A First Course in Corporate Finance

764 Pages·2006·6.375 MB·English

by  Welch I.

A First Course in
Corporate Finance
Preview,Monday9th October,2006
116175494417370260 Wed Oct 25 01:46:38 2006
A First Course in Corporate Finance
©2003–2006byIvoWelch. Allrightsreserved.
CartoonsarecopyrightandcourtesyofMikeBaldwin. Seehttp://www.cornered.com/.
ISBN:nonumberyet.
LibraryofCongress: nonumberyet.
BookWebsite: http://welch.econ.brown.edu/book/
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ThereferencedspreadsheetsareExcel(Microsoft)andOpenOffice(free).
Printed: Monday9thOctober,2006(frombookc.tex).
Warning: This book is in development.
It is not error-free.
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A First Course in
Corporate Finance
Preview,Monday9th October,2006
Ivo Welch
ProfessorofFinanceandEconomics
BrownUniversity
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Far and away, the most important contributor to this book was Mary-Clare McEwing. As editor, she helped me
improvethesubstanceofthebooktremendously.
There are also a large number of other individuals who have helped me with this book. Among them were Rick
Antle,DonnaBattista,RandolphBeatty,WolfgangBühler,KangbinChua,DiegoGarcia,StanGarstka,RogerIbbotson,
LudovicPhalippou,MatthewSpiegel,JohnStrong,JulieYufe,andmanyanonymous(victim)studentswhohadtouse
earliererror-riddendrafts.
Thereviewersofearlierdraftsofthebookspentanenormousamountoftimeandprovidedmewithmanygreat
ideas. Iowethemmydeepgratitudefortheirengagement:
TonyBernardo MarkKlock TimSullivan
JamesGatti
ThomasChemmanur AngelineLavin ChrisStivers
SimonGervais
BillChristie JosephMcCarthy MarkStohs
TomGeurtz
JenniferConrad JamesNelson JohnStrong
RobertHansen
JoshCoval MichaelPagano MichaelTroege
MiltHarris
AmyDittmar MitchPetersen JoelVanden
RonaldHoffmeister
RichardFendler SarahPeck JaimeZender
KurtJesswin
DiegoGarcia RobertRitchey Miranda(Mei)Zhang
DarrenKisgen
SharonGarrison BruceRubin
A list ofarticlesupon which the ideasin the bookarebased, and a listofarticles thatdescribe currentongoing
academicresearchwilleventuallyappearonthebook’swebsite.
Warning: This book is in development.
It is not error-free.
Dedicatedtomyparents,ArthurandCharlotte.
Lastfilechange:Jul19,2006(11:13h)
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A Quick Adoption Checklist For Instructors
This is the recommended checklist for this book (AFCIc) while the book is in beta test mode. This
checklist will not apply after AFCIc is published (with full supplementary materials) by Addison-
Wesley-Pearson.
✓ Read this prologue and one or two sample chapters to determine whether you like the AFCIc
approach. (Althoughnotrepresentative,Irecommendthatyoualsoreadtheepilogue.)
IfyoudoliketheAFCIcapproach,thenpleasecontinue. IfyoudonotlikeAFCIc(orthechapters
youread),[email protected]. IpromiseIwillnotshoot
themessenger: Iwanttolearnhowtodoitbetter.
✓ Continuetoassignwhateverotherfinancetextbookyouwereplanningtouse,justaddAFCIc. Use
itasasupplementarytext,orassignjustafewchapters.
AlthoughAFCIcisafull-servicetextbookforanintroductoryfinancecourse,itshouldalsowork
•
wellasacomplementtoanexistingtextbook. Yourstudentsshouldrelativelyeasilybenefitfrom
havingaccesstoboth,becausethisbookisbothdifferentfromandsimilartothecompetition. I
believethatrelativetorelyingonlyonyouroldtextbook, AFCIcwillnot increase, butdecrease
yourstudent’sconfusionandworkload.
TakethelowriskrouteandseehowwellAFCIcworks! (TakethePepsichallenge!) Keepingyour
•
old textbook is also your insurance against using a novel textbook. And it will make students
lesscriticaloftheremainingshortcomingsinAFCIc,suchasthelimitednumberofexercises(and
theiroccasionallyerroneoussolutions). Perhapsmostimportantly,AFCIcdoesnotyet havefull
supplementarymaterials. ItwillwhenAddison-Wesleywillpublishit,butuntilthen,theauxiliary
materialsfromothertextbooksmayhelp.
