrawn lines of credit
Trade letters of credit
Standby letters of credit
Purchase obligations
8,665
5,279
2,006
1,396
32,928
665
3,029
2,006
1,396
10,502
Total commercial commitments
$ 78,633
$
24,199
Long-term debt
Commercial paper
Capital lease obligations
$
5,106
-
$
2,609
-
846
808
2,150
2,250
1,072
Thereafter
$
9,387
3,002
5,678
-
-
-
13,550
8,855
21
$ 23,002
$ 13,344
$ 18,088
Capital Resources: Management believes that cash flows from operations and proceeds from the
sale of commercial paper will be sufficient to finance any seasonal buildups in merchandise
inventories and meet other cash requirements.
At January 31, 2004, Standard & Poors (“S&P”), Moody’s Investors Services, Inc. and Fitch
Ratings rated our commercial paper A-1+, P-1 and F1+ and our long-term debt AA, Aa2 and
Intro to Valuation: 27
AA, respectively. As of January 31, 2004, we had $6 billion of debt securities remaining under a
shelf registration statement previously filed with the US SEC.
Future Expansion: In the US, we plan to open approximately 40 to 45 new discount stores and
approximately 230 to 240 new Supercenters in fiscal 2005. (Approximately 150 will be from
conversions or relocations of existing Wal-Mart Stores.) We also plan to further our
Neighborhood Market concept by adding approximately 20 to 25 new units during fiscal 2005.
The Sam’s Club segment plan to open 30 to 35 Clubs during fiscal 2005, (Approximately 20 will
be from expansions or relocations of existing Sam’s Club stores.) Internationally, the company
plans to open 130 to 140 new units (of which 30 will be conversions or relocations).
The planned square footage of growth for fiscal 2005 represents approximately 50 million square
feet of new retail space, which is more than an 8% increase over current square footage. We
estimate that our capital expenditures in fiscal 2005 relating to these new units and distribution
centers will be approximately $12 billion in the aggregate. We plan to finance expansion
primarily out of cash flows from operations and with a combination of commercial paper and the
issuance of long-term debt.
Market Risk: Market risks relating to operations include changes in interest rates and changes
in foreign exchange rates. We enter into interest rate swaps to minimize the risks and costs
associated with financing activities, as well as to maintain an appropriate mix of fixed- and
floating-rate debt.
We hold currency swaps to hedge our net investment in the United Kingdom.
Summary of Significant Accounting Policies:
Cost of Sales: Cost of sales includes actual product cost, change in inventory, the cost of
transportation to the Company’s warehouses from suppliers, the cost of transportation from the
Company’s warehouse to the stores and Clubs and the cost of warehousing for our Sam’s Club
segment.
Litigation: The Company is involved in a number of legal proceedings, which include
consumer, employment, tort and other litigation.
The Company is a defendant in Dukes v. Wal-Mart Stores, Inc., a putative class-action lawsuit
commenced in June 2001 and pending in the United States District Court for the Northern
District of California. The case was brought on behalf of all past and present female employees
in all of the Company’s retail stores and wholesale Clubs in the United States. The complaint
alleges that the Company has engaged in a pattern and practice of discriminating against women
in promotions pay, training, and job assignments. The complaint seeks, among other things,
injunctive relief, compensatory damages including front pay and back pay, punitive damages,
and attorneys’ fees. If the Court certifies a class in this action and there is and adverse verdict on
the merits, or in the event of a negotiated settlement of the action, the resulting liability could be
material to the Company, as could employment-related injunctive measures, which would result
in increased costs of operations on an ongoing business.
Intro to Valuation: 28
Segments: Page 51 contains a break down of revenues by segment for fiscal years ending 2004,
2003 and 2002.
Quarterly Financial Data: Page 52 contains income statements broken down by quarters.
Fiscal Year: February 1 to January 31.
Intro to Valuation: 29
Teaching Note Four: Free Cash Flow Valuation
With forecasted financial statements in hand we are ready to tackle the valuation of our
company. Just as in earlier stages, we will want to follow sound economic principles as we
evaluate our company, or more specifically, as we construct the intrinsic value of their common
stock shares. Three economic principles play an influenciary role in what we do at this stage:
first, more cash is preferred to less cash; second, cash today is preferred to cash in the future
(hence the need of discounting future cash flows); and third, a more risky cash flow is less
valuable than a less risky or certain cash flow (risk premium). While these economic concepts
appear simple and intuitive, their application can be challenging and difficult. The precise
measure of cash flows relevant to a valuation will also prove to be a complex exercise,
particularly given the various accounting policies that firms follow and that regulations allow.
