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CHAPTER 5Bonds and Their Valuation

Bonds: Facts and Motivations Bond valuation

Finding price and yield Yield-to-maturity: Details A relationship between price and yield Premium, discount, and par bonds

Assessing risk Default risk, interest rate risk, and

reinvestment rate risk Bond ratings

Types of bonds Bond contract terms and bankruptcy process

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Top Five Largest U.S. Corporate Bond Financings, as of July 1999

Issuer

Ford Motor Co.

AT&T

RJR Holdings

WorldCom

Sprint

Date

July 1999

Mar 1999

May 1989

Aug 1998

Nov 1998

Amount

$8.6 billion

$8.0 billion

$6.1 billion

$6.1 billion

$5.0 billion

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Advantage of Debt over Equity

Interest expense is tax-deductible but dividend is not.

Avoid earning/ownership dilutionAvoid a high flotation cost for

issuing stock. Flotation cost = Underwriting fee,

Fee to investment banker

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Example of Tax Saving with Debt

Income StatementRevenue−COGSProfit Margin

− Op. Cost Firm w/o Debt Firm w/ Debt EBIT$5 $5

−Int. Exp 0 1EBT 5 4−Tax (30%) 1.5 1.2 Net Income 3.5 2.8

30 cents savings for every dollar of interest expense

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Who Issue a Bond?

Domestically, Treasury bill, note, or bond: Issued by federal

government, Called “risk-free” securities, about $4 trillion market

Municipal bond: “munis”Corporate bond: our focus, about $5 trillion market

Internationally,Euro bond (Dollar-denominated bonds sold in

Germany by GM)Foreign bond: “Yankee” bond (dollar-denominated

bond sold in U.S. by non-U.S. issuer), “Samurai” bond (Yen bonds sold in Japan by a non-Japanese borrower), etc

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AMD(Issuer, Seller, or

Borrower)

Investor(Buyer, Lender)

Price?

Coupons at t=1,2, …. T

Face Value at T

Main Question: How much would be the fair price a buyer is willing to pay for this bond?

Bond Pricing: Cash Flow

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Elements of Bond Pricing

1. Par value (par): Face amount. paid at maturity. Assume $1,000.

2. Coupon interest rate (C or INT): Stated interest rate on the bond certificate. Multiply by par value to get dollars of interest to be paid. Generally fixed.

3. Maturity (N): Years until bond must be repaid. Declines over time.

4. Yield-to-Maturity (YTM, rd): The current market interest rate that is used to discount the future coupon payments and face amount. Or, the required rate of return to be earned from other bonds with same level of risk.

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Financial Asset Valuation

PV =

CF

1+ r ... +

CF

1+r1 n

12

21

CF

rn .

0 1 2 nr

CF1 CFnCF2Value

...

+ ++

The value of any financial asset (e.g., a bond, a stock, a loan, etc) is simply the present value of the cash flows the asset is expected to produce.

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An AMD Bond

Suppose AMD issues a bond with a par value of $1,000 at a coupon rate of 10% for five years. That is, AMD promises to pay you $100 at the end of each of 5 years and $1,000 at the end of 5th year. Suppose the current market interest rate is 10%. How much would you pay for a bond now?

AMD Bond

10% Coupon

$1,000 Par

5-year Maturity

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The Value of AMD bonds

0 1 2 5r=10%

100=$1,000*10%

1,100100PresentValue

...

1 2 5 5

100 100 100 1,000......

(1 10%) (1 10%) (1 10%) (1 10%)

90.91 + 82.64 + ...... + 62.09 + 620.92

$1000

PV

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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 lump sum at t = 10:

$ 614.46 385.54

$1,000.00

PV annuity PV maturity value Value of bond

===

INPUTS

OUTPUT

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What if a price is given?: What’s the YTM on a 10-year, 9% annual coupon, $1,000

par value bond that sells for $887?

90 90 90

0 1 9 10rd=?

1,000PV1 . . .PV10

PVM

887 Find rd that “works”!

...

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10 −887 90 1000N I/YR PV PMT FV

10.91

V

INT

r

M

rB

dN

dN

1 11

... +INT

1+ r d

887

90

1

1000

11 10 10

r rd d

+90

1+r d

,

+ + + +

++++

INPUTS

OUTPUT

...

Watch out a negative sign on PV.

Find rd

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Semiannual Bonds

1. Multiply years by 2 to get periods = 2n.2. Divide nominal rate by 2 to get periodic rate = rd/2.3. Divide annual INT by 2 to get PMT =

INT/2.

2n rd/2 OK INT/2 OK

N 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

INPUTS

OUTPUT

N Multiply by 2

YTM Divide by 2

INT Divide by 2

Find the value of 10-year, 10% coupon,semiannual bond if rd = 13%.

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What if a price is given with semiannual coupons?: What’s the YTM on a 10-year, 9% semiannual coupon, $1,000 par value bond

that sells for $887?

45 45 45

0 1 920In 6 mth periodsrd=?

1,000PV1 . . .PV10

PVM

887 Find rd that “works”!

...

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20 -887 45 1000N I/YR PV PMT FV

5.44 x2 =10.88

887

45

1

1000

11 20 20

r rd d

+45

1+r d

,++

++

INPUTS

OUTPUT

...

Watch out a negative sign on PV.

Don’t forget multiplying 5.44 by 2.

Find rd for Semiannual Bonds

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Coupon rate = A stated interest rate on the bond at the time of issuance, Usually fixed. Can be used to compute periodic cash flows to investors. Easier to understand.