Fornow,studentscandownloadthebookchapters,sothereisnoprintingcostinvolved. Af-
•
fordabilityshouldnotbeaconcern.
ItshouldbearelativelysimplemattertolinkAFCIcchaptersintoyourcurriculum,becausethe
•
chaptersarekeptrelativelystraightforwardandsuccinct.
YoucannotgowrongifyoutryoutatleastafewchaptersofAFCIcinthismanner.
✓ YoucanreceivepermissiontoposttheelectronicAFCIconyourclasswebsite. (Thewebsitemust
be secured to allow only university-internal distribution.) Students can carry the files on their
notebookcomputerswiththem.
✓ Youcanaskyourcopycentertoprintandbindtheversiononyourwebsite. Youcanalsoobtain
anicelyprintedandboundversionfor$40fromlulu.com.
AlthoughversionsontheAFCIcwebsiteathttp://welch.econ.brown.edu/bookwillalwayshave
•
someimprovements,itisagoodideaforeachclasstoagreeononedefinitivereferenceversion.
✓ If you are using AFCIc and you are looking for lecture notes, feel free to “steal” and adapt my
lecture notes (linked at http://welch.econ.brown.edu/book) to your liking. You can change and
modifythelecturenotesanywayyoulike,withoutcopyrightrestrictions.
✓ Of course, I hope that the majority of your students (and you) will prefer reading AFCIc instead
of your old textbook. At the end of the course, please ask your students which textbook they
found more helpful. Please email your conclusions and impressions [email protected]. Any
suggestionsforimprovementareofcoursealsoverywelcome. Anyfeedbackwouldbeappreciated,
butitwouldbeparticularlyhelpfulformetolearninwhatrespectstheyprefertheirothertextbook.
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To The Instructor
Thisbookis Most corporate finance textbooks cover a similar canon of concepts, and this textbook is no
intentionallydifferent. exception. AquickglanceattheTableofContentswillshowyouthatmost—thoughnotall—of
the topics in A First Course in Corporate Finance overlap with those in traditional finance
textbooks. But this does not mean that this book is not different. Although I cover similar
conceptualterritory,therearealsoimportantdepartures.
InnovationsinApproach
Here is my view of how this book differs from what is currently out there. I do not claim
that other traditional textbooks do not teach any of what I will list, but I do maintain that my
emphasisonthesepointsismuchstrongerthanwhatyouwillfindelsewhere.
ConversationalTone. ConversationalTone: Thetoneismoreinformalandconversational,which(Ihope)makesthe
subjectmoreaccessible.
Themethodof Numerical-ExampleBased: Ilearnbestbynumericalexample,andfirmlybelievethatstudents
instructionis do, too. Whenever I want to understand an idea, I try to construct numerical examples
“step-by-step
formyself(thesimpler,thebetter). Idonotparticularlycareforlongalgebraorcomplex
numericalexamples.”
formulas,precisethoughtheymaybe. Idonotmuchlikemanydiagramswithlongtextual
descriptionsbutnospecificexamples,either—Ioftenfindthemtoovague,andIamnever
sure whether I have really grasped the whole mechanism by which the concept works.
Therefore, I wanted to write a textbook that relies on numerical examples as its primary
tutorialmethod.
This approach necessitates a rearrangement of the tutorial textbook progression. Most
conventionalfinancetextbooksstartwithabird’seyeviewandthenworktheirwaydown.
The fundamental difference of this book is that it starts with a worm’s eye view and
worksitswayup. Theorganizationisbuiltaroundcriticalquestionlike“Whatwoulditbe
worth?,”whichisthenansweredinnumericalstep-by-stepexamplesfromfirstprinciples.
Right under numerical computations are the corresponding symbolic formulas. In my
opinion, this structure clarifies the meaning of these formulas, and is better than either
an exclusively textual or algebraic exposition. I believe that the immediate duality of
numericswithformulaswillultimatelyhelpstudentsunderstandthematerialonahigher
levelandwithmoreease. (Ofcourse,thisbookalsoprovidessomeoverviews,andordinary
textbooksalsoprovidesomenumericalexamples.)
