. 37
( 39)


3. You can increase PepsiCo™s eternal earnings growth rate estimate E(g), thereby changing
its growth pro¬le. Doing so would assume that PepsiCo has more of the characteristics of
a growth ¬rm than a value ¬rm. Increasing the eternal growth rate is just as powerful as
reducing the long-term cost of capital. In the perpetuity, g and r enter only as a di¬erence.

In the real world, you would probably choose a combination of these tools to increase the pro
forma value to reach the actual market value. Table 29.7 contains one calibrated version of
the PepsiCo pro forma that increases the initial cash ¬‚ow growth rate from 10% to 15%, and
reduces the cost of capital by 0.5%. Together, these two changes push the market value from
$57 billion to $90 billion”and you could make up others. If you push it up a little more,
PepsiCo™s management would be pleased with your calibrated pro forma”it would indicate to
them that their market value is justi¬ed. (Of course, you would not show them your original
uncalibrated pro forma. )
You must be conceptually clear about what it is that you are doing if you calibrate your pro
Know what you are
doing here when you are forma: you are “fudging” numbers to make the outcome ¬t a market value. This is justi¬ed if
doing this!
you believe that the ¬nancial market™s value of PepsiCo is e¬cient and better than your own
pro forma estimate. You can “fudge” appropriately and responsibly or inappropriately and
irresponsibly (and be on the lookout if someone else is handing you their pro forma estimates).
For example, by adopting Coca Cola™s 3% growth rate as appropriate, you are accepting the
market™s assessment of Coca Cola at face value”even though this seems economically like an
optimistically low cost of capital and optimistically high growth rate. In one sense, you are
adopting a “deus ex machina””a number that is dropped on you from another part of the
stage (the ¬nancial markets) and that you therefore do not fully understand. In another sense,
you are just doing what you have always done: you are doing relative valuation, accepting the
known market-value of a comparable as a good baseline in your quest to compute another
project™s valuation.
Section 29·5. Complete Pro Formas.
Table 29.7. Calibrated Economic Cash Flow Projections

Pro Forma Cash Flow Statement

Cash Flow Model Terminal Value
Growth at 15% Growth at 3%

2002 2003 2004 2005
2000 2001

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

¬le=proformas.tex: RP
Projected Annual Asset Cash Flows1 $1,969 $2,264 $2,604 $2,994 next row
$1,556 $1,712

$2, 994
Terminal Market Value for 2005 to eternity at E(g) = 3%: ≈ $99.8 billion
6.5% ’ 3.0%

Total Cash Flows $2,058 $2,366
≈ $102.4 billion

Discount Factor, based on 6% cost of capital 0.943 0.890 0.840

2001 Present Value of Cash Flows $1,857 $2,015 $85,989

≈ $90 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.)

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752 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

29·6. Alternative Assumptions and Sensitivity Analysis

What should you learn from this chapter? Perhaps most importantly: do not trust any single
You need sensitivity
analysis pro forma estimate. But you can do more analysis to help you understand how robust your
estimates actually are. Most such techniques are easiest to perform in spreadsheets, which
allow you to try out di¬erent assumptions and scenarios.

29·6.A. Fiddle With Individual Items

Always keep your ultimate goal in mind”you want to ¬nd the best value estimate for your
You want to ¬nd a best
estimate of value”not business. Your goal is not an exercise in NPV analysis. It is not beauty or simplicity, either.
the simplest or most
Though both are nice to have, if elegance requires sacri¬cing important value drivers, you
complex, easiest or
cannot do it. Use your imagination, your head, and your good common sense!
hardest pro forma.

You should pay attention to other information”and even your personal opinion. For example,
You can use ad-hoc
assumptions if you in our PepsiCo valuation, $2,506 (or $2,994) was the estimated expected cash ¬‚ow in 2005. If
believe they offer better
you have good reason to believe that this is a low estimate, you can adjust (“fudge”) it. For
example, if you believed that a new drink were to come on-line and give cash ¬‚ows a one-time
upward value transition of $500 million, then you can use $3,000 or even $3,500. Your estimate
does not have to be based on formal, scienti¬c forecasting, either. Of course, whoever is the
consumer of your pro forma may not agree with your estimate, so you™d better be ready to
mount a good and credible defense of your number.
Similarly, there are no laws that say that you have to use the growing perpetuity formula on
You can use alternative
terminal value estimates, cash ¬‚ows to obtain your terminal market value. Instead of using the assumption that growth
will remain eternally the same (say, 3%/year), you could develop another formula that assumes
high growth rates for a few years (say, 5% next year), followed by growth rate declines until
the growth rate reaches the in¬‚ation rate (say, 2% per year). Or, you might deem it best if you
assumed that you could ¬nd a buyer for PepsiCo who will be paying $200 billion in 2005”
ultimately, it is this quantity that you seek to model with your terminal value. Again, you™d
better be ready to argue why your $200 billion should be the best estimate.
Modeling the pro forma as a spreadsheet will also allow you to consider speci¬c future scenarios.
More analysis can help
to determine expected For example, what would happen if the new product were to be wildly successful, or if it were
(rather than just most
to fall on hard times (though few pro formas in the real world consider complete failure“a
likely) cash ¬‚ows.
mistaken omission)? What would happen in a recession, based on what has happened in past
recessions? What would happen if sales were to decline by 5% next year, rather than grow by
3.6% per year? What would happen if sales were to decline for a number of years, not just
for one year? How bad would one or many inputs have to be for you to regret having bought
into the project in the ¬rst place? And, of course, you can ask the venerable payback question:
how long will it take before you get your money back? Admittedly, with more time, technology,
and printing space, you really should look at many di¬erent modi¬ed scenario analyses to
understand our PepsiCo pro forma better. Computer spreadsheets were invented precisely to
make such analyses relatively easy.
¬le=proformas.tex: RP
Section 29·6. Alternative Assumptions and Sensitivity Analysis.

29·6.B. Do Not Forget Failure

The biggest problem in most pro formas, however, is not even in the details. It is the fact that The biggest problem.
This is a scenario, not an
a pro forma is just one particular scenario, and usually a reasonably optimistic one. Many pro
expected value! Overall
formas are modeling just a “typical” or median outcome (recall Section 7·3). This would not be failure is often not
dissimilar to an average outcome but conditional on the project not aborting altogether. considered.

Obviously, this is more important for entrepreneurial ventures or startups than it is for PepsiCo. Entrepreneurial
ventures”especially tech
For example, if someone pitches you a new magazine, most of the time, the pro forma will
ventures”often have
project a mildly optimistic scenario”on condition that the magazine succeeds. It probably almost all value in the
does not take into account the fact that 50% of all magazines fold within a year. It is your task terminal value estimate.
as the consumer of the pro forma to determine for yourself the probability of overall magazine
failure, or you will end up misled. (Immediate death does not matter for our PepsiCo pro forma.
PepsiCo is likely to stay around for a few more years.)

