. 10
( 39)


“ “
NPV = $6.776M ⇐ PV(E (C1 )) = $45.454M PV(E (C2 )) = $41.322M

Real options come in many guises. Many projects are nothing but strategic options: For exam- Strategic Options are
ple, the value of unused land around cities is essentially the option that the city might expand
enough to make building on the land economically worthwhile. Research and development
often has no immediate usefulness, or even usefulness in the most likely scenario”but there
is a chance that it might yield a highly pro¬table discovery. This strategic option value has
to be properly considered in the expected cash ¬‚ow computation, or the project value will be
underestimated. Silly as it may sound, the most common mistake that managers commit when
it comes to real options is to just not recognize that they are there.

7·4.E. Summary

The proper valuation of strategic options is as important as it is di¬cult. The fact that the Strategic options are
tough to value.
¬rst step to valuing your real options is to recognize them does not mean that the rest is easy.
Strategic options become both economically more important and more di¬cult to value when
there are many periods and many possible economic scenarios. Valuation is especially di¬cult
if your decisions in each time period cannot be made independently but in turn depends on
possible futures. For example, if it costs money to close and reopen a plant, then your decision
to close the plant must also depend on your assessment of how quickly the product price will
recover. If there is a good chance of recovery soon, you may choose to operate the plant even
at a small loss right now. In such problems, the optimal decision rule itself can be very di¬cult
to ¬nd.
¬le=npvadvice.tex: LP
174 Chapter 7. Capital Budgeting (NPV) Applications and Advice.

Figure 7.9. Value of an Expansion Technology With Di¬erent Parameters

Retail P=$800, Cost C=$200
Decision: Run Plant Double
Revenues: $180,000,000
Fixed Costs: $100,000,000
Rent: $10,000,000
Retail P=$600, Cost C=$100
Net: $70,000,000

Decision: Run Plant
Revenues: $75,000,000
Fixed Costs: $50,000,000
d Retail P=$400, Cost C=$100
Rent: $10,000,000
d Decision: Do Not Run Plant

Net: $15,000,000
Revenues: $0
Rent: $10,000,000
¡ Net: ’$10, 000, 000
Retail P=$500 (known)
Flexibility: Build Capacity?
Fixed Costs: $3,000,000
e Retail P=$600, Cost C=$100
e Decision: Run Plant
… Revenues: $75,000,000
Fixed Costs: $50,000,000
Retail P=$400, Cost C=$100

  Rent: $10,000,000
Decision: Do Not Run Plant
  Net: $15,000,000
Revenues: $0
Rent: $10,000,000
Net: ’$10, 000, 000
‚ Retail P=$200, Cost C=$100
Decision: Do Not Run Plant
Revenues: $0
Rent: $10,000,000
Net: ’$10, 000, 000

“ “
NPV = $12.702M ⇐ PV(E (C1 )) = $2.272M PV(E (C2 )) = $13.429M

The correct valuation method for real options is the decision tree. In a spreadsheet, this is
Use Scenario
Analysis”The accomplished with scenario analysis, which allows you to specify di¬erent scenarios, one at a
Management Name for
time, each resulting in its own cash ¬‚ows. (Financial managers do this regularly, as we noted in
Chapter 1.) The appropriate project NPV would be the average over many di¬erent scenarios”
each with di¬erent probabilities and possibly di¬erent managerial responses”given a best
managerial strategy. Working this out is not easy. Think about how di¬cult it was just to
¬gure out how many di¬erent project combinations you could choose today. Now, ¬gure out
what you could do in the future under an in¬nite variety of possible future scenarios”which
you have to do when you value strategic options. Out of necessity, most businesses consider
only the most obvious strategic options.
Solve Now!
Q 7.5 List “strategic options” that a ¬rm needs to incorporate in its project valuation.

Q 7.6 A business produces 100,000 gadgets, costing $1 each to produce and sellable for $1.80
each (last year and just now). To produce another 100,000 gadgets requires running the machine
at night, which increases production costs from $1 to $2. The business can last for up to 2 years
(but think about how you would solve this for 5 years). In every year, with 10% probability, the
output price doubles; with 10% probability, the output price halves; with 80% probability, the
price stays the same as in the previous year. Shutting down the factory for 1 year costs $9,000.
Reopening it costs $10,000. The cost of capital is a constant 5% per year. What is the value of
this factory? (This is a di¬cult problem, but unfortunately not an unrealistic one.)
¬le=npvadvice.tex: RP
Section 7·5. Mental Biases.

7·5. Mental Biases

Most cash ¬‚ow and cost-of-capital estimates rely on judgments. Unfortunately, it is often Model inputs are usually
not what they should be.
di¬cult to obtain accurate judgments. Our brains tend to commit systematic decision errors.
Managers who do not recognize these biases will systematically make poor decisions.
There are literally dozens of well-known behavioral errors, but limited space allows us to high- Innate Human Decision
Biases cause predictable
light just three: overcon¬dence, relativism, and compartmentalization.
valuation mistakes.

1. Overcon¬dence is the tendency of people to believe that their own assessments are more
accurate than they really are. In lab experiments, ordinary people are found to be dra-
matically overcon¬dent. When asked to provide a 90% con¬dence interval”which is just
a range within which they are con¬dent that their true value will lie in nine out of ten
tries”most people end up being correct only ¬ve out of ten times.
It is di¬cult to empirically document overcon¬dence”after all, if it were easy, managers
would recognize it themselves and avoid it. However, we do have evidence that many
managers who are already heavily invested in their own company tend to throw caution
overboard and voluntarily invest much of their own money into the corporation”and even
in companies going bankrupt later on. There is also good empirical evidence that those of
us who are most optimistic in overestimating our own life-expectancy disproportionately
become entrepreneurs. Even if optimism is a disease, it seems to be a necessary one for
To understand this better and to test your own susceptibility to these problems, you
can take a self-test at the book website, http://welch.econ.brown.edu/book. Doing so
will likely make you remember this problem far more than reading long paragraphs of
text in this book. Incidentally, the only population segments who are known not to be
systematically overcon¬dent are weather forecasters and clinically depressed patients.

2. Relativism is the tendency of people to consider issues of relative scale when they should
not. For example, most people are willing to drive 15 minutes to a store farther away
to save $20 on the purchase of $30 worth of groceries, but they would not be willing to
drive the 15 minutes to a car dealer farther away to save $100 on the purchase of a new
$20,000 car. The savings appears to be less important in the context of the car purchase
than in the context of a grocery purchase. This is ¬‚awed logic, similar to comparing
IRR™s while ignoring project scale. The marginal cost is driving 15 minutes extra, and the
marginal bene¬t is a higher $100 in the context of the car than the $20 in the context of
the groceries. Put di¬erently, the problem is that we tend to think in percentages, and the
$20 is a higher percentage of your grocery bill than it is of your car purchase. The smaller
the amount of money at stake, the more severe this problem often becomes. When a gas
station advertises a price of $2 per gallon rather than $2.10, customers often drive for
miles and wait in long lines”all to ¬ll a 20 gallon gas tank at a total savings that amounts
to a mere $2.

