Bond Types,Values 2014

8/18/2019 Bond Types,Values 2014

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The Valuation ofThe Valuation of

Long-TermLong-Term

SecuritiesSecurities


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The Valuation ofThe Valuation of

Long-Term SecuritiesLong-Term Securities

Distinctions Among ValuationConcepts

Bond Valuation

Preferred Stock Valuation

Common Stock Valuation

Rates of Return (or ields!


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What is Value? What is Value?

"oing-concern #alue"oin

g-concern #alue represents theamount a firm could $e sold for as acontinuing operating $usiness%

Li&uidation #alueLi

&uidation #alue represents theamount of mone' that could $e

realied if an asset or group ofassets is sold separatel' from itsoperating organiation%


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()! a firm* total assets minus lia$ilitiesand preferred stock as listed on the$alance sheet%

Book #alueBook #alue represents either

(+! an asset * the accounting #alueof an asset -- the asset,s costminus its accumulateddepreciation


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.ntrinsic #alue.ntrinsic #alue represents theprice a securit' /ought to ha#e0$ased on all factors $earing on#aluation%

1arket #alue1arket #alue represents themarket price at 2hich an asset

trades%


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Bond ValuationBond Valuation

.mportant Terms

T'pes of Bonds Valuation of Bonds

3andling SemiannualCompounding


7/814-7

Important Bond TermsImportant Bond Terms

The maturit' #aluematurit' #alue (1V1V! 4or face

#alue5 of a $ond is the stated#alue% .n the case of a 6%S% $ond7the face #alue is usuall' 8+7999%

A $ond$ond is a long-term de$tinstrument issued $' acorporation or go#ernment%


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Important Bond TermsImportant Bond Terms

The discount rate (discount rate (kkdd !(capitaliation

rate! is dependent on the risk of the$ond and is composed of the risk-freerate plus a premium for risk%

The $ond,s coupon ratecoupon rate is the statedrate of interest the annual interest

pa'ment di#ided $' the $ond,s face#alue%


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Different Types of BondsDifferent Types of Bonds

A perpetual $ondperpetual $ond is a $ond that never matures% .t has an infinite life%

(+ : kd!+ (+ : kd!

) (+ : kd!

V ; : : %%% :. ..

;t;+

(+ : kd!t

.or . (PV.


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4-10

!erpetual Bond "#ample!erpetual Bond "#ample

Bond P has a 8+7999 face #alue and pro#ides an>? annual coupon% The appropriate discount rateis +9?% @hat is the #alue of the perpetual $ondperpetual $ond

.. ; 8+7999 ( >?! ; 8>98>9%

kkdd ; +9?+9?%

VV ; .. = kkdd 4Reduced orm5

; 8>98>9 = +9?+9? ; 8>998>99%


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A non-ero coupon-pa'ing $ondnon-ero coupon-pa'ing $ond is acoupon pa'ing $ond 2ith a finite life%

(+ : kd!+ (+ : kd!

) (+ : kd!nn

V ; : : %%% :. . : 1V.

;nn

t;+(+ : kd!

t

.

V ; . (PV.


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Bond C has a 8+7999 face #alue and pro#idesan >? annual coupon for 9 'ears% The

appropriate discount rate is +9?% @hat is the#alue of the coupon $ond

%oupon Bond "#ample%oupon Bond "#ample

VV ; 8>9 (PV.++%+G8>++%+G%


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A ero coupon $ondero coupon $ond is a $ond that pa'sno interest $ut sells at a deep discount

from its face #alue it pro#idescompensation to in#estors in the form

of price appreciation%

(+ : kd!nn

V ;1V

; 1V (PV.


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VV ; 8+7999 (PV.<

+9?7 9!; 8+7999 (%9FE!; 8FE%998FE%99

&ero-%oupon&ero-%oupon

Bond "#ampleBond "#ample

Bond H has a 8+7999 face #alue anda 9 'ear life% The appropriate

discount rate is +9?% @hat is the#alue of the 'ero-coupon $ond


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Types of BondsVanilla – xed coupons, repaid at maturity

Zero Coupon – pay no explicit interest but

instead, sell at a deep discountConvertible – can be converted into to stock


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Types of Bonds Junk Bonds – below investment rade


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!overnment Bonds Treasury "ecurities # $ederal overnment

debt Treasury Bills %T&bills' (ure discount bonds)riinal maturity of one year or less

Treasury notes %T&notes'Coupon debt)riinal maturity between one and ten years

Treasury bonds %T&bonds'Coupon debt

)riinal maturity reater t*an ten years


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Bond +atinsoody-s , "tandard . (oor-s and $itc*

reularly monitor issuer-s nancialcondition and assin a ratin to t*e debt

.n#estment"rade

Belo2.n#estment"rade(Iunk!