29·6.C. Assessing the Pro Forma

By now, you should have realized that the question, “Which PepsiCo pro forma is correct?” is What you should ask and
what I can tell you.
not a good one . No pro forma is correct! A better question is, “What kind of PepsiCo pro forma
is better?” But perhaps the best question is, “How can I judge how good a pro forma is?” There
is no easy answer.
You should de¬nitely contemplate your uncertainty about each input. Often, the most in¬‚uen- An interesting
diagnostic: what fraction
tial source of uncertainty is the long-run value. For PepsiCo, it came into play in your terminal
of the value comes from
value. An interesting statistic is, therefore, what fraction of the value comes from the terminal the ¬nal value estimate?
value. In PepsiCo™s case, the present value estimate was $57 billion, of which roughly $53 bil-
lion came from the terminal value. After calibration, the value estimate was about $90 billion,
of which $86 billion came from the terminal value. So 95% of your PepsiCo pro forma value was
buried in your terminal value estimate. To the extent that you do not trust this terminal value,
you should be particularly careful. Of course, if you had stretched T , more value would have
been part of the detailed period rather than the terminal value”but this would not mean that
your forecast would have had more reliability. Consequently, the fraction of terminal value
in the overall value is only one interesting diagnostic. But then again, a large in¬‚uence of the
terminal value is fairly common, even for established companies. And startup companies typi-
cally have even more of the future cash ¬‚ows far in the future, although they also have higher
costs of capital early on. Many entrepreneurial venture business plans have 80% to 95% of their
value in this “dark-gray box” called terminal value. Watch out!
Are there any tools that can help? Even though a spreadsheet is the right tool for presenting and Monte-Carlo Estimation.
playing with one pro forma at a time, it is really the wrong tool to incorporate your uncertainty
in a more systematic way. Your input into each cell of your pro forma spreadsheet should
really contain not just one number for your best estimate, but also a second number that tells
you how reliable you deem your best estimate to be. This is what an even more sophisticated
method of analysis”called Monte-Carlo Simulation”does. It allows you to associate your
uncertainty with each cell in your pro forma spreadsheet. The Monte-Carlo procedure then
simulates a whole range of possible scenarios (NPV values), and gives you a distribution of
outcomes. Think of it as an automated sensitivity analysis. But this is beyond the scope of a
¬rst textbook in ¬nance.

Monte-Carlo Analysis is explained in the web chapter on real options.
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754 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

29·7. Proposing Capital Structure Change

Return to the scenario in which you are an investment banker seeking to propose a capital struc-
We want to propose
capital structure ture change. Equipped with your calibrated pro forma, you can now go in front of PepsiCo™s
management and present two capital structure scenarios”the current structure and the pro-
posed change. Your exposition of any proposed capital structure change will again be through
a hypothetical pro forma, including the full balance sheet and ¬nancing section on the cash
¬‚ow statement, but space constraints in this textbook limits our discussion.
Let™s begin evaluating PepsiCo™s current capital structure. In 2001, it had short-term debt of
The current situation.
$354 and long-term debt of $2,651. Other liabilities and deferred income taxes added another
$5,372. The income statement tells you that this caused PepsiCo to pay $219 in interest and
$1,367 in corporate income taxes (provisionally). With $4,029 in pre-tax earnings, this is a 34%
average tax rate.
Of its asset market value of over $100 billion, $87 billion was in equity and only $3 billion was
Judge the reasons pro
and con capital in ¬nancial debt. (The rest were other liabilities.) With so little ¬nancial debt, the only question
of real interest is whether it would make sense for PepsiCo to take on more. To answer this
question, you must weigh the various capital structure rationales from Part IV”questions like:

• How likely is PepsiCo to go into ¬nancial distress if it increases its leverage?

• How much could it save in corporate income taxes if it takes on more debt?

• How important are free cash ¬‚ow e¬ects? How much in value would PepsiCo gain by
operating more e¬ciently?

And so on.
In PepsiCo™s case, many of these questions are relatively easy. For example, the probability that
To sell to PepsiCo, you
must estimate the cost PepsiCo will experience ¬nancial distress if it took on a couple of billion dollars in extra debt
of debt.
is very low. Moody™s rated PepsiCo™s current debt an A1, just below Aa3; Standard and Poor™s
rated it an A. To pitch a new debt issue, you would have to inform PepsiCo what you believe
its cost of debt would be if it took on more debt. You would probably begin by looking at the
credit ratings of other companies. For example, Table 29.8 gives some relevant statistics for
¬rms with di¬erent credit ratings, debt ratios and interest coverages. In 2001, PepsiCo had a
book-value based debt/assets ratio of 14%, and its EBIT/interest ratio was about 25. In fact,
PepsiCo seemed like an outlier”its S&P rating should have been AA, not just A+.
Table 29.8 suggests that ¬rms with long-term debt of about 30% and an EBIT/Interest ratio
Let™s speculate on
alternative capital of 7 still tend to rank as “investment grade,” a category that many investment professionals
structure interest rates.
consider an important break. How much debt could PepsiCo take on to reach this high a level?
The answer is around $4 billion. With about $4 billion additional debt, and even if PepsiCo
had to pay an 8% interest rate, it would still likely remain BBB-rated. A quick look at prevailing
interest rates on ¬nancial websites further reveals that AAA bonds promised to pay about 7%,
BB bonds about 7.95% on average. Consequently, a PepsiCo with $6.5 billion in debt may have
to promise an interest rate of about 7.7% (which seems high relative to our cost of capital). Of
course, to really convince PepsiCo, you should spend many more hours researching a good
interest rate estimate for PepsiCo™s new debt.
Against these costs of borrowing, management should weigh the potential bene¬ts of more
The dollar effect of
releveraging”long term debt. What would the e¬ect of such leveraging be on PepsiCo™s value? Fortunately, we even
and short term tax
have formulas to help us assess the tax savings. For each dollar extra in debt rather than equity
¬nancing forever, you know that the corporate income tax savings would have a present value
of „ · DT. Speci¬cally, with an interest rate of 7.7% on $4 billion of new debt, PepsiCo™s interest
See Section 22·7.B.
proceeds would increase by $300 million. In turn, at its „ = 33% tax rate, this would create a
net present value of tax savings of about $100 million in the ¬rst year alone”about 4% of net
income. If PepsiCo maintained the extra $4 billion in perpetuity, the present value of these tax
savings would come to over $1.5 billion”not bad for a day™s work.
¬le=proformas.tex: RP
Section 29·7. Proposing Capital Structure Change.

Table 29.8. Characteristics of Firms by S&P Bond Ratings, December 2001

Investment Grade Speculative Grade
Mean 23% 26% 34% 43% 54% 62%
Std.Dev. 15% 16% 16% 20% 26% 56%
Long-Term Debt
Quart 1 11% 15% 23% 30% 36% 22%
Median 20% 26% 33% 42% 52% 56%
Quart 3 32% 37% 44% 53% 67% 86%

Mean 17 11 7 5 4 1
Std.Dev 15 15 11 14 25 4
Quart 1 6 4 3 2 0 -1
Median 14 7 5 3 1 0
Quart 3 24 12 8 5 3 1

PepsiCo had an equivalent total debt over assets ratio of ($2, 651 + $354)/$21, 695 ≈ 14%, and an equivalent oper-
ating income over interest ratio of $5, 490/$219 ≈ 25. Assets are book value based, and, for an old ¬rm such as
PepsiCo, severely understate assets.

