. 36
( 39)


concepts in ¬nance (such as present value or the capital-asset pricing model), ¬nancials
and pro formas are messy and unique for each business. Forecasting the ¬nancials for
a new cancer drug is di¬erent from forecasting the ¬nancials for a new toy fad, which
is di¬erent from forecasting the ¬nancials for a retail store, which is di¬erent from fore-
casting the ¬nancials for aluminum mining, and so on. So, many of the guidelines for
creating good pro formas are necessarily less universal and more ad hoc.

2. Relativity: The di¬culties of making good ¬nancial projections for a speci¬c project are
often tremendous. It is important that you realize the limits of what you can and cannot
do. You should be able to do it better than your peers”a relative rather than an absolute
standard. Looking in retrospect at what later actually happened in relation to what you
predicted in your pro forma is often a great lesson in humility. You are not alone in this

3. Learning by doing: The best way to learn how to do a pro forma is to struggle designing
one. Such a case-based approach is considerably more e¬ective than a passive listening

Still, this chapter seeks to prepare you a little by giving you some general guidance, because
in the end, you must learn how to design good pro formas: to be an e¬ective entrepreneur,
manager, or analyst, you must learn both how to produce and how to critically consume ¬nan-
cial pro formas. After reading this chapter, your next step in learning pro formas should be
to work through and critique many case studies”necessarily a trial-and-error-and-experience
¬le=proformas.tex: RP
Section 29·1. The Goal and Logic.

29·1.A. The Template

The standard method for creating a pro forma separates the future into a “detailed projection” Decide on a detailed
projection period and a
time period, for which you forecast the ¬nancials in great detail, and a terminal value, which
terminal value period.
you can think of as the “then market value” of the business”a going-concern value of the
business if you were to sell it at this point in the future. You have to decide for how many
years you want to project ¬nancials in detail before capping your value analysis with your
terminal value.
As our guinea pig, let™s use PepsiCo, because you have already studied its historical ¬nancials Here is the template of
what we need to do.
in Chapter 9. (Recall its ¬nancial statements on Pages 200“205.) Your goal now is to construct
a good pro forma as of December 2001 to estimate PepsiCo™s market value, presuming you
already know the 2001 ¬nancials. The construction template is in Table 29.1. It shows the
three big areas you must work on:

1. A choice of horizon T , up to which you estimate in great detail.

2. The detailed ¬nancials during the initial projection phase, from time +1 to T ’ 1.

3. A terminal market value at time T ’ 1, which is a standin for the cash ¬‚ows from time T
to eternity.

Table 29.1. The Pro Forma Problem for PepsiCo
To b e
Pro Forma Income Statement

’2 ’1 +1 +2 +3 +T
Year 0 ... Value

1999 2000 2001 2002 2003 2004

Net Sales $22,970 $25,479 $26,935

pro lesale

ded on
“ COGS $10,326 $10,226 $10,754


... “wh
= Net Income $2,505 $2,543 $2,662
Pro Forma Cash Flow Statement

pro lesale

Net Income $2,505 $2,543 $2,662
ded on


+ Depreciation $1,156 $1,093 $1,082 ec

... ... ... ...

= Operating Cash Flow $3,605 $4,440 $4,201

The numbers for PepsiCo™s income statement were taken from Table 9.13 (Page 228). The numbers for PepsiCo™s
cash ¬‚ow statement were taken from Table 9.14 (Page 229).
Your goal is to project future cash ¬‚ows”T periods worth of detailed ¬nancials”followed by a wholesale market
value estimate of the remaining cash ¬‚ows until eternity.

We shall begin our analysis by presuming that you have the perspective of an external analyst The main purpose is to
determine independently
who has to construct a pro forma to value a ¬rm for which you do not know the current market
a market value.
value. That is, we pretend that you do not know PepsiCo™s market value. Such a perspective
is also taken by analysts of buyout companies, who try to assess whether the market value
of a publicly traded company is low enough to warrant a takeover. In addition, we presume
that because you are an external analyst”an outsider”you do not have detailed knowledge of
PepsiCo™s operation, and certainly not enough to pretend you are an insider or manager.
¬le=proformas.tex: LP
732 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

Although entrepreneurs who need to design a pro forma often share the dilemma of not know-
PepsiCo is an imperfect
ing the publicly traded market value of their proposed projects, they face two more big issues
example, because it
that are not very important in your analysis of PepsiCo:
could be done a lot more

Inside Knowledge As an entrepreneur, chances are that you know in great detail the oper-
ational details of your proposed project. As an external analyst (or venture capitalist
considering funding the project), this is rarely the case.

Upstart vs. Mature Phase PepsiCo is an established company, so its projects have long prior
histories. Its cash ¬‚ows will not start with a sharp initial business growth curve to be
followed only later by a more stable period. As ¬rms mature and grow, they are less
likely to default. The decline in credit risk will allow their promised rates of return to
decline. In addition to having to pay higher default premia, many young, small ¬rms also
have to pay higher expected rates of return. The reason is that they tend to be especially
vulnerable to downturns in economy-wide conditions, which re¬‚ects itself in higher betas
and higher costs of capital.
The end of the upstart growth phase is often a natural break and thus a possible choice
for T , the break of your pro forma into a detailed projection period and ¬nal market value.
But PepsiCo is already in its mature, stable state and, as an outsider, you really have no
detailed knowledge of how the next year will be di¬erent from what will happen in ten
Therefore, you could even just rely on a terminal value right now and dispense with the
initial detailed projection phase altogether. Nevertheless, we will work out the detailed
projections to illustrate the process.

Working Capital Issues Another issue that is relatively less important for PepsiCo is working
capital projection and management”PepsiCo is so big, stable, and unlevered that it can
easily borrow more capital whenever it needs more. In contrast, a small entrepreneurial
¬rm would have to pay close attention to avoid running out of cash”which could lead to
loss of the entire business even if its underlying real business economics were sound.

I have surreptitiously introduced one more unusual feature”our pro forma is constructed as if
We can peek at “illegal”
information. we stand at the end of 2001. This shall allow us later to use hindsight knowledge to “autopsy”
how good or bad your forecasts turned out.
¬le=proformas.tex: RP
Section 29·2. The Detailed Horizon vs. The Terminal Time Break.