Studentsshouldhave ProblemSolving: An important goal of this book is to teach students how to approach new
amethodofthinking, problemsthattheyhavenotseenbefore. Ourgoalshouldbesendstudentsintothereal
notjustformulas.
worldwiththeanalyticaltoolsthatallowthemtodisectnewproblems,andnotjustwitha
chestfullofformulas. Ibelievethatifstudentsadoptthenumericalexamplemethod—the
“startsimpleandthengeneralize”method—theyshouldbeabletosolveallsortsofnew
problems. It should allow them to figure out and perhaps even generalize the formulas
thattheylearninthisbook. Similarly,ifstudentscanlearnhowtoverifyothers’complex
new claims with simple examples first, it will often help them to determine whether the
emperoriswearingclothes.
Webuildafoundation Deeper,YetEasier: Ibelievethatformulaicmemorizationisultimatelynotconducivetolearn-
first—soweare ing. In my opinion, such an alternative “canned formula” approach is akin to a house
deeper!
without a foundation. I believe that shoring up a poorly built house later is more costly
thanbuildingitrighttobeginwith.
Giving students the methods of how to think about problems and then showing them
howtodeveloptheformulasthemselveswillmakefinanceseemeasierandsimplerinthe
end, even if the coverage is conceptually deeper. In my case, when I haved learned new
subjects,IhaveoftenfounditespeciallyfrustratingifIunderstandasubjectjustalittle
but I also suspect that the pieces are really not all in place. A little knowledge can also
be dangerous. If I do not understand where a formula comes from, how would I know
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whetherIcanorcannotuseitinanewsituation? AndIbelievethatevenaveragestudents
canunderstandthebasicideasoffinanceandwheretheformulascomefrom.
Brevity: Sometimes,lessismore. Brevityisimportant.
Thebookfocusison
This book is intentionally concise, even though it goes into more theoretical detail than
explanations,not
otherbooks! Institutionaldescriptionsareshort. Onlytheconceptsareexplainedingreat institutions.
detail.
Myviewisthatwhenstudentsareexposedtotoomuchmaterial,theywon’treadit,they
won’t remember it, and they won’t know what is really important and what is not. Ten
years after our students graduate, they should still solidly remember the fundamental
ideasoffinance,beabletolookupthedetailswhentheyneedthem,andbeabletosolve
new (financial) problems. Many institutional details will have changed, anyway—it is the
ideas,concepts,andtoolsthatwilllastlonger.
Self-ContainedforClarity: Financeisasubjectthateverystudentcancomprehend,regardless Self-containedmeans
of background. It is no more difficult than economics or basic physics. But, it is often studentscan
backtrack.
a problem that many students come into class with a patchwork on knowledge. We, the
instructors,thenoftenerroneouslybelievethestudentshaveallthebackgroundcovered.
Alongtheway,suchstudentsgetlost. Itiseasytomistakesuchthemfor“poorstudents,”
especiallyifthereisnoreferencesource,wheretheycanquicklyfillinthemissingparts.
In this book, I try to make each topic’s development self-contained. This means that I
try to explain everything from first principles, but in a way that every student can find
interesting. For example, even though the necessary statistical background is integrated
in the book for the statistics novice, the statistics-savvy student also should find value
in reading it. This is because statistics is different in our finance context than when it is
taughtforitsownsakeinastatisticscourse.
CloserCorrespondencewiththeContemporaryCurriculum: Ibelievethatmostfinancecore LessChapter
courses taught today follow a curriculum that is closer in spirit to this book—and more Reordering.
logical—thanitistotheorderinolder,traditionalfinancetextbooks. Intheplaceswhere
thisbookcoversnovelmaterial(seebelow),Ihopethatyouwillfindthatthenewmaterial
hasmerit—andifyouagree,thatcoveringitismucheasierwiththisbookthanwithearlier
books.
InnovationsinParticularTopics
Thebookalsooffersanumberoftopicalandexpositionalinnovations. Hereisaselection:
ProgressiontoRiskandUncertainty: Thebookstartswithaperfectrisk-freeworld,thenadds First,norisk;then
horizon-dependentinterestrates,uncertaintyunderriskneutrality,imperfectmarketfric- risk-neutralattitudes
torisk;then
tions(e.g.,taxes),uncertaintyunderrisk-aversion,andfinallyuncertaintyunderriskaver-
risk-averseattitudesto
sionandwithtaxes(e.g.,WACCandAPV). Frictions(Ch6): risk.