It is more di¬cult to judge the operational savings that more debt could bring. For example, Other Ef¬ciency-Related
PepsiCo™s unions might see a seemingly less pro¬table company (lower earnings), which would
make them more willing to accept lower wages. Management might work harder, too”perhaps
even cut a few corporate airplanes. In deciding whether it would make sense value-wise to
relever, you would add these tax savings to any e¬ciency gains from debt, and subtract any
dead-weight losses.
Finally, there is another issue at hand. To take advantage of the tax savings, the money would You can return the cash
to shareholders either as
need to be returned to shareholders”or else it would earn more taxable net income. This
dividends or in a
can be done either through dividend payments or through a share repurchase. Both have the repurchase. This makes
disadvantage that if PepsiCo were overvalued in the market, as the original pro forma suggested, sense primarily if you do
not believe that shares
PepsiCo should raise more money in the equity markets, too, and not repurchase our shares. As
are already overvalued.
you learned, overvalued shares allow you to raise capital at very low expected rates of return.
See Section 19·3.C.
But, as a junior investment banker looking out to create value for PepsiCo shareholders, your In real life, your
problem would not be
most important problem would almost surely be elsewhere. It would be the problem of convinc-
maximizing ¬rm value;
ing PepsiCo™s management that more leverage is good for them. You could tell management that your problem would be
if they raised $4 billion in debt to repurchase $4 billion in equity, they would probably create an convincing
instant corporate value increase of $1 billion”more than just one-year™s $100 million savings,
example of an agency
but less than the $1.5 billion perpetuity income tax savings. Unfortunately, this is unlikely to issue.
sway management. Clearly, with more debt and less equity, they would have less ability to take
over other companies, start new projects, purchase corporate airplanes, or build corporate em-
pires. As an investment banker, in thinking about how to pitch to PepsiCo™s management, you
would have to ask yourself”what™s in it for PepsiCo™s management? (Any productive answer
would most likely have to lie in the compensation package of management.) One good choice
for an investment banker is to identify potential candidate ¬rms to take over”not only will
this create issuing fees, but it will also create advice fees. (And the investment banker can
suggest acquisitions that can create value even for the acquiror, too!) But on an equity value
of $87 billion, even $1 billion in more value is only about 1% of PepsiCo™s stock market value”
clearly, you would have an uphill struggle on your hands, even though a debt-for-equity issue
would just as clearly create shareholder value. (And hindsight knowledge tells us not only that
PepsiCo maintained its capital structure, but also that it continues to pay around $300 million
in interest expense, and continues to incur tax obligations of around $1.4 billion every year.)
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756 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

So, your best shot may be to convince PepsiCo to take over another company and lever up in the
process. (There is another alternative, too: you could try to convince a third party to take over
PepsiCo and relever. Unfortunately, this is not very attractive, because PepsiCo may already
have been overvalued by the market, if you believe your original pro forma.)

29·8. Hindsight

Let™s now switch perspective again. This time, you will look at the preceding analysis as an
Hindsight allows us to
autopsy! economist with hindsight. Remember that in our previous perspective, PepsiCo was a publicly
traded ¬rm. Consequently, you had a real market value upon which you could calibrate your pro
forma estimate. But why was this real market value so much higher than our original unbiased
pro forma estimate? Were the ¬nancial markets too optimistic, or were you too pessimistic?
In fact, we wanted to work with PepsiCo as of 2001, because you can now see how your ¬nancial
This is unfair”you
would not have this forecasts turned out in hindsight. But before we delve into what happened to PepsiCo from 2002
to 2005, you should realize that the actual realized ex-post performance would not necessarily
have been the best ex-ante estimate, because it contains subsequent and possibly unexpected
developments. For example, if you had believed defense contractors to be poor investments
in 2000, it might have been the right bet, but the events of and following September 11, 2001
would have proved you wrong. This does not mean that your 2000 forecast was bad, or that
you should have bet on a growing defense sector in 2000. (It may be of little consolation
to you if your bet would have lost you a lot of money.) Nevertheless, more often than not,
the best forecast is more likely to be borne out by the events of the future. Analyzing one
realization of the subsequent events is not giving you a perfect assessment of what you should
have predicted”but it is informative. In our case, PepsiCo™s actual 2002-2005 performance can
help tell you why the ¬nancial markets in 2001 were more optimistic than your pro forma was,
though not perfectly so. An autopsy can therefore give you some good but not perfect hints
where our forecast was wrong.
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Section 29·8. Hindsight.

Table 29.9. Actual Vs. Forecast Cash Flows and Earnings for PepsiCo


Year 2002 2003 2004
1999 2000 2001

Actual Econ. Cash Flow $4,242 $2,169 $2,817
$1,641 $2,501 $1,556

Projected, Direct, Tables 29.2 and 29.6 $1,883 $2,071 $2,278
Projected, Detailed, Table 29.4

Actual Net Income $3,000 $3,568 $4,212
$2,505 $2,543 $2,662

Projected, Direct, Page 737 $2,742 $2,824 $2,909
Projected, Detailed. Table 29.3 $2,828

: The detailed projected cash ¬‚ow omits interest paid, and is therefore a little too low.

If your cash ¬‚ow forecasts were too low, your pro forma forecast would have been too pes- Your cash ¬‚ow and
especially earnings
simistic. Indeed, Table 29.9 shows this turned out to be the case. In 2002, PepsiCo sold o¬
forecasts were too low!
some subsidiaries and therefore produced cash of over $4.2 billion. In 2003, PepsiCo invested
more than usual, and its cash ¬‚ows dropped back to just above $2 billion. This con¬rms what
you already knew”cash ¬‚ows are too lumpy to be well suited to direct projections. But what
about your earnings forecasts? They grew more smoothly than cash ¬‚ows”but also much
faster than what you had projected. By 2004, actual earnings were almost 50% higher than
your detailed forecast. No wonder that your pro forma was too pessimistic!
A closer reading of the 2002 annual report reveals what happened. After adjusting for changes Further information.
in the reporting of sales and COGS, PepsiCo™s 2002 sales actually increased by about $1.6 billion,
much more than the projected $971 million sales growth (from $26,935 million to $27,906
million) in the detailed pro forma in Table 29.1. Almost all of the increased sales ended up as
pro¬t. Higher sales in later years, too, can explain why most of the pro forma forecasts were
so mistakenly low. Our method”mechanistic projection models from past ¬nancial data”is
rarely very good, and PepsiCo was no exception. Unless you had known the business and
market well enough to forecast sales this high, you would have stood no chance!
You can also autopsy the pro forma estimate of E(r ’ g). As of mid 2005, PepsiCo had an How to reach the $100
asset market cap of $100 billion ($87 billion in equity) on earnings of $4.3 billion, plus another
$300 million in interest payments. Consequently, it is now capitalized at about E(r ’ g) =
E(CF )/PV ≈ 4.5%”in line with our own forecasts. Next, autopsy the forecast for E(r ), again
as of 2005. PepsiCo had a lower beta of only about 0.35”closer to the optimistic historical 0.7
beta than the pessimistic, shrunk beta of 0.9. Interest rates also turned out to have remained
low, so the 2005 cost of capital estimate might be

E (r ) = 5% + 3% · 0.35 ≈ 6% ,

which was lower than our unbiased 7% cost of capital estimate. Together with the E(r ’ g) ≈
4.5%, this implies that PepsiCo is capitalized as if its earnings were to grow only by about 1.5%
per year”not a very optimistic valuation, and indeed even lower than both the 2005 rate of
in¬‚ation and the estimate in your unbiased pro forma. So, we did not do too badly on our
E(r ’ g) forecast.
In sum, in hindsight, the primary driver of PepsiCo™s higher value was its higher sales. Let this This was an “easy” pro
forma”and we were still
be a lesson in humility: even for a large and established company with a solid history, valuation
off by a factor of two.
is di¬cult and su¬ers from plenty of uncertainties”though economic knowledge could have
done much to improve our estimates. But how much more uncertain are pro formas of upstart
projects, in which even more of the value lies far in the future?! This uncertainty should not
discourage you, however. Just as the CAPM is the premier model for the cost of capital, the
pro forma is the premier model to write business plans”simply, there is no better alternative.
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758 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

Forecasting the future is the tough job that economic value is all about. Fortunately, you don™t
even need to be able to forecast well. All that matters is that you can forecast better than the
rest of us. If you can, you will become rich.