29·2. The Detailed Horizon vs. The Terminal Time Break

Your ¬rst goal is to understand how to choose a suitable value for the horizon choice T in How many years of
Table 29.1. Remember that the horizon is the span of time up to which you project detailed
¬nancials and beyond which you substitute your “wholesale” terminal value estimate.
As an initial step, let us take a brief detour into forecasting. There is one surprising and key In relative terms, the
very-long run may not
insight to note: you may be able to project future cash ¬‚ows as well in the very long term as in
be more daunting than
the intermediate term. This would imply that you would be able to estimate the present value the intermediate run.
of long-term cash ¬‚ows better than that of intermediate-term cash ¬‚ows. This is best explained Future cash ¬‚ows may
be equally uncertain,
by example.
and present values
would be less uncertain.
If you have to forecast the temperature in two hours, your (short-term) forecast will be pretty
Uncertainty may not
good, and much better than your six-month forecast. But how would your six-month forecast grow dramatically with
compare to your ¬fty-year forecast? Most likely, both your prediction and level of accuracy horizon.
would be similar. For example, your temperature forecast for August of next year should
probably be the same 80 degrees, plus or minus 10 degrees, as your forecast for August in ¬fty
years. Thus, if the business and environment are stable, then your uncertainty is not likely to
grow with your horizon after some point.
Now say you want to value an ice cream store. How does your temperature forecast a¬ect In NPV terms, long-term
uncertainty can often be
your store™s estimated present value? The e¬ect of the temperature uncertainty for August
less problematic.
of next year is less discounted and thus more important than the e¬ect of the temperature
uncertainty in August in ¬fty years. If your store expects to earn $100,000, and a 10 degree
temperature di¬erence can cause you to earn anything between $75,000 and $125,000, then
the temperature uncertainty for August of next year can cause a present value di¬erence of
about $50, 000/(1 + 15%)1 ≈ $43, 478 at a 15% discount rate (cost of capital). But the same
temperature uncertainty in ¬fty years hence causes only a present value di¬erence of about
$50, 000/(1 + 15%)50 ≈ $46. Consequently, if you want to estimate your store™s value today,
your intermediate-term uncertainty should worry you more than your long-term uncertainty.
The role of intermediate term vs. long term uncertainty generalizes beyond ice cream stores, Economics and Strategy:
Scarce resources make
because knowledge of economics and strategy allows you to put reasonable bounds on long-
term future pro¬tability (in 20 or 50 years). At such far-out horizons, you should not expect
businesses to still have unusually large growth rates and to earn economic rents”where eco-
nomic rents are de¬ned as investment rates of return that are much higher than the cost of
capital. Economic rents can only be achieved when a ¬rm has assets and capabilities that are
scarce, valuable, and di¬cult to imitate. Examples of such scarce resources are the presence
of a unique and excellent manager (e.g., a Jack Welch of General Electric), economies of scale
(e.g., Microsoft™s computer software or Walmart™s mass logistics and buying power), unduplica-
ble corporate reputation (e.g., Sony™s brand name), legally protected intellectual property (e.g.,
Glaxo™s retroviral drug patents or Disney™s Mickey Mouse), or consumer switching costs (e.g.,
Comcast™s cable television). In the very long run, over decades, scarce resources tend to be-
come less scarce, as new technologies and consumers make old advantages obsolete. Wal-Mart
Stores (WMT) may seem like a juggernaut today, but in 50 years, it will almost surely not have
the scarce resources that will allow its owners to continue earning rates of return much above
their investment cost of capital. (If Wal-Mart did maintain its historical growth rate, it would
have to colonize other planets!)
To determine how long it might take before a product becomes a commodity and thus produces The force (of economics)
has worked on products
only normal pro¬ts, you need to apply economic thinking to your speci¬c business knowledge.
historically, too.
If there are few scarce resources and entry barriers, then it may only take a couple of years
before unusually high corporate growth rates slow down and there are no more economic
rents. For example, there are few entry barriers to ¬‚at-screen television technology today.
Consequently, you can count on the industry that produces ¬‚at-screen televisions to earn few
excess rents within 10 years. (If you do not believe this, think back to 1997, when the average
DVD player sold for $800; today, all entry barriers have disappeared, and you can purchase a
DVD player for $20.) Other products, however, can enjoy more scarcity and entry barriers for
longer periods of time. For example, if you can get a patent on an e¬ective cancer drug, you
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734 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

will be able to earn economic rents for 15 to 25 years”although better competitors™ drugs will
eventually come onto the scene and your patent will eventually run out.
Your ¬rst reaction might be to dismiss such a long-term perspective. Walmart, Microsoft,
Don™t get caught up in
today™s perspective. Google, and General Electric just seem too good to believe in their eventual demise. It is tempt-
ing to let your present-day experience color your long-term forecasts. But look back ¬fty years
and ask yourself whether the fast-growing exciting juggernaut companies operating then are
still the same. Or just 25 years. Can you even name the companies from the 1980s that still
earn large economic rents? If you had picked two companies that looked similar in 1985, are
both companies still around? For example, Dell may still be doing well, but Gateway looked
just as good in 1985”and there are literally dozens of now bankrupt companies that looked no
di¬erent then, either. Standing in 1985, you should not have expected to earn large economic
rents if you had bet on any one computer hardware vendor then.
The economics that help you decide on when a ¬rm is likely to settle into a lower economic
The strategy model:
what delays erosion of growth rate is taught in great detail in business strategy courses and carries di¬erent labels
economic rents?
(e.g., Porter™s ¬ve forces). To determine when economic rents are likely to dry up, strategy
suggests you ask such questions as:

• How long before your entry barriers will erode?
• How long before your success will be mimicked by the competition?
• How long before you can be squeezed by suppliers or customers?

So, to choose your horizon T , you must consider the underlying ¬rm economics. If you set T
The two considerations
for setting T : business at a point where long-run economic forces will have eroded most of the economic edge of the
economics and discount
company”where growth will return from the initial but unsustainably high short-term rates to
sustainable, ordinary, long-term rates”then you can assume that the company will earn only
“ordinary pro¬ts” thereafter. This suggests that your goal should be to capture the initial rapid
and possibly unstable growth phase with detailed ¬nancial forecasts, and the stable period
with the terminal value. Another way to say this is that a good T is the point in time when you
expect the present value of growth opportunities (PVGO) to be low (or even zero). But there
is also a second consideration to your choice of T . You want to pick a horizon such that the
discount factor is high enough so that the precise choice of T would not matter too much. For
example, at a 10% discount rate, each dollar in 20 years is worth only about 15 cents in present
value today. The high discount factor can help plaster over the errors that your crude terminal
value estimate will inevitably commit. Whether you choose 20 years or 25 years as the detailed
horizon, then, would likely not matter too much in terms of your present value. After all, when
it comes to exit values on horizons that are so far away, the best you can hope for is a halfway
reasonable estimate of market value, anyway.
For most businesses, you would pick a terminal value somewhere between 3 and 20 years, with
Typical values for T :
5“10 years. 5 to 10 years being most common. Let™s apply economic intuition to choose a T for PepsiCo.
PepsiCo is a very stable company, so it is not necessary to project 20 years of ¬nancials in
great detail. You can instead “lump” the value created in all future years into one terminal
market (sale) value fairly soon. This is a relief”it saves you from guessing too many years and
lots of numbers about which you”as an outsider”really have no clue. Thus, for expositional
convenience, let us choose a horizon of T = 3 years. That is, we will try to project in detail
from 2002 to 2004, and summarize all cash ¬‚ows from 2005 to forever with one value estimate
at the end of 2004.
¬le=proformas.tex: RP
Section 29·3. The Detailed Projection Phase.

Important: The choice of break point T between a detailed projection period
and a terminal market value is often dictated by two considerations:

1. A desire to distinguish between an upfront strong growth phase and a sub-
sequent mature and stable phase.

2. A desire to have a small discount factor on the terminal market value to
reduce the present value importance of estimation errors.

In practice, most pro formas choose a T between 5 and 20 years.

29·3. The Detailed Projection Phase

You have now dealt with the ¬rst goal of choosing the horizon T . Your second goal is to In real life, you must use
all your economic
determine the project value during the beginning growth period, from next year (+1) up to
knowledge to do a good
some year T ’ 1. The good news is that, if you were an actual analyst, you would probably projection.
know your business quite well and thus be able to reasonably predict the immediate future.
You could use historical cash ¬‚ows for some guidance about future cash ¬‚ows. Of course,
to do this well, you would have to understand a lot about the underlying economics of the
business, although you would still have to make many assumptions. In this process, you could
use much additional information that you have so far mostly ignored”such as the speci¬c
industry economics or the corporate balance sheet.
The bad news is that illustrating this process in a textbook is di¬cult. There are no clear Initial growth
projections are highly
rules that apply to all companies, and this book is not about PepsiCo. You probably do not
know much about PepsiCo™s business”and even if we could fully explain and analyze PepsiCo™s External analysts can use
many businesses, it would not help you elsewhere. Pharmaceutical drug research, aluminum the historical ¬nancials
as one of their inputs.
mining, fad toys, and a new stamping machine each have their unique business, ¬nancial, and
accounting patterns. There is little generality here. In contrast to the terminal value, long-run
economic forces are unlikely to apply in the projection phase period.
Even though we lack speci¬c information, our exposition and forecast demand that we not The detailed projections
will also in¬‚uence your
simply brush over the initial growth phase. We need accurate, detailed projection period fore-
terminal values.
casts. They have a signi¬cant impact on project wealth, and not just because they have a direct
contribution to the present value over the next ¬ve years, but also because the terminal value
itself is (usually) relative to a baseline expected cash ¬‚ow in year T . This baseline must be
established from your initial detailed projections. Here, however, we are going to have to make
up some numbers to illustrate the process. Be warned: our ¬nancial projections for PepsiCo
will necessarily remain naïve. Again, because we know very little about PepsiCo™s business or
the plans of its managers, accuracy is not the goal”illustration is.
The two primary methods of projecting ¬nancials are explained in the next two subsections: Projecting economic
cash ¬‚ows directly or
indirectly (via detailed
1. Direct extrapolation of the accounting component that you are interested in (i.e., the ¬nancials).
economic NPV cash ¬‚ows for the project, though sometimes also the earnings).