AAA Best Quality

AA High Quality A Upper Mediu !rade

BBB Mediu !rade

BB "pe#ulati$e

B %ery "pe#ulati$e&&& %ery %ery "pe#ulati$e

&&

& '( )*terest Bei*g +aid

, &urre*tly i* ,eault


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Semiannual %ompounding Semiannual %ompounding

(+! Di#ide kkdd $' ))()! 1ultipl' nn $' ))

(! Di#ide .. $' ))

1ost $onds in the ()S) pa' interestt2ice a 'ear (+=) of the annual

coupon!%

AdJustments needed*


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(+ : kd =)) !))Knn(+ : kd =)) !

+

Semiannual %ompounding Semiannual %ompounding

A non-ero coupon $ondnon-ero coupon $ond adJusted forsemiannual compounding%

V ; : : %%% :. = )) . = )) : 1V

;))Knn

t;+(+ : kd =)) !

t

. = ))

; . =)) (PV.


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VV ; 89 (PV.F%)

Semiannual %ouponSemiannual %oupon


Bond C has a 8+7999 face #alue and pro#idesan >? semiannual coupon for +F 'ears% The

appropriate discount rate is +9? (annual rate!%

@hat is the #alue of the coupon $ond


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Let us use another 2orksheet on 'ourcalculator to sol#e this pro$lem% Assume

that Bond C 2as purchased (settlementdate! on +)-+-)99 and 2ill $e redeemedon +)-+-)9+% This is identical to the +F-

'ear period 2e discussed for Bond C%

@hat is its percent of par @hat is the#alue of the $ond


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Bond "#ampleBond "#ample+% @hat is its

percent of par

)% @hat is the

#alue of the$ond

>%G)>? of par(as &uoted in

financial papers!

>%G)>?

8+7999 face#alue ; *+,).+


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Preferred StockPreferred Stock is a t'pe of stockthat promises a (usuall'! fied

di#idend7 $ut at the discretion ofthe $oard of directors%

!referred Stoc/ Valuation!referred Stoc/ Valuation

Preferred Stock has preference o#ercommon stock in the pa'ment ofdi#idends and claims on assets%


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!referred Stoc/ Valuation!referred Stoc/ Valuation

This reduces to a perpetuity perpetuity M

(+ : kP!+ (+ : kP!

) (+ : kP! VV ; : : %%% :

Di#P Di#PDi#P

;t;+ (+ : kP!

t

Di#P or Di#P(PV.


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!referred Stoc/ "#ample!referred Stoc/ "#ample

Di#Di#PP ; 8+99 ( >? ! ; 8>%998>%99%

kkPP ; +9?+9?%VV ; Di#Di#PP = kkPP ; 8>%998>%99 = +9?+9?

; 8>98>9

Stock PS has an >?7 8+99 par #alueissue outstanding% The appropriate

discount rate is +9?% @hat is the #alueof the preferred stockpreferred stock


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%ommon Stoc/ Valuation%ommon Stoc/ Valuation

Pro rata share of future earningsafter all other o$ligations of the

firm (if an' remain!% Di#idends may may $e paid out of

the pro rata share of earnings%

Common stockCommon stock represents aresidual o2nership position in the

corporation%


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%ommon Stoc/ Valuation%ommon Stoc/ Valuation

(+!


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Dividend Valuation 0odel Dividend Valuation 0odel

Basic di#idend #aluation model accountsfor the PV of all future di#idends%

(+ : ke!+ (+ : ke!

) (+ : ke!

