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Chapter 3

Financial Decision

Making and theLaw of One Price

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Valuation Principle

• !oal o" "inancial decision #a$ing%

• Costs vs. &ene"its

• Co#plications

•

'et Present (alue

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3.1 Valuing Decisions

• Identi"y Costs and &ene"its – )ay need help "ro# other areas in identi"ying the

relevant costs and *ene"its• )ar$eting• Econo#ics• +rgani ational &ehavior• -trategy• +perations

•

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!nal (ing Costs and &enefits

• -uppose a e elry #anu"acturer has theopportunity to trade 10 ounces o" gold andreceive 20 ounces o" palladiu# today.

• Is this a good deal%

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!nal (ing Costs and &enefits)cont*d+

• !old can *e *ought and sold "or a current #ar$et priceo" 51, 00 per ounce.

– 610 ounces o" gold7 8 651, 00/ounce7 9 51 ,000 today• :he current #ar$et price "or palladiu# is 5 00 per

ounce. – 620 ounces o" palladiu#7 8 65 00/ounce7 9 512,000

• 'et value o" the pro ect today is –

512,000 ; 51 ,000 9 ;53,000

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!lternati,e - a/ple 3.1

• Pro$le/ – hich pri e should you choose%

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• Pro$le/ – ould

your decision change i" you *elieved the value o"the euro ould rise over the ne?t #onth%

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3.0 nterest 2atesand the i/e Value of Mone

• :i#e (alue o" )oney – Consider an invest#ent opportunity ith the

"ollo ing certain cash "lo s.• Cost 5100,000 today• &ene"it 510 ,000 in one year

– -uppose the current annual interest rate is F. &yinvesting or *orro ing at this rate, e can e?change 51today "or 51.0 one year.

•

=is$;@ree Interest =ate 6Giscount =ate7,r

f :he interest rateat hich #oney can *e *orro ed or lent ithout ris$. – Interest =ate @actor 9 1 r f – Giscount @actor 9 1 / 61 r f 7

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he nterest 2ate4 !n - change 2ate!cross i/e )cont*d+

• (alue o" Invest#ent in +ne

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he nterest 2ate4 !n - change2ate !cross i/e )cont*d+

• Giscount @actors and =ate – >e can interpret

as the price today o" 51 in one year. :he a#ount iscalled the one year discount factor . :he ris$ "ree rate isalso re"erred to as the discount rate "or a ris$ "reeinvest#ent.

1 1 0.934581 1.07r

= =+

1

1 r +

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• Pro$le/ – :he cost o" replacing a "leet o" co#pany truc$s

ith #ore energy e""icient vehicles as 5100#illion in 2012.

– :he cost is esti#ated to rise *y B. F in 2013. – f the interest rate was 56" what was the

cost of a dela in ter/s of dollars in 0710'

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• %olution – I" the pro ect ere delayed, its cost in 2013

ould *e• 5100 #illion 61.0B 7 9 510B. #illion

– Co#pare this a#ount to the cost o" 5100 #illionin 2012 using the interest rate o" 4F

• 510B. #illion H 1.04 9 5104.33 #illion in 2012dollars.

– :he cost o" a delay o" one year ould *e• 5104.33 #illion ; 5100 #illion 9 54.33 #illion in 2012

dollars.

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Figure 3.1 Converting &et een Gollars :odayand !old, Euros, or Gollars in the @uture

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3.3 Present Valueand the 8PV Decision 2ule

• :he 8et Present Value )8PV+ o" a pro ector invest#ent is the di""erence *et een thepresent value o" its *ene"its and the presentvalue o" its costs.

• >hen #a$ing an invest#ent decision, ta$e thealternative ith the highest 'P(.

• =e ect those pro ects ith negative 'P(

(Benefits) (Costs)= − NPV PV PV (All project cash flows)= NPV PV

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e t$ook - a/ple 3.9

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a$le 3.1 Cash Flows and 8PVs forWe$ %ite &usiness !lternati,es

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a$le 3.0 Cash Flows of :iring and&orrowing Versus %elling and n,esting

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3.5 !r$itrage and the Law of OnePrice

• Ar*itrage – :he practice o" *uying and selling e uivalent

goods in di""erent #ar$ets to ta$e advantage o"a price di""erence. An ar$itrage opportunitoccurs hen it is possi*le to #a$e a pro"it

ithout ta$ing any ris$ or #a$ing anyinvest#ent.