OftenMeaningless.
PV0 = VariousModifications.

(cid:0)(cid:18)  @
(cid:0) @R
PerfectWorld(Ch2): Uncertainty(Ch5): CorporateTaxes(Ch18):
PV0 = 1CF1r +(1CFr2)2 +··· PV0 = 1E(CF(1r˜)1)+1E(C(Fr˜20),2)+··· - PV0 = 1 (r˜1,EQE)(C(F11,FMτ)) (r˜1,DT)+···
+ + +E +E +E + − ·E
@ (cid:0)(cid:18) @ (cid:0)(cid:18)
@ (cid:0) @ (cid:0)
@R (cid:0) @R (cid:0)
Horizon-DependentRates(Ch4): Risk-Aversion(PartIII):
PV0 = 1+CFr10,1 +1+CFr20,2 +··· PV0 = 1+r1,F+[EE(r˜(1C,MF1))−r1,F]·βi,M+···
Each step builds on concepts learned earlier. I believe it is an advantage to begin simply
andthengraduallyaddcomplexity. Theuniquerolesofthemoredifficultconceptsofrisk
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measurement, risk-aversion, and risk-aversion compensation then become much clearer.
(Thereare someforward hintsin thetext thatdescribe howthemodel willchange when
theworldbecomesmorecomplex.)
Drivehome“default AStrongDistinctionbetweenExpectedandPromisedCashFlows: Ihavealwaysbeenshocked
risk.” byhowmanygraduatingstudentsthinkthataBostonCelticsbondquotes400basispoints
in interest above a comparable Treasury bond because of the risk-premium, which they
cancalculateusingtheCAPMformula. Learningtoavoidthisfundamentalerrorismore
importantthanfancytheories: themainreasonwhytheBostonCelticsbondpromises400
extrabasispointsis,ofcourse,primarilyitsdefaultrisk(compensationfornon-payment),
not a risk-premium (compensation for risk-averse investors that comes from the corre-
lation with the market rate of return). And for bonds, simple ICAPM-like equilibrium
modelssuggestthatthelattershouldbeanorderofmagnitudesmallerthantheformer.
The CAPM itself can definitely not be used to claim a 400 basis point risk premmium.
Although many instructors mention this difference at some point, 5 minutes of default
riskdiscussionisoftenlostin5hoursworthofCAPMdiscussion. Butifstudentsdonot
understandthebasicdistinction,the5hoursofCAPMdiscussionarenotjustwastedbut
haveonlymademattersworse.
Traditionaltextbookshavenothelped,becausetheyhavenotsufficientlyemphasizedthe
distinction. In contrast, in this book, default risk is clearly broken out. The difference
betweenquoted(promised)andexpectedreturns,andquoteddefaultcompensationand
riskcompensationareimportantthemescarriedthroughout.
Understand FinancialsfromaFinancePerspective: Finance students need to solidly understand the re-
accountingwithout lationship between financial statements and NPV. Although it is not bad if they also
beinganaccounting
understand all the accounting nooks and crannies, it is more important that they under-
textbook.
stand the basic logic and relationship between finance and accounting. It is essential if
they want to construct pro formas. Yet, when I was writing this book, I could not find
good, concise, and self-contained explanations of the important aspects and logic of ac-
counting statements from a finance perspective. Consequently, this book offers such a
chapter. It does not just show students some financial statements and names the finan-
cialitems;instead,itmakesstudentsunderstandhowtheNPVcashflowsareembedded
intheaccountingstatements.
Afundamentalunderstandingoffinancialsisalsonecessarytounderstandcomparables:
for example, students must know that capital expenditures must be subtracted out if
depreciation is not. (Indeed, the common use of EBITDA without a capital expenditures
adjustment is often wrong. If we do not subtract out the pro-rated expense cost, we
should subtract out the full expenses. Factories and the cash flows they produce do not
fallfromheaven.)
ProFormas: In any formal financial setting, professionals propose new projects—whether it
istheexpansionofafactorybuildingwithinacorporation,oranewbusinessforpresen-
tation to venture capitalists—through pro formas. A good pro forma is a combination
of financial expertise, business expertise, and intuition. Both art and science go into its
construction. The book’s final chapter, the capstone towards which the book works, is
the creation of such a pro forma. It combines all the ingredients from earlier chapters—
capitalbudgeting,taxes,thecostofcapital,capitalstructure,andsoon.