V ; : : %%% :Di#+ Di# Di#)

;t;+

(+ : ke!t

Di#t Di#t* Cash Di#idendat time t

ke* N&uit' in#estor,s

re&uired return

Di#t* Cash Di#idendat time t

ke* N&uit' in#estor,s

re&uired return


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1d2usted Dividend 1d2usted Dividend

Valuation 0odel Valuation 0odel

The $asic di#idend #aluation modeladJusted for the future stock sale%

(+ : ke!+ (+ : ke!

) (+ : ke!nn

V ; : : %%% :Di#+ Di#nn : PricennDi#)

nn* The 'ear in 2hich the firm,sshares are epected to $e sold%

Pricenn* The epected share price in 'ear nn%

nn* The 'ear in 2hich the firm,sshares are epected to $e sold%

Pricenn* The epected share price in 'ear nn%


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Dividend 3ro4thDividend 3ro4th

!attern 1ssumptions!attern 1ssumptions

The di#idend #aluation model re&uires theforecast of all future di#idends% The

follo2ing di#idend gro2th rate assumptionssimplif' the #aluation process%

Constant "ro2thConstant "ro2th

Oo "ro2thOo "ro2th

"ro2th Phases"ro2th Phases


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%onstant 3ro4th 0odel %onstant 3ro4th 0odel

The constant gro2th modelconstant gro2th model assumes thatdi#idends 2ill gro2 fore#er at the rate g%

(+ : ke!+ (+ : ke!

) (+ : ke!

V ; : : %%% :D9(+:g! D9(+:g!

;(ke - g!

D+D+* Di#idend paid at time +%

g * The constant gro2th rate%

ke* .n#estor,s re&uired return%

D+* Di#idend paid at time +%

g * The constant gro2th rate%


D9(+:g!)


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%onstant 3ro4th%onstant 3ro4th

0odel "#ample0odel "#ample

Stock C" has an epected di#idendgro2th rate of >?% Nach share of stock

Just recei#ed an annual 8%) di#idend%The appropriate discount rate is +F?%@hat is the #alue of the common stockcommon stock

DD++ ; 8%)8%) ( + : %9> ! ; 8%F98%F9

VVC"C" ; DD++ = ( kkee - g ! ; 8%F98%F9 = ( %+F%+F - %9> !

; 8F98F9

Stock C" has an epected di#idendgro2th rate of >?% Nach share of stock

Just recei#ed an annual 8%) di#idend%The appropriate discount rate is +F?%@hat is the #alue of the common stockcommon stock

DD++ ; 8%)8%) ( + : %9> ! ; 8%F98%F9

VVC"C" ; DD++ = ( kkee - g ! ; 8%F98%F9 = ( %+F%+F - %9> !

; 8F98F9


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&ero 3ro4th 0odel &ero 3ro4th 0odel

The ero gro2th modelero gro2th model assumes thatdi#idends 2ill gro2 fore#er at the rate g ; 9%

(+ : ke!+ (+ : ke!

) (+ : ke!

VH" ; : : %%% :D+ D

;ke

D+ D+* Di#idend paid at time +%ke* .n#estor,s re&uired return%

D+* Di#idend paid at time +%


D)


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&ero 3ro4th&ero 3ro4th


Stock H" has an epected gro2th rate of9?% Nach share of stock Just recei#ed an

annual 8%) di#idend per share% Theappropriate discount rate is +F?% @hat

is the #alue of the common stockcommon stock

DD++ ; 8%)8%) ( + : 9 ! ; 8%)8%)

VVH"H" ; DD++ = ( kkee - 9 ! ; 8%)8%) = ( %+F%+F - 9 !

; 8)+%G98)+%G9


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D9(+:g+!t Dn(+:g)!t

3ro4th !hases 0odel 3ro4th !hases 0odel

The gro2th phases modelgro2th phases model assumesthat di#idends for each share 2ill gro2

at t2o or more different gro2th rates%

(+ : ke!t (+ : ke!

tV ; t;+

n

t;n:+

:


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D9(+:g+!t Dn:+

3ro4th !hases 0odel 3ro4th !hases 0odel

Oote that the second phase of the gro2thgro2th

phases modelphases model assumes that di#idends 2ill

gro2 at a constant rate g)% @e can re2ritethe formula as*

(+ : ke!t (ke - g)!