3. Compartmentalization Compartmentalization is the tendency of people to categorize deci-
sions. Most people are more inclined to spend more when the same category has produced
an unexpected windfall earlier. For example, winning a lottery prize while attending a
baseball game often makes winners more likely to purchase more baseball tickets, even

Anecdote: Small Business Failures
In New York City, two of every ¬ve new restaurants close within one year. Nationwide, the best estimates
suggest that about 90% of all restaurants close within two years. If successful, the average restaurant
earns a return of about 10% per year. So, owners seem to lose money on average. So, why open yet another
restaurant? We mentioned earlier (Page 12) that restauranteurs may just enjoy owning restaurants. But
a more likely explanation is that restauranteurs are over-optimistic, and just do not realize how tough it
is to pro¬tably run a restaurant.
More generally, a Small Business Administration study of small business failures from 1989 to 1992
found that 33% of businesses failed within 2 years, 50% within 4 years, and 66% within 6 years. Yet in a
survey of about 3,000 entrepreneurs, 81% of entrepreneurs believed that their chances of success were
at least 70%, and 33% believed that they had zero chance of failure!
¬le=npvadvice.tex: LP
176 Chapter 7. Capital Budgeting (NPV) Applications and Advice.

though the project “baseball game” has not changed in pro¬tability. Similarly, an unex-
pected loss may stop people from an otherwise pro¬table investment that they should
make. For example, say an individual likes to attend a particular baseball game. If she
loses her baseball game ticket, she is less likely to purchase a replacement, even though
the cost and bene¬t of purchasing the ticket are the same as they were when the original
ticket was purchased.

Know thyself to avoid these errors!
Solve Now!
Q 7.7 Describe common mental decision biases, and how they are likely to bias NPV calculations.

7·6. Incentive (Agency) Biases

Mental biases are not our only bias. Another kind of bias arises when one person is acting on
Incentive problems arise
when the information behalf of another. This is called an agency problem”a situation in which the owner of a project
provider has incentives
has to rely on someone else for information, and this someone else has divergent interests. An
that are different from
example may be shareholders who rely on corporate management to undertake projects on
those of the project
their behalves, or a division manager who has to rely on department managers for information
about how pro¬table their proposed projects really are. A cynical synopsis of agency biases
would be “all people act and lie in their own self-interest.” Now, although everyone does have
incentives to lie”or at least color the truth”corporations are especially rife with such agency
distortions. Of course, few people sit down and contemplate how to best and intentionally lie.
Instead, they convince themselves that what is in their best interest is indeed the best route to
take. Thus, mental biases often reinforce incentive problems: “wishful thinking” is a disease
from which we all su¬er.
You can take the fact that we have already had to mention agency issues repeatedly in this
These problems are
pervasive and important. chapter as an indication of how important and pervasive these are. But, again, lack of space
forces us to highlight just a few issues with some examples:

1. Competition for Capital Managers often compete for scarce resources. For example, divi-
sion managers may want to obtain capital for their projects. A less optimistic but more
accurate estimate of the project cash ¬‚ows may induce headquarters to allocate capital
to another division instead. Thus, division managers often end up in a race to make their
potential projects appear in the most favorable and pro¬table light.

2. Employment Concerns Managers and employees do not want to lose their jobs. For exam-
ple, scientists tend to highlight the potential and downplay the drawbacks of their areas
of research. After all, not doing so may cut the project and thereby cost them their jobs.

3. Perks Managers do not like to give up perks. For example, division managers may like
to have their own secretaries or even request private airplanes. Thus, they are likely
to overstate the usefulness of the project “administrative assistance” or “private plane

4. Power Managers typically love to build their own little “empires.” For example, they may
want to grow and control their department because bigger departments convey more
prestige and because they are a stepping stone to further promotion, either internally or
externally. For the same reason, managers often prefer not to maximize pro¬ts, but sales.

5. Hidden Slack Managers like the ability to be able to cover up problems that may arise in
the future. For example, division managers may want to hide the pro¬tability of their
divisions, fearing that headquarters may siphon o¬ “their” pro¬ts into other divisions.
They may prefer to hide the generated value, feeling that the cash they produced in good
times “belongs” to them”and that they are entitled to use it in bad times.
¬le=npvadvice.tex: RP
Section 7·6. Incentive (Agency) Biases.

6. Reluctance to Take Risk Managers may hesitate to take on risk. For example, they may not
want to take a pro¬table NPV project, because they can only get ¬red if it fails”and may
not be rewarded enough if it succeeds. A popular saying used to be “no one was ever ¬red
for buying IBM,” although these days Microsoft has taken over IBM™s role.

7. Direct Theft Managers and employees have even been known to steal outright from the
company. For example, a night club manager may not ring sales into the cash register. Or
a sales agent may “forget” to charge her relatives. In some marginal cases, this can be a
¬ne line. For example, is taking a paper clip from the company or answering a personal
e-mail from the company account really theft? In other cases, theft is blatantly obvious.
In September 2002, Dennis Kozlowski, former CEO, was charged with looting $600 million
from Tyco shareholders. His primary defense was that he did so in broad daylight”with
approval from the corporate board that he had helped put in place.

We do know where agency problems play a bigger role and where they play a lesser role. Where agency problems
are big, and where they
are not.
I. Scale and Owner Engagement In a small company with one owner and one employee, agency
con¬‚icts are less important than they are in big corporations with their many layers of
management and disengaged owners.
Do you believe that professionally run companies really make the best decisions on behalf
of their public shareholders? Remember that agency issues do not just arise between
shareholders and management”they start with the lowest level employee and bubble all
the way up to the top-level CEO. Decision-making is often based on a chain of deception.
It is a testament to the importance of sharing risks among many investors that large,
publicly traded companies still manage to net-in-net create shareholder value!

II. Project Duration If the project is short-term and/or comes with good interim progress
points, it is easier to reward managers appropriately for success and punish them for
failure. For example, think how you would judge and reward a manager who is (sup-
posedly) working on an R&D project that is not likely to have visible results for decades.
This is a di¬cult task. Agency problems for large and very long-term projects may be so
intrinsically high that they cannot be undertaken.

III. External Noise If good luck is an integral and important part of the project, it becomes
more di¬cult to judge managerial performance, which in turn aggravates agency issues.
For example, we can relatively easily measure the productivity of a line worker in a factory.
We know whether she works or slacks o¬. Therefore, agency problems matter less. In
contrast, it is more di¬cult to determine if our sales agent worked hard but the customer
just did not bite, or if our sales agent just failed. Similarly, our nightwatch security guard
may or may not be working hard, and it could take years before we could learn (probably
the hard way) whether she regularly stayed awake or just dozed o¬.

IV. Opaqueness If information is very di¬cult for outsiders to come by, agency problems will
be worse. For example, if only your manager sees what projects are available, he can
present only those that he would like to undertake and not mention those that have
higher NPV, but require di¬erent skills that he may not have or more work that he ¬nds

We also know that there are mechanisms that can help alleviate agency problems.

A. Audits If the company runs independent assessments or audits, managers can make de-
cisions based on better information, even if their employees are unwilling to provide it.
However, many consultants su¬er from the same disease as employees: they know that
they are most likely to be rehired if they tell the manager what she wants to hear.

B. Truth-Telling Incentives If managers can be rewarded for telling the truth, agency con¬‚icts
will become less important. For example, if your company has a research scientist who has
expertise in alpha-proteins and works on an alpha-protein project, your goal as manager
should be to allow this scientist to say without su¬ering any negative consequences: “Do
¬le=npvadvice.tex: LP
178 Chapter 7. Capital Budgeting (NPV) Applications and Advice.

not waste your money putting any more research dollars into alpha-proteins.” This means
that the scientist™s salary and promotion chances must remain the same or even increase”
even if this means that she no longer has a good alternative use for her time and e¬ort. You
might even o¬er a reward for any scientists who are voluntarily cancelling their projects.
Would you really be willing to carry through on such a promise? Would your research
scientists believe you?
Some companies also undertake post audits, which are designed not only to evaluate the
quality of the ¬nancial numbers (like a usual audit), but also the quality of managers™ up-
front forecasts. Knowing that such post audits will be held will strengthen the incentives
of managers to give accurate forecasts to begin with.