Robustness: The book discusses the robustness of methods—the relative importance of er-
rorsandmistakes—andwhatfirst-orderproblemsstudentsshouldworryaboutandwhat
second-orderproblemstheycanreasonablyneglect.
ANewerPerspectiveonCapitalStructure: Theacademicperspectiveaboutcapitalstructure
hasrecentlychanged. A$1millionhousethatwasoriginallyfinancedbya50%mortgage
andthendoublesinvaluenowhasonlya25%debtratio. Inanalogousfashion,Chapter20
shows how stock price movements have drastically changed the debt ratio of IBM from
2001 to 2003. Students can immediately eyeball the relative importance of market influ-
ences, issuing and other financial activities. The corporate market value changes are an
important and robust factor determining capital structure—at least equal in magnitude
tofactorssuggestedinacademictheoriesinvolvingthepeckingorderortrade-offs. More-
over,wenowknowthatmostnewequitysharesappearinthecontextofM&Aactivityand
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as executive compensation, not in the context of public equity offerings. Part IV of our
bookexplainswhattheknownfirst-orderdeterminantsofcapitalstructureare,whatthe
(important)second-orderdeterminantsare,andwhatthefactorsstillunderinvestigation
are.
ManyOtherTopicalImprovements: Forexample,theyieldcurvegetsitsown(optional)chap- ...andmanymore.
terevenbeforeuncertaintyisdescribedinmuchdetail,sothatstudentsunderstandthat
projectsoverdifferenttimehorizonscanofferdifferentratesofreturnevenintheabsence
of risk. There is a self-contained chapter on comparables as a valuation technique—a
technique that many of our students will regularly have to use after they graduate. The
corporategovernancechapterhasaperspectivethatisdarkerthanitisinothertextbooks.
WACC,APV,anddirectproformaconstructionallincorporatethetaxadvantageofdebt
into valuation. This is bread-and-butter for CFOs. This book offers a clear explanation
of how these methods usually come to similar results (and when not!). Throughout the
book, I try to be open and honest about where our knowledge is solid and where it is
shaky—andhowsensitiveourestimatesaretotheerrorsweinevitablycommit.
Althoughmostofourcurriculumsaresimilarintheircoverageofthebasics,timeconstraints Webchapterswillallow
usually force us to exclude some topics. Your preferences as to what to cut may differ from a-la-cartechoice.
mine. For example, I find the financials part very important, because this is what most of
our graduates will do when they become analysts, brokers, or consultants. However, you may
instead prefer to talk more about international finance. It is of course impossible to satisfy
everyone—andinstructorshavealwayschosentheirownfavorites,addinganddeletingtopics
astheyseefit.
Thisbooktriestoaccommodatesomechoice. SomechaptersareavailableontheWebsite(“Web
Chapters”) accompanying this book. Chapter style and formatting are unmistakably identical
to the book itself. Every instructor can therefore choose his/her own favorite selection and
ask students to download it. These chapters are free and access is easy. The menu right now
containsthefollowingchapters:
RealOptions: RealoptionsarebrieflycoveredinChapter7inthetext,butnotingreatdetail.
Thiswebchaptershowshowtousespreadsheets,time-seriesanalysis,MonteCarlosimu-
lation,andoptimizationtodeterminethevalueofaplantthatcanshutdownandreopen
(foracost)asoutputpricesfluctuate.
OptionandDerivativePricing: This is a difficult subject to cover in an introductory course,
because it really requires a minimum of 4-6 class sessions to do it well. This chapter
tries to help you cover the basics in 2 class sessions. It explains option contracts, static
arbitrage relations (including put-call parity), dynamic arbitrage and the Black-Scholes
formula,andbinomialtrees.
InternationalFinance: Thischapterexplainstheroleofcurrencytranslationsandinternational
marketsegmentationforbothinvestmentsandcorporatebudgetingpurposes.
Ethics: This chapter is experimental—and provocative. There is neither a particular set of
must-covertopicsnoratemplateonhowtopresentthismaterial. Yourchoicesandviews
may differ from mine. However, I believe that ethical considerations are too important
forthemnevertoberaised.
