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 $ou just won a perpetuity that will pay you %&!'''
every three months( )hat is the present value o thisperpetuity! i you can earn &'* return per year!compounded +uarterly,
( &!'''
B( .!'''
/( &'!'''
D( .'!'''
0ow say that you want the 1rst payment o %&!''' to
be paid 23 months 4or &5 +uarters6 rom today, Didmoving the start o the scholarship bac8 in timepositively or negatively impact the value, )9$,
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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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