Finally, how would I, as an investor in 2001, have looked at your pro forma? Most of my
A reasonable way to
approach public market faith would have been in the market value of PepsiCo, not in your pro forma value analysis. I
would not have trusted your ability to forecast the economics. However, if you had had more
knowledge of the underlying sales dynamics, your value analysis could have raised enough
doubts in me to believe that PepsiCo might be a little overvalued. After all, any public market
value is the clearing price where the bears and bulls on PepsiCo are in equilibrium”and your
analysis would have led me to join the bears. But I would have kept it all in proper perspective”
it would have been irrational for me to believe that the appropriate market price of PepsiCo
would be the pro forma $57 billion, when I could have seen the market value of $100 billion”
a reasonable synthesis of the PepsiCo value estimates would instead have concluded a value
closer to the market value than to the pro forma value”say, a synthesis of $95 billion.

29·9. Caution ” The Emperor™s New Clothes

Did our projections seem arbitrary to you? They should, because they were arbitrary”and this
Do not automatically
trust pro formas! They chapter made a point of telling you so throughout. But look back at the ¬nancials in Tables 29.3
often look very
and 29.4. If you did not round but quoted a few more digits (for pseudo-accuracy), if you
professional even if they
expanded the footnotes with some more mumbo-jumbo, and if you added a few more columns
are not credible.
of future years, a naïve reader might be fooled into thinking that you were a sophisticated
analyst who knew what you were doing! It is important that you not end up being such a naïve
consumer of pro formas. A well-written pro forma can easily convey an image of professional
knowledge where there is none. (Form over content may work here!) In the case of pro formas,
even the best emperor wears only a bathing suit.
Another danger for the unwary pro forma reader is falling into the trap of looking at the trees,
Do not lose the forest
and discuss mini-details. rather than the forest. You can easily get involved in endless discussions of a particular pro-
jected item in someone else™s pro forma. In real life, most pro formas rely on plenty of heroic
assumptions”in some cases, there are just one or two critical assumptions, in other cases,
there may be many. You must look at the big picture as well as at the minor assumptions.
There is devil in both detail and in the sum-total.
I hope I have not been sounding dismissive of pro formas. On the contrary”again, you really
What a good pro forma
is and is not. have no alternative, and forecasting the future is inherently a di¬cult but important task. The
universal use of heroic assumptions does not mean that there is no di¬erence between a good
and a bad pro forma. A less naïve reader can certainly distinguish a good one from a bad
one. A good pro forma pitched to a sophisticated audience must use solid economics and have
detailed footnotes explaining and justifying just about every important line item. It is a starting
point for a good discussion, not an end in itself.
Ultimately, ¬nance is about value, so it must revolve around projections, and pro formas are a
Closing the circle.
good tool to organize projections. Projecting is very hard. Remember how the book started? I
told you then that valuation is both an art and a science. The formulas are easy; the application
is hard. I trust that you believe me now. Welcome to the club of ¬nanciers!
¬le=proformas.tex: RP
Section 29·10. Summary.

29·10. Summary

The chapter covered the following major points:

• The purpose of pro formas is to project ¬nancials, which are then often used to com-
pute a project™s NPV today. You can also use pro formas to perform a ratio analysis to
test the ¬nancial soundness of a business plan or to analyze a project™s working capital

• Pro formas are usually split into a detailed forecast period and a terminal value.

• A good horizon choice for the detailed forecast period depends on the economics of the
business and the prevailing discount rate.

• A quick-and-dirty pro forma analysis may just project the line items of direct use. A more
complete pro forma analysis can try to project many intermediate components.

• A useful distinction is to think of ¬xed vs. variable (sales-contingent) forecasts for indi-
vidual components.

• Scenario analysis helps you to better understand the uncertainty in your pro forma.

• Pro formas are often idiosyncratic and not very reliable. But you have no better alternative.
So, use caution in constructing and interpreting pro formas.
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760 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.


A. Appendix: In-a-Pinch Advice: Fixed vs. Variable Compo-

Is it possible to predict in general how ¬rms™ income statements and cash ¬‚ow statements are
What is ¬xed, what is
variable? Some advice. likely to develop in the future? Is depreciation better modeled as consisting of ¬xed+variable
components, or is it better modeled as a ¬xed component only, or as a variable component
only? Is COGS more sales-variable or more stable, or are dividends? Of course, every business
is di¬erent, so there are no uniform answers here. Some ¬rms rely more on ¬xed-cost technolo-
gies, others on variable cost technologies. However, rather than not provide any guidance, I will
now describe how corporate ¬nancials have evolved on average in publicly traded companies.
Our speci¬c interest is whether particular accounting items have been better explained by their
own history or by sales growth. Although such knowledge of how the average publicly traded
¬rm has evolved can sometimes help you in a pinch (when you need something quickly and
without much thought), it is better if you regard this section as a “jumpstart” to get you to do
more economic thinking, exploration, and business modeling of your particular company.

Important: If you can, ignore the crutches provided for you in this section.
Instead, execute your modeling based on speci¬c and sound intelligence about
your business.

Our basic public company ¬nancial item prediction model will be
Our projections consist
only of a ¬xed
component and a E ( salest+1 )
E ( X t+1 ) ≈ γ¬xed · X t + γvariable · X t · (29.14)
variable (sales-related)

where X is a ¬nancial statement number, such as COGS or SG&A, and t is a year index. For
example, statistical history suggests that

E ( salest+1 )
E ( SG&At+1 ) ≈ 36% · SG&At + 68% · SG&At ·
E ( salest+1 )
= γ¬xed · SG&At + γvariable · SG&At · .

This says that the typical ¬rm™s SG&A was about one-third related to its own past SG&A value,
and two-thirds related to SG&A adjusted for sales growth. How would you use this prediction in
our PepsiCo pro forma? In 2001, PepsiCo had SG&A of $11,608, and sales of $26,935. Projected
2002 sales were $27,906 for a 3.6% increase. Thus, Formula 29.15 suggests

$27, 906
E ( SG&A2002 ) ≈ 36% · $11, 608 + 68% · $11, 608 · .
$26, 935
≈ 36% · $11, 608 + 68% · [$11, 608 · (1 + 3.6%)]

≈ 36% · $11, 608 + 68% · $12, 025 ≈ $12, 356 .

The left part in the formula measures the “¬xed e¬ect,” i.e., the degree to which SG&A remains
the same as last year™s SG&A, independent of PepsiCo™s 2002 sales growth. The right part in
the formula measures the “variable e¬ect,” i.e., how SG&A has to increase with sales growth in
¬le=proformas.tex: RP
Section A. Appendix: In-a-Pinch Advice: Fixed vs. Variable Components.

Side Note: The reason why the coe¬cients in formula 29.16 do not add up to 1 is that SG&A increased on
average in the sample”perhaps due to in¬‚ation. If γ¬xed is 1 and γvariable is 0, then the best prediction of X
next year is the same as X this year. If γ¬xed is 0 and γvariable is 1, then the best prediction of X next year is
obtained by multiplying last year™s X by the observed or predicted sales increase from this year to next year.