V ; t;+

n

:+

(+ : ke!n


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3ro4th !hases3ro4th !hases


Stock "P has an epected gro2thrate of +G? for the first 'ears and

>? thereafter% Nach share of stock Just recei#ed an annual 8%)

di#idend per share% The appropriate

discount rate is +F?% @hat is the#alue of the common stock under

this scenario


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Stock "P has t2o phases of gro2th% The first7 +G?7 startsat time t;9 for 'ears and is follo2ed $' >? thereafterstarting at time t;% @e should #ie2 the time line as t2o

separate time lines in the #aluation%

Stock "P has t2o phases of gro2th% The first7 +G?7 startsat time t;9 for 'ears and is follo2ed $' >? thereafter starting at time t;% @e should #ie2 the time line as t2o

separate time lines in the #aluation%

9 + ) F G

D+ D) D D DF DG

"ro2th of +G? for 'ears "ro2th of >? to infinit'M


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Oote that 2e can #alue Phase ) using the %onstant3ro4th 0odel

9 + )

D+ D) D

D DF DG

9 + ) F G

"ro2th Phase+ plus the infinitel'

long Phase )


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Oote that 2e can no2 replace all di#idends from 'ear to infinit' 2ith the value at time t;7 VM SimplerMM

V ;

D DF DG

9 + ) F G

D

k-g

@e can use this model $ecausedi#idends gro2 at a constant >?

rate $eginning at the end of ear %


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Oo2 2e onl' need to find the first four di#idends tocalculate the necessar' cash flo2s%

9 + )

D+ D) D

V

9 + )

5e4 TimeLine

D

k-g

@here V ;


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Determine the annual di#idends%

D9 ; 8%) (this has $een paid alread'!

DD66 ; D9(+:g+!+ ; 8%)(+%+G!+ ;*7)8 *7)8

DD. . ; D9(+:g+!) ; 8%)(+%+G!) ;*,)7 *,)7

DD7 7 ; D9(+:g+!B ; 8%)(+%+G!B ;*9): *9):

DD, , ; DB(+:g)!+ ; 8F%9G(+%9>!+ ;*9), *9),


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Oo2 2e need to find the present #alueof the cash flo2s%

9 + )

%EG %G F%9G

E>

9 + )

1ctual Values

F%G%+F-%9>@here 8E> ;

3 h !h


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@e determine the PV of cash flo2s%

PV(DD66! ; DD66(PV.E9! ; * * 7).8 7).8

PV(DD. . ! ; DD. . (PV.! ; 8E> 4C" 1odel5

PV(! ! 7 7 ! ; ! ! 7 7 (PV.! ; * * 96)7. 96)7.


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D9(+:%+G!t D



!V ;

t;+

:

+

(+:%+F!n

V ; 8%)E : 8%9 : 8% : 8F+%)

V ; *6).. V ; *6)..

% l l ti R t f


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%alculating Rates of%alculating Rates of

Return Return

+% Determine the epected cash flo2scash flo2s%

)% Replace the intrinsic #alue (V! 2ith the

market price (Pmarket price (P99!!%

% Sol#e for the mar/et reuired rate ofmar/et reuired rate of

returnreturn that e&uates the discounted cashdiscounted cash

flo2sflo2s to the market pricemarket price%

Steps to calculate the rate ofreturn (or ield!%


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Determining Bond =T0 Determining Bond =T0

Determine the ield-to-1aturit'(T1! for the annual coupon pa'ing

$ond 2ith a finite life%

P9 ; nn

t;+ (+ : kd !t

.

; . (PV.


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Determining the =T0 Determining the =T0

Iulie 1iller 2ant to determine the T1for an issue of outstanding $onds at

Bas/et Wonders % BW has anissue of +9? annual coupon $onds2ith +F 'ears left to maturit'% The

$onds ha#e a current market #alue of*[email protected]: *[email protected]: %

What is the =T0? What is the =T0?


