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Copyright 2002 Harcourt, Inc. All rights reserved.

CHAPTER 9Bonds and Their Valuation

Key features of bonds

Bond valuation

Measuring yield

Assessing risk

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Key Features of a Bond

1. Par value: Face amount; paid

at maturity. Assume $1,000.

2. Coupon interest rate: Statedinterest rate. Multiply by parvalue to get dollars of interest.Generally fixed.

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3. Maturity: Years until bondmust be repaid. Declines.

4. Issue date: Date when bondwas issued.

5. Default risk: Risk that issuer

will not make interest orprincipal payments.

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How does adding a call provision

affect a bond?

Issuer can refund if rates decline.

That helps the issuer but hurts theinvestor.

Therefore, borrowers are willing topay more, and lenders require more,on callable bonds.

Most bonds have a deferred call anda declining call premium.

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Whats a sinking fund?

Provision to pay off a loan over itslife rather than all at maturity.

Similar to amortization on a termloan.

Reduces risk to investor, shortens

average maturity.But not good for investors if rates

decline after issuance.

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1. Call x% at par per year for sinking

fund purposes.2. Buy bonds on open market.

Company would call if kd is below the

coupon rate and bond sells at apremium. Use open market purchaseif kd is above coupon rate and bondsells at a discount.

Sinking funds are generally handled

in 2 ways

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Financial Asset Valuation

PV =

CF

1 + k . . . +

CF

1 + k

1 n

1

2

21

CF

k n .

0 1 2 nk

CF1 CFnCF2Value

...

+ ++

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The discount rate (ki) is theopportunity cost of capital, i.e.,the rate that could be earned on

alternative investments of equalrisk.

ki = k* + IP + LP + MRP + DRP

for debt securities.

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Whats the value of a 10-year, 10%

coupon bond if kd = 10%?

V

k k

B

d d

$100 $1,1

000

1

1 10 10. . . +$100

1+ kd

100 100

0 1 2 10

10%

100 + 1,000V = ?

...

= $90.91 + . . . + $38.55 + $385.54= $1,000.

++

++

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10 10 100 1000N I/YR PV PMT FV

-1,000

The bond consists of a 10-year, 10%

annuity of $100/year plus a $1,000 lumpsum at t = 10:

$ 614.46

385.54$1,000.00

PV annuity

PV maturity valueValue of bond

=

==

INPUTS

OUTPUT

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10 13 100 1000N I/YR PV PMT FV-837.21

When kd rises, above the coupon rate,the bonds value falls below par, so itsells at a discount.

What would happen if expected

inflation rose by 3%, causing k =13%?

INPUTS

OUTPUT

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What would happen if inflation fell, and

kd declined to 7%?

10 7 100 1000N I/YR PV PMT FV

-1,210.71

If coupon rate > kd, price rises abovepar, and bond sells at a premium.

INPUTS

OUTPUT

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Suppose the bond was issued 20years ago and now has 10 years tomaturity. What would happen to itsvalue over time if the required rate

of return remained at 10%, or at13%, or at 7%?

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M

Bond Value ($)

Years remaining to Maturity

1,372

1,211

1,000

837

775

30 25 20 15 10 5 0

kd

= 7%.

kd = 13%.

kd = 10%.

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At maturity, the value of any bondmust equal its par value.

The value of a premium bond woulddecrease to $1,000.

The value of a discount bond wouldincrease to $1,000.

A par bond stays at $1,000 if kdremains constant.

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Whats yield to maturity?

YTM is the rate of return earned on

a bond held to maturity. Alsocalled promised yield.

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Whats the YTM on a 10-year, 9%

annual coupon, $1,000 par value bondthat sells for $887?

90 9090

0 1 9 10kd=?

1,000PV1...

PV10PVM887 Find kdthat works!

...

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10 -887 90 1000N I/YR PV PMT FV

10.91

VINT

k

M

kB

d

N

d

N1 1

1... +

INT

1+ k d

887 901 1 00011 10 10k kd d+ 901 + kd ,

Find kd

++++

++++

INPUTS

OUTPUT

...

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If coupon rate < kd, bond sells at adiscount.

If coupon rate = kd, bond sells at

its par value.

If coupon rate > kd, bond sells at apremium.

If kd rises, price falls.

Price = par at maturity.

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Find YTM if price were $1,134.20.

10 -1134.2 90 1000

N I/YR PV PMT FV7.08

Sells at a premium. Becausecoupon = 9% > kd = 7.08%,bonds value > par.

INPUTS

OUTPUT

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Definitions

Current yield =

Capital gains yield =

= YTM = +

Annual coupon pmtCurrent price

Change in priceBeginning price

Exp totalreturn

ExpCurr yld

Exp capgains yld

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Find current yield and capital gains

yield for a 9%, 10-year bond when thebond sells for $887 and YTM = 10.91%.

Current yield =

= 0.1015 = 10.15%.

$90$887

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YTM = Current yield + Capital gains yield.

Cap gains yield = YTM - Current yield

= 10.91% - 10.15%= 0.76%.

Could also find values in Years 1 and 2,get difference, and divide by value in

Year 1. Same answer.

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Whats interest rate (or price) risk?

Does a 1-year or 10-year 10% bondhave more risk?

kd 1-year Change 10-year Change

5% $1,048 $1,38610% 1,000 4.8% 1,000 38.6%

15% 956 4.4% 749 25.1%

Interest rate risk: Rising kd causesbonds price to fall.