2. Detailed ¬nancial modeling of all or most items in the ¬nancial statements.

The ¬rst is a drastic shortcut, used by analysts only when time and knowledge are severely lim-
ited, whereas the second is more common. Incidentally, computer spreadsheets were originally
invented primarily to facilitate the projections in pro formas, and are therefore the preferred
tool for designing them.
¬le=proformas.tex: LP
736 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

29·3.A. Method 1: Direct Extrapolation of Historical Cash Flows

The ¬rst method is really a “cheat,” in that it is a shortcut which avoids having to do the full-
Directly project the ¬nal
cash ¬‚ows themselves blown ¬nancial pro forma analysis. It directly projects the historical cash ¬‚ows forward, e.g.,
forward. Here, it gives
by assuming a constant growth rate forever. For example, using Formula 9.18, PepsiCo™s cash
bad results. Recognize
¬‚ows for 1999 to 2001, you can compute the cash ¬‚ows that accrued to both debt and equity:
such problems!

Asset Cash Flow1999 = ’ + (’$792) = $1, 641
$3, 605 $1, 172

Asset Cash Flow2000 = ’ + (+$57) = $2, 501
$4, 440 $1, 996
From Formula 9.18: (29.1)
Asset Cash Flow2001 = ’ + = $1, 556
$4, 201 $2, 637
Economic Project Operating Investing Interest
= Cash Flow + Cash Flow ’ Income .
Cash Flow

Over the three years, PepsiCo showed a cash ¬‚ow decline of about $1, 556/$1, 641 ’ 1 ≈ 5%.
Warning: You really
This comes to an annual decline of about ($1, 556/$1, 641)1/2 ’ 1 ≈ 2.6%. Over the most recent
need to understand the
business. Mechanical
12 months, cash ¬‚ows even dropped by one-third! You could assume that PepsiCo™s cash ¬‚ows
extrapolation rarely
will continue to decline at this rate forever. But do you really believe that PepsiCo™s cash ¬‚ow
decline will continue, or do you believe that it will reverse? If you investigate PepsiCo™s cash
¬‚ow statement in Table 9.14 further, you can learn that much of PepsiCo™s decline was due to
a heavy increase in (other) investing activity, not to a decline in its business (sales). Some of
it was due to the acquisition of Quaker, which PepsiCo hopes will eventually pay o¬ in more
cash, not less cash. This demonstrates how hazardous simplistic extrapolation of cash ¬‚ows
can be: You really need to know more about the business itself and the reasons behind the
¬nancial trends. Purely mechanical rather than economic models of the business usually just
don™t work well. Again, always remember that valuation requires much economic and common
sense and that it is as much an art as science.

Table 29.2. Pro Forma: Direct Cash Flow Projections

“Detailed” Model Terminal Value
Growth at 10% See Next Section

2002 2003 2004 2005 2006-
2000 2001

Year +1 Year +2 Year +3 Year +4 to ∞
Year ’1 Year 0

Projected CF1 $1,883 $2,071 $2,278 $2,506 ?
$1,556 $1,712

Explanations (Notes):
: Projecting 10% due to investments, until (incl.) 2005.

You have encountered another solution to issues arising from the lumpiness of cash ¬‚ows. In
You could project
earnings instead of cash Chapter 10, you considered forecasting earnings rather than cash ¬‚ows. In the very long-run,
¬‚ows”which has
earnings and cash ¬‚ows should be roughly equal”after all, earnings “just” shift the time-series
advantages and
accruals. The question is whether historical net income growth or historical cash ¬‚ow growth
represents the present value of the future cash ¬‚ow growth stream better if you have to work
with truncated cash ¬‚ow forecasts.

Net income On the positive side, the accountants have tried to capitalize future already-
transacted for cash ¬‚ows with good accrual judgment. On the negative side, this human
intervention also means historical net income could have beeen more easily manipulated
than historical cash ¬‚ows. Earnings are also less lumpy than cash ¬‚ows, allowing for more
reliable forecasts.
Cash Flows Cash ¬‚ows are the gold standard if you can project them out accurately to in¬nity.
But if you have to truncate your forecast in the future, or rely on a ¬nite number of cash
¬le=proformas.tex: RP
Section 29·3. The Detailed Projection Phase.

¬‚ows as representation of the future, it is not clear whether your history would paint a
more accurate picture of the future.

The simplest of projects makes this clear”a plant that costs $20 million and then delivers $2
million a year with 20 year accounting depreciation. This plant does not have an $22 million
economic value increase between years 0 and 1 that you should project forward as a sustainable
path. In contrast, the earnings will not show such a negative spike followed by high growth,
but a smooth and constant pattern of $1 million pro¬t each year. Thinking that earnings will
continue at $1 million would be more representative of the future cash ¬‚ows (truly $2 million
per year) than projecting cash ¬‚ows of $2 + $22 = $24, $2 + $22 · 2 = $46, and so on. There is
some academic evidence that earnings-based terminal value projections are on average superior
to pure cash ¬‚ow based terminal value projections.
PepsiCo had earnings of $2,662 in 2001, having grown at rates of 1.5% and 4.7% over the two Let™s do PepsiCo with
prior years. If PepsiCo were to grow its earnings by 3% per year, the following earnings trend
would emerge:

“Detailed” Model Terminal Value
Known Growth at 3% See Next Section
2000 2001 2002 2003 2004 2005 2006-
Year ’1 Year +1 Year +2 Year +3 Year +4 to ∞
Year 0
Projected Earnings $2,543 $2,662 $2,742 $2,824 $2,909 $2,996 ?

In this future, earnings would reach $3 billion by 2005”about 20% higher than the equivalent
cash ¬‚ow projection. Because earnings are more stable (have lower variance), their forecasts
are also often more reliable than cash ¬‚ow forecasts.

29·3.B. Method 2: Pro Forma Projections With Detailed Modeling of Financials

The second and more common method of projecting economic cash ¬‚ows during the initial A more sophisticated
method attempts to
period is to project entire ¬nancial statements, which provide the individual components for
model the entire
the economic cash ¬‚ows you seek. Doing so is often (but not always) better than projecting ¬nancials, not just the
economic cash ¬‚ows directly for three reasons: “end product,” the
economic cash ¬‚ows.

1. As we just noted, on the one hand, cash ¬‚ows are di¬cult to directly project, because
they tend to be volatile. Capital expenditures occur in lumps, and thus do not follow
steady, constant growth paths. On the other hand, the smoother net income contains
many ¬ctional accounting accruals that are not really cash. We are caught between a rock
and a hard place.

2. The full projection method can make it easier to intelligently incorporate any knowledge
of the underlying business into the economic cash ¬‚ow estimates. For example, you may
happen to know that unusual expenses will be zero next year, or that a new payment
system may speed the collection of receivables. By forecasting the individual items, you
can integrate your economic knowledge, so that it ¬‚ows in an optimal fashion into your
cash ¬‚ow estimates.