• 'or#al )ar$et – A co#petitive #ar$et in hich there are no

ar*itrage opportunities.

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3.5 !r$itrage and the Law ofOne Price )cont*d+

• Ja o" +ne Price – I" e uivalent invest#ent opportunities trade

si#ultaneously in di""erent co#petitive #ar$ets,then they #ust trade "or the sa#e price in *oth #ar$ets.

• (aluing a -ecurity ith the Ja o" +ne Price – Assu#e a security pro#ises a ris$ "ree pay#ent o" 51000

in one year. I" the ris$ "ree interest rate is F, hat cane conclude a*out the price o" this *ond in a nor#al

#ar$et%

– Price6&ond7 9 5 2.3B

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dentif ing !r$itrageOpportunities with %ecurities

• >hat i" the price o" the *ond is not 5 2.3B% – Assu#e the price is 5 40.

–

:he opportunity "or ar*itrage ill "orce the price o" the*ond to rise until it is e ual to 5 2.3B.

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dentif ing !r$itrageOpportunities with %ecurities

• >hat i" the price o" the *ond is not 5 2.3B% – Assu#e the price is 5 0.

– :he opportunity "or ar*itrage ill "orce the price o" the*ond to "all until it is e ual to 5 2.3B.

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Deter/ining the 8o;!r$itragePrice

• Knless the price o" the security e uals thepresent value o" the securityLs cash "lo s,an ar*itrage opportunity ill appear.

•

'o Ar*itrage Price o" a -ecurityPrice( ec!rit") (All cash flows pai# $" the sec!rit")= PV

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!lternati,e - a/ple 3.<

• Pro$le/ – Consider a security that pays its o ner 52,000

today and 53,000 in one year, ithout any ris$. – -uppose the ris$ "ree interest rate is F. – What is the no;ar$itrage price of the

securit toda )$efore the =0"777 is paid+'f the securit is trading for =5">97" what

ar$itrage opportunit is a,aila$le'

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!lternati,e - a/ple 3.< )cont?d+

• %olution – Present value o" the "irst cash "lo 9 52,000 – Present value o" the second cash "lo 9

53,000 / 61.0 7 9 52,B30.1 – :otal present value o" the cash "lo s 9

• 52,000 52,B30.1 9 54,B30.1 9 no ar*itrage price o" the security.

– :he security is trading "or 54, 0,

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!lternati,e - a/ple 3.< )cont?d+

• %olution – E?ploit its overpricing *y selling it "or 54, 0. – Kse 52,000 o" the sale proceeds to replace the

52,000 e ould have received "ro# the securitytoday

– Invest 52,B30.1 o" the sale proceeds at F toreplace the 53,000 e ould have received inone year.

– :he re#aining 511 .B1 is an ar*itrage pro"it.54, 0 52,000 52,B30.1 9 511 .B1

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Deter/ining the nterest 2ateFro/ &ond Prices

• I" e $no the price o" a ris$ "ree *ond, ecan use

to deter#ine hat the ris$ "ree interestrate #ust *e i" there are no ar*itrageopportunities.

Price( ec!rit") (All cash flows pai# $" the sec!rit")= PV

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he 8PV of rading %ecuritiesand Fir/ Decision Making

•

In a nor#al #ar$et, the 'P( o" *uying or selling asecurity is ero.

• -eparation Principle – >e can evaluate the 'P( o" an invest#ent decision

separately "ro# the decision the "ir# #a$es regardingho to "inance the invest#ent or any other securitytransactions the "ir# is considering.

(B!" sec!rit") (All cash flows pai# $" the sec!rit") Price( ec!rit")

0

= −

=

NPV PV

( ell sec!rit") Price( ec!rit") (All cash flows pai# $" the sec!rit")

0

= −

=

NPV PV

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Valuing a Portfolio

• :he Ja o" +ne Price also has i#plications"or pac$ages o" securities.

– Consider t o securities, A and &. -uppose athird security, C, has the sa#e cash "lo s as Aand & co#*ined. In this case, security C ise uivalent to a port"olio, or co#*ination, o" thesecurities A and &.