The essence of all valuation techniques is that when an investor purchases a security, they
anticipate sometime in the future recovering their initial investment along with financial
compensation for the risk of their investment and compensation for investing rather than
consuming (time-value of money).
Valuation models often aid a potential investor by
formalizing their beliefs and assumptions regarding the prospects of the firm’s securities which
lead to a fair price for a security’s anticipated future stream of cash flows. This formalization
can follow a myriad of alternatives given the valuation complications noted above. This note
only acts as a simple introduction to valuation and should not be taken as a comprehensive
treatment. We refer interested readers to texts such as Damodaran (2002) for a broad and
extensive valuation treatment.
In the first section we introduce valuation concepts and models. We start with the wellknown dividend discount valuation models; discuss their applications and short comings, which
Intro to Valuation: 30
naturally lead us to our preferred valuation method of discounted free cash flows. In section two
we define relevant measures of free cash flows, constructing forecasts of free cash flows from
our forecasted financial statements, and the basics of free cash flow valuation. In section three
we cover two key inputs of any DCF valuation: estimation of the cost of equity which is used to
discount forecasted free cash flows and the estimation of the steady state growth rate of free cash
flows. The final section integrates discounting with expected future free-cash flows providing
the value estimates and discusses extensions to our simple model.
Valuation Concepts and Introduction:
In general valuation methods can be categorized into three broad classes: discounted
cash flow (DCF) methods, relative valuation methods, and abnormal return valuation methods.3
While each of the three broad classes has their place in valuation, DCF is at the foundation of all
virtually all valuation methods and consequently will be the primary method covered in this note.
DCF valuations can all be traced back to the following relationship:
n
Intrinsic Value  
t 1
CFt
(1)
(1  r ) t
Where CFt = cash flow in period t, n = number of periods of asset’s life, r = discount rate that
reflects the riskiness of the anticipated cash flows, and the Intrinsic Value is the true value of the
security given the investor’s assumptions and beliefs. In our case of valuing equities, anticipated
future cash flows include possible dividends or futures cash flows from sale of the equity at the
end of the holding period. Future case flows are rarely known with certainty and consequently
must be estimated or forecasted. Note three, which introduced financial statement forecasting
methods, will provide the necessary account forecasts required to construct future cash flows to
investors.
3
Damodaran (2002) Chapter 2 provides a comprehensive overview of various valuation models.
Intro to Valuation: 31
As a special case to equation (1), assume that the holding period is infinite (n) and
that all future cash flows are dividends which grow at a constant rate for all future periods.
Under these well-know assumptions equation (1) will simplify to the well-known Gordon growth
model,

(2)
Div1
t
t 1 (1  r )
Div1

rg
Intrinsic Value  
where Div1, is next year’s expected dividend, r is the appropriate discount rate for the expected
dividend, and g is the assumed constant growth rate in dividends. The Gordon growth model,
while simple and intuitive, assumes away many interesting and relevant potential paths for future
cash flows and investor holding periods. Simple contradictions to equation (2) include expected
dividends whose growth rates vary over time or finite anticipated holding periods. A more
complicated contradiction includes the case where a company decides to use some of their
current period’s earnings to engage in share repurchases. No one would reasonably argue that
these repurchases are valuable to equity holders, but there is no mechanism in equation (2) for
this to increase equity value. In fact, given that the cash flows are not paid as dividends, the
Gordon growth model would predict that this act would decrease share value relative to the case
where all cash flows are paid to equity holders.4
Free Cash Flows
Scenarios such as the one described above have led to a more general approach to
defining cash flows (in particular cash flows available to equity holders). One of the more
popular generalizations has been termed Free Cash Flows, defined as cash flows that the
4
One could argue that the Gordon growth model could capture the positive impact on this purchase through the
future sale of the security at a higher price.
Intro to Valuation: 32
company has available to certain claim holders even if the cash flows are not directly transferred.
Generally speaking two types of free cash flows can be constructed and used in valuation
exercise: Free Cash Flow to the Firm (FCFF), and Free Cash Flow to Equity (FCFE). Our
interest will be the latter, but we briefly discuss FCFF models first.
Free-Cash Flows to the Firm (FCFF)
FCFF method constructs expected cash flows to all claimholders in the firm, including
equity holders, bondholders, and preferred stock holders. The simple way of constructing FCFF
is to estimate the cash flows prior to any cash flows going to these claimholders. Thus one
would start with earnings before interest and taxes, and then subtract off any taxes and/or
reinvestment needs. This would lead us to FCFF defined formally as:
FCFF = EBIT(1-tax rate) – (Capital Expenditures – Depreciation) –
(3)
(Change in working capital).
To value a company using this model, we construct forecasts of FCFF for each year in our
anticipated holding period and then discount the expected cash flows at the appropriate discount
rate, weighted-average cost of capital (WACC).
