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Chapter 5

Bonds, Bond Valuation, and

Interest Rates

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Topics in Chapter Key features of bonds Bond valuation Measurin yield !ssessin ris"

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Value = + + +FCF1 FCF2 FCF∞

(1 + WACC)1 (1 +WACC)∞

(1 + WACC)2

Free cash fow(FCF)

Mar"et interest rates

$ir%&s business ris"Mar"et ris" aversion

$ir%&s debt'e(uity %i)Cost o debt

Cost of e(uity

Weighted average

cost o caital(WACC)

*et operatinpro+t after ta)es

Re(uired invest%entsin operatin capital

!

=

"eter#i$a$ts o %$tri$sic Value& 'he Cost o"ebt

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Key $eatures of a Bond -ar value. $ace a%ount/ paid at

%aturity0 !ssu%e 1,0 Coupon interest rate. 3tated

interest rate0 Multiply by par valueto et dollars of interest0 4enerally

+)ed0

(More…)

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Maturity. ears until bond %ust berepaid0 6eclines0

Issue date. 6ate 7hen bond 7asissued0

6efault ris". Ris" that issuer 7ill

not %a"e interest or principalpay%ents0

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Call -rovision Issuer can refund if rates decline0 That helps the issuer but hurts the

investor0 Therefore, borro7ers are 7illin to

pay %ore, and lenders re(uire

%ore, on callable bonds0 Most bonds have a deferred call

and a declinin call pre%iu%0

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:hat&s a sin"in fund; -rovision to pay o< a loan over its

life rather than all at %aturity0 3i%ilar to a%orti=ation on a ter%

loan0 Reduces ris" to investor, shortens

averae %aturity0 But not ood for investors if rates

decline after issuance0

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enerally handled in 2

7ays Call )? at par per year for sin"in

fund purposes0 Call if rd is belo7 the coupon rate and

bond sells at a pre%iu%0

Buy bonds on open %ar"et0 @se open %ar"et purchase if rd is

above coupon rate and bond sells at adiscount0

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Value of a 1year, 1?coupon bond if r

d

1?

VB

1 1,

0 0 0 D

1

100 100

0 1 2 10

10%

100 + 1,000V = ?

...

A0A1 D 0 0 0 D #>055 D #>505

1,0

DDE1 D rdF1 E1 D rdF* E1 D rdF*

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10 10 100 1000

N I/YR PV PMT FV

-1,000

8108

#>505 1,0

-V annuity

-V %aturity valueValue of bond

=

==

INPUTS

OUTPUT

The bond consists of a 1year, 1?annuity of 1'year plus a 1,

lu%p su% at t 1.

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:hen rd rises, above the coupon

rate, the bond&s value falls belo7par, so it sells at a discount0

10 13 100 1000N I/YR PV PMT FV

-3!.21

INPUTS

OUTPUT

:hat 7ould happen if e)pectedinGation rose by #?, causin r

1#?;

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inGation fell, and rd

declined to 9?;

If coupon rate H rd, price rises above

par, and bond sells at a pre%iu%0

10 ! 100 1000N I/YR PV PMT FV

-1,210.!1

INPUTS

OUTPUT

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1#

3uppose the bond 7as issued 2years ao and no7 has 1 years to

%aturity0 :hat 7ould happen toits value over ti%e if the re(uiredrate of return re%ained at 1?, or

at 1#?, or at 9?; 3ee ne)t slide0

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M

1,3!2

1,211

1,000

3!

!!"

30 2" 20 1" 10 " 0

r # = !%.

r # = 13%.

r # = 10%.

Bond Value EF vs ears

re%ainin to Maturity

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!t %aturity, the value of any bond%ust e(ual its par value0

The value of a pre%iu% bond7ould decrease to 1,0

The value of a discount bond 7ould

increase to 1,0 ! par bond stays at 1, if rd

re%ains constant0

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:hat&s yield to

%aturityJ; TM is the rate of return earned on

a bond held to %aturity0 !lso

called pro%ised yield0J It assu%es the bond 7ill not

default0

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TM on a 1year, A? annualcoupon, 1, par value bondsellin for >>9

$0 $0$0

0 1 $ 10r #=?

1,000PV1

.

. .PV10

PVM

! $ind rd that 7or"sJ

...