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=T0 Solution =T0 Solution

8+7)F98+7)F9 ; 8+99(PV.9G%+9 : 8)EF%99; 8+79>+%+98+79>+%+9

44Rate is too highC Rate is too highC 55


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8+7)F98+7)F9 ; 8+99(PV.9 : 8G)%99; 8+7)E)%>98+7)E)%>9

44Rate is too lo4C Rate is too lo4C 55


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%9E 8+7)E

%9) .RR 8+7)F9 8+)

%9 8+79>+

Q 8)%9) 8+)


8)Q

;


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4-53

%9E 8+7)E

%9) .RR 8+7)F9 8+)

%9 8+79>+

Q 8)%9) 8+)


8)Q

;


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4-54

%9E 8+)E

%9) T1 T1 8+)F98+)F9 8+)

%9 8+9>+

(8)!(9%9)! 8+)


8)Q

Q ; Q ; %99)

T1 T1 ; %9E : %99) ; %9E) or E%)?E%)?

D t i i S i lD t i i S i l


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Determining SemiannualDetermining Semiannual

%oupon Bond =T0 %oupon Bond =T0

P9 ; )nn

t;+ (+ : kd =) !t

. = )

; (. =)!(PV.


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Determining the SemiannualDetermining the Semiannual


Iulie 1iller 2ant to determine the T1for another issue of outstanding

$onds% The firm has an issue of >?semiannual coupon $onds 2ith )9

'ears left to maturit'% The $onds ha#e

a current market #alue of *A9: *A9: %What is the =T0? What is the =T0?

D t i i S i lDetermining Semiann al


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4 + : (/ d . !) 5 -+ ; T1

Determine the ield-to-1aturit'(T1! for the semiannual coupon

pa'ing $ond 2ith a finite life%

4 + : (%9)G)G!) 5 -+ ; %9>E+ or >%E+?

Oote* make sure 'ou utilie the calculatorans2er in its DNC.1AL form%

D t i i S i lDetermining Semiannual


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4 + : (kd = )!) 5 -+ ; T1

This techni&ue 2ill calculate kd%

ou must then su$stitute it into the

follo2ing formula%

4 + : (%9>F)F+ =)!) 5 -+ ; %9>E+ or >%E+? (same resultM!

B d ! i =i ldBond !rice =ield


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Bond !rice - =ieldBond !rice - =ield

RelationshipRelationship

Discount BondDiscount Bond -- The market re&uiredrate of return eceeds the coupon rate

(Par P9 !%Premium BondPremium Bond ---- The coupon rateeceeds the market re&uired rate of

return (P9 Par!%

Par BondPar Bond ---- The coupon rate e&uals themarket re&uired rate of return (P9 ; Par!%

Bond !rice =ieldBond !rice =ield


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%oupon Rate%oupon Rate

1ARNT RN6.RND RATN U< RNT6RO (?!

B U O D

P R . C

N

( 8 !

+999 Par

+G99

+99

+)99

G99

99 ) G > 6: 6: +) + +G +>

F ear F ear

+F ear +F ear



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Bond !rice-=ieldBond !rice-=ield


Assume that the re&uired rate of return on

a +F 'ear7 +9? annual coupon pa'ing $ondrisesrises from +9? to +)?% @hat happens tothe $ond price

@hen interest rates riserise7 then themarket re&uired rates of return riserise

and $ond prices 2ill fall fall %

@hen interest rates riserise7 then themarket re&uired rates of return riserise

and $ond prices 2ill fall fall %



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B U O D

P R . C

N

( 8 !

+999 Par

+G99

+99

+)99

G99

99 ) G > 6: 6: +) + +G +>

+F ear +F ear

F ear F ear


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Bond !rice-=ieldBond !rice-=ield


Assume that the re&uired rate of

return on a +F 'ear7 +9? annualcoupon pa'ing $ond fallsfalls from +9? to>?% @hat happens to the $ond price

@hen interest rates fall fall 7 then themarket re&uired rates of return fall fall

and $ond prices 2ill riserise%

@hen interest rates fall fall 7 then themarket re&uired rates of return fall fall

and $ond prices 2ill riserise%



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B U O D

P R . C

N

( 8 !

+999 Par

+G99

+99

+)99

G99

99 ) G > 6: 6: +) + +G +>

+F ear +F ear

F ear F ear

Bond !rice =ield RelationshipBond !rice =ield Relationship


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Bond !rice-=ield RelationshipBond !rice-=ield Relationship

Therefore7 the $ond price has

risenrisen from 8+999 to 8++E+%

The re&uired rate of return on a +F'ear7 +9? coupon pa'ing $ond

has fallenfallen from +9? to >?%


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The Role of Bond 0aturity The Role of Bond 0aturity

Assume that the re&uired rate of return

on $oth the F and +F 'ear7 +9? annualcoupon pa'ing $onds fall fall from +9? to>?% @hat happens to the changes in

$ond prices

The longer the $ond maturity@ thegreater the change in $ond price for a

given change in the mar/et reuiredrate of return%

The longer the $ond maturity@ thegreater the change in $ond price for a

given change in the mar/et reuiredrate of return%



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B U O D

P R . C N

( 8 !