3. The full projection method can help you judge other important information”such as
working capital availability, suitable debt-equity ratios, and interest rate coverage. Espe-
cially for entrepreneurs who are often in danger of a liquidity crisis, such information can
be just as important as the economic cash ¬‚ows themselves. In fact, all the ratio analysis,
such as the ¬nancial health and pro¬tability ratios, are often more useful when applied See Section 10·4.B
to pro forma ¬nancials than when applied to current ¬nancials. Such analysis can help
you judge whether the ¬rm is on a sound or critical path.
¬le=proformas.tex: LP
738 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

The Income Statement: Sales

Table 29.3. A Possible PepsiCo Pro Forma Income Statement Model for 2002

Income Statement Estimated
1999 2000 2001 2002 2003
Sales1 ··· ···
= $25,093 $25,479 $26,935 $27,906
COGS2 ··· ···
$10,326 $10,226 $10,754 $10,760
··· ···
+ SG&A $11,018 $11,104 $11,608 $12,279
+ Deprec/Amort4 ··· ···
$193 $147 $165 $168
··· ···
+ Unusual Expenses $73 $184 $387 $279
= Operating Expenses6 ··· ···
“ $21,610 $21,661 $22,914 $23,486
Operating Income7 ··· ···
= $3,483 $3,818 $4,021 $4,420
··· ···
+ Net Interest Income $792 “$57 $8 $0
··· ···
Income Before Tax
= $4,275 $3,761 $4,029 $4,420
Corporate Income Tax10 ··· ···
“ $1,770 $1,218 $1,367 $1,591
··· ···
Income After Tax
= $2,505 $2,543 $2,662 $2,828
Extraordinary Items12 ··· ···
“ $0 $0 $0 $0
··· ···
Net Income
= $2,505 $2,543 $2,662 $2,828

Explanations (Notes):

1 6 10
: grows by historical 3.6%. : sum the above. : 36% of IBT.
2 7 11
: $3,506+26% of sales. : subtract the above. : subtract the above.
3 8 12
: 44% of sales. : too ignorant and lazy. : too ignorant and lazy.
4 9 13
: 3-year historical average. : subtract the above. : subtract the above.
: 1% of sales.

The detailed projection method usually starts by forecasting future sales in the income state-
The base for detailed
pro formas is sales ment. This sales forecast is the single most critical aspect of any pro forma, because it becomes
the baseline number from which many other ¬nancial item estimates will follow. In PepsiCo™s

• You could use a mechanistic model that extrapolates sales growth from historical ¬nan-
cials. For example, in Table 29.3, you can compute that PepsiCo sales grew at an annu-
alized rate of ($26, 935/$25, 093)1/2 ’ 1 ≈ 3.6% from 1999 to 2001. Let us assume that
PepsiCo sales will continue in 2002 at the same growth rate. Therefore, projected PepsiCo
sales in 2002 would be $26, 935 · (1 + 3.6%) ≈ $27, 906.
Like other pro forma line items, sales has a footnote that explains our assumption. In-
deed, every good pro forma must have detailed footnotes explaining the assumptions
behind each and every line item projection. Admittedly, our notes in Table 29.3 are too
perfunctory and do not even explain where the 3.6% came from. But, in the real world,
you must carefully explain the background assumptions behind each and every critical
component of your pro forma!

• You could and should use an economic model that uses detailed business knowledge. For
example, as a real-world analyst, you might know whether PepsiCo was about to launch
many exciting new products or whether it had few new projects in the pipeline. You
might use knowledge of how much PepsiCo did not pay out in dividends but kept in
retained earnings for reinvestment into its operations”which eventually would turn into
more sales or pro¬tability. You might look at the forecast of the macroeconomic climate,
which might tell you something about how PepsiCo sales would perform next year, e.g.
during the then-predicted recession of 2002. And so on. Any such information would
help you to adjust the sales estimates for more accurate projections.
¬le=proformas.tex: RP
Section 29·3. The Detailed Projection Phase.

In a real pro forma where your money is on the line, it would be reckless to forecast sales
through a mechanistic model without an economic model!

The Income Statement: Other Components
You would then go down item by item on the income statement, the next being COGS. You have Direct extrapolation of
COGS is possible. But it
a whole range of options:
can now also be
projected in relation to
(as a fraction of) sales.
• You could repeat the sales exercise with COGS: a pure growth model would project that
COGS™ historical growth rate of ($10, 754/$10, 326)1/2 ’ 1 ≈ 2.05% will continue in 2002.
If applied to the year 2001 COGS of $10,754, your 2002 COGS forecast would thus be
$10, 754 · (1 + 2.05%) ≈ $10, 975.

But, armed with the sales scenario of $27,906 in 2002, you can now consider a much wider set
of models.

• You could forecast COGS not only relative to its own history, but also relative to projected
sales for 2002, which you have already estimated. You also know the historical relation-
ship between COGS and sales, which you can use to predict a relationship between 2002
sales and 2002 COGS. For example, PepsiCo™s COGS was $10, 326/$25, 093 ≈ 41.15% of
sales in 1999, 40.14% of sales in 2000, and 39.93% of sales in 2001. The simplest sales-
based model might just project that COGS would be a slowly declining fraction of sales
in 2002. In this case, your COGS forecast might be

E ( COGS2002 ) ≈ 0 + 39.5% · E ( sales2002 )
= 39.5% · ≈ $11, 023 .
27, 906

• A more sophisticated model might pose that there are economies of scale. In this case,
COGS would not go up one-to-one with sales. Instead, COGS would have both a “¬xed
component,” whose cost would not change with sales (e.g., the factories), and a “variable
component,” whose costs would increase with sales (e.g., the cola syrup). You might try to
plot COGS against sales for 1999“2001, and determine visually that a good line ¬t would
E ( COGS2002 ) = $3, 500 + 25% · E ( sales2002 )
= + b · E ( sales2002 )
a .

This says that $3.5 billion is unalterable factory costs, but for each extra dollar of sales,
you have to purchase only 25 cents of syrup. Substituting in our estimated 2002 sales of
$27,906 million, you would project COGS for 2002 to be

E ( COGS2002 ) ≈ $3, 500 + 25% · ($27, 906) ≈ $10, 500 .

Or, you could use heavier statistical artillery and run a regression relating PepsiCo™s COGS
to sales over its most recent three years. (Don™t worry if you do not know what this is.)
Such a regression suggests that a better line ¬t would be

E ( COGS2002 ) ≈ $3, 506 + 26% · E ( sales2002 ) ,

so your prediction would change to

E ( COGS2002 ) ≈ $3, 506 + 26% · $27, 906 ≈ $10, 760 .

• You could draw on information from other ¬rms, such as Coca Cola. In 2001, Coca Cola
had COGS of $6,044 on sales of $20,092, a ratio of 30%, which is much lower than PepsiCo™s.
¬le=proformas.tex: LP
740 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

This may not only suggest that Coca Cola™s business is di¬erent, but also that PepsiCo
may be able to lower its COGS in the future to meet “better practice” standards. Thus,
you might want to lower PepsiCo™s COGS estimate from $10,760.
• If you were even more sophisticated, you could recognize that COGS contains some depre-
ciation. Thus, the history of PepsiCo™s past capital expenditures could also in¬‚uence your
COGS estimate. You could throw past capital expenditures into your statistical regression,
too, to come up with a better prediction equation.

The sky”your economic and econometric background knowledge”is your limit. For illustra-
tion™s sake, let™s adopt $10,760 as our predicted COGS in Table 29.3.
You can repeat these forecasting processes to predict other income statement items. Like
Other items in the table
may follow other models. COGS, SG&A contains both ¬xed and variable expenses, as well as depreciation that relates to
past investments. SG&A might thus best be modeled as a combination of a ¬xed component,
plus a sales-variable component, plus a past capital-expenditure-based component. But given
that no money (only scarce book space) is at stake, for the rest of the income statement, let™s
play it simple. The footnotes describe the method of projection for each item. Clearly, if your
money was at stake, you would want to know as much about the business as possible and use
this knowledge to come up with better models for PepsiCo™s business relations. Again, the limit
is your business knowledge, your imagination, and your economic and accounting knowledge.
Di¬erent items could receive totally di¬erent treatments, too. For example, you could relate
net interest income to how much debt PepsiCo currently has, and what you know current and
what you believe future interest rates to be.

In the appendix to this chapter, there are similar formulas for many pro forma components
Side Note:
estimated with data from the universe of publicly traded companies. These can be used “in-a-pinch””or even
help you gain some intuition about how important the ¬xed and variable components are in a particular data
item. However, the formulas there are mechanistic and therefore de¬nitely not particularly reliable in any
individual case”so be careful.

