Bond Valuation.ppt

7/23/2019 Bond Valuation.ppt

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CHAPTER 8

Bonds and TheirValuation



7-2

What is a bond? A long-term debt instrument in

which a borrower agrees to make

payments of principal andinterest, on specic dates, to theholders of the bond



7-3

Bond Valuation A bond issue represents borrowing

from many lenders at one time

under a single agreement While one person may not be willing

to lend a single company !"# million,

"#,### in$estors may be willing tolend the rm !",### each



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Bond Terminology A bond%s term &or maturity' is the time fromthe present until the principal is to be returned Bonds mature on the last day of their term

A bond%s face $alue &or par' represents theamount the rm intends to borrow &theprincipal' at the coupon rate of interest Bonds typically pay interest &coupon rate' e$ery si(

months

Bonds are non-amorti)ed &meaning the principal isrepaid at once when the bond matures rather thanbeing repaid in increments throughout the bond%slife'



7-5

Bond Terminology *oupon interest rate + stated interest

rate &generally (ed' paid by the issuer

ultiply by par to get dollar payment ofinterest ssue date + when the bond was issued



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Bond Valuation.Basic

deas Ad/usting to interest rate changes

Bonds are sold in both primary &original

sale' and secondary markets&subse0uent trading among in$estors'

nterest rates change all the time

ost bonds pay a (ed interest rate What happens to the price of a bond paying

a (ed interest rate in the secondarymarket when interest rates change?



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1ther types &features' of

bonds *on$ertible bond + may be e(changed for

common stock of the rm, at the holder%soption

Warrant + long-term option to buy astated number of shares of common stockat a specied price

2utable bond + allows holder to sell the

bond back to the company prior tomaturity

ncome bond + pays interest only wheninterest is earned by the rm



7-8

The $alue of nancial

assets

n

n

3

3

"

"

k'&"*4

k'&"*4

k'&"*4 Value

+

++

+

+

+

=

0 1 2 nk

CF1 CFnCF2Value

...



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What is the $alue of a "#-year,"#5 annual coupon bond, if kd 6

"#5?

!",###V!7899 !7899 !;#;" V

&""#'

!",###

&""#'

!"##

&""#'

!"##

V

B

B

"#"#"B

=

+++=

+++=

0 1 2 nk

100 100 + 1,000100VB = ?

...



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<etermining the 2rice of aBond

The Bond Valuation 4ormula The price of a bond is the present

$alue of a stream of interestpayments plus the present $alue ofthe principal repayment

2B 6 2V&interest payments' = 2V&principal

repayment'

Interest payments are

annuities—can use thepresent value of an annuity

formula: PMT[PVFAk,n]

Principal repayment is a lump

sum in the future—can usethe future value formula:

FV[PVFk,n]



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*ash 4low Time >ine for aBond

This is a

sinle

sum!

This is an

or"inary

annuity!



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Value of a Bond

VB 6 2T @"- &"&"=kd''C kd D = &

&"=kd' '



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<etermining the 2rice of a

Bond Two nterest Eates and 1ne ore

*oupon rate

<etermines the si)e of the interest payments F.the current market yield on comparable

bonds The appropriate discount rate that makes the

present $alue of the payment e0ual to the price of

the bond in the market AFA yield to maturity &GT'

*urrent yield.annual interest paymentdi$ided by bond%s current price



7-14

Bond * has a !",### face $alue and pro$ides an85 annual coupon for 7# years The appropriate

arket Eate is "#5 What is the $alue of the

coupon bond?

VV = $80 (PVIFA10%, 30) + $1,000 (PVIF10%, 30)

= $80 (9.427) + $1,000 (.07)

!!Table IV Table IV "" !!Table II Table II ""

= $74.1# + $7.00 = $811.1#$811.1#.

Value of the bond



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A )ero-coupon bond)ero-coupon bond is a bond that pays nointerest but sells at a deep discount from its face

$alue it pro$ides compensation to in$estors in the form

of price appreciation

(1 + k)nn

V =V

= V (PVIFk, nn)

Hero *oupon Bond



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&"' <i$ide kkdd by 33&3' ultiply nn by 33

&7' <i$ide by 33

&' &n' *a ne-e' /e aea- (12 & e annual /&u*&n).

Au'en' neee5

Iemi-annual *ompounding



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(1 + k 22 ) 226nn(1 + k 22 )1

A non-)ero coupon bondnon-)ero coupon bond ad/usted forsemiannual compounding

V = + + ... +I 22 I 22 + V

=226nn

=1(1 + k 22 )

I 22

= I 22 (PVIFAk

22

,226nn

) + V (PVIFk

22

, 226nn

)

(1 + k 22 ) 226nn+ V

I 22(1 + k 22 )2




7-18

B&n C a' a $1,000 a/e alue an *-&e' an8% 'eannual /&u*&n &- 1 ea-'. e

a**-&*-ae a-ke -ae ' 10% (annual -ae). a' e alue & e coupon bond ?