+999 Par

+G99

+99

+)99

G99

99 ) G > 6: 6: +) + +G +>

+F ear +F ear

F ear F ear


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The Role of Bond 0aturity The Role of Bond 0aturity

The F 'ear $ond price has risenrisen from 8+7999 to8+79>9 for the F 'ear $ond (:>%9?!%

The +F 'ear $ond price has risenrisen from 8+7999 to8+7+E+ (:+E%+?!% T4ice as fast T4ice as fast C C

The re&uired rate of return on $oth the Fand +F 'ear7 +9? annual coupon pa'ing

$onds has fallenfallen from +9? to >?%

The Role of theThe Role of the


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The Role of theThe Role of the



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4-71

"#ample of the Role of"#ample of the Role of

the %oupon Ratethe %oupon Rate

Assume that the market re&uired rate ofreturn on t2o e&uall' risk' +F 'ear $onds

is +9?% The annual coupon rate for Bond3 is +9? and Bond L is >?%

@hat is the rate of change in each of the$ond prices if market re&uired rates fall

to >?

"#ample of the Role of the"#ample of the Role of the


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4-72

"#ample of the Role of the"#ample of the Role of the


The price for Bond 3 2ill rise from 8+7999

to 8+7+E+ (:+E%+?!%The price for Bond L 2ill rise from 8>> to

8+7999 (:+E%?!% aster Increaseaster IncreaseC C

The price on Bond 3 and L prior to thechange in the market re&uired rate of

return is 8+7999 and 8>> respecti#el'%

Determining the =ield onDetermining the =ield on


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4-73


!referred Stoc/ !referred Stoc/

Determine the 'ield for preferredstock 2ith an infinite life%

P9 ; Di#P = kP

Sol#ing for kP such thatkP ; Di#P = P9

!referred Stoc/ =ield!referred Stoc/ =ield


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!referred Stoc/ =ield!referred Stoc/ =ield

"#ample"#ample

kP ; 8+9 = 8+99%

/ / ! ! ; 6:6:%

Assume that the annual di#idend oneach share of preferred stock is *6: %

Nach share of preferred stock iscurrentl' trading at *6:: % @hat is

the yield on preferred stock



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%ommon Stoc/ %ommon Stoc/

Assume the constant gro2th modelis appropriate% Determine the 'ield

on the common stock%

P9 ; D+ = ( ke - g !

Sol#ing for ke such that

ke ; ( D+ = P9 ! : g

%ommon Stoc/%ommon Stoc/


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%ommon Stoc/%ommon Stoc/

=ield "#ample=ield "#ample

ke ; ( 8 = 89 ! : 9

//ee

; +9? : F? ; 6969

Assume that the epected di#idend(D+! on each share of common stock

is *7% Nach share of common stockis currentl' trading at *7: and has anepected gro2th rate of 9% @hat is

the yield on common stock


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/*at a0ects Bond

prices1+isk2nterest rates

3efault risk


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/*at is t*e 4term structure of interest

rates51 /*at is a 4yield curve51

Term structure6 t*e relations*ipbetween interest rates %or yields' and

maturities7

8 rap* of t*e term structure is called

t*e yield curve7


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3raw a normal yield

curve


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3'pothetical Treasur' ield Cur#e

9

F

+9

+F

+ +9 )9

ears to 1aturit'

.nterestRate (?! + 'r >%9?

+9 'r ++%?

)9 'r +)%GF?

Real risk-free rate

.nflation premium

1aturit' risk premium


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/*at factors can explain t*e s*ape

of t*is yield curve1

T*is constructed yield curve is upward

slopin7 T*is is due to increasin expected

in9ation and an increasin maturityrisk premium7

Bond Types,Values 2014

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Transcript of Bond Types,Values 2014