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10 -! $0 1000

N I/YR PV PMT FV

10.$1

VI*T M

B

E1 D rdF1

E1 D rdF*

000 DI*T

>>9 A

E1 D rdF1

1,

E1 D rdF*

DA

E1 D rdF*

DD

D D

INPUTS

OUTPUT

000

$ind rd

E1 D rdF*

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1A

If coupon rate L rd, bond sells at a

discount0 If coupon rate rd, bond sells at its

par value0 If coupon rate H rd, bond sells at a

pre%iu%0 If rd rises, price falls0

-rice par at %aturity0

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$ind TM if price 7ere1,1#020

3ells at a pre%iu%0

Because coupon A? H rd 90>?, bond&s value Hpar0

10 -113.2 $0 1000

N I/YR PV PMT FV!.0

INPUTS

OUTPUT

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6e+nitions

Current yield

Capital ains yield

TM D

!nnual coupon p%tCurrent price

Chane in priceBeinnin price

)p totalreturn

)pCurr yld

)p capains yld

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A? coupon, 1year bond, - >>9, and TM 10A1?

Current yield

0115 1015?0

A>>9

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Cap ains yield TM Currentyield 10A1? 1015? 098?0

Could also +nd values in ears 1 and2,et di<erence, and divide by value in

ear 10 3a%e ans7er0

TM Current yield DCapital ains yield0

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3e%iannual Bonds

10Multiply years by 2 to et periods

2*0206ivide no%inal rate by 2 to etperiodic rate rd'20

#06ivide annual I*T by 2 to et -MT I*T'202Nr # /2 O& INT/2 O&

N I/YR PV PMT FV

INPUTS

OUTPUT

a ue o year

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2(10) 13/2 100/2

20 '." "0 1000

N I/YR PV PMT FV

-3.!2

INPUTS

OUTPUT

a ue o year,coupon, se%iannual bond ifrd 1#?0

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3preadsheet $unctionsfor Bond Valuation

3ee Ch05 Mini Case.xls for details0 -RIC IN6

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Callable Bonds and ieldto Call

! 1year, 1? se%iannualcoupon,

1, par value bond is sellin for1,1#50A 7ith an >? yield to%aturity0

It can be called after 5 years at1,50

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10 -113".$ "0 10"0

N I/YR PV PMT FV

3.!'" 2 = !."3%

INPUTS

OUTPUT

*o%inal ield to Call ETCF

If you bouht bonds 7ould you

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2A

If you bouht bonds, 7ould yoube %ore li"ely to earn TM or

TC;

Coupon rate 1? vs0 TC rd

905#?0 Could raise %oney by

sellin ne7 bonds 7hich pay905#?0

Could thus replace bonds 7hich

pay 1'year 7ith bonds that payonly 950#'year0 Investors should e)pect a call,

hence TC 905?, not TM >?0

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In eneral, if a bond sells at apre%iu%, then coupon H rd, so a

call is li"ely0 3o, e)pect to earn.

TC on pre%iu% bonds0 TM on par O discount bonds0

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rd rP D I- D 6R- D N- D

MR-0

Qere.

rd Re(uired rate of return on a

debt security0

rP Real ris"free rate0

I- InGation pre%iu%0

6R- 6efault ris" pre%iu%0

N- Ni(uidity pre%iu%0

MR- Maturity ris" pre%iu%0

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#2

:hat is the no%inal ris"free rate;

rR$ E1DrPFE1DI-F1

rPD I- D ErP)I-F

rPD I-0 EBecause rP)I- iss%allF

rR$

Rate on Treasury securities0

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sti%atin I-

Treasury InGation-rotected3ecurities ETI-3F are inde)ed to

inGation0 The I- for a particular lenth

%aturity can be appro)i%ated as

the di<erence bet7een the yieldon a noninde)ed Treasury securityof that %aturity %inus the yield on

a TI-3 of that %aturity0

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Bond 3preads, the 6R-,and the N-

! bond spreadJ is often calculated asthe di<erence bet7een a corporate

bond&s yield and a Treasury security&syield of the sa%e %aturity0 Therefore. 3pread 6R- D N-0

Bond&s of lare, stron co%panies often

have very s%all N-s0 Bond&s of s%allco%panies often have N-s as hih as2?0

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#5

Bond Ratins ? defaultin 7ithin.