C. Contingent Compensation If managers are rewarded more if the project succeeds and pun-
ished if the project fails, agency con¬‚icts will become less important. For example, if you
pay your managers only when their projects succeed (or throw them into jail when their
project fails!), then managers will work harder and choose projects that they believe are
more likely to succeed.
Of course, like any other mechanism to control agency problems, this control strategy
has its costs, too. Managers have to feed their families and you may not be able to attract
the best managers if you force them to take on so much risk. (The capital markets are
probably better at taking risk than individual families!) And such managers may also be
more reluctant to take good risks on behalf of the company”risks that they should take
in the interest of shareholders”if they are themselves risk averse and compensated by

D. Reputation If managers can build a reputation for truth-telling and capable management,
they are less likely to undertake bad projects. For example, agency concerns are likely
to be a worse problem when it comes to secret one-shot projects, where your managers
cannot build a track record that will help them with future projects. On the other hand,
sometimes reputational considerations can themselves become the problem. Witness the
many dysfunctional but beautifully artistic o¬ce buildings that are primarily monuments
to some famous architectural ¬rm.

There is no obvious solution to these decision bias problems. Again, do not believe that just
The best “solution” is
ample skepticism and because we have spent only a few pages on agency issues that they are not important”they are
common sense.
both ubiquitous and very important in the real world. The website, http://welch.econ.brown.-
edu/book, has a full chapter on corporate governance, which is all about agency con¬‚icts. As a
manager or principal, you must be skeptical of all estimates and judgments and take the biases
and incentives of each information provider into account.
¬le=npvadvice.tex: RP
Section 7·6. Incentive (Agency) Biases.

Solve Now!
Q 7.8 The CEO projects earnings of $100 million next year. List three reasons why this is not a
good input into an NPV valuation.

Q 7.9 Describe common agency biases, and how they are likely to bias NPV calculations.

Anecdote: Fiduciary Responsibility, or the Fox guarding the Hen House.
On Wednesday, December 29, 2004, The Wall Street Journal reported on page 1:

In the biggest U.S. merger this year, J.P. Morgan Chase&Co. announced last January it would acquire
Bank One Corp. To assure investors it was paying fair price, J.P. Morgan told them in a proxy ¬ling
it had obtained an opinion from one of “the top ¬ve ¬nancial advisors in the world.”
The in-house bankers at J.P. Morgan endorsed the $56.9 billion price”negotiated by their boss”as

Next to it was a sidebar called Passing Muster, which explained

A ˜fairness™ opinion tells a company™s board that a deal™s terms are fair to shareholders.
Purpose: Legal protection from an investor claim that a deal was done without due care.
Cost: A few hundred thousand dollars to a few million.
Potential Con¬‚icts
• Bankers may have incentives to call a deal fair because most of their advisory fee is paid only
if deal closes.
• Bankers™ fee is tied to the deal price.
• Bankers may support a deal where executives will personally pro¬t, in hopes of securing
future work.
• Bankers use ¬nancial data supplied by client that wants deal to go through.
• When deal maker is a bank, its own bankers often write the fairness opinion.

Remember that everyone”in-house bankers, management, and the corporate boards”are employed by the
shareholders, to whom they owe ¬duciary responsibility, and for whom they are supposed to look out for.
It is a clear agency con¬‚ict for an employee to provide a fairness opinion. But it would also be di¬cult for
management to have these in-house bankers ¬red for doing them a personal favor”another agency con¬‚ict.
And there is also the original agency con¬‚ict: the incentive of acquiring managers to pay too high a price or of
target managers to accept too low a price. Here is how the WSJ story continues:

But during the negotiations, Bank One Chief Jamie Dimon had suggested selling his bank for
billions of dollars less if, among other conditions, he immediately became chief of the merged ¬rm,
according to a person familiar with the talks. That suggestion wasn™t accepted by J.P. Morgan.

Obviously, Jamie Dimon did not o¬er to pay his own personal billions for the privilege of becoming CEO, but
Bank One™s shareholders™ billions. Obviously, the J.P. Morgan management did not decline the billions on behalf
of their own pockets, but on behalf of their J.P.M. shareholders.
Still, there are of course the corporate boards which could have ¬red either the in-house bankers or their
management teams. Neither happened.
¬le=npvadvice.tex: LP
180 Chapter 7. Capital Budgeting (NPV) Applications and Advice.

7·7. Summary

The chapter covered the following major points:

• Attribute to each project™s NPV its in¬‚uence on other projects, either positive or negative.

• Think about how you can take advantage of or create positive externalities among projects.
If you cannot, there is no reason for these to be organized inside the same ¬rm.

• Think “on the margin.” Take all projects that contribute more marginal bene¬ts than they
create marginal costs.

• Consider economies of scale.

• Ignore sunk costs.

• Realize that real-world implementation problems”which range from di¬erences in short-
term marginal costs and long-term marginal costs, to political reasons and agency consid-
erations inside corporations”often make taking the best set of projects di¬cult.

• Compare long-term projects in terms of their rental equivalents if these projects are easily

• Use the expected cash ¬‚ows, not the most likely cash ¬‚ows in the NPV numerator.

• Take “strategic options” (or “real options”) into account. This is the value of your ability
to change course depending on future conditions. It includes your ¬‚exibility to delay or
accelerate projects, and to expand or shut down projects.

• Realize that common human and agency biases usually distort expected cash ¬‚ow esti-

• Design your operations so as to reduce agency con¬‚icts when it is marginally pro¬table
to do so.

No doubt about it: good capital budgeting is a di¬cult problem. Each subsection covered in
The problem is tough!
We can only offer some this chapter can easily be expanded into a full chapter or even a full book”and real options
and corporate governance already have their own web chapters. There are pitfalls everywhere.
To make your task a little easier, Appendix 2·1 contains an NPV checklist. In the end, though,
capital budgeting is an art as much as a science and has to rely as much on common sense and
intuition as on rules. The best analysis combines both.
¬le=npvadvice.tex: RP
Section 7·7. Summary.

Solutions and Exercises

1. The answer is yes, because it will cost the company $120,000 to move division DA. Moving saves $10,000/10%=
$100,000 in division DA costs and $3,000/10%=$30,000 in division DB costs. The total savings are $130,000
which is $10,000 greater than the cost of the building.
2. The answer is no, because the press earns $2,000/0.10=$20,000. But the press costs $10,000 to purchase and
eliminates $1,500/0.10=$15,000 of pro¬ts from the screw machines. So the total cost of the press, including
the $15,000 in opportunity costs, is $25,000. The project™s value is $20, 000 ’ $25, 000 = ’$5, 000.
3. Yes. The PV of the division™s pro¬ts will be $50,000/0.10=$500,000. The division costs are $210,000
for new equipment and $20,000 per year in increased overhead. The PV of the increased overhead is
$20,000/0.10=$200,000. So the total PV cost of the new division is $210, 000 + $200, 000 = $410, 000, and
the PV of the bene¬ts equal $500,000.


PV( Cost ) = $10, 000 + Annuity( $1, 000, 18 years, 12% )

$1, 000 1
= $10, 000 + · 1’ = $17, 249.67 .
(1 + 12%)18
PV( Cost ) = $15, 000 + Annuity( $800, 22 years, 12% )

$1, 000 1
= $15, 000 + · 1’ = $21, 115.72 .
(1 + 12%)22

(b) The equivalent rental values are

Annuity(x, 18 years) = $17, 249.67 x = $2, 379.37 .