It is important that you do not believe that the precise coe¬cient estimates of 36% and 68% are Again, use the estimates
for guidance, and”if
applicable to your company. They are based on mechanical statistical models, which rely only
need be”as stand-ins,
on historical information for publicly trading companies that may be totally unrelated to your but do not believe they
own, and on a time period that is ancient history. The coe¬cient estimates can serve only as ¬t your project well.
“quick-and-dirty” stand-ins until you use your skills and smarts to produce something better.
They are here only to help give you some initial guidance in your own economic exploration of
whether a particular ¬nancial item in your ¬rm tends to be more ¬xed or more variable.
Moreover, keep in mind that most of the time, you will be asked to create a pro forma when Projection formulas can
de¬nitely be hazardous
the company contemplates a change in policy, or when you want to propose a new project. The
to your wealth. Watch it.
historical behavior of large publicly traded companies is unlikely to be a good representation
of what will happen in such circumstances. Instead, your pro forma forecasts must be speci¬c
in addressing contemplated policy changes. So, please do better than the formulas below.
Enough words of caution. Here are some nuggets of forecasting advice:

Sales This is the most important variable. You must forecast this number as diligently as you
possibly can. Other variables below can depend on this critical estimate. For illustration,
we shall forecast PepsiCo™s 2002 sales to be $27,906, which means that PepsiCo™s 2002
sales growth is $27, 906/$26, 935 ’ 1 ≈ 3.6%.

COGS In our average publicly traded companies,

E ( salest+1 )
E ( COGSt+1 ) ≈ 6% · COGSt + 95% · COGSt · (29.17)

Coe¬cients so close to 0 and 1, respectively, suggest that cost of goods sold is best
explained as a constant ratio of sales (unless the ¬rm deliberately shifts production into
di¬erent [¬xed cost] production). Like all other formulas below, this formula is based on
the history of reasonably large publicly traded U.S. ¬rms (and thus is neither necessarily
applicable to smaller ¬rms nor to the future).
To use this formula to forecast PepsiCo™s COGS for 2002, you would compute

E ( sales2002 )
E ( COGS2002 ) ≈ 6% · COGS2001 + 95% · COGS2001 · .
≈ 6% · $10,754 + 95% · {$10,754 · [1.036]}

≈ $11, 229 .

SG&A Selling, general & administrative expenses tend to have both a ¬xed and a variable com-
ponent. A typical ¬rm may be modeled by assuming that two-thirds is related to the sales
increase, and one-third is related to historical SG&A. A formula estimated on reasonably
large publicly traded U.S. ¬rms suggests that

E ( salest+1 )
E ( SG&At+1 ) ≈ 36% · SG&At + 68% · SG&At · (29.19)

For PepsiCo,

E ( sales2002 )
E ( SG&A2002 ) ≈ 36% · SG&A2001 + 68% · SG&A2001 · .
≈ 36% · $11,608 + 68% · {$11,608 · [1.036]}

≈ .
$12, 356
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762 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

Unusual Expenses No particular advice.
Operating Income Either construct from the items above (i.e., use the accounting identities),
or forecast as
E ( salest+1 )
E Oper.Inc.t+1 ≈ ’41% · Oper.Inc.t + 120% · Oper.Inc.t · (29.21)

Note that operating income is extremely sensitive to sales growth: any extra sales on
the margin has more than a one-to-one e¬ect on operating income. This is why the ¬rst
coe¬cient is negative and the second is above 1. It makes economic sense: operating
income goes positive only above some break-even sales point. (A strong sensitivity to sales
growth also appears in some other variables below.) However, there is one unusual feature
of this formula that you should understand: the two coe¬cients sum up to considerably
less than 100%. This means that the formula indicates a strong “drift” of operating income
towards zero. For example, for PepsiCo,

E ( sales2002 )
E Oper.Inc.2002 ≈ ’41% · Oper.Inc.2001 + 120% · Oper.Inc.2001 · .
≈ ’41% · $4,021 + 120% · {$4,021 · [1.036]}

≈ .
$3, 350
You would estimate declining operating income even in the face of increasing sales! This
also occurs in a number of formulas below. You must watch out for this”and think about
whether such a drift towards zero would make sense for your particular company and pro
Interest Income/Payments Either construct from debt and/or previous year™s interest pay-
ments, or forecast as
E ( salest+1 )
E ( Intst Inc.t+1 ) ≈ 22% · Intst Inc.t + 67% · Intst Inc.t · (29.23)

Remember: If a change in capital structure policy is contemplated, this item needs to
re¬‚ect it.
E ( sales2002 )
E ( Intst Inc.2002 ) ≈ 22% · Intst Inc.2001 + 67% · Intst Inc.2001 · .
≈ 22% · $8 + 67% · {$8 · [1.036]}

≈ .

Income Before Tax Either construct from items above, or forecast as
E ( salest+1 )
E ( Inc.bef.Taxt+1 ) ≈ ’32% · Inc.bef.Taxt + 116% · Inc.bef.Taxt · .
For PepsiCo,

E ( sales2002 )
E ( Inc.bef.Tax2002 ) ≈ ’32% · Inc.bef.Tax2001 + 116% · Inc.bef.Tax2001 · .
≈ ’32% · $4,029 + 116% · {$4,029 · [1.036]}

≈ .
$3, 553

Income Tax Either construct from items above, or forecast as
E ( salest+1 )
E ( Income Taxt+1 ) ≈ ’55% · Income Taxt + 123% · Income Taxt · .
¬le=proformas.tex: RP
Section A. Appendix: In-a-Pinch Advice: Fixed vs. Variable Components.

For PepsiCo,

E ( sales2002 )
E ( Income Tax2002 ) ≈ ’55% · Income Tax2001 + 123% · Income Tax2001 · .
≈ ’55% · $1,367 + 123% · {$1,367 · [1.036]}

≈ .

Income After Tax Either construct from items above, or forecast as
E ( salest+1 )
E ( Inc.aft.Taxt+1 ) ≈ ’30% · Inc.aft.Taxt + 113% · Inc.aft.Taxt · (29.29)

For PepsiCo,

E ( sales2002 )
E ( Inc.aft.Tax2002 ) ≈ ’30% · Inc.aft.Tax2001 + 113% · Inc.aft.Tax2001 · .
≈ ’30% · $2,662 + 113% · {$2,662 · [1.036]}

≈ .
$2, 318

Extraordinary Items No speci¬c advice.

Net Income Either construct from items above, or forecast as
E ( salest+1 )
E ( Net Inc.t+1 ) ≈ ’42% · Net Inc.t + 114% · Net Inc.t · (29.31)

For PepsiCo,

E ( sales2002 )
E ( Net Inc.2002 ) ≈ ’42% · Net Inc.2001 + 114% · Net Inc.2001 · .
≈ ’42% · $2,662 + 114% · {$2,662 · [1.036]}

≈ .
$2, 026

Depreciation, Depletion, Amortization Either construct from items above, or forecast as

E ( salest+1 )
E ( DDAt+1 ) ≈ 42% · DDAt + 62% · DDAt · (29.33)

For PepsiCo,

E ( sales2002 )
E ( DDA2002 ) ≈ 42% · DDA2001 + 62% · DDA2001 · .
≈ 42% · $1,082 + 62% · {$1,082 · [1.036]}

≈ .
$1, 149

Deferred Taxes Very strongly related to sales growth and/or capital investment.

Non-Cash Items Very sticky, but negatively related to sales growth.

Changes in Working Capital In Chapter 9, we discussed that changes in working capital can
use up cash quite quickly, especially when the ¬rm is growing fast! Consequently, this
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764 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

is one of the cases where a negative coe¬cient on the sales-growth-adjusted term makes
sense! And, indeed, we ¬nd that a decent model for large ¬rms is

E ( salest+1 )
E ( ∆W C t+1 ) ≈ 46% · ∆W C t + (’43%) · ∆W C t · (29.35)

For PepsiCo,

E ( sales2002 )
E ( ∆W C 2002 ) ≈ 46% · ∆W C 2001 + (’43%) · ∆W C 2001 · .
≈ 46% · $84 + (’43%) · {$84 · [1.036]}

≈ .