The Cash Flow Statement
Next, you might model the cash ¬‚ow statement. Table 29.4 is an attempt for PepsiCo. It
The cash ¬‚ow statement
model would rely on the starts by transferring the projected net income from the pro forma income statement model
income statement model.
into the cash ¬‚ow statement model. For the remaining cash ¬‚ow items, we can only remain
perfunctory”after all, this is only an illustration without real economic knowledge. Although
we really have no idea what causes depreciation and depletion, a number on the order of $1,100
looks “reasonably reasonable,” given that you know nothing about PepsiCo™s physical plant, and
given the stabilities of PepsiCo™s prior history of depreciation and capital expenditures. (We
also ignore the fact that some parts of depreciation have already been modeled in components
of the income statement, although we really should check consistency.)
Working down the cash ¬‚ow statement, you must adopt a ratio for your model for deferred
Other cash ¬‚ow
statement components. taxes, which ¬ts the history reasonably well”let™s go with around 18% of PepsiCo™s income
taxes. You know nothing about non-cash items, and PepsiCo™s history does not suggest a clear
pattern, so choose zero. Changes in working capital are more noteworthy, because their relation
to sales contain interesting economics. We know that it is not the absolute level of sales, but
sales growth that determines the working capital that the business consumes”but not one-
to-one. For example, you may have to carry more inventory to satisfy sales growth, although
economies of scale may allow you to grow inventory less than one-to-one. Your receivables
collection policies and technologies (and your willingness to sell to dubious customers) may
in¬‚uence how much your receivables should grow with sales. Your willingness to pay your
suppliers may in¬‚uence your payables, and so on. With a projected sales increase for 2002 of
just under $1 billion, it would suggest that PepsiCo will need more working capital. Yet, PepsiCo
also grew in prior years, and still managed to pull working capital out of the business, rather
than put it in! This is rather unusual, and may contain some interesting choices PepsiCo has
made. We could dig further to ¬nd out, but without further knowledge, and after much (pretend)
analysis of the underlying business, just presume that PepsiCo will need to put $200 million into
the business to ¬nance sales growth. The result of all these forecasts is a projected operating
¬le=proformas.tex: RP
Section 29·3. The Detailed Projection Phase.

Table 29.4. A Possible PepsiCo Pro Forma Cash Flow Statement Model

Cash Flow Statement Estimated

1999 2000 2001 2002
Net Income $2,505 $2,543 $2,662 $2,828
Depreciation and Depletion2 ···
+ $1,156 $1,093 $1,082 $1,100
Deferred Taxes3 ···
+ $573 $33 $162 $300
Non-Cash Items4 ···
+ “$708 $355 $211 $0
’$200 ···
+ Changes in Working Capital $79 $416 $84
Total Operating Activity6 ···
= $3,605 $4,440 $4,201 $3,700
Capital Expenditures7 ···
“$1,341 “$1,352 “$1,324 “$1,300
Other Investing8 ···
+ $169 “$644 “$1,313 $0
Total Investing Activity9 ···
= “$1,172 “$1,996 “$2,637 “$1,300
Operating Plus Investing $2,400

Explanations (Notes):

1 4 7
: ’$1, 200 + 4% · Earnings.
: transfer $2,828 from IS. : too ignorant and lazy.
2 5 8
: cat in the hat. : 27% of revenue Increase. : too ignorant and lazy.
3 6 9
: 15%-20% of Income Tax, rounded. : sum of above, rounded. : sum the above, rounded.

cash ¬‚ow of $3.7 billion. Finally, after equally long consideration of PepsiCo™s business, and
equally long interviews with PepsiCo management, you determine that PepsiCo is planning to
invest $1.3 billion into capital expenditures, and nothing into other activities.

Financing Policy, the Balance Sheet, and Linkages
Your next step would be to think more about your ¬nancing policy. This will in¬‚uence not only More Linkages arise.
the remainder of your cash ¬‚ow statement (the ¬nancing cash ¬‚ows), but also your balance
sheet (debt and equity positions) and even your income statement (interest payments). In fact,
depending on what you assume, you may have to go back to the income statement and go
through your forecasts again. Other linkages will arise, too. For example, what you assume
about ¬nancing cash ¬‚ows will force your end-of-period cash position on your balance sheet,
because the cash position next year is the cash position this year plus the net of all cash
¬‚ows. For another example, you must also think hard about what you believe current assets
and current liabilities will be”e.g., how your technology may change your inventory or your
collection abilities. This assumption has direct implications not only for your balance sheet,
but also for your changes in working capital on your cash ¬‚ow statement. Of course, you would
also need to provide detailed projections for the remaining detailed projection period, 2003“
2005. The principles are the same as they were for your projection of 2002. We will skip all
these for lack of space.
¬le=proformas.tex: LP
742 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

29·3.C. Policy and Calculations o¬ the Pro Forma Components

After you have projected your balance sheet and the statement of owners™ equity, i.e., a full set
of detailed ¬nancial forecasts up to the terminal value, T , what can you do with these numbers?

Economic Project Cash Flows
The ¬rst important use of the pro forma is project value analysis. Having guestimated the
The projected cash ¬‚ow
is now much higher, due components of the cash ¬‚ow statement for 2002, you can now compute the economic cash
to our Other Investing
¬‚ow for your NPV analysis, using the basic cash ¬‚ow formula 9.18 from Page 221: economic
project cash ¬‚ow for PepsiCo is the sum of operating cash ¬‚ows and investing cash ¬‚ows plus
interest expense, which comes to around $2.4 billion”about 50% higher than your alternative
$1.7 billion direct projection in Table 29.2. This is not because the forecasting technique is
di¬erent, but primarily because here you projected other investing activity to be zero. (It
accounted for around $1 billion of consumed cash in 2001.)

Ratio and Soundness Analysis
A second common use for detailed ¬nancial projections is forward-looking ratio and soundness
Ratio or Financial Health
Analysis. analysis. Such an analysis can serve to check the reasonableness of your forecasts”and the
viability of the ¬rm under your presumed scenario. For example, if an upstart ¬rm were to end
up with a very high debt/equity ratio and very little cash, the implied future interest coverage
ratio should ring an alarm. Or, a growth path may have an interim negative cash position”
which would doom the ¬rm. The ¬rm may be on a collision course with reality, and management
should change course to preserve cash before the entire ¬rm evaporates. However, because
most ratio analysis requires aspects of the ¬nancials that we do not have space to model”
speci¬cally, the ¬nancing policy on the cash ¬‚ow statement, and the full balance sheet”we
will not discuss this any further. Once you have the full pro forma model, the ratio analysis
principles and soundness principles remain exactly the same as they were in Chapter 10.

Policy In¬‚uences
Pro forma projections depend not only on external factors”for example, whether the economy
Historical projections
work only if the world is is going into a recession”but also on many choices that managers make”for example, how
quickly to pay for or collect outstanding bills, how much to invest into new projects vs. how
much to pay out in dividends, how much to ¬nance with debt vs. how much to ¬nance with
equity, and so on. You have to be careful to realize that historical extrapolations may no longer
work if either the external environment or the corporate policy is changing.
This is even more important to recognize when you are not an external analyst, but a manager
If policy is changing, the
world may no longer be constructing a pro forma in order to contemplate a corporate policy change. For example, if
you invest more in new factories, all sorts of relationships”some of them nonobvious”may
change. For instance, the relation between COGS and sales may change if the consumers of
your product ask for more or less complementary products from other producers, which in
turn may change the cost of raw materials that you require for production. Just be careful.
¬le=proformas.tex: RP
Section 29·4. Pro Forma Terminal Values.