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0

500

1,000

1,500

0% 5% 10% 15%

1-year

10-year

kd

Value

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What is reinvestment rate risk?

The risk that CFs will have to bereinvested in the future at lower rates,

reducing income.

Illustration: Suppose you just won$500,000 playing the lottery. Youll

invest the money and live off theinterest. You buy a 1-year bond with a

YTM of 10%.

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Year 1 income = $50,000. At year-end get back $500,000 to reinvest.

If rates fall to 3%, income will dropfrom $50,000 to $15,000. Had youbought 30-year bonds, income

would have remained constant.

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Long-term bonds: High interest raterisk, low reinvestment rate risk.

Short-term bonds: Low interest rate

risk, high reinvestment rate risk.Nothing is riskless!

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True orFalse: All 10-year bondshave the same price andreinvestment rate risk.

False! Low coupon bonds have lessreinvestment rate risk but moreprice risk than high coupon bonds.

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Semiannual Bonds

1. Multiply years by 2 to get periods = 2n.

2. Divide nominal rate by 2 to get periodicrate = kd/2.

3. Divide annual INT by 2 to get PMT =INT/2.

2n kd/2 OK INT/2 OKN I/YR PV PMT FV

INPUTS

OUTPUT

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2(10) 13/2 100/220 6.5 50 1000N I/YR PV PMT FV

-834.72

Find the value of 10-year, 10% coupon,

semiannual bond if kd = 13%.

INPUTS

OUTPUT

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You could buy, for $1,000, either a 10%,

10-year, annual payment bond or anequally risky 10%, 10-year semiannualbond. Which would you prefer?

The semiannual bonds EFF% is:

10.25% > 10% EFF% on annual bond, so buysemiannual bond.

EFFi

m

Nom

m

%.

. 1 1 10 10

21 10 25%

2

.

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If $1,000 is the proper price for the

semiannual bond, what is the properprice for the annual payment bond?

Semiannual bond has kNom

= 10%, withEFF% = 10.25%. Should earn sameEFF% on annual payment bond, so:

INPUTS

OUTPUT

10 10.25 100 1000N I/YR PV PMT FV

-984.80

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At a price of $984.80, the annualand semiannual bonds would bein equilibrium, because investors

would earn EFF% = 10.25% oneither bond.

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kNom = 7.53% is the rate brokerswould quote. Could also calculateEFF% to call:

EFF% = (1.03765)2 - 1 = 7.672%.

This rate could be compared tomonthly mortgages, and so on.

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If you bought bonds, would you be

more likely to earn YTM or YTC?

Coupon rate = 10% vs. YTC = kd =

7.53%. Could raise money by sellingnew bonds which pay 7.53%.

Could thus replace bonds which pay$100/year with bonds that pay only$75.30/year.

Investors should expect a call, henceYTC = 7.5%, not YTM = 8%.

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In general, if a bond sells at apremium, then (1) coupon > kd, so(2) a call is likely.

So, expect to earn:

YTC on premium bonds.

YTM on par & discount bonds.

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Disney recently issued 100-yearbonds with a YTM of 7.5%--thisrepresents the promised return. Theexpected return was less than 7.5%

when the bonds were issued. If issuer defaults, investors receive

less than the promised return.

Therefore, the expected return oncorporate and municipal bonds isless than the promised return.

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Bond Ratings Provide One Measure

of Default Risk

Investment Grade Junk Bonds

Moodys Aaa Aa A Baa Ba B Caa C

S&P AAA AA A BBB BB B CCC D

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What factors affect default risk and

bond ratings?

Financial performance

Debt ratio

TIE, FCC ratios

Current ratios

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Provisions in the bond contractSecured versus unsecured debt

Senior versus subordinated debt

Guarantee provisions

Sinking fund provisions

Debt maturity

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Other factorsEarnings stability

Regulatory environment

Potential product liability

Accounting policies

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Top Ten Largest U.S. Corporate

Bond Financings, as of July 1999

Issuer

Ford Motor Co.AT&T

RJR Holdings

WorldComSprint

Date

July 1999Mar 1999

May 1989

Aug 1998Nov 1998

Amount

$8.6 billion$8.0 billion

$6.1 billion

$6.1 billion$5.0 billion

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Bankruptcy

Two main chapters of Federal

Bankruptcy Act:Chapter 11, Reorganization

Chapter 7, Liquidation

Typically, company wants Chapter 11,creditors may prefer Chapter 7.

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If company cant meet its obligations, itfiles under Chapter 11. That stopscreditors from foreclosing, takingassets, and shutting down the

business.Company has 120 days to file a

reorganization plan.Court appoints a trustee to

supervise reorganization.Management usually stays in control.

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Company must demonstrate in itsreorganization plan that it isworth more alive than dead.

Otherwise, judge will orderliquidation under Chapter 7.

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If the company is liquidated, heresthe payment priority:

1. Secured creditors from sales ofsecured assets.

2. Trustees costs

3. Wages, subject to limits4. Taxes

5. Unfunded pension liabilities

6. Unsecured creditors7. Preferred stock

8. Common stock

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In a liquidation, unsecured creditors

generally get zero. This makes themmore willing to participate inreorganization even though their claims

are greatly scaled back.Various groups of creditors vote on the

reorganization plan. If both the majorityof the creditors and the judge approve,company emerges from bankruptcywith lower debts, reduced interestcharges, and a chance for success.

Documents

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