Financial Management - Bonds 2014

8/9/2019 Financial Management - Bonds 2014

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ecap: egular! "mmediate anddelayed perpetuity

Regularperpetuity is when the first payment arrives nextperiod(e.g., next year,

month etc)

Immediateperpetuity is when the first payment arrives today

Delayed (or deferred)perpetuity is when the first payment arrives at some

future period t

periodper

periodper

r

PMTPV

)Perpetuity( =

Note: r is theper periodinterest rate. The formula assumes that r can be used to discount all

future cash flos, and that the first payment arri!es next period

periodper

periodper

periodperPMT

r

PMTmmediatePV )i( +=

1

)1(

1)(

+=

t

periodperperiodper

periodper

rx

r

PMT"elayedPV


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#roblems $ou just won a perpetuity that will pay you %&!'''

every three months( )hat is the present value o thisperpetuity! i you can earn &'* return per year!compounded +uarterly,

( &!'''

B( .!'''

/( &'!'''

D( .'!'''

0ow say that you want the 1rst payment o %&!''' to

be paid 23 months 4or &5 +uarters6 rom today, Didmoving the start o the scholarship bac8 in timepositively or negatively impact the value, )9$,

-2


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;eneral nnuity


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Assume that you are 3 years old today! and that you are planning onretirement at age "#$ %o save for your retirement! you plan on ma&ing'3!" in annual contributions to a retirement account each year until you

reach age "#$ our first contribution will be made on your 31st birthday sothat you ma&e 3# annual contributions$ Assume that the rate of interest is*$

1$ %he present value (P+) (at age 3) of your retirement savings is closest to:

a$ ',"!"11 b$ '-!

c$ '1-! d$ '1."! e$ '#!.3

.$ %he future value (/+) at age "# of your retirement savings is closest to:

a$ '1."! b$ ',0!"#3

c$ '1!! d$ '3!--!."


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0ow to bonds and valuation


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Bond is debt contract withcertain standard eatures

Face amount orpar value whichis re-paid atmaturity

Typically %&!'''

or most bonds

Coupon interest rate:Stated interest rateand does not changeduring the lie o thebond=sually > $T? atissue

Maturity:

$ears until

bond must

be repaid


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Bond ?ar8ets

#rimarily over-the-countertransactions with dealers connectedelectronically

Ctremely large number o bondissues! but generally low dailyvolume in single issues

;etting up-to-date prices dicult!particularly on small company ormunicipal issues

Treasury securities are an eCception3-E


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;overnment Bonds

Treasury Securities > government debt

Treasury Bills 4T-bills6 #ure discount bonds

Original maturity o one year or lessTreasury notes

/oupon debt

Original maturity between one and ten years

Treasury bonds /oupon debt

Original maturity greaterthan ten years

3-&'


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+aluation of oupon 2onds:

A typical example: hat is the mar&et price of a corporate bond that has a coupon

rate of 0*! a face value of '1! and matures exactly 1 years from today if theinterest rate is 1* compounded semiannually4 %imeline of coupons and face value repayment loo&s li&e this

1 . 3 , $$$ . time

',# ',# ',# ',# '15 ',# payment

es! the cash flow from the bond loo& li&e:

a) an annuity: . identical payments of ',# for 1 years (or . semi6annualpayments)

b) Plus a lump6sum amount of '1 at the end of the period


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Bond Falue

Bond Falue > #F4coupons6 G #F4par6

Bond Falue > #F4annuity6 G #F4lumpsum6

emember:

s interest rates increase present valuesdecrease

4 r H #F 6

s interest rates increase! bond pricesdecrease and vice versa

3-&5


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The Bond-#ricing +uation

3-&2

tt r)(1

/

r)(1

161

r

+alue2ond

++

+=

PV(Annuity) PV(lump sum)

C = Coupon payment; F = Face value,

r=discount rate (yield-to-maturity)

#urrent yield$#oupon%&ond Value


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Cample o /oupon BondFaluation

ou are considering the purchase of a # year! 1* coupon bond with a face value

of '1$ %he bond pays coupons annually$ our cost of capital (discount rate) is

-*$ hat is the highest price that are you willing to pay for the bond4

tt r)(1

/

r)(1

161

r

+alue2ond

++

+=


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Iero /oupon Bonds

ample* ou are considering the purchase of a 3 year%reasury bond with a face value of '1 and 8ero6coupons$ %he mar&et interest rate on similar ris& andmaturity bonds is #*! compounded semi6annually$ hatis the highest price that are you willing to pay for the

bond4 9ote:

ero6oupon 2onds ma&e no interest payments (oupon;)

3-&3

tt r)(1

/

r)(1

161

r

+alue2ond ++

+=


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The $ield to ?aturity 4$T?6

TheYield to maturity (YTM o a bond isthe discount rate that e+uates the todayAsbond price with the present value o theuture cash fows o the bond(

The yield to maturity is the average annualrate o return that a bondholder will earn ibond held to maturity

=sually coupon rate at issue e+uals $T?