Given that this method values the entire firm, a challenge arises when using this method
to construct intrinsic values of stock price, we are left with an estimated total value of the firm,
and to construct values of equity, we must subtract the market value of debt as well as preferred
stock both of which can be time coming and difficult to obtain. This challenge will lead us to
other definitions to free cash flow that can avoid valuing debt and other non equity securities.
Intro to Valuation: 33
Free-Cash Flows to Equity (FCFE)
FCFE, are available cash flows to equity holders of the firm, therefore we must subtract off debt
flows.5 This subtracting off debt flows brings two beneficial generalizations: first, we are able
to forecast changes in debt holding of firm that do not show up in equity valuations that follow
from FCFF valuations (generally assumed to be constant), and second, we do not have to
construct market values of debt to convert a firm value to equity value. Hence, FCFE models are
well-suited for many stock valuations applications; accounting for cash flow decisions of the
firm – including cash flow retention or share repurchases – and allowing an equity valuation to
follow in a more straightforward setting than FCFF.
To construct FCFE, we start with net income, the measure of stockholder’s earnings, and
then convert the measure to a cash flow by subtracting out any reinvestment needs as follows,
FCFE = Net income – (Capital Expenditures – Depreciation) – (Change in
(4)
working capital) + (New Debt issued – Debt repayments).
These are the cash flows that are available to the firm to pay out as dividends and will become
the uncertain cash flows that we will use to construct the intrinsic value of the firm as noted in
the equation below,
Intrinsic Value 
FCFE1
FCFE2
FCFE3
FCFE4 TV 5  FCFE5




1
2
3
(1  ke)
(1  ke)
(1  ke)
(1  ke) 4
(1  ke) 5
(5)
where our assumption of including five years of forecasts is based on our pro forma analysis in
note three that went out five years. Using equation (4) and our forecasted financial statement, we
can construct the forecasted free cash flows in equation (5). However, to construct the intrinsic
value, we still need some measure of terminal value, TV5. We suggest assuming that the firm
5
Two other common cash flow measures used in DCF valuation that we do not discuss include earnings before
interest, taxes, depreciation, and amortization (EBITDA) and net operating profit or loss after taxes (NOPLAT).
Intro to Valuation: 34
will follow a version of a Gordon growth model from year six forward which simplifies TV5
value to
FCFE6
, just the six-year forecast of free cash flows divided by the cost of equity, ke,
k e  g FCFE
minus the constant growth rate in FCFE, gFCFE. Notice relative to the FCFF model, our risk
adjusted discount rate, ke, will be simpler to construct than WACC. Intuitively, the Gordon
growth terminal value is based on the notion that the value of $1 of free cash flow received in the
coming year, 1 + growth rate (gFCFE), divided by the cost of equity, ke, will lead to the enterprise
minus the growth rate (ke – gFCFE) when taken to perpetuity.
Key Valuation Inputs
The introduction of this note stated that valuation models help to formalize an investor’s
beliefs and assumptions. Two key assumptions in any DCF valuation include values for the cost
of equity capital and the constant growth rate in cash flows. You will find that not only are these
inputs critical to an assumption, but they can prove difficult to estimate as well. We introduce
some simple methods for their estimation below.
Cost of Equity Capital
The cost of equity can be estimated a number of way, but the standard approach involves using
the well-known capital asset pricing model,6
ke = Rf + β(Rm – Rf).
(6)
The risk free rate, Rf, is typically taken to be the yield on a comparable maturity US-Treasury
bond or Bill. Given that the cost of equity equation is typically applied to return horizons from
one month to one year, this suggests that using yields from 90-day US T-bills up to one-year
6
Bodie, Kane, and Marcus (2004) chapter 7 provides a comprehensive treatment of the capital asset pricing model,
as well as a discussion into its implementation.
Intro to Valuation: 35
Treasury bonds is reasonable and unless the slope of the yield curve is quite dramatic, any choice
in the relevant range should suffice.
The magnitude of the equity risk premium, Rm – Rf, on the other hand, is subject of much
debate. For simplicity, we suggest a common starting point is to assume the risk premium is 6.0
percent, and then one may use current conditions to deviate from this number. Beta, β, the
measure of systematic risk, is a unique measure for each stock. Betas are not observed and
therefore must be estimated. A common method for constructing your own estimate of beta is to
run a regression of equation (6) using historical returns on stocks, risk-free securities, and market
index returns. Alternatively, a number of financial sources provide estimates of betas. These
can be found by searching the company’s financial information on a Bloomberg terminal or at a
host of financial websites (Yahoo Finance, MSN Finance, etc.). These providers of financial
information follow a variety of methods to construct their beta estimates:
regression beta
estimation, fundamental beta estimation, and accounting beta estimation method are prominent
methods for calculation of betas. For example, the cost of equity using the CAPM for Wal Mart
is roughly approximated as ke = 3.65 + 0.6(6) = 7.25 percent, assuming a beta of 0.6 (Yahoo
Finance website), a risk-free rate of 3.65 percent (T-bill yield) and a risk-premium of 6 percent
using equation (6) as our model.