Annuity(x, 22 years) = $21, 115.72 x = $2, 762.16 .

(c) The 18-year machine has the lower rental cost, so it is the better deal.

5. See Page 165.
6. Problems like this need to be solved “backwards.” You can start in period 2 with a prevailing price of $0.45,
$0.90, $1.80, $3.60, or $7.20; and your factory can be either open or closed. In this ¬nal period,
• If the price is $0.90 or lower, you de¬nitely want to close the factory, because $9,000 loss is better than
$10,000 loss. If the factory is already closed, lucky you.
• If the price is $1.80 or higher, you de¬nitely want the factory to be open, because $80,000 pro¬t fortu-
nately outweighs all opening and closing costs. If the factory is already open, lucky you.
Now consider what to do in year 1. If the price drops to $0.90, you have a decision to make: operate the
factory for a year, hoping that the future will be better, or close the factory. Operating losses would be
$10,000. Closing immediately would cost only $9,000. So, if you operate today, you incur an extra $1,000
loss. In exchange, there is a 10% chance that the price will go back up, in which case you got lucky. In this case,
you will have saved $10,000 reopening costs. Thus, you are exactly indi¬erent between closing and operating
if the price has dropped. (Of course, if the price is higher today, operating today is the correct choice.)
The problem of determining optimal choices as a function of environmental variables can get incredibly
complex very easily. Scenario analysis (or just plain real-world experience and intuition) is really the only
analysis method. This goes beyond the scope of an introductory textbook.

7. See Page 175.

8. First, it is probably the most likely outcome, not the expected outcome. It is probably more likely that the
¬rm goes bankrupt due to totally unforeseen circumstances than it is likely that the ¬rm will have a windfall.
Second, the CEO has an incentive to distort the truth, and report better projections than are most likely. This
is an agency problem. And, third, the CEO is probably subject to mental biases, too.
¬le=npvadvice.tex: LP
182 Chapter 7. Capital Budgeting (NPV) Applications and Advice.

9. See Page 176.

(All answers should be treated as suspect. They have only been sketched, and not been checked.)
Other Important Capital Budgeting Topics

The Internal Rate of Return (IRR), Duration, and Other Capital Budgeting Rules
last ¬le change: Feb 23, 2006 (14:32h)

last major edit: Apr 2004, Dec 2004

The CFO survey in Chapter 1 mentioned a number of other popular capital budgeting rules
(methods to decide among projects) other than NPV. Of course, even at their best, these mea-
sures can only be as good as NPV”we know that NPV, when correctly applied, yields the right
Two of these alternative capital budgeting techniques often”but not always”yield the same
correct answer, because they are really based on the same equation as NPV. They are the prof-
itability index and the internal rate of return, abbreviated IRR. Chapter 1 mentioned that IRR is
used as often as NPV. Actually, you have already seen it in another context, where it was called
the yield-to-maturity (YTM). You can interpret IRR as a “sort of average rate of return” when a
project has di¬erent cash ¬‚ows at di¬erent times. You will encounter IRR many times in your
Unfortunately, there are also some incorrect capital budgeting rules that are in common use,
¬rst and foremost the payback rule mentioned in Chapter 1. You thus need to know what they
are, and when and why they are bad.

¬le=irr.tex: LP
184 Chapter 8. Other Important Capital Budgeting Topics.

8·1. Pro¬tability Index

The ¬rst important alternative capital budgeting measure is the pro¬tability index. It divides
How it is computed.
the present value of future cash ¬‚ows by the project cost (the negative of the ¬rst cash ¬‚ow).
For example, if you have a project with cash ¬‚ows

Time 0 1 2 3 PV 1 to 3
Project A Cash Flow $70 $60 $50 $128.94

and the interest rate is 20% per annum, you would ¬rst compute the present value of future
cash ¬‚ows as
$70 $60 $50
PV = + + ≈ $128.94
1 + 20% (1 + 20%)2 (1 + 20%)3 (8.1)
= PV(CF1 ) + +
PV(CF1 ) PV(CF1 ) .

The NPV is $28.94. The pro¬tability index is
Pro¬tability Index = ≈ 1.28 .
PV( Future Cash Flows )
Pro¬tability Index =

A positive NPV project usually has a pro¬tability index above 1””usually” because the prof-
itability index is meaningful only if the ¬rst cash ¬‚ow is a cash out¬‚ow. When this is the case,
you can use either NPV or the pro¬tability index for a simple “accept/reject” decision: the
statements “NPV > 0” and “Pro¬tability Index > 1” are the same.
Some managers like the fact that the pro¬tability index gives information about relative perfor-
Here it does nicely.
mance and use of capital. For example,

Time 0 1 2 3 PV 1 to 3
Project B Cash Flow $21.14 $18.12 $15.10 $38.94

has the same NPV of $28.94 as our original project, but a higher pro¬tability index than 1.28
because it requires less capital upfront.
Pro¬tability Index = ≈ 3.89 .
PV( Future Cash Flows )
Pro¬tability Index = .

The reason is that two measures value the scale of the project di¬erently. It is intuitively
appealing that we would prefer the second project, even though it has the same NPV, because
it requires less capital. It may even be less risky, but this can be deceiving, because we have
not speci¬ed the risk of our future cash ¬‚ows.
Unfortunately, the very same feature that we just considered as an advantage can also be a
But here is where it can
go wrong. disadvantage. You cannot use the pro¬tability index to choose among di¬erent projects. For
example, assume that your ¬rst project returns twice as much in cash ¬‚ow in all future periods,
so it is clearly the better project now.

PV(CF1 , CF2 , CF3 )
Time 0 1 2 3
Project B Cash Flow $21.14 $18.12 $15.10 $38.94
Project C Cash Flow $140 $120 $100 $257.87

But the pro¬tability index of project C is only

Pro¬tability Index = ≈ 2.57 . (8.4)
¬le=irr.tex: RP
Section 8·2. The Internal Rate of Return (IRR).

which is below the 3.89 pro¬tability index of project B. The reason is that, when compared to
NPV, the pro¬tability index really “likes” lower upfront investment projects. It can indicate
higher index values even when the NPV is lower. So, you should really consider the pro¬tability
index to choose among projects only if the NPV of the two projects is equal (or at least very

8·2. The Internal Rate of Return (IRR)

The second important alternative to NPV is the Internal Rate of Return, often abbreviated Why study IRR if we
already know the correct
as IRR. You already know it”it is the same measure as the yield-to-maturity (YTM) that we
encountered in Section 4·6. It is important that you understand how to work it”and what its
drawbacks are, because it is in wide use.

8·2.A. De¬nition

Important: The Internal Rate of Return is the quantity IRR, which, given a
complete set of project cash ¬‚ows, solves the NPV equation set to zero,

0 = CF0 + + + + ... (8.5)
1 + IRR (1 + IRR)2 (1 + IRR)3

The IRR capital budgeting rule states that if a project™s IRR is above its appropriate
interest rate (cost of capital), it should be taken.