29·4. Pro Forma Terminal Values

Your third goal is to determine the ¬rm™s terminal market value. The growing perpetuity for- We have decided on T
and the cash ¬‚ows up to
mula 3.13 from Page 40 is the most common way to estimate it. That is, you would take your
T ”let™s work on the
detailed estimated value of cash ¬‚ows for time T , presume that it will grow forever at some terminal value.
sustainable, long-term growth rate E(g), and discount it back:
E (Cash FlowT =2005 ) (29.7)
E (Terminal Value’1=2004 ) = .
E (r ) ’ E (g)

For illustration™s sake, the remainder of the chapter will rely only on the direct cash ¬‚ow fore-
casts from Table 29.2. (This means, for example, that Cash FlowT =2005 is $2,506.) We now need
a combined estimate for the eventual, stable, and eternal growth rate E(g) and the eternal cost
of capital E(r ).

29·4.A. The Cost of Capital

To determine the cost of capital for PepsiCo as of late 2001, you would probably rely on the The ¬rst
goal”determine the
CAPM. If PepsiCo is publicly traded, you can use its own historical return data. You can also use
appropriate expected
information from one or more comparables, such as Coca Cola”and this would be your only rate of return for
good option if PepsiCo were a privately held company. Table 29.5 gathers a couple of years of PepsiCo”or, if you do
not have historical data,
(dividend-adjusted) stock prices from Yahoo!Finance for the S&P500, PepsiCo, and Coca Cola.
a company like PepsiCo
that is in its stable

Table 29.5. Four Years of Historical Stock Prices

Date S&P500 PEP KO Date S&P500 PEP KO
2-Jan-98 980.28 $32.86 $58.87 3-Jan-00 1,394.46 $31.94 $53.21
2-Feb-98 1,049.34 $33.20 $62.39 1-Feb-00 1,366.42 $30.07 $45.05
2-Mar-98 1,101.75 $38.95 $70.56 1-Mar-00 1,498.58 $32.79 $43.65
1-Apr-98 1,111.75 $36.22 $69.12 3-Apr-00 1,452.43 $34.49 $43.94
1-May-98 1,090.82 $37.24 $71.40 1-May-00 1,420.60 $38.25 $49.64
1-Jun-98 1,133.84 $37.70 $78.04 1-Jun-00 1,454.60 $41.92 $53.58
1-Jul-98 1,120.67 $35.64 $73.48 3-Jul-00 1,430.83 $43.22 $57.19
3-Aug-98 957.28 $25.52 $59.44 1-Aug-00 1,517.68 $40.23 $49.11
1-Sep-98 1,017.01 $27.06 $52.73 1-Sep-00 1,436.51 $43.54 $51.59
1-Oct-98 1,098.67 $31.02 $61.82 2-Oct-00 1,429.40 $45.85 $56.51
2-Nov-98 1,163.63 $35.56 $64.24 1-Nov-00 1,314.95 $42.95 $58.78
1-Dec-98 1,229.23 $37.70 $61.43 1-Dec-00 1,320.28 $47.06 $57.19
4-Jan-99 1,279.64 $35.97 $59.88 2-Jan-01 1,366.01 $41.84 $54.43
1-Feb-99 1,238.33 $34.64 $58.57 1-Feb-01 1,239.94 $43.75 $49.77
1-Mar-99 1,286.37 $36.26 $56.42 1-Mar-01 1,160.33 $41.86 $42.53
1-Apr-99 1,335.18 $34.18 $62.56 2-Apr-01 1,249.46 $41.59 $43.51
3-May-99 1,301.84 $32.85 $62.97 1-May-01 1,255.82 $42.63 $44.64
1-Jun-99 1,372.71 $35.94 $57.13 1-Jun-01 1,224.38 $42.23 $42.55
1-Jul-99 1,328.72 $36.17 $55.80 2-Jul-01 1,211.23 $44.55 $42.17
2-Aug-99 1,320.41 $31.70 $55.11 1-Aug-01 1,133.58 $44.91 $46.02
1-Sep-99 1,282.71 $28.44 $44.59 4-Sep-01 1,040.94 $46.48 $44.30
1-Oct-99 1,362.93 $32.35 $54.53 1-Oct-01 1,059.78 $46.68 $45.27
1-Nov-99 1,388.91 $32.23 $62.36 1-Nov-01 1,139.45 $46.61 $44.57
1-Dec-99 1,469.25 $32.99 $53.96 3-Dec-01 1,148.08 $46.80 $44.75

Index values and prices on December 1, 1997, were 970.43, $60.64, and $32.98, respectively . All prices were obtained
from Yahoo!Finance.
¬le=proformas.tex: LP
744 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

Augment this table by computing historical rates of returns from historical prices to obtain the
Compute the Historical
Beta. following table:

rS&P500 rKO rPEP
˜ ˜ ˜
Date S&P500 KO PEP
2-Jan-98 980.28 $58.87 $32.86 1.015% “2.919% “0.3639%
2-Feb-98 1,049.34 $62.39 $33.20 7.045% 5.979% 1.0347%
2-Mar-98 1,101.75 $70.56 $38.95 4.995% 13.095% 17.3193%
··· ··· ··· ··· ··· ··· ···

With these rates of return, you can compute the relevant historical statistics:

rS&P500 rKO rPEP
˜ ˜ ˜
Mean 0.49% “0.21% 1.08%
Variance 27.77%% 84.46%% 67.03%%
Standard Deviation 5.27% 9.19% 8.19%
Cov with rS&P500
˜ 27.77%% 12.76%% 19.30%%
Corr with rS&P500
˜ 100% 26% 45%

These statistics make it easy to calculate the historical equity beta of PepsiCo and Coca Cola:
0.001276 0.001930
βKO,S&P500 = = 0.46 , βPEP,S&P500 = = 0.70
0.002777 0.002777
Cov(˜i , rS&P500 )

βi,S&P500 =
Var(˜i , rS&P500 )

So, what would be your best estimate of PepsiCo™s future equity beta?

• You could just adopt PepsiCo™s historical equity market-beta of 0.7 (if you know the his-
torical value data for PepsiCo).

• You could believe that equity betas should be shrunk towards the average beta in the
market, which is βM,M = 1. In this case, you might want to choose a market beta of
βPEP,S&P500 = (0.7 + 1)/2 ≈ 0.85.

• You could compute an industry beta, which might be more reliable than even PepsiCo™s
own beta. After all, PepsiCo™s data can be noisy because it relies on just one realization
of history for just one ¬rm. (Well, you do not have this information here, so let™s skip this

• You could assume that Coca Cola is similar to PepsiCo, which gives you information about
PEP™s future market-beta, too. You might then choose a market-beta of 0.46, or an average
between PepsiCo™s and Coca Cola™s market-betas. This would give you an equity-beta
estimate of around 0.58.

Let™s presume you adopt βPEP,S&P500 = 0.7 as your equity beta. But this is not the estimate
number you need. You really want to value the assets and not just the equity of PepsiCo.
About 10% of PepsiCo™s market value was in various liabilities, which likely would have had
market-betas close to zero. Therefore, with an equity beta of 0.7, PepsiCo™s asset-beta would
likely have been around βPEP (FM) = 90% · βPEP (EQ) + 10% · βPEP (DT) = 90% · 0.7 + 10% · 0 ≈ 0.6.
So, henceforth, let us assume that your best asset beta estimate for PepsiCo is βPEP,S&P500 = 0.6.
(For convenience we omit subscripting the asset beta di¬erently from the equity beta.)
To use the CAPM, you also need an estimate of the economy-wide risk-free rate and equity
CAPM inputs: risk-free
rate choice. premium.

The Risk-Free Rate At the end of 2001, the 5-year Treasury Yield was about 4.4%, and the 20-
year Treasury Yield was about 5.7%, holding pretty steady throughout 2001. Given that
PepsiCo is likely to be around for a while, maybe a 10-year interest rate would be a good
choice. You could choose a rate of around 5% per annum, perhaps plus or minus 1-2%.
¬le=proformas.tex: RP
Section 29·4. Pro Forma Terminal Values.