One will quickly see that while the CAPM provides an elegant, model-based method for
estimating the cost of equity capital, there are many unknown inputs that the use of the model
requires (i.e., beta, risk-premium, risk-free rates) and that one should not take any output of the
CAPM as anything more than an estimate. In fact, many will test the sensitivity of a particular
CAPM cost of equity capital, using simulation techniques over the various inputs.
Growth Rate
Intro to Valuation: 36
Our pro forma analysis on financial statements provides forecasted growth rates in free
cash flows over the next five years. However, to correctly value common shares in the stock, we
are required to estimate steady-state growth rate in FCFE for years six forward that is used in our
construction of TV5. To estimate a growth rate in free cash flows that is consistent with the
assumptions of the FCFE model, we will have to extend the growth rate assumptions of the
simple dividend discount model as noted below,
g = Retention Ratio x ROE.
(7)
This equation assumes that what earnings not paid out as dividends are retained in the firm, an
assumption that should be relaxed to be consistent with FCFE models, to what is called the
equity reinvestment rate (ERR),
ERR = 1 – (Net Capital Expenditures + Change in Working Capital – Net Debt
(8)
Issues)/Net Income.
In addition, the ROE on equity in equation (7) is also relaxed to the Noncash ROE (NROE) to
reflect the fact that in FCFE models, there is no excess cash left in the firm and the ROE should
only measure return on noncash investments,
NROE = (Net Income – After-tax income from cash and marketable securities)/(Book
(9)
value of equity – Cash and marketable securities).
A combination of equations (8) and (9) will lead to a model for estimated steady state growth
rate in free cash flows to equity that can be used as the input for the TV5,
gFCFE = ERR x NROE.
(10)
As a starting point to constructing our estimates for gFCFE, we can use equations (8), (9), and (10)
along with our forecasted financial statements to see our implicit growth rate forecasts over the
coming five years. These forecasts can help to guide our estimate of gFCFE, given that the steady
Intro to Valuation: 37
state growth rate from year six on is likely to be less than the forecasted growth rates but perhaps
in a range around our current forecasts. You can also use information taken from notes in
financial statements or understanding of industry dynamics and life-cycle may help to inform or
adjust your estimate of gFCFE. You will find that this rate is a key input into a valuation and
varying your growth rate estimates will lead to profound changes in our intrinsic value estimates.
This sensitivity should be quantified as carefully as possible using simulation or other sensitivity
analysis.
Looking at our example company of Wal Mart, we can observe how to construct
estimates of gFCFE.
On the spreadsheet titled “Walmart.xls” there is a sheet labeled
“Performance and Valuation” that, among other things, lists forecasts of equation (8) the ERR,
equation (9), and equation (10) the noncash ROE. Given the assumptions we made to construct
the forecasts, gFCFE ranges from 5.8% to 7.7% over the next five years. These growth rates are
substantially lower that anticipated growth rates in dividend that would be backed out of a
Gordon growth models which range around 15%. The large difference between dividend growth
rates and free cash flow growth rates illustrate the need to estimate growth rates in free cash
flows specifically as opposed to relying on traditional methods.
With growth rate and cost of capital estimates, we are ready to construct an intrinsic
value. For our sample company, Wal Mart, the “Performance and Valuation sheet” provides an
estimate of the Intrinsic Value based on equation (5), which given our assumptions leads to an
share price of $61, reasonably close to the current price of Wal Mart shares ($51 on 3/31/2005).
Spend time with the “Performance and Valuation” sheet to see how the formulas
represent the equations listed in this note. This sheet can be used as a template for valuing other
company’s shares of stock. In addition, understanding the formulas in this sheet will better allow
Intro to Valuation: 38
you to test various assumptions and conduct simulation studies to help inform you regarding the
importance of particular assumptions in your particular valuation.
References:
Bodie, Z., A. Kane, and A. Marcus, 2004, Essentials of Investments, McGraw-Hill/Irwin,
New York, New York.
Clarke, R., and G. McQueen, 2001, “Forecasting Financial Statements: Proforma
Analysis,” working paper, Brigham Young University.
Damodaran, A., 2002, Investment Management, John Wiley & Sons, New York, New
York.
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