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<iscount Bond<iscount Bond -- The market re0uired rate of returne(ceeds the coupon rate &2ar J 2# '

2remium Bond2remium Bond ---- The coupon rate e(ceeds themarket re0uired rate of return &2# J 2ar'

2ar Bond2ar Bond ---- The coupon rate e0uals the marketre0uired rate of return &2# 6 2ar'

f interest rate rise so that market re0uired rate ofreturn increases, the bond%s price will fallf interest rate fall, so that market re0uired rate ofreturn decreases, the bond%s price will rise

Bond 2rice-Gieldrelationship



7-20

The price path of a bond

What would happen to the $alue of thisbond if its re0uired rate of return remainedat "#5, or at "75, or at K5 until maturity?

:ea-'& au-

1,372

1,211

1,000

837

77

30 2 20 1 10 0

k = 7%.

k = 13%.

k = 10%.

VB



7-21

Bond $alues o$er time

At maturity, the $alue of any bond muste0ual its par $alue

f kd remains constantL The $alue of a premium bond would

decrease o$er time, until it reached!",###

The $alue of a discount bond wouldincrease o$er time, until it reached!",###

A $alue of a par bond stays at !",###



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<enitions

+

==

=

=

*MG

N(pected

*G

N(pected GT,returntotalN(pected

price Beginning

pricein*hange &*MG'yieldgains*apital

price*urrent

payment coupon Annual &*G'eld*urrent yi



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An e(ampleL*urrent and capital gains yield

4ind the current yield and the capitalgains yield for a "#-year, ;5 annual

coupon bond that sells for !88K, andhas a face $alue of !",###

*urrent yield 6 !;# !88K

6 #"#"9 6 "#"95



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*alculating capital gainsyield

GT 6 *urrent yield = *apital gains yield

*MG 6 GT + *G6 "#;"5 - "#"95

6 #KO5

*ould also nd the e(pected price one yearfrom now and di$ide the change in price by thebeginning price, which gi$es the same answer



7-25

*all 2ro$isions

f interest rates ha$e dropped substantially sincea bond was originally issued, a rm may wish toPrenance,% or retire their old high interest bond

issue Qowe$er, the issuing corporation would ha$e to

get all the bondholders to agree to this

4rom the bondholder%s $iewpoint, this could be

a bad idea.they would be gi$ing up highcoupon bonds and would ha$e to rein$est theircash in a market with lower interest rates

To ensure that the corporation can renance theirbonds should they wish to do so, the corporation

makes the bonds Pcallable%



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*all pro$ision

Which gi$es the issuing corporation the rightto call the bond for redemption

The call pro$ision generally states thatcompany must pay the bondholders anamount greater than the par $alue if theyare called

The additional sum, which is termed a callpremium

t is often set e0ual to one year%s interest ifthe bonds are called during the rst year,and the premium declines at a constant rateof T e$ery year there after



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*all 2ro$isions

*all pro$isions allow bond issuers toretire bonds before maturity by paying

a premium &penalty' to bondholders any corporations oRer a deferred call

period &meaning the bond won%t becalled for at least ( years after theinitial issuing date' Fnown as the call-protected period



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*all 2ro$isions

The NRect of A *all 2ro$ision on2rice When $aluing a bond that is probably

going to be called when the call-protected period is o$er *annot use the traditional bond $aluation

procedure *ash Sows will not be recei$ed through

maturity because bond will probably be called



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The Eefunding <ecision

When current interest rates fall belowthe coupon rate on a bond, company

has to decide whether or not to call inthe issue *ompare interest sa$ings of issuing a new

bond to the cost of making the call *alling in the bond re0uires the payment of a

call premium ssuing a new bond to raise cash to pay oR the

old bond re0uires payment of administrati$ee(penses and Sotation costs



7-30

Gield to *all

To calculate the GT*, sol$e thise0uation for F d,

VB = PMT [ {1- (1/(1+k d))! / k d " + (C#$$ P%&' /

(1+k d) )



7-31

What is rein$estment raterisk?

The risk of an income decline dueto drop in interest rates is called

rein$estment risk This risk is high on callable bonds

t is also high on short term

maturity bonds



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*onclusions about interest rateand rein$estment rate risk

*1*>I1L othing is risklessU

Ihort-termA<1E Qighcoupon bonds

>ong-termA<1E >ow

coupon bonds

nterest

rate risk>ow Qigh

Eein$estment rate risk

Qigh >ow



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<efault Eisk

f an issuer defaults, in$estors recei$eless than the promised return

nSuenced by the issuer%s nancialstrength and the terms of the bondcontract

n$estor need to asses a bond%sdefault risk before making apurchase



7-34

Bond Eefunding

Bond may be refunded by thecompany prior to maturity through

either the issuance of serial bondor e(ercising a call pri$ilege on astraight bond



7-35

Bond ndentures.*ontrolling <efault Eisk

As a bondholder, you would like to ensurethat you will recei$e your promised interestand principal payments