3O- and$itch

Moody&s

1 yr0 5 yrs0

Investment grade bonds:

!!! !aa 0 0

!! !a 0 01

! ! 01 08

BBB Baa 0# 20A

Junk bonds:

BB Ba 10 >02

B B 10> A02

CCC Caa 220# #80A

Source: Fitch Ratings

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Bond Ratins and Bond3preads Eahoo$inance, March 2AF

Nonter% Bonds ield E?F 3pread E?F

1ear Tbond 208>

!!! 505 20>2 !! 5082 20A

! 509A #011

BBB 905# 0>5 BB 11082 >0A

B 1#09 1102

CCC 280# 2#082

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#9

:hat factors a<ect defaultris" and bond ratins;

$inancial ratios 6ebt ratio

Coverae ratios, such as interestcoverae ratio or BIT6! coveraeratio

-ro+tability ratios Current ratios

(More…)

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Bond Ratins MedianRatios E3O-F

Interestcovera

e

Return oncapital

6ebt tocapital

!!! 2#0> 2908? 120?

!! 1A05 290? 2>0#?

! >0 1905? #905?

BBB 09 1#0? 205?

BB 205 110#? 5#09?

B 102 >09? 950A?

CCC 0 #02? 11#05?

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#A

Sther $actors that !<ectBond Ratins

-rovisions in the bond contract 3ecured versus unsecured debt

3enior versus subordinated debt 4uarantee provisions 3in"in fund provisions

6ebt %aturity

(More…)

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Sther factors arnins stability

Reulatory environ%ent -otential product liability !ccountin policies

n eres ra e or pr ce r s or

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n eres ra e or pr ce r s or1year and 1year 1?bonds

rd 1year Chane 1yearChane

5? 1,> 1,#>81? 1,

0>?1,

#>08?

15? A580?

9A2501?

Interest rate ris". Risin rd

causes bond&s price to fall0

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0

"00

1,000

1,"00

0% "% 10% 1"%

1-e*r

10-e*r

r #

Value

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:hat is reinvest%ent rateris";

The ris" that C$s 7ill have to bereinvested in the future at lo7er

rates, reducin inco%e0 Illustration. 3uppose you ust 7on

5, playin the lottery0 ou&ll

invest the %oney and live o< theinterest0 ou buy a 1year bond7ith a TM of 1?0

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ear 1 inco%e 5,0 !t yearend et bac" 5, to reinvest0

If rates fall to #?, inco%e 7ill dropfro% 5, to 15,0 Qad youbouht #year bonds, inco%e

7ould have re%ained constant0

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The Maturity Ris" -re%iu%

Nonter% bonds. Qih interest rateris", lo7 reinvest%ent rate ris"0

3hortter% bonds. No7 interest rateris", hih reinvest%ent rate ris"0 *othin is ris"less ields on loner ter% bonds usually are

reater than on shorter ter% bonds, sothe MR- is %ore a<ected by interestrate ris" than by reinvest%ent rate ris"0

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Ter% 3tructure ield Curve

Ter% structure of interest rates.the relationship bet7een interest

rates Eor yieldsF and %aturities0 ! raph of the ter% structure is

called the yield curve0

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Qypothetical Treasury ieldCurve

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Ban"ruptcy

T7o %ain chapters of $ederalBan"ruptcy !ct. Chapter 11, Reorani=ation Chapter 9, Ni(uidation

Typically, co%pany 7ants Chapter

11, creditors %ay prefer Chapter 90

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If co%pany can&t %eet its obliations, it+les under Chapter 110 That stops

creditors fro% foreclosin, ta"inassets, and shuttin do7n the business0 Co%pany has 12 days to +le a

reorani=ation plan0 Court appoints a trusteeJ to supervise

reorani=ation0 Manae%ent usually stays in control0

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Co%pany %ust de%onstrate in itsreorani=ation plan that it is

7orth %ore alive than dead0J Sther7ise, ude 7ill order

li(uidation under Chapter 90

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li(uidated, here&s thepay%ent priority.

-ast due property ta)es 3ecured creditors fro% sales of secured assets0 Trustee&s costs )penses incurred after ban"ruptcy +lin :aes and unpaid bene+t contributions,

subect to li%its @nsecured custo%er deposits, subect to li%its Ta)es @nfunded pension liabilities @nsecured creditors -referred stoc" Co%%on stoc"

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In a li(uidation, unsecured creditorsenerally et =ero0 This %a"es the%%ore 7illin to participate inreorani=ation even thouh their clai%sare reatly scaled bac"0

Various roups of creditors vote on thereorani=ation plan0 If both the %aorityof the creditors and the ude approve,co%pany e%eresJ fro% ban"ruptcy7ith lo7er debts, reduced interestchares, and a chance for success0

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