For example, for a project with cash ¬‚ows ’$100 and +$130 today and next year, the IRR is IRR generalizes returns!
obtained by solving
’$100 + =0.
1 + IRR
Of course, this means that IRR is just the simple rate of return of 30%. In this sense, a simple
rate of return is a special case of the more general IRR concept. But here is an example of IRR,
where a simple return is not applicable. A project has cash ¬‚ows ’$100, +$55, and +$60.50 in
successive years. How can you characterize the “rate of return” (loosely speaking) embedded
in its cash ¬‚ows? You do so by ¬nding the IRR,

$55 $60.50
’$100 + + =0. (8.7)
1 + IRR (1 + IRR)2

For this particular set of cash ¬‚ows, the solution is an internal rate of return of 10%, because

$55 $60.50
’$100 + + =0. (8.8)
1 + 10% (1 + 10%)2

If the project™s appropriate cost of capital over all years is 9%, then the IRR capital budgeting
rule states that the project should be accepted; if the cost of capital is 11%, it should be rejected.
As with NPV, it is important with IRR that you know whether you are computing it based on
expected or promised cash ¬‚ows. If you want to use the IRR for capital budgeting, you must
use expected cash ¬‚ows. YTM is most often computed for promised cash ¬‚ows”thus, it really
should be called “quoted YTM” rather than just “YTM.”
Even though the internal rate of return is quoted as a percentage and compared against an IRR is a characteristic of
a project™s cash ¬‚ows. (It
interest rate (the cost of capital or hurdle rate), the IRR itself is usually not an interest rate.
is not an interest rate.)
Instead, IRR is a characteristic of a project™s cash ¬‚ow stream. A given cash ¬‚ow stream directly
implies an IRR. In fact, you can compute the IRR for a project, never having looked at ¬nancial
markets, interest rates, or costs of capital. This is IRRs most important advantage over NPV: it
can be calculated before you know what the appropriate interest rate (cost of capital) is. It thus
¬le=irr.tex: LP
186 Chapter 8. Other Important Capital Budgeting Topics.

can give you useful project information in and of itself. It is also helpful in judging project
pro¬tability and thereby allows you to judge the performance of a manager”it may be easier
to hold her to her earlier promise of delivering an IRR of 20% than it is to argue with her about
what the appropriate cost of capital for her project would be. Armed with the IRR, you can
then contact various capital providers to see if the project is worthwhile. This is especially
useful if your project can be easily scaled but your cost of capital is increasing with your level
of investment (markets are imperfect). In this case, NPV is somewhat cumbersome to use, but
IRR makes it easy to help you determine an optimal scale for your investment.

Important: The IRR is best thought of as a characteristic of project cash ¬‚ows. It
is not a simple rate of return, even though it is often compared to a cost of capital
(which is rate of return) when it is used for capital budgeting purposes.

The IRR capital budgeting rule often yields the same (correct) decision as the NPV capital bud-
IRR is safe to use when
there is only one geting rule. IRR is guaranteed to work if
positive or only one
negative cash ¬‚ow.
1. the ¬rst, up-front cash ¬‚ow is a single negative number (an investment) followed only by
positive cash ¬‚ows (paybacks), or vice-versa.

2. the relevant yield curve for your cost of capital is uniformly above or below the IRR.

This is why IRR has survived as a common method for “capital budgeting”: most projects have
precisely such cash ¬‚ow patterns”an upfront investment followed by future pro¬ts. Of course,
you cannot do any better than doing right, so always using NPV is safer. It is just that if you
use IRR correctly and in the right circumstances, it can often work equally well and sometimes
gives you nice intuition.
You can ¬nd IRRs either by trial and error”as we did in Section 4·6”or you can use a common
Here is how to get the
IRR. spreadsheet function, which does this in a relatively painless manner. For example, Table 8.1
shows how to obtain an IRR in a simple example”cell A4 will become 0.13. (It may be painless
for you, but ¬nding IRR is actually not a trivial function. The spreadsheet must ¬nd the solution
to a polynomial equation that is of an order equal to the number of periods.)

Table 8.1. IRR Calculation in Excel

1 “1000
2 600
3 600
4 =IRR(A1:A3) ← will become 13%
¬le=irr.tex: RP
Section 8·2. The Internal Rate of Return (IRR).

8·2.B. Problems with IRR

Unfortunately, like the pro¬tability index, IRR does not always work. There are a number of
problems that you may encounter.

1. Project Comparisons and Scale In fact, the IRR shares the ¬rst shortcoming with the prof-
itability index. It can mislead when projects are exclusive alternatives. For example, would
you prefer a project with a 100% IRR, or a project with a 10% IRR? Think about it.
What if the ¬rst project is an investment opportunity of $5 (returning $10), and the second
project is an investment opportunity of $1,000 (returning $100)? The latter is the better
project, even though its IRR is worse.

2. Direction If a project starts with in¬‚ows and continues with out¬‚ows, it may be that a lower
IRR is better than a higher IRR. For example, if you have one project that receives $100
and has to pay $105 next year, its IRR is 5%. If you have another project that receives $100
and has to pay $106, its IRR is 6%. Obviously, you would rather pay less in the future”but
the IRR for the second project is higher.

3. Multiple Solutions When projects have both future positive and negative cash ¬‚ows (there
are often multiple and sometimes no solutions), all hell can break loose. For example,
return to our earlier project from Section 2·4.B on Page 28, where our project cost $900
today, yielded $200/year for two years, then $400/year for two years, and ¬nally required
a cleanup expense of $100. There are at least two internal rates of return: r = 8% and
r = ’79.6% (round to ’80%). Con¬rm this:

$200 $200 $400 $400
’$900 + + + + + ≈0,
(1 + 8%)2 (1 + 8%)3 (1 + 8%)4 (1 + 8%)5
1 + 8%
$200 $200 $400 $400
’$900 + + + + + ≈0.
2 3 4 (1 ’ 80%)5
1 ’ 80% (1 ’ 80%) (1 ’ 80%) (1 ’ 80%)

So, does this project yield an internal rate of return of 8% or an internal rate of return of
-80%? The fact is that both IRRs are valid according to the de¬nition. Should you accept
the project if the prevailing interest rate is 5%? The answer is not obvious, and we need
to go back to the NPV rule to learn that the correct answer is yes.
What does Excel do if there are multiple IRRs? You will never know. Excel will just pick
one for you.
There is also “modi¬ed IRR” (or MIRR) measure that can sometimes eliminate multiple
Side Note:
solutions. It is not worth the bother. If you have alternating-sign cash ¬‚ows, use NPV instead.

4. No Solution What is the proper IRR of a project that yields $10 today and $20 tomorrow,
and never demands an investment? There is no IRR that makes it zero. Or a project that
costs $10 today and $20 tomorrow, and never yields a positive cash¬‚ow? These projects
have no economically sensible IRR solutions, though they are admittedly far-fetched. But
neither does a project with cash ¬‚ows ’10, +$28, and ’$20 in consecutive years, where
the non-existence is not so obvious.

5. Cost of Capital Comparison When the term structure of interest rates is not ¬‚at (e.g., when
the annualized two-year interest rate is di¬erent from the one-year interest rate), and the
IRR lies between them, there is no rule as to which one to compare the IRR to. For example,
the yield curve may have the 1-year interest rate at 10%, the 2-year interest rate at 9%, the
3-year interest rate at 8%, the 4-year interest rate at 7%, and the 5-year interest rate at 6%.
Should you accept a 5-year project with an 8% IRR? After all, its project IRR is above its
5-year cost of capital (interest rate) but below the 1-year cost of capital. There is no clear

These problems may seem obvious when highlighted in isolation. But in the context of complex
real-world multiple project analysis, they are surprisingly often overlooked. Don™t!
¬le=irr.tex: LP
188 Chapter 8. Other Important Capital Budgeting Topics.

Solve Now!
Q 8.1 A project has cash ¬‚ows of -$100, $55, and $70 in consecutive years. What is the IRR?

Q 8.2 From memory, write down the equation that de¬nes IRR.

Q 8.3 Give an example of a problem that has multiple IRR solutions.

Q 8.4 Give an example of a problem that has no IRR solution.