Of course, the CAPM demands a purely risk-free interest rate and not PepsiCo™s interest
Side Note:
rate (which already contains a default and risk premium). For curiosity, how does your risk-free return
estimate compare to PepsiCo™s historical average interest rate? The income statement suggests an interest
expense of $219 in 2001 on balance sheet short-term borrowings of $354 and long-term debt of $2,651.
This interest debt ratio suggests a nominal interest rate of about 7.3%”although we do not know whether
some of the interest expense went to pay for other liabilities, when PepsiCo contracted to its debt, what
the interest rate would be if it could re¬nance in 2001, or what PepsiCo bonds™ relative liquidity premium
would be. A quick look at Yahoo!Finance would show you that PepsiCo™s bond rating was A+, which at
the time carried nominal interest rates of just about 7.5%. Of course, these are promised interest rates,
not expected interest rates.

Computing the Levered
Equity Cost of Capital.
The Equity Premium It is more di¬cult to settle on an appropriate equity premium. Pretend
that the board of PepsiCo and your own management have unanimously declared that 3%
per annum is the standardized estimate.

Putting the three inputs together yields an appropriate CAPM cost of capital for PepsiCo”the
¬rm (not the equity)”of

E (˜PEP ) ≈ 5% + · ≈ 7.1%
Asset Cost of Capital: 3% 0.7
E (˜PEP ) ≈ rF + [E (˜M ) ’ rF ] · βPEP,S&P500 .
r r

Let™s just round this to 7%”the CAPM is not a model with accuracy after the decimal point,
anyway. You must keep in mind that reasonable variations on the estimate for PepsiCo™s market
beta, for the risk-free rate, and for the equity premium could easily justify other cost of capital
estimates, say between about 5% and 10%.

29·4.B. The Cost of Capital Minus the Growth Rate of Cash Flows

To compute a terminal value estimate via a perpetuity calculation, you need an estimate of the For choice of E (g), a
wide range is often easy
cost of capital (E(r )) minus the eternal expected growth rate of cash ¬‚ows (E(g)). It is easy
to come up with.
to come up with high upper limits for sustainable growth rates. For example, E(g) cannot
be above the ¬rm™s cost of capital, or PepsiCo™s value would be in¬nite. You would also not
expect E(g) to be much above the growth rates of world GDP”you would not expect our world
to consist of nothing but PepsiCo. In sum, a number like 5“6% is probably an upper bound
on PepsiCo™s E(g). You can also think of low lower bounds. Although it is not impossible
to imagine PepsiCo fading away in terms of its importance, this probably will not happen
too quickly, so we might want to choose a growth rate of no less than, say, ’1% per annum.
Sometimes, it is more intuitive to think of such changes not in terms of nominal growth rates,
but in terms of real growth rates. With an assumption of an in¬‚ation rate of 2% per annum, the
’1% growth rate would correspond to a real rate of decline of about 3% per annum.
But you need to do better than these wide limits, or your valuation will have too large a range For choice of E (g), a
narrow range is more
of possible values to be useful. To improve your eternal growth estimate, you can draw on
dif¬cult”and subjective.
information from two sources:

1. Within Company Information: For example, you can assume that managers will not be dras-
tically overinvesting or underinvesting forever. This means you should be consistent in
your choice of expected cash ¬‚ows and the expected growth rate of your cash ¬‚ows. Would
you really want to assume that a ¬rm invests 20% of its value each year forever, but will
grow its cash ¬‚ows by only 1% forever? Probably not.
In PepsiCo™s case, cash ¬‚ow from investing activity was $2,637 million in 2001. This is
a reinvestment rate of around 3% per annum, measured in terms of PepsiCo™s value. (I
peaked at PepsiCo™s asset market value of $100 billion, which allowed me to compute
$2,637/$100,000. I could have equally well used other market value estimates”such as
the number that our pro forma will come up with in the end.) This is a reinvestment rate
of about 3% per annum. A number in this vicinity for E(g) would make sense.
¬le=proformas.tex: LP
746 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

2. Industry or Comparable Firm Information: For example, you can analyze the publicly traded
Coca Cola to better understand PepsiCo. Its economic cash ¬‚ows were computed on
For Coca Cola™s
¬nancials, see Page 228. You can learn that Coca Cola had earnings of $2,431 in 1999, $2,177 in 2000,
Tables 9.11 and 9.12.
and $3,969 in 2001. Its economic cash ¬‚ows were $799, $2,867, and $3,211, respectively”
driving home yet again how lumpy cash ¬‚ows are compared to earnings! Moreover,
throughout 2001, Coca Cola was valued at just about $100 billion.
If you think of Coca Cola in 2000 or 2001 as a comparable for a then-stable PepsiCo as of
2005, you can back out an estimate of E(r ’ g) from Coca Cola™s value. For example,
$3, 211
= ’ E (r ’ g) = 3.2%
$100, 000
E (r ’ g)
≈ .
Terminal Value2000
E (r ) ’ E (g)

This contains a small error, in that you should formally have used the cash ¬‚ow forecasts
for 2002, not those for 2001. However, this error is minor compared to the real problem. If
you had computed this just two years earlier, the same calculation would have yielded not
3.2% but 0.8%! Clearly, the lumpiness of cash ¬‚ows makes backing out eternal growth rates
hazardous. This is the reason why many analysts prefer to use the smoother earnings as
a standin for cash ¬‚ows, similar to why many analysts do comparables (Chapter 10) in
terms of earnings, not in terms of cash ¬‚ows.

Remarkably, your two numbers for the eternal growth rates agree on an estimate for E(g) of
Wow! We do not have a
dilemma for a change! about 3% per annum. (Such agreement is, unfortunately, quite rare.) Moreover, this is about
1“2% above the in¬‚ation rate, and roughly in line with generally predicted long-run real growth
rates of GDP. This gives us some con¬dence in our estimates (or, more likely, overcon¬dence).
You can now combine the estimate of your eternal growth rate with your estimate for the
You could have easily
used other estimates. cost of capital. At an appropriate expected rate of return at 7%, you would expect E(r ’ g) =
E(r )’E(g) ≈ 7% ’3% = 4% per annum. It is important for you to contemplate the importance
of your estimate of E(r ’ g). You should recall that your cost of capital estimate could easily
have been 10% instead of 7%, which would have meant E(r ’ g) ≈ 10% ’ 3% = 7% per annum
on the high end; or 5%, which would have meant E(r ’ g) ≈ 5% ’ 3% = 2% per annum on the
low end. So how big is the value di¬erence that would come from di¬erent costs of capital and
di¬erent eternal growth rates of earnings? Do you have to worry about it?
Unfortunately, the answer is yes. The uncertainty in your E(r ’ g) estimate is not only wide,
Differences in estimates
of E (r ’ g) matter even but it also has a signi¬cant in¬‚uence on your valuation. (This is often the case in the real
for a company as large
world, too.) To see this, let us consider a cash ¬‚ow estimate for 2005 of $2,506 million (from
as PepsiCo, which does
Table 29.2). Then, your base estimate of E(r ) ≈ 7% and E(r ) ’ E(g) ≈ 4% would translate into
not have almost all its
earnings power far in
a terminal value estimate (in millions of dollars) of
the future.
$2, 506 $2, 506
Terminal Value2004 ≈ = ≈ $62, 650
E (r ) ’ E (g) 4%
≈ .
Terminal ValueT ’1
E (r ) ’ E (g)

Again, this terminal value (TV) represents the 2004 value of all future cash ¬‚ows that PepsiCo
will create from Year 2005 to eternity”the presumed market value if you had to sell PepsiCo
at the end of 2004. Now vary the denominator and see how this terminal value changes:

E(r ) E(r ) ’ E(g) E(r ) E(r ) ’ E(g)
TVT =2004 TVT =2004
5% 2% $125.3 billion 8% 5% $50.1 billion
6% 3% $83.5 billion 9% 6% $41.8 billion
7% 4% $62.7 billion 10% 7% $35.8 billion

Of course, because the terminal value estimates are as of 2004, you have to discount them
back to 2001. One issue we will not have to confront in PepsiCo™s case is that of time-changing
¬le=proformas.tex: RP
Section 29·5. Complete Pro Formas.