Bond indentures attempt to pre$ent rms frombecoming riskier after the bonds are purchased,and includes such protecti$e co$enants asL >imits to management%s salary >imits to di$idends

aintenance of certain nancial ratios Eestrictions on additional debt issues

Iinking funds pro$ide money for the repaymentof bond principal



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Iinking 4und s a series of payments made into an account that%s

dedicated to paying oR a bond%s principal at maturity <eposits are planned so that the amount in the bank

on the date the bonds mature will /ust e0ual theprincipal due f lenders re0uire a sinking fund for security, it%s

included a pro$ision in the bond agreement

*ompany can call randomly call in some bonds forretirement before maturity Another approach is to issue serial bonds, splitting

the total amount borrowed into se$eral separateissues



7-37#$

The Bond ndenture ndenture + Written agreement between the company &the

borrower' and the bondholders &the lenderscreditors' andincludesL The rights of the bondholders and the duties of the

issuing corporation

The basic terms of the bonds 4ace $alue, coupon rate, maturity, etc

The total amount of bonds issued A description of property used as security, if applicable

<escribes collateral &bonds, stocks, etc' andor mortgage&real property, ie, land, buildings, etc' used as pledge

The repayment arrangements + schedule of repayments *all pro$isionsL gi$ing the issuer the option to repurchase

the bond at a specic price prior to maturity

<etails of protecti$e co$enants + positi$e &should' andnegati$e &should not '



7-38

Bond ndenture Itandard pro$ision

Ipecify certain record keeping and generalbusiness practices that the bond issue must

follow The borrower commonly must

aintain satisfactory accounting records inaccordance with generally accepted accounting

principles &MAA2' 2eriodically supply audited nancial statements

2ay ta(es and other liabilities when due

aintain all facilities in good working order



7-39

Bond ndenture

Eestricti$e pro$isions Which place operating and nancial constraints on the

borrower

Theses pro$isions help protect the bondholder againstincrease in borrower risk Ee0uire a minimum le$el of li0uidity 2rohibit the sale of accounts recei$ables to generate cash

mpose (ed asset restrictions &maintain a specic le$elof (ed assets' *onstrain subse0uent borrowing &subordination' >imit the rm%s annual cash di$idend payments to a

specied percentage or amount



7-40

Bond ndenture

Iinking 4und Ee0uirements 1b/ecti$e is to pro$ide for the systematic retirement of

bonds prior to their maturity

Iecurity nterest The bond indenture identies any collateral pledged

against the bond species how it is to be maintained

Trustee A trustee is a third party to a bond indenture The trustee can be one indi$idual, a corporation, or a

commercial bank trust department



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Types of bonds

nsecured bonds <ebentures

Iubordinated debentures ncome bonds

Iecured bonds

ortgage bonds *ollateral trust bonds N0uipment trust certicate

%&



7-42

<ebentures

nsecured bonds that only creditworthy rms can issue

*on$ertible bonds are normallydebentures

*laims are the same as those of any

general creditors ay ha$e other unsecured bonds

subordinated to them

%'



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Types of bonds

Iubordinated debentures *laims are not satised until those of the creditors holdings

certain &senior' debts ha$e been fully satised

*laims is that of a general creditor but not as good as asenior debt claim

ncome bonds 2ayment of interest is re0uired only when earnings are

a$ailable *laims is that of a general creditor

Are not default when interest payments are missed, because

they are contingent only on earnings being a$ailable



7-44

Types of bonds ortgage bonds

Iecured by real estate or buildings

*laims is on proceeds from sale of mortgaged assets if

not fully satised, the lender becomes general creditors

A number of mortgages can be issued against the samecollateral

*ollateral trust bonds Iecured by stocks or bonds that are owned by the issuer

*ollateral $alue is generally 395 to 795 greater thanbond $alue



7-45

Types of bonds

N0uipment trust certicate sed to nance rolling stock +

airplanes, trucks, boats, railroad cars *laim is on proceeds from the sale of

the asset if proceeds do not satisfyoutstanding debt, trust certicatelenders become general creditors

%(



7-46

*ontemporary types ofbonds

Hero coupon bonds is a bond that pays no interest but sells at adeep discount from its face $alue it pro$ides compensation to in$estors in theform of price appreciationMenerally callable at par $alue Treasury Bills are good e(amples of )eroes

unk bondsQigh risk bonds high yields + often yielding 35 to75 more than the best 0uality corporate debt



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4loating rate bonds Itated interest rate is ad/usted periodically

within stated limits in response to changesin specied money market and capitalmarket rates

Tend to sell at close to par because of theautomatic ad/ustment to changing marketsconditions

Iome issues pro$ide for annual redemptionat par at the option of the bondholder



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N(tendible notes Ihort maturities, typically " to 9 years, that

can be renewed for a similar period at theoption of holders

An issue might be a series of 7 year renewablenotes o$er a period of "9 years e$ery 7

years the notes could be e(tended foranother 7 years, at a new rate competiti$ewith market interest rates at the time ofrenewal




2utable bonds Bonds that can be redeemed at par at the

option of their holder either at specied datesafter the date of issue and e$ery " to 9 yearsthereafter or when and if the rm takesspecied actions, such as being ac0uired,ac0uiring another company, or issuing a largeamount of additional debt

The bond%s yield is lower than that of a nonputable bond

Documents

Bond Valuation.ppt