8·3. So Many Returns: The Internal Rate of Return, the Cost
of Capital, the Hurdle Rate, and the Expected Rate of

It is time to recap four rates that are commonly used in ¬nance: the Internal Rate of Return,
Finance professors like
to use terms the Cost of Capital, the Expected Rates of Return and the Hurdle Rate. The di¬erences are
sometimes subtle, and they are sometimes used interchangeably”which is okay in many, but
not all, situations. So, here is a summary.

• Internal Rate Of Return The internal rate of return is a feature of cash ¬‚ows, and has nothing
to do with capital markets. It can be calculated before the appropriate cost of capital is
known. It is the most di¬erent from the three rates below.
• Cost of Capital Always think of it as the opportunity cost of capital. It is also determined by
the prevailing rates for loans of your type in capital markets. It is determined by demand
and supply of capital in the economy”the expected rate of return that investors demand
in order to give us money willingly. In perfect capital markets, with many lenders and
borrowers, loans are usually zero net present value (or the borrower or lender is giving
away free money). The cost of capital is sometimes called the “required expected rate of
• Expected Rate of Return The expected rate of return is a generic term. It could mean your
project™s expected rate of return, or the cost of capital (the lenders™ expected rate of
return). If your project™s actual expected rate of return is above the required expected rate
of return, it is a positive NPV project. If management makes smart decisions, projects™
expected rates of return are above the cost of capital. The very last, marginal project
often has an expected rate of return just above the cost of capital.
• Hurdle Rate The appropriate project hurdle rate is the expected rate of return above which
management decides to accept and go forward with the project. It is set neither by the
¬nancial markets, nor by the project, but by management. Bad management could choose
any arbitrary and even idiotic hurdle rates. Good management should accept all projects
that have positive net present value.
Usually, this means that good managers should set a project™s hurdle rate to be equal to
the project™s cost of capital, and management should then determine whether the project™s
IRR exceeds this hurdle rate.
If management makes smart decisions, taking all positive NPV projects, the “hurdle rate,”
“cost of capital,” and “required expected rate of return” are all the same.

We already know that expected project returns are di¬cult to come by. Managers often in-
correctly use promised rates of return. Because corporations are aware that claims based on
expected project returns are regularly in¬‚ated (agency issues again!), many of them have estab-
lished hurdle rates high above the ¬rm™s cost of capital. It is not uncommon to ¬nd project
hurdle rates of 15% on claimed project rates of returns in corporations that face costs of capital
on the order of 10%. Venture capitalists even regularly employ project hurdle rates as high as
¬le=irr.tex: RP
Section 8·4. Other Capital Budgeting Rules.

8·4. Other Capital Budgeting Rules

8·4.A. The Problems of Payback

Although most corporations in the real world rely on NPV and IRR, some follow a whole variety Alternative Capital
Budgeting Rules: Power!
of di¬erent capital budgeting rules. In some corporations, power rules: the most in¬‚uential
employees get most new funding. In other corporations, even stranger historical methods for
deciding whether to take projects have taken hold.
One commonly used alternative rule is the payback rule. Projects are assumed to be better if Alternative Capital
Budgeting Rules:
they recover their original investment faster. For the most part, this is a stupid idea. Consider
the following three projects:

Year 1 Year 2 Year 3 Year 4
’$5 +$8
Project A
’$5 +$4
Project B $1,000
’$5 +$4 +$1 million
Project C $0

Project A has the shortest (best) payback period, but it is the worst of the three projects. Pro-
ject B has the next shortest payback period, but it is the second-worst of the three projects
(assuming reasonable interest rates). Project C has the longest (worst) payback period, but is
the best project. (There is also a version of payback in which future paybacks are discounted.
This measure asks not how long it takes you to get your money back, but how long it takes you
to get the present value of your money back.)
To be fair, payback can be an interesting number. Pluses and Minuses.

1. There is a beautiful simplicity to payback. It is easier for managers not trained in ¬nance
to understand “you will get your money back within 5 years” than it is to understand “the
NPV is $50 million.”

2. Payback™s emphasis on earlier cash ¬‚ows helps ¬rms set criteria when there are agency
problems inside the ¬rm. For instance, if your department manager claims that you will
get your money back within 1 year, and 3 years have already passed without your having
seen a penny, then something is probably wrong and you may need a better manager.

3. Payback can also help if you have limited capital”an imperfect market situation”so that
your cost of capital is very high and getting your money back in a short amount of time
is paramount. In this sense, payback helps you assess your future “liquidity.”

4. Finally, in many ordinary situations, in which the choice is a pretty clear-cut yes or no,
the results of the payback rule do not lead to severe mistakes, but just to mild mistakes
(as would, for example, a rule that ignores all time-value of money). If you have a project
in which you get your money back within one year, chances are that it™s not a bad one,
even from an NPV perspective. If you have a project in which it takes 50 years to get your
money back, chances are that it™s not a good one.

Having said all this, if you use payback to make decisions, it will lead you to take the wrong
projects and ruin your company. So, why take a chance when you know better capital budgeting
methods? Feel free to work out the payback period and use it as “interesting side information,”
but do not base your project choices on it”and certainly don™t compare projects merely on the
basis of payback.
¬le=irr.tex: LP
190 Chapter 8. Other Important Capital Budgeting Topics.

8·4.B. More Rules

There are an in¬nite number of other possible capital budgeting rules. A set of measures is
Accounting Based
Measures. based on accounting information (which we will cover next, so do not worry if the following
makes little sense to you). For example, some ¬rms choose projects based on the book rate of
return”net income divided by the book value of equity. Some ¬rms want to choose projects to
maximize the book value of equity. Some ¬rms want to choose projects to maximize reported
earnings. As you will learn soon, all of these measures are based on complex accounting con-
ventions, and not on economics. Therefore, I can only recommend against using them. I have
no idea what kind of projects you will end up with if you use any of these measures”except
that in many cases, if the measures are huge (e.g., if your accounting rate of return is 90% per
annum), then chances are that the project is also positive NPV.
A more sensible managerial practice is to think about what resources are constrained in the
Sensible Measures.
¬rm, given that we do not live in a perfect market. If the ¬rm is highly levered and has di¬culty
borrowing more, then the contribution of the new project to the ¬rm™s leverage ratio would be
an interesting measure. If the ¬rm™s management is already stretched thin, then measuring the
managerial time required to run the project would be an interesting measure. If the ¬rm is cash-
constrained, then the payback time and cash outlay [e.g., the pro¬tability index] would make
interesting measures. Of course, all these issues should have already appropriately entered the
cash ¬‚ows that you use in your NPV calculations”but the fact is that this is often di¬cult to
do or was entirely overlooked to begin with. Therefore, even though these measures should
not be used as primary capital budgeting tools, you can use them to help you make informed

Important: Simple Advice: Stick to net present value and, if need be, to the
internal rate of return. Do not use alternative capital budgeting rules for invest-
ment decisions. Use alternative measures to help you make decisions, but do not
be mechanically driven by them.
¬le=irr.tex: RP
Section 8·5. Summary.

8·5. Summary

The chapter covered the following major points:

• The pro¬tability index rearranges the NPV equation. If used by itself, it often provides the
same capital budgeting advice as NPV. But relative to NPV, the pro¬tability index favors
projects that have a lower upfront scale.

• The IRR (internal rate of return) is computed from a project™s cash ¬‚ows”and without
the use of any cost-of-capital information. It solves the NPV formula to equal zero.

• IRR can be interpreted as a “sort of” average rate of return implicit in project cash ¬‚ows.

• Projects with an IRR above the cost of capital often, but not always, have positive net
present value (NPV), and vice-versa.