Capital Expenditures Capital expenditures seem to be strongly related to sales growth.

E ( salest+1 )
E CapExpt+1 ≈ 0% · CapExpt + 100% · CapExpt · (29.37)

For PepsiCo,

E ( sales2002 )
E CapExp2002 ≈ 0% · CapExp2001 + 100% · CapExp2001 · .
≈ 0% · $1,324 + 100% · {$1,324 · [1.036]}

≈ .
$1, 324

Note: If a change in capital expenditures policy is contemplated, this item needs to re¬‚ect

Other Investing Very sticky, but negatively related to sales growth.

Total Cash Flows From Investing Activity

E ( salest+1 )
E ( CF-Invt+1 ) ≈ (’320%) · CF-Invt + 340% · CF-Invt · (29.39)

For PepsiCo,

E ( sales2002 )
E ( CF-Inv2002 ) ≈ (’320%) · CF-Inv2001 + 340% · CF-Inv2001 · .
≈ (’320%) · $2,637 + 340% · {$2,637 · [1.036]}

≈ .

Very strongly related to sales growth.

Financing Cash Flow Items No useful relationship.

Dividends Very sticky, but negatively related to sales growth.

E ( salest+1 )
E ( Dividendst+1 ) ≈ 159% · Dividendst + (’82%) · Dividendst · . (29.41)

This estimated formula often does not make much economic sense: Why would dividends
go down if sales go up? It is not altogether impossible, of course. For example, if the ¬rm
experiences great sales surprises, it may decide that it needs the money to cover working
capital or that it wants to reinvest the money rather than pay it out as dividends. However,
you should consider this on a case-by-case basis. You might be better o¬ just assuming
last year™s dividends.

Net Stock Issuing No useful relationship. Strongly related to sales growth.
¬le=proformas.tex: RP
Section A. Appendix: In-a-Pinch Advice: Fixed vs. Variable Components.

Net Debt Issuing Strongly related to sales growth.

E ( salest+1 )
E ( Debt-Issuet+1 ) ≈ (’192%) · Debt-Issuet + 195% · Debt-Issuet · .

Total Cash Flows From Financing Activity Mildly related to sales growth.

E ( salest+1 )
E ( CF-Fint+1 ) ≈ (’0.07) · CF-Fint + 0.25 · CF-Fint · (29.43)

For PepsiCo,

E ( sales2002 )
E ( CF-Fin2002 ) ≈ (’0.07) · CF-Fin2001 + 0.25 · CF-Fin2001 · .
≈ (’0.07) · $1,919 + 0.25 · {$1,919 · [1.036]}

≈ .

Foreign Exchange E¬ects Sticky.

E ( salest+1 )
E ( FXt+1 ) ≈ 0.75 · FXt + (’0.52) · FXt · (29.45)

For PepsiCo,

E ( sales2002 )
E ( FX2002 ) ≈ 0.75 · FX2001 + (’0.52) · FX2001 · .
≈ 0.75 · $4 + (’0.52) · {$4 · [1.036]}

≈ .

Total Net Cash Flows
E ( salest+1 )
E ( Net CFt+1 ) ≈ 272% · Net CFt + (’267%) · Net CFt · (29.47)

Here is an example of an estimated formula that serves as a warning: a negative coef-
¬cient on the sales-growth adjusted number probably makes little sense for most large
companies. Yes, it could be that the company does consume more working capital as it
grows, but it just does not seem to be applicable in many cases”such as PepsiCo. You
might just want to avoid this formula.

The formulas are estimated using “regression analysis.” For super-nerds, to normalize
Digging Deeper:
¬rms, all variables were normalized by sales, regressions were run ¬rm-by-¬rm, and the coe¬cients were then
averaged over ¬rms. Even more sophisticated modeling assumptions and techniques did no better than the simple
regression approach adopted here.

In conclusion, do not trust these formulas. They are merely tools you can use for constructing
a ¬rst draft of your pro forma”they are not good blueprints. Forecasting the performance
of any business, but especially a new business, remains an art that relies on the underlying
sciences of economics, statistics, accounting and ¬nance. Don™t just rely on statistics alone.
Use common sense. Use good knowledge of the economics of the business and the industry.
Document your reasoning in informed and detailed footnotes. And then”pray!
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766 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.

Solve Now!
Q 29.1 Complete the 2002 forecast in the cash ¬‚ow statement model in Table 29.4. Create a
forecast for 2003. (Iterate on depreciation and investing to determine sensible inputs into both.)
¬le=proformas.tex: RP
Section A. Appendix: In-a-Pinch Advice: Fixed vs. Variable Components.

Solutions and Exercises

1. There is no clear and unique answer to this question. Here is a reasonable attempt.

Income Statement December
2001 2002 2003 Model Used
= Sales $26,935 $27,906 $28,911 grows by 3.6%
COGS $10,754 $10,761 $11,023 $3,506+26% of revenue
+ SG&A $11,608 $12,279 $12,721 44% of revenue
+ Deprec/Amort $165 $168 $168 3-year average
+ Unusual Expenses $387 $279 $289 1% of revenue
= Operating Expenses
“ $22,914 $23,486 $24,201 Sum The Above
Operating Income
= $4,021 $4,420 $4,710 Subtract The Above
+ Net Interest Income $8 $0 $0 Too Ignorant and Lazy
Income before Tax
= $4,029 $4,420 $4,710 Subtract The Above
“ Corporate Income Tax $1,367 $1,591 $1,696 36% of IBT
Income After Tax
= $2,662 $2,828 $3,014 Subtract The Above
“ Extraordinary Items $0 $0 $0 Too Ignorant and Lazy
Net Income
= $2,662 $2,828 $3,014

Cash Flow Statement December
2002 2003 Model Used
= Net Income $2,828 $3,014 transferred
+ Depreciation and Depletion $1,149 $1,216 formula
+ Deferred Taxes $286 $305 18% of Income Tax
+ Non-Cash Items “$46 “$46 Average Historical
+ Changes in Working Capital $43 $71 27% of Revenue Increase
Total Operating Activity
= $4,260 $4,560 Sum Above
’$1, 200 ’ 4% · Earnings
= Capital Expenditures “$1,313 “$1,321
+ Other Investing “$1,000 “$1,000 Arbitrary. Sticky.
Total Investing Activity
= “$2,313 “$2,321 Sum The Above

Depreciation: 42% times prior year depreciation plus 62% times sales-grossed-up prior depreciation.

(All answers should be treated as suspect. They have only been sketched, and not been checked.)
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768 Chapter 29. Corporate Strategy and NPV Estimation With Pro Forma Financial Statements.
Part VI



The Appendix

(A part of all versions of the book.)

Afterthoughts and Opinions. Preliminary
last ¬le change: Feb 23, 2006 (15:37h)

last major edit: n/a

You have traveled a long distance with me throughout this book. We have now reached the
Epilogue, where by tradition, I am allowed to voice my own personal and perhaps unscienti¬c
opinions. I want to leave you with some of my thoughts on business and ¬nance education,
¬nance as a discipline, and ¬nancial research.

Anecdote: Yogi Berra™s Theory and Practice

In theory, there is no di¬erence between theory and practice. In practice, there is.

” Yogi Berra

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774 Chapter A. Epilogue.