costs of capital. In upstart ¬rms, the early discount rate would often be higher than the long-
run discount rate (used in the growing perpetuity formula). The reason is that there is more
uncertainty and market dependence before the ¬rm reaches its more stable phase, causing a
higher cost of capital early on. In contrast, for PepsiCo, the market risk is probably the same in
2001 as it is after 2004, so you can use the same discount rate. Therefore, you can just adopt
the same E(r ) for both early and late years. This gives 2001 equivalent present values of

E(r ) E(r ’ g) E(r ) E(r ’ g)
PVT =2001 ( TVT =2004 ) PVT =2001 ( TVT =2004 )
5% 3% $108.2 billion 8% 5% $39.8 billion
6% 3% $70.1 billion 9% 6% $32.2 billion
7% 4% $51.1 billion 10% 7% $26.9 billion

A present value spread as large as $26 billion and $108 billion is a problem. Clearly, your
uncertainty about the di¬erence between the cost of capital and the appropriate eternal growth
rate has a big impact on your valuation. What should you do now? In real life, you would
probably entertain a range of possible values, do more research, and pick estimates based on
the purpose for which you wanted to use the pro forma. If you wanted to sell the company,
you would pick a low discount and high growth rate to make the value appear large. If you
wanted to buy the company, you would want to claim a high discount and low growth rate in
your negotiations with the seller. Yes, you would probably choose whatever suits you. It is not
all science!

29·5. Complete Pro Formas

You now have the ingredients necessary to produce a pro forma with a market value: economic
cash ¬‚ow forecasts, a terminal value based on the cost of capital and eternal growth, and
discount factors. Let™s put it all together.

29·5.A. An Unbiased Pro Forma

Table 29.6 uses one set of assumptions that we deemed to be reasonable. It starts with the Reasons why our pro
forma value estimate for
projected asset cash ¬‚ows from Table 29.2.
PepsiCo is too low.

2002 2003 2004 2005

Year +1 Year +2 Year +3 Year +4
Year 0

Annual Cash Flows $1,883 $2,071 $2,278 $2,506

The terminal market value estimate, as of 2004 for all cash ¬‚ows from 2005 to eternity, is
$62.65 billion, assuming a 7% cost of capital and 3% eternal growth rate. Add the 2004 cash
¬‚ows, and you obtain a value of $65.0 billion for 2004. Finally, you must discount all cash
¬‚ows, which gives you an estimated market value as of 2001 of

PV2001 ≈ + + ≈ $57 billion
$1.7 $2.4 $53.0
= PV(CF2002 ) + PV(CF2003 ) + PV(CF2004 ) .

Incidentally, this assumes that if you bought PepsiCo at the end of 2001, you would not receive
the 2001 cash ¬‚ows of $1,712.
¬le=proformas.tex: LP
Table 29.6. Direct Economic Cash Flow Projections

Pro Forma Cash Flow Statement

Cash Flow Model Terminal Value

Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.
Growth at 10% Growth at 3%

2002 2003 2004 2005
2000 2001

to ∞
Year +1 Year +2 Year +3 Year +4
Year ’1 Year 0

Projected Annual Asset Cash Flows1 $1,883 $2,071 $2,278 $2,506 next row
$1,556 $1,712

$2, 506
Terminal Market Value for 2005 to eternity at E(g) = 3%: ≈ $62.650 billion
7% ’ 3%

Total Cash Flows $1,883 $2,071
≈ $65.0 billion

Discount Factor, based on 7% cost of capital 0.935 0.873 0.816

2001 Present Value of Cash Flows $1,712 $2,372 $53,001

≈ $57 billion
Total Present Value in 2001 of Asset Cash Flows from 2002 to Eternity:

Explanations (Notes):
Unless otherwise stated, values are in million dollars.
: Projecting 10% growth due to investments, until (incl.) 2005. These particular estimates were derived in Table 29.2. (You could
alternatively use the cash ¬‚ows from the detailed projections, instead.)
¬le=proformas.tex: RP
Section 29·5. Complete Pro Formas.

29·5.B. A Calibrated Pro Forma

Now switch your perspective to that of an analyst who is analyzing not the hypothetical privately If PepsiCo was public,
then we could use
held company, but the actual publicly traded PepsiCo. This allows you to check whether your
information about its
pro forma value is in line with the actual market value. It turns out that PepsiCo™s stock market- market value!
value was actually around $87.4 billion in 2001 (plus about $3 billion of debt and another $10
billion in other liabilities) for a total asset value of about $100 billion. This suggests that
your pro forma value estimate was way low. (In Section 29·8, we will investigate using as-yet-
unavailable ex-post information why this is so.)
Why would you want to ¬nd a pro forma market value for a ¬rm for which you already have We need to “calibrate”
our model to the
a public market value? Here is one scenario: you want to suggest capital structure changes
current market value.
that would not only increase PepsiCo™s value, but also generate fees for your employer, an
investment bank. The pro forma is the language of proposing corporate changes. Naturally,
you will have to present your pro forma to PepsiCo™s management. But before you can do so,
you will want to have a value estimate that ¬ts the current market value of PepsiCo”otherwise,
PepsiCo™s management would likely be so displeased with your original low pro forma value
estimate that they will not listen to any of your proposals. It would also be silly for you to
pretend that you believe that PepsiCo is worth only $54 billion when it is trading for $100
billion. You must somehow coerce the inputs in your model to ¬t the reality of PepsiCo™s
current market value better. You should look for reasons why PepsiCo is worth more than
what your original pro forma suggests. Although this should rightly be called model “fudging,”
the technical term is model calibration.
You have basically three tools at your disposal that can do the job: We can tinker with the

1. You can depart from your current projected cash ¬‚ow path. The original pro forma relied
on the direct-projection cash ¬‚ows that assumed a growth rate of 10%. Altering the cash
¬‚ow growth rate changes both the initial period cash ¬‚ow projections and the 2005 cash
¬‚ow projection of $2,506, upon which your terminal value was based. There are a number
of alternative choices you can entertain.
One way to justify higher cash ¬‚ows is to argue for higher sales, lower expenses, higher
future cash ¬‚ows, etc. This can ¬‚ow into a faster growth path for directly projected cash
¬‚ows. For example, your calibrated model can assume that PepsiCo should be valued o¬
cash ¬‚ows that grow faster than 10%”say, 15%:

2002 2003 2004 2005
Projected Year +1 Year +2 Year +3 Year +4
Year 0
Economic CF@ 15% growth $2,058 $2,366 $2,721 $3,130

Another way to increase value is to work o¬ the detailed ¬nancials from Table 29.4 rather
than the direct projections, because the former were higher, reaching $2,400 as early as
Yet another way is to shift your focus to earnings, either from the detailed ¬nancials
or from the direct projection. You know that in the very long-run, discounted earnings
and discounted cash ¬‚ows should be roughly equal”after all, earnings “just” shift the
time-series accruals. You also know that earnings may be more suitable to a growing-
perpetuity valuation, because they are less a¬ected by temporary and possibly lumpy
investment patterns. Perhaps PepsiCo accelerated its investments in 2001, sacri¬cing
immediate cash ¬‚ows for higher future cash ¬‚ows. So, relying on earnings growing at 3%
per annum, you have the following revised ¬gures:

2001 2002 2003 2004 2005
Year +1 Year +2 Year +3 Year +4
Projected Year 0
Earnings (not CF) $2,662 $2,742 $2,824 $2,909 $2,996

Or, you can rely on the detailed earnings projections, which were even higher, reaching
$2,828 as early as 2002.
¬le=proformas.tex: LP
750 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

2. You can reduce your estimate of PepsiCo™s cost of capital from 7% to a lower number. This
has two e¬ects: it makes future cash ¬‚ows more valuable, and it increases your estimated
terminal market value. The ¬rst e¬ect is relatively unimportant”we know that present
values over short horizons are reasonably robust to modest changes in the cost of capital.
It is the second e¬ect that gives you a lot of valuation “bang for the buck.” Referring back
to Page 747, you can see that reducing the cost of capital by just 1% gives you an extra
$20 billion in present value. Reducing the cost of capital by 2% gives you an extra $60


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