• IRR can su¬er from serious computation problems, having multiple or no solutions. IRR
su¬ers from comparison problems, because it does not adjust for project scale.

• In the context of bonds, IRR is called the “yield to maturity.”

• The information that other capital budgeting measures provide can sometimes be “inter-
esting.” However, they often provide non-sensical results and therefore should generally
be avoided”or at least consumed with great caution.
¬le=irr.tex: LP
192 Chapter 8. Other Important Capital Budgeting Topics.

Solutions and Exercises

1. Using Excel, the answer pops out as 16%. Check: ’$100 + $55/1.16 + $70/1.162 = 0.
2. See equation 8.5 on Page 185.
3. For example, ’$100, +$120, ’$140, +$160, ’$1. (The solutions are ’99.3716% and 16.796%. The important
aspect is that your example has multiple in¬‚ows and multiple out¬‚ows.)
4. ’$100 at time 1, ’$50 at time 2. There are no economically sensible rates of return that can possibly make
this a zero net present value.

(All answers should be treated as suspect. They have only been sketched, and not been checked.)
Part II

Corporate Financials

(A part of all versions of the book.)



You now know all the important capital budgeting concepts. The next issue on the agenda is to
learn to apply them with the information that companies provide, which is rarely the cash ¬‚ows
that you need as direct inputs into your NPV analyses. So, the goal now is to teach you how to
work with the information in corporate ¬nancial statements”and how to translate what you can
¬nd in ¬nancials into what you need for a net present value analysis. Our analysis primarily takes
the perspective of the corporate manager, although outside analysts often also need to analyze
corporate ¬nancials from the same perspective.

We will also try to use some of the information in the ¬nancials to perform a different type
of valuation estimation, which is based on ¬nancials and relies on proper market valuation of
comparable ¬rms.

What we want to Accomplish in this Part
The goal of this part of the book is to teach the meaning and intelligent use of corporate ¬nancial

• Chapter 9 shows how to extract economic cash ¬‚ow estimates from corporate ¬nancial
statements. We will build up some hypothetical ¬rms to show what they would report in
their ¬nancials. This will help you understand how to translate back from the ¬nancials
to the ¬rm.

Typical question: What are the economic cash ¬‚ows in PepsiCo™s ¬nancial state-
ments that we would use to estimate the net present value of PepsiCo?

• Chapter 10 shows how to assemble information about your own ¬rm, using publicly avail-
able information from comparable ¬rms.

Typical questions: How do “comparables” di¬er from NPV? When is the P/E
(price earnings) ratio a good number to look at? What should be the P/E ratio
of our project? How and when can you average P/E ratios? What can you learn
from other ¬nancial ratios?
Understanding Financial Statements

Translating Accounting into Finance (Economic Cash Flows)
last ¬le change: Feb 18, 2006 (19:54h)

last major edit: Apr 2004, Dec 2004

Financial Accounting is the “language of business.” Although this book is not about ¬nancial
statements, you must understand both their logic and their fundamentals. They contain in-
formation about the cash ¬‚ows we need for an NPV analysis, as well as a lot of other useful
information. Without understanding accounting, you also cannot understand corporate income
taxes, a necessary NPV input.
This chapter begins with a simple hypothetical project. Its economics make computing NPV
easy. It then explains how accountants would describe the project in a ¬nancial statement. We
then translate between the ¬nance and the accounting descriptions. Finally, the chapter applies
the same analysis to the ¬nancial statement of a real corporation, PepsiCo (PEP).
This chapter also gently introduces some more details on corporate income taxes and capital
structure, which will be explained in greater detail in Chapter 22.

¬le=¬nancials.tex: LP
198 Chapter 9. Understanding Financial Statements.

9·1. Financial Statements

We already know that the value of our ¬rm is determined by its underlying projects. We already
accounting also matters
to ¬nance. know that these projects have cash ¬‚ows that we use in our NPV analyses. So, why should you
bother with learning about what companies say in their ¬nancials? A rose is a rose is a rose,
isn™t it? The projects and thus the ¬rm have the same value no matter what we report.
Yes and no. There are many good reasons why you should understand ¬nancial statements:

1. If you want to have an intelligent conversation with someone else about corporations, you
must understand the language of accounting. In particular, you must understand what
earnings are”and what they are not.

2. Subsidiaries and corporations report ¬nancial statements, designed by accountants for
accountants. They rarely report the exact cash ¬‚ows and cash ¬‚ow projections that you
need for PV discounting. How can you make good decisions which projects to take if you
cannot understand most of the information that you will ever have at your disposal?

3. It may be all the information you will ever get. If you want to get a glimpse of the operation
of a publicly traded corporation, or understand its economics better, then you must be
able to read what the company is willing to tell you. If you want to acquire it, the corporate
¬nancials may be your primary source of information.

4. The IRS levies corporate income tax. This tax is computed from a tax-speci¬c variant of the
corporate income statement, which relies on the same accounting logic as the published
¬nancials. (The reported and tax statements are not the same!) Because income taxes are
de¬nite costs, you must be able to understand and construct ¬nancial statements that
properly subtract taxes from the cash ¬‚ows projected from projects when you want to
compute NPV. And, if you do become a tax guru, you may even learn how to structure
projects to minimize the tax obligations, although most of this is beyond the scope of our

5. Many contracts are written on the basis of ¬nancials. For example, a bond covenant may
require the company to maintain a price-earnings ratio above 10. So, even if a change in
accounting rules should not matter theoretically, such contracts can create an in¬‚uence
of the reported ¬nancials on your projects™ cash ¬‚ows.

6. There is no doubt that managers care about their ¬nancial statements. Managerial com-
pensation is often linked to the numbers reported in the ¬nancial statements. Moreover,
managers can also engage in many maneuvers to legally manipulate their earnings. For
example, ¬rms can often increase their reported earnings by changing their depreciation
policies (explained below). Companies are also known to actively and expensively lobby
the accounting standards boards. For example, in December 2004, the accounting stan-
dards board ¬nally adopted a mandatory rule that companies will have to value employee
stock options when they grant them. Until 2004, ¬rms™ ¬nancial statements could treat
these option grants as if they were free. This rule was adopted despite extremely vigorous
opposition by corporate lobbies, which was aimed at the accounting standards board and
Congress. The reason is that although this new rule does not ask ¬rms to change projects,
it will drastically reduce the reported net income (earnings) especially of technology ¬rms.
But why would companies care about this? After all, investors can already determine that
many high-tech ¬rms (including the likes of Microsoft a few years ago) may have never
had positive earnings if they had had to properly account for the value of all the stock
options that they have given. This is a big question. Some behavioral ¬nance researchers
believe that the ¬nancial markets value companies as if they do not fully understand
corporate ¬nancials. That is, not only do they share the common belief that ¬rms manage
their earnings, but they also believe that the market fails to see through even mechanical
accounting computations. Naturally, the presumption that the ¬nancial markets cannot
understand accounting is a very controversial hypothesis”and, if true, this can lead to
all sorts of troublesome consequences.
¬le=¬nancials.tex: RP
Section 9·1. Financial Statements.

For example, if the market cannot understand ¬nancials, then managers can legally ma-
nipulate their share prices. A ¬rm would especially bene¬t from a higher share price
when it wants to sell more of its shares to the public. In this case, managers could and
should maneuver their ¬nancials to increase their earnings just before the equity issue.
There is good evidence that ¬rms do this”and also that the ¬nancial markets are regularly
disappointed by these ¬rms™ performances years after their equity issues.
Even more troublesome, there is also evidence that managers do not take some positive
NPV projects, if these projects harm their earnings. Does this sound far-fetched? In fact, in
a survey of 401 senior ¬nancial executives Graham, Harvey, and Rajgopal found that 55%
would delay starting a project and 80% would defer maintenance and research spending
in order to meet earnings targets. Starting projects and doing maintenance and R&D are
presumably the right kind of (positive NPV) projects, so not taking them decreases the
underlying real value of the ¬rm”even though it may increase the ¬nancial image the
¬rm projects.