A·1. Thoughts on Business and Finance Education

By nature, most disciplines in business schools, but especially ¬nance, are closely related to
practice. It is not an overstatement to claim that the majority of ideas in ¬nance were either
invented or developed in Academia, before they crossed over into practice. Unfortunately, over
the years, fundamental misunderstandings have developed, which have become the source of
much frustration among both faculty and students. Let me try to correct some of them.

A·1.A. Common Student Misconceptions

Some students seem to believe that business schools exist primarily to increase salaries and to
enhance job opportunities. As a result, they expect a “vocational education.” It is no wonder
that they are especially fond of some practitioner-teachers, who can share plenty of war stories,
vouch for the importance of their own teaching in their business environment, and may even
help some students to get a job at their own or their friends™ businesses.
This is a sad and limited view of what business schools have to o¬er. It will necessarily cause
their ¬nance education to be a rather unrewarding experience. Vocational training is not what
top business schools are good at. The top business schools are without exception not vocational
training centers, but research centers. Community colleges teach job-speci¬c skills; universities
do not!
Business schools provide”or at least should provide”a profoundly intellectual experience.
Such an experience allows students to take a fresh look at the world, to explore other business
areas for the ¬rst time, to learn how to think in economic and business terms, to consider the
intellectual foundations of business, and to learn about the most novel ideas”those that have
not yet permeated practice. Chances are that the practice in any given company is based on
knowledge that the previous generation of managers learned in business schools ten to twenty
years ago.
So, the value of an M.B.A. graduate”even to the ¬rst employer”is not his/her immediate busi-
ness knowledge. It makes no sense for M.B.A. students to learn how the ¬xed-income depart-
ment at Goldman Sachs works this year, which is well known by anyone working there (including
the secretaries), and which will surely be best explained by the Goldman Sachs traders to any
new hire upon arrival. Instead, the value of M.B.A. students to an employer is the intellec-
tual ability; knowledge of the fundamentals, basic theories and their application; cutting edge
ideas; human skills; team skills; sales skills, etc. Some of these skills are native, but most can
be taught or at least improved upon by studying. In the end, it is an individual™s versatility and
curiosity, an ability to generalize and synthesize, and a talent for bringing an aerial perspective
to speci¬c problems that will allow the newly minted M.B.A. to be of value for many years to
Naturally, many students feel a great deal of anxiety about job prospects, and therefore they
tend to prefer skills that they believe will facilitate immediate placement upon graduation.
Trust me: pretending to have been taught business practice in business schools is not what
employers want. Employers ¬rst and foremost want to hire smart, curious, and enthusiastic
individuals, who are solid on the basic concepts and who can apply them to new situations.
They can teach their own practices better than business schools can.

Anecdote: The Time Warp
Do you really want to just learn what the CFO knows today? In October 2003, City&Guilds (U.K.) released their
study of 405 random ¬nancial directors. One in seven needs help even switching his or her computer on and
o¬. One in ¬ve struggle to save a document. More than one in ¬ve need assistance in printing. And a quarter
cannot understand spreadsheets. (Source: The Register.)
¬le=epilogue.tex: RP
Section A·1. Thoughts on Business and Finance Education.

Student Heterogeneity
There is another factor at play which may make you initially unhappy in your introductory Realize that there are
distinct student
¬nance class”but it is important that you realize why this is so. Chances are that you will
¬nd yourself in a classroom with considerable heterogeneity in student preparation. Some
students will be more comfortable with math then other students. If you are taking this course
in business school, half the students may have come from a background in which their prime
function was ¬nance-related. Usually, such ¬nance work experience will not have left them
with solid enough knowledge to skip the ¬nance core course, but it will have left them with
the knowledge to help them better integrate the new information. Large and distinct student
populations are a fact of life in many introductory ¬nance courses. It is thus inevitable that
you ¬nd yourself in a classroom in which many students ¬nd the tempo of the ¬rst course
¬nance too fast and many other students ¬nd it too slow. On the plus side, I have found that
it can work very well if students with worse backgrounds are tutored by students with better
backgrounds. On the minus side, the temptation is high to just let the “¬nance jocks” take care
of the group assignments. Do not let this happen, or the preparation problem will accumulate
and become unsurmountable.
Now put yourself into the shoes of your ¬nance instructor. There is plenty of material that can It is impossible to time a
¬nance course in a
absolutely not be skipped. Interviewers expect students to have a solid grasp of the ¬nance
business school core, so
basics (but fortunately not of practical esoterics). It is not uncommon for an interviewer to that both the
ask questions that could go right onto the midterm or ¬nal. To appreciate the di¬cult task well-prepared ¬nance
nerds and novices will be
of the instructor, now add the heterogeneity in student background. The need to grade does
happy all the way.
not improve student happiness much, either. The well-prepared students start out with a
considerable headstart when it comes to test performance relative to students who come from
non-quantitative and non-¬nancial backgrounds. The world is not fair”and neither is the grade
competition in such a course.
In the end, there is no way around it: it will be a challenge for previously unprepared and Advice to the
“non-quants”: As a less
non-technically inclined students to keep up. It is the task of the instructor to make this a
prepared student, you
surmountable challenge. This is the most important goal of a ¬nance course”all motivated must struggle.
students must be able to acquire a solid ¬nance background. But if you are one of those
students without quantitative and ¬nancial preparation, you will inevitably feel overwhelmed
by your class experience. Let me advise patience, practice, and re¬‚ection: it will all eventually
fall into place, kemosabe, and you can do well in the end. Some of my best and brightest
students felt frustrated during the course, but they kept at it, studied and learned twice as
hard, and ended up at the top of their class. Struggling and anxiety along the way are necessary,
maybe even desirable, and in the end unavoidable.

A·1.B. Common Faculty Misconceptions

Some faculty are as mistaken as students. They seem to believe that ideas in Academia are
too di¬cult to communicate to M.B.A. students in an exciting and interesting fashion. They
deemphasize current academic research in their classes. They rarely talk about what it is that
drew themselves to business schools rather than to practice: the excitement of new knowl-
edge and research, and the opportunity to convey ideas to students and the world at large. If
academic research is not universally incorporated into the curriculum and identi¬ed as such,
then it is not surprising that students ¬nd little value in it. In fact, if the research ideas are so
obscure that they cannot be explained to and appeal to M.B.A. students, they probably are of
little interest to begin with.
So, here is my personal appeal to faculty in core courses: in addition to integrating current
research throughout the curriculum, please reserve your ¬nal teaching session of class to talk
about academic research in ¬nance in general terms”and the academic research in your own
department, speci¬cally. My own experience tells me that students will ¬nd this to be the single
most popular session of the entire course.
¬le=epilogue.tex: LP
776 Chapter A. Epilogue.