• (alue Additivity

Price(C) Price(A B) Price(A) Price(B)= + = +

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!lternati,e - a/ple 3.@

• Pro$le/ – )oon Moldings is a pu*licly traded co#pany ith

only three assets• It o ns 0F o" Gue &everage Co., 0F o" )ountain

Industries, and 100F o" the +?"ord &ears, a "oot*alltea#.• :he total #ar$et value o" )oon Moldings is 5200

#illion, the total #ar$et value o" Gue &everage Co. is5 #illion and the total #ar$et value o" )ountainIndustries is 5100 #illion.

– What is the /arket ,alue of the O ford&ears'

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!lternati,e - a/ple 3.@ )cont*d+

•

%olution – :hin$ o" )oon as a port"olio consisting o" a

• 0F sta$e in Gue &everage – 0F 5 #illion 9 53 . #illion

• 0F sta$e in )ountain Industries – 0F 5100 #illion 9 5 0 #illion

• 100F sta$e in +?"ord &ears – Knder the (alue Added )ethod, the su# o" the value o"

the sta$es in all three invest#ents #ust e ual the 5200

#illion #ar$et value o" )oon.• :he +?"ord &ears #ust *e orth

– 5200 #illion N 53 . #illion N 5 0 #illion 9 5 2. #illion

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Valuing a Portfolio

• (alue Additivity and @ir# (alue – :o #a?i#i e the value o" the entire "ir#,

#anagers should #a$e decisions that #a?i#i e'P(.

– :he 'P( o" the decision represents itscontri*ution to the overall value o" the "ir#.

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Where Do We Ao Fro/ :ere'

• I#pact o" =is$ on (aluation – >hen cash "lo s are ris$y, e #ust discount

the# at a rate e ual to the ris$ "ree interest rateplus an appropriate ris$ pre#iu#.

– :he appropriate ris$ pre#iu# ill *e higher the#ore the pro ectLs returns tend to vary ithoverall ris$ in the econo#y.

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!ppendi 4 he Price of 2isk

• =is$y (ersus =is$ "ree Cash @lo s

– Assu#e there is an e ual pro*a*ility o" either a

ea$ econo#y or strong econo#y.

! di 4 h P i f 2i k

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!ppendi 4 he Price of 2isk)cont*d+

• =is$y (ersus =is$ "ree Cash @lo s 6contLd7

– E?pected Cash @lo 6)ar$et Inde?7• O 65B007 O 6514007 9 51100

I#plies investors are ris$ averse andre uire a ris$ pre#iu#.

Price(%is&'free Bon#) P (Cash lows) (*1100 in one "ear) (1.04 * in one "ear + * to#a")

*1058 to#a"

=

= ÷

=

2i k ! i

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2isk !,ersionand the 2isk Pre/iu/

– )ar$et return i" the econo#y is strong• 61400 ; 10007 / 1000 9 40F

– )ar$et return i" the econo#y is ea$• 6B00 ; 10007 / 1000 9 ;20F

–

E?pected #ar$et return• O 640F7 O 6;20F7 9 10F

,-pecte# ain at en# of "ear ,-pecte# ret!rn of a ris&" in/est ent

nitial Cost=

h 8 ! $it P i f 2i k

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Copyright ©2014 Pearson Education, Inc. All rights reserved. 3 3B

he 8o;!r$itrage Price of a 2isk%ecurit

– I" e co#*ine security A ith a ris$ "ree *ond that pays5B00 in one year, the cash "lo s o" the port"olio in oneyear are identical to the cash "lo s o" the #ar$et inde?.

– &y the Ja o" +ne Price, the total #ar$et value o" the*ond and security A #ust e ual 51000, the value o" the#ar$et inde?.

h 8 ! $it g P i

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he 8o;!r$itrage Priceof a 2isk %ecurit )cont*d+

•

!iven a ris$ "ree interest rate o" 4F, the #ar$etprice o" the *ond is

– 65B00 in one year7 / 61.04 5 in one year/5 today7 9 5today

–

:here"ore, the initial #ar$et price o" security A is51000 ; 5 9 5231.

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BDC03blh