It is of course impossible for this book about ¬nance to explain all the nuances of accounting.
Instead, we will focus on only one goal of importance to a ¬nancier: how do we obtain the cash
¬‚ows that we need for an NPV analysis, and why can we not use earnings? Accounting has,
of course, more to o¬er than just this”and fortunately you can learn more about its broader
scope in your accounting course.

9·1.A. The Contents of Financials

Publicly traded companies report their ¬nancial results (or ¬nancials) in ¬nancial reports to Companies communicate
their internals through
their shareholders and to the public. The most important ¬nancial report is the Annual Report,
standardized ¬nancial
which is ¬led with the SEC in Form 10-K. (There is also a Quarterly Report, called 10-Q .) Almost reports.
all Annual Reports begin with a general description of the business and business developments,
followed by the more formal presentation of the ¬rm™s ¬nancials. We are interested primarily
in the ¬nancials: after all, ¬nanciers are primarily interested in how much money the ¬rm
makes rather than how it makes it. However, as much as we would prefer to keep the ¬rm a
black box, we usually cannot: knowledge of “how money is made” is usually necessary for good
knowledge of the “how much money is made””and “how can we make more money.”
If you have not seen a company™s Annual Report (which includes the ¬nancial statements), Read some!
please spend some time reading one. Any business library should have a selection. Most large
corporations also publish their ¬nancials on their websites. If you own shares of stock in a
publicly traded company, the Annual Report will automatically be mailed to you once a year.
And the SEC runs EDGAR, a very comprehensive electronic repository of corporate ¬nancials,
including annual and quarterly reports.
¬le=¬nancials.tex: LP
200 Chapter 9. Understanding Financial Statements.

Table 9.1. Consolidated Balance Sheet PepsiCo, Inc. and Subsidiaries
December 29, 2001 and December 30, 2000

2001 2000
(in millions except per share amounts)

Current Assets
Cash and cash equivalents $ 683 $ 1,038
Short-term investments, at cost 966 467
1,649 1,505

Accounts and notes receivable, net 2,142 2,129
Inventories 1,310 1,192
Prepaid expenses and other current assets 752 791
Total Current Assets 5,853 5,617

Property, Plant and Equipment, net 6,876 6,558
Intangible Assets, net 4,841 4,714
Investments in Unconsolidated A¬liates 2,871 2,979
Other Assets 1,254 889
Total Assets $21,695 $20,757

Liabilities and Shareholders™ Equity
Current Liabilities
Short-term borrowings $ 354 $ 202
Accounts payable and other current liabilities 4,461 4,529
Income taxes payable 183 64
Total Current Liabilities 4,644 4,593

Long-Term Debt 2,651 3,009
Other Liabilities 3,876 3,960
Deferred Income Taxes 1,496 1,367

Preferred Stock, no par value 26 49
Deferred Compensation ” preferred - (27)

Common Shareholders™ Equity
Common stock, par value 1 2/3 c per share 30 34
(issued 1,782 and 2,029 shares, respectively)
Capital in excess of par value 13 375
Deferred compensation - (-21)
Retained earnings 11,519 16,510
Accumulated other comprehensive loss (1,646) (1,374)

Less: repurchased common stock, at cost (1,268) (7,920)
(26 and 280 shares, respectively)
Total Common Shareholders™ Equity 8,648 7,604
Total Liabilities and Shareholders™ Equity $21,695 $20,757

See accompanying notes to consolidated ¬nancial statements.
¬le=¬nancials.tex: RP
Section 9·1. Financial Statements.

Table 9.2. Consolidated Statement of Common Shareholders™ Equity PepsiCo, Inc. and
Fiscal years ended December 29, 2001, December 30, 2000 and December 25, 1999.

2001 2000 1999
Shares Amount Shares Amount Shares Amount
(in millions)

Common Stock
Balance, beginning of year 2,029 $ 34 2,030 $ 34 2,037 34
Share repurchases   (9)  (13) 
Stock option exercises 6  -  - 
Quaker stock option exercises 3  8  6 
Shares issued to e¬ect merger (256) (4) 0  - 
Balance, end of year 1,782 30 2,029 34 2,030 34
Capital in Excess of Par Value
Balance, beginning of year 375 559 904
Share repurchases  (236) (370)
Stock option exercises(a) 82 52 (21)
Reissued shares 150  
Shares issued to e¬ect merger (595)  
Other 1  46
Balance, end of year 13 375 559
Deferred Compensation
Balance, beginning of year (21) (45) (68)
Net activity 21 24 23
Balance, end of year  (21) (45)
Retained Earnings
Balance, beginning of year 16,510 14,921 13,356
Net income 2,662 2,543 2,505
Shares issued to e¬ect merger (6,644)  
Cash dividends declared  common (1,005) (950) (936)
Cash dividends declared  preferred (4) (4) (4)
Balance, end of year 11,519 16,510 14,921
Accumulated Other Comprehensive Loss
Balance, beginning of year (1,374) (1,085) (1,139)
Currency translation adjustment (CTA) (218) (289) (136)
CTA reclassi¬cation adjustment   175
Cash ¬‚ow hedges, net of tax:
Cumulative e¬ect of accounting change 3  
Derivative (losses)/gains, net (21) - -
Minimum pension liability adjustment, (38) (2) 17
net of tax

Other 2 2 (2)
Balance, end of year (1,646) (1,374) (1,085)
Repurchased Common Stock
Balance, beginning of year (280) (7,920) (271) (7,306) (255) (6,535)
Shares repurchased (35) (1,716) (38) (1,430) (36) (1,285)
Stock option exercises 20 751 29 816 20 514
Reissued shares 13 374    “
Shares issued to e¬ect merger 256 7,243    “
Balance, end of year (26) (1,268) (280) (7,920) (271) (7,306)
Total Common Shareholders™ Equity $ 8,648 $ 7,604 $ 7,078

(a) Includes total tax bene¬t of $212 in 2001, $177 in 2000 and $105 in 1999.
See accompanying notes to consolidated ¬nancial statements. These include a closing stock price of $49.05/share,
which indicates a market capitalization of $87.4 billion.
¬le=¬nancials.tex: LP
202 Chapter 9. Understanding Financial Statements.

Table 9.3. Consolidated Statement of Income PepsiCo, Inc. and Subsidiaries
Fiscal years ended December 29, 2001, December 30, 2000 and December 25, 1999.

2001 2000 1999
(in millions except per share amounts)

Net Sales
New PepsiCo $ 26,935 $25,479 $22,970
Bottling Operations “ “ 2,123
Total Net Sales 26,935 25,479 25,093

Costs and Expenses
Cost of sales 10,754 10,226 10,326
Selling, general and administrative expenses 11,608 11,104 11,018
Amortization of intangible assets 165 147 193
Merger-related costs 356 “ “
Other impairment and restructuring charges 31 184 73
Total Costs and Expenses 22,914 21,661 21,610

Operating Pro¬t
New PepsiCo $ 4,021 $3,818 $3,430
Bottling Operations “ “ 2,123
Total Operating Pro¬t $ 4,021 $3,818 $3,483

Bottling equity income and transaction gains/(loss), net 160 130 1,083
Interest expense (219) (272) (421)
Interest income 67 85 130


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