A·1.C. Business School vs. Practice

Table A.1. Advantages and Disadvantages of Business Schools over Business Practice

Some Examples of
What Business School Teaches Better Than Practice What Practice Teaches Better Than Business School
General, universal knowledge Job speci¬c knowledge
Concepts of business The speci¬c business
General tools (statistics, data, economics, etc.) Speci¬c tools (e.g., a particular accounting system)
Marketing methods Our product or service marketing
Method of thinking Method of company™s practice
Concepts of ideas for the next 20 years Implementation of ideas from the last 10 years
Knowledge for a lifetime Knowledge for this year
Leadership principles and theories Learning how to lead a particular Set of people
Source of con¬‚ict Con¬‚ict resolution with a speci¬c person
Learning by study Learning by doing
Re¬‚ection Action
Selling principles Selling our product or service
Negotiation principles Negotiating with speci¬c customers
Forests trees

Business schools can teach some subjects better than practice, but not all. This is not to say
that practice is any less interesting than Academia. It is to say that practice is best taught by
practice (the employer) than by business schools. As an M.B.A. student, be patient: the ¬xed
income department at Goldman Sachs will explain in its own training program the specialized
¬xed income and institutional knowledge that it will require. The ¬xed income department
does not seek individuals who already know what Goldman Sachs will teach in its ¬rst week.
Instead, the ¬xed income department seeks smart, ¬‚exible, and open-minded individuals, with
a solid understanding of fundamentals”of forests, not of trees. Table A.1 is my perspective
on who does what better.
Business schools should focus on subjects that they can teach both well and better than practice.
One or the other is not enough. For example, there is ample research that has shown that taller
people are more successful. But height is not something that business schools can contribute
much to, so we should not teach it. Take the second: I wish I knew how to teach you how to
“sell” anything”products, services, ideas. In my opinion, the ability to sell to other people”to
get them excited”may be the single most important skill and key for success in life. Now, some
people are naturally adept at selling, others can learn it, and still others will never be good at
it. Unfortunately, although selling ability is undoubtedly enormously important, this does not
mean that business schools can and should teach it. It may be better learned by following the
company™s best salesperson. (I will let you know when I ¬gure this one out!) In sum, do not
expect to learn everything you need for success either only in practice or only in school! If you
do, you will be disappointed.

Anecdote: Success in Business: Grow up!
Timothy Judge, a University of Florida management professor, ¬nds that controlling for gender, weight, and
age, each inch in height seems to add about $789 a year in salary. In his study, greater height boosted subjective
ratings of work performance, including supervisors™ evaluations of how e¬ective someone was on the job. It
also raised objective measures of performance, such as sales volume. The relationship between height and
earnings was particularly strong in sales and management, but was also present in less social occupations such
as engineering, accounting and computer programming.
Source: Yahoo.
¬le=epilogue.tex: RP
Section A·1. Thoughts on Business and Finance Education.

A·1.D. The Rankings

In 1988, Business Week (BW) began to publish a bi-annual ranking of business schools. This
rankings issue has become one of BW™s top sellers. Unfortunately, the quality of the rankings
is only mediocre. Worse, the in¬‚uence of the rankings on business education has been both
enormous and negative.
The BW rankings are based primarily on “customer satisfaction” surveys of students and re-
cruiters. Consequently, the BW ratings end up mostly as a popularity contest, and are not
based on criteria that measure the quality of education. For example, consider another promi-
nent survey: students at California State University at Chico were #1 in Playboy™s Party School
Rankings. They would probably rate their satisfaction very highly”but this does not make Cal-
State Chico a good school. The same issue applies to recruiters sampled by BW. Most recruiters
are themselves alums of one of the schools they are asked to rank. Most business school alums
have never studied at any school beyond their own”a fact that naturally makes them relatively
ill-equipped to make comparisons. (They also see themselves re¬‚ected in the students from
their alma mater.) Because larger schools have more alums that are sampled, the size of the
pool of alums ends up being the primary predictor of “recruiter opinion” in the BW survey. The
result is inevitable: the average recruiter ranks his or her own alma mater highest (or at least
very highly). Finally, all schools, students, and alums are now catering to and manipulating the
BW rankings. Students and alums know that if they do not rank their own school highly, the
values of their degrees will go down. And in almost every school, some faculty member will
explain this to those students who have not yet understood this basic fact. In sum, popularity
ratings are not a great measure of educational quality.
But the most important error of the BW survey is that it treats education as if it were a consump-
tion good sold by vendors. Instead, education is something that is coproduced by the school
and the student. Almost anyone with an above-average IQ can get a degree in a business school
today, but its usefulness is largely determined by the depth of engagement of the student. A
student who coasts will gain little, no matter how good the school is.
This is not to say that there are no quality di¬erences between schools. There are quality di¬er-
ences, but the BW rankings do not fairly re¬‚ect them. My advice to any student is to consider
many rankings only as useful supplementary indicators. For example, Harvard Business School
(HBS) should probably be ranked as the #1 business school for a general M.B.A. education to-
day, although a ranking somewhere between #1 and #5 would be more appropriate. But HBS
is not #1 in every ¬eld. Its ¬nance education, though superb, is not the world™s #1. There
are other schools that are at least as good. In contrast, HBS™ education in corporate strategy”
where its world-renowned case method works well”is undoubtedly #1. Yale, my prior school,
may not boast a top 3 M.B.A. program, but it o¬ers the #1 ranked education for management
of not-for-pro¬t organizations today. And so on. Finally, quality di¬erences among similarly
ranked schools are often modest: most schools teach similar curricula. The material in this
book should appeal to students of any school. My personal guess is that the educational quality
di¬erence between the #1 school and the #10 school is very small (as it would be between #10
and #30, or between #30 and #100). The variation in what an individual gets out of an M.B.A.
program within one individual school just swamps the average quality variations across schools.
It is up to you to make your education top-ranked.
Fortunately, although deciding on the right school is a tough problem, there are many good
choices to pick from. It is especially encouraging to me that many schools that never show up
in any of the rankings are o¬ering excellent business educations. Again, by selection of classes
and instructors, a student can easily get a worse business education at, say, Harvard Business
School, than at, say, Notre Dame, even though Harvard clearly outranks Notre Dame in any

In my opinion, there are no good distance-learning universities in existence today. (This may
Side Note:
change in the future.) The most prominent, the so-called University of Phoenix, is a great business for its owners,
but not for its students. Its degrees are not recognized by others and it is not accredited by the AACSB. (This
is not an absolute necessity for an established top-10 school, but it is necessary for an upstart school.)
¬le=epilogue.tex: LP
778 Chapter A. Epilogue.

A·2. Finance: As A Discipline

A·2.A. Art or Science?

I have stated several times throughout the book that ¬nance is as much an art as it is a science.
All three parts of ¬nance”valuation, investments, and ¬nancing”have simple conceptual un-
derpinnings, but their applications in real life are di¬cult. And for all three of them, there is
no alternative: ¬nding the proper value, the proper portfolio, the proper capital structure may
be tough, but this is what it is all about. The di¬culty of these questions is good news for
practitioners and academics alike: it means that computers will not replace them for a long
time to come.
What to do for now? Given that all methods have their errors, the best advice is to use common
sense, to employ a number of di¬erent techniques to come up with a whole range of possible
answers, and then to make a judgment at the end of the day as to what appears most reasonable
in light of di¬erent models and estimates.

A·2.B. Will We Ever Fully Understand Finance?

No! It is the nature of the beast. Most of ¬nance is a social science. When there are no
arbitrage conditions to constrain permissible behavior and prices, behavior and prices can
and will deviate from the theory. On occasion, this leads some to conclude that ¬nance is
less worthy of study or even a lesser science than, say, mathematics or physics. This is a
mistake. The questions are di¬erent. Finance is not interested in the big bang, and physics is
not interested in the behavior of C.F.O.™s. The study of one is not more or less worthy than the
study of the other.
Finance and physics even share many similar philosophical issues: Some questions permit more
precise answers than others. Some systems (like the weather and stock prices) are chaotic and
di¬cult to predict, while others (like Newtonian mechanics and option prices) are more exact.
It may even surprise you that I am comfortable stating that economics and ¬nance ask many
questions to which the answers are more di¬cult and complex than those often pondered
in mathematics and physics. For example, economic agents can react to economic forecasts,
which makes predicting the stock market even harder than predicting the weather. Imagine
how much more di¬cult it would be for atmospheric physicists to predict the weather if the


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