CapitalStructureEventStudies: Thischapterdescribestheevidence(up-to-2003!) ofhowthe
stock market reacts to the announcements of new debt offerings, new equity offerings,
anddividendpayments.
The title of the book is optimistic. A one-quarter course cannot cover the vast field that our
profession has created over the last few decades. The book requires at least a one semester
course, or, better yet, a full two-quarter sequence in finance—although I would recommend
that the latter type of course sequence use the “general survey” version of this book, which
goesintomoredetailintheinvestmentspart.
I hope that this book will become your first choice in finance textbooks. If you do not like it,
please drop me an email to let me know where it falls short. I would love to learn from you.
(AndevenifIdisagree,chancesarethatyourcommentswillinfluencemynextrevision.)
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SIDE NOTE
Ifyouusethisbookorsomechapterstherefrom,pleasepermitmetouseandpostyour homeworkandexam
questionswithanswers. (Ofcourse,thisisnotarequirement,onlyapleaforhelp.) MyintentisfortheWebsite
to become collaborative: you will be able to see what other faculty do, and they can see what you do. The
copyrightwillofcourseremainwithyou.
To The Student
Prerequisites
Thisbookandthe What do you need to understand this book? You do not need any specific background in
subjectitselfare finance. Youdoneedtobethoroughlycomfortablewitharithmeticandgenerallycomfortable
tough,buttheyarenot
withalgebra. Youdoneedmathematicalaptitude,butnoknowledgeofadvancedmathematical
forbidding,eventoan
averagestudent. The constructs, such as calculus. Knowledge of statistics would be very helpful, but the book will
mainprerequisiteis explaintherelevantconceptswhentheneedarises. Youshouldowna$20scientificcalculator.
mathematicalaptitude,
butnotmathematical A financial calculator is not necessary and barely useful. Instead, you should learn how to
sophistication. operateaspreadsheet(suchasExcelinMicrosoft’sOfficeorthefreeOpenCalcspreadsheetin
OpenOffice). Thefinancialworldismovingrapidlyawayfromfinancialcalculatorsandtoward
computer spreadsheets—it is easier to work with information on a large screen with a 2,000
MHzprocessorthanonasmall2-linedisplaywitha2MHzprocessor. BecauseIhavetriedhard
tokeepthebookself-containedandtoexplaineverythingfromfirstprinciples,youshouldnot
need togohuntingfordetailsinstatistics,economics,oraccountingtextbooks. Butthisisnot
to say that you do not need to take courses in these disciplines: they have way more to offer
thanjustbackgroundknowledgeforafinancetextbook.
Jargoncantripupthe One word of caution: the biggest problem for a novice of any field, but especially of finance,
reader. is jargon: the specialized terminology known only to the initiated. Worse, in finance, much
jargon is ambiguous. Different people may use different terms for the same thing, and the
same term may mean different things to different people. You have been warned! This book
attemptstopointoutsuchambiguoususage. Luckily,thebarkofjargonisusuallyworsethan
itsbite. Itisonlyatemporarybarriertoentryintothefieldoffinance.
HowtoReadTheBook
Thisbookisconcise, Thistextbooktriestobeconcise. Itwantstocommunicatetheessentialmaterialinastraight-
focusingonthe forward(andthuscompact),butalsoconversational(andthusmoreinteractive)andaccessible
essenceofarguments.
fashion. There are already many finance textbooks with over a thousand pages. Much of the
content of these textbooks is interesting and useful but not essential to an understanding of
finance. (Ipersonallyfindsomeofthisextracontentdistracting.)
Thelayoutofthebook. The book is organized into four parts: the basics consist of return computations and capital
budgeting. Nextarecorporatefinancials,theninvestments(assetpricing),andfinancing(capital
structure). Majorsectionswithinchaptersendwithquestionsthataskyoutoreviewthepoints
justmadewithexamplesorquestionssimilartothosejustcovered. You should not proceed
beyond a section without completing these questions (and in “closed book” format)! Many,
but not all, questions are easy and/or straightforward replications of problems that you will
have just encountered in the chapter. Others are more challenging. Each chapter ends with
answers to these review questions. Do not move on until you have mastered these review
questions. (Thepublishedversionofthisbookwillcontainmanymorestudentquestions,and
therewillbeaseparatestudenttestbank.)
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