)e use $T? as the discount rate to value abond


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/omputing $ield-to-?aturity$T?6(


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/omputing $ield-to-?aturity 4$T?6

$ield to ?aturity o a Iero-/oupon Bond

The yield to maturity or a Kero-couponbond is the return you will earn as an

investor by buying the bond at is currentmar8et price! holding the bond to maturity!and receiving the promised ace valuepayment(

$ield to ?aturity o an n-$ear Iero-/oupon

Bond

17

1

n

n

'ace Value(TM

Price + =


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Cample: $ield-to-?aturity4$T?6

" the #rice o 2 year maturity ris8-ree!Kero-coupon bond is %E&(J2! what is itsyield to maturity, ssume that &'' and annual compounding( ( )

1P

+alue/ace

%>1

+alue/aceP

71

=

+=

n

n

riceTM

rice


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Bond #rices:elationship Between /oupon and $ield

/oupon rate > $T? #rice >#ar

/oupon rate L $T? #rice L#ar

MDiscount bondN )hy,

/oupon rate P $T? #rice P#ar

M#remium bondN )hy,

3-5&

hi l l i hi


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;raphical elationshipBetween #rice and $ield-to-

maturity

3-55

&o!d

Pr

i(e

.ieldtomaturity


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"nterest ate is8

#rice is8

/hange in price due to changes ininterest rates

Rong-term bonds have more priceris8 than short-term bonds

Row coupon rate bonds have moreprice ris8 than high coupon ratebonds

3-5.


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Treasury uotations

"" Fe# $% &'% $%'$ $%'$% )*+',+"

?aturity > J(* per year Bid price > &.:&5 > &. &525 * o par

#rice at which dealer is willing to buy rom you

s8 price > &.:& > &. &25 * o par #rice at which dealer is willing to sell to you

Bid-s8 Spread > DealerAs pro1t

/hange > 3.25nds MTic8 SiKeN > &25

s8ed $ield > 2(.Q2'*

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#roblems &( )hat is the yield to maturity o a one-year!

ris8-ree! Kero-coupon bond with a %&'!''' acevalue and a price o %E3'' when released,

5( ris8-ree! Kero-coupon bond with a ace valueo %&!''' has & years to maturity( " the $T? is

(J*! what is the price this bond will trade at, 2( )hat must be the price o a %&'!''' bond

with a 3(* coupon rate! semiannual coupons!and two years to maturity i it has a yield tomaturity o J* #,

3-5Q


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Say 9ello to the $ield /urvehttp:1nance(yahoo(combondscompositeUbondUrates

=S Treasury Bonds

Maturity &ield &esterday ast *ee+ ast Mont

2 ?onth '(' '('Q '('5 '('.

3 ?onth '(' '(' '(' '('

5 $ear '(2' '(2' '(5E '(2J

2 $ear '(32 '(32 '(35 '(Q2

$ear &(.Q &(.Q &(.. &(35

&' $ear 5(3Q 5(3E 5(J 5(J3

2' $ear 2(3 2(3J 2(2 2(J'


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#ossible Term Structure Shapes

hat do each of these shapes say about the relation between

current and future interest rates4

Flat Term Structure

r7

i!terestrate

/erm to maturity

Rising Term Structure

Declining (Inverted)

Term Structure


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)hy Does the Term Structureo "nterest ates ?atter,

%he term structure of interest rates tells us what interest rate

we could earn over different investment hori8onsE

=ow can we use this information4

PV = CF1

(1+ r1)1+ CF2

(1+ r2)2+ CF3

(1+ r3)3+ CF4

(1+ r4 )4+ ...+

CFN

(1+ rN)N

= CF

n

(1+ ri)nn=1

4

?f weFre going to calculate the P+ of cash flows occurring in

the future! we should use the discount rate that applies to

cash flows arriving in that period


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Financial Management - Bonds 2014

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