We are dealing with two rates: Coupon rate and YTM

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We are dealing with two rates: Coupon rate and YTM

Yield-to-maturity The compounded rate of return earned on a

bond held to maturity if an investor re-invests all the coupon payments until maturity.

Usually, same as the current market interest rate for a similar investment. Also known as the opportunity cost of capital, i.e., the rate that could be earned on alternative investments of equal risk.

The discount rate that equates a bond’s price with the present value of its future cash flows.

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YTM: Example

2−year @ 10% annual coupon bonds, YTM = 15% Price = $918.71

Now, assume that an investor re-invest first coupon income (t = 1) at 15% for one year.

Then, total cash inflows upon maturity in year 2 is equal to 100*1.15 = 115 plus100 plus1,000= 1215

Find I that makes a PV of 918.75 equal to FV of 1215 when N = 2N = 2, PV = −918.75 , PMT = 0, FV= 1,215 I = 15%

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rd = (r* + DRP) + IP + Others.

rd = Required rate of return on a debt security.

r* = Real risk-free rate. T-bond rate if no inflation; 1% to 4%.

DRP = Default risk premium. IP = Inflation premium.Others = Liquidity premium and/or

Maturity risk premium.

YTM is a function of many factors!

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Graphical Relationship Between Price and Yield-to-Maturity

600

700

800

900

1000

1100

1200

1300

1400

1500

0% 2% 4% 6% 8% 10% 12% 14%

Yield

Pri

ce

Microsoft Excel Worksheet

Price and Yield move in an opposite direction!

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Any explanation?

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10 13 100 1000N I/YR PV PMT FV

-837.21

When rd rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount.

INPUTS

OUTPUT

What would happen if expected inflation rose by 3%, causing rd = 13%?

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What would happen if inflation fell, and rd declined to 7%?

10 7 100 1000N I/YR PV PMT FV

-1,210.71

If coupon rate > rd, price rises above par, and bond sells at a premium.

INPUTS

OUTPUT

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Premium, Discount, Par Bonds

If coupon rate < rd, bond sells at a discount. (Price < Par)

If coupon rate = rd, bond sells at its par value. (Price = Par)

If coupon rate > rd, bond sells at a premium. (Price > Par)

If rd rises, price falls - very important.

Price = par at maturity.

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Examples: Premium, Discount, and Par Bond

Example 1: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 10%.

Example 2: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 13%.

Example 3: Find the value of 10%, 10-year, $1,000 par value annual bond. Assume YTM = 7%.

Now plot three bonds. Put price on the y-axis and yield on the x-axis.

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Definitions

Current yield =

Capital gains yield =

= YTM = +

Annual coupon pmtCurrent price

Change in priceBeginning price

Exp totalreturn

Exp Curr yld

Exp capgains yld

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Find current yield and capital gains yield for a 8%, 10-year bond when the

bond sells for $827.97 and YTM = 10.91%.

Current yield =

= 0.0966 = 9.66%.

$80 $827.97

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YTM = Current yield + Capital gains yield.

Cap gains yield = YTM - Current yield = 10.91% - 9.66% = 1.25%.

Could also find values in Years 0 and 1,get difference, and divide by value inYear 1. Same answer.

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Premium and Discount Bonds

All 10-year Bonds

Premium

C = 15%

YTM = 10.91%

Discount

C = 8%

YTM = 10.91%

Current

Yield

12.08% 9.66%

Capital Gain or Loss Yield

─1.17% 1.25%

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Change in price of a bond over time: Suppose the bond was issued 20

years ago and now has 10 years to maturity. What would happen to its value over time if the required rate

of return remained at 10%, or at 13%, 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

rd = 7%.

rd = 13%.

rd = 10%.

ChangeInPriceOverTime

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

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

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

At maturity, the value of any bond must equal its par value. Any economic rationale?

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Changes in Bond Price over Time: Reality

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Three Risks in the Bond Market

Default risk: A seller may not pay me coupons and principal.

Interest rate risk: A volatile interest movement may depress the value of my bonds. (also called price risk)

Reinvestment risk: I may be forced to re-invest my coupon payments at a lower interest rate.

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Bond Ratings Provide One Measureof Default Risk

Investment Grade Junk Bonds

Moody’s Aaa Aa A Baa Ba B Caa C

S&P AAA AA A BBB BB B CCC D

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Importance of Bond Ratings

A rating is an indicator of default riskA lower rating means difficulty in

selling new bonds as the company needs new financing.

A lower rating means a higher interest expense in the future funding.

A downgrades may have negative impact on equity prices.

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Bond Rating and Market Interest Rates

Rating Interest Rate Spread over Long Bond Rate

AAA 7.20% 0.20%

AA 7.50 0.50

A 8.00 1.00

BBB 8.50 1.50

BB 9.00 2.00

B 10.25 3.25

CCC 12.00 5.00

CC 13.00 6.00

C 14.50 7.50

Source: Applied Corporate Finance by Aswath Damodaran, 1997

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What’s interest rate (or price) risk? Does a 1-year or 10-year 10% bond

have more risk?

rd 1-year Change 10-year Change

5% $1,048 $1,386

10% 1,000 4.8% 1,000 38.6%

15% 956 4.4% 749 25.1%

Interest rate risk: Rising rd causes bond’s price to fall.

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0

500

1,000

1,500

0% 5% 10% 15%

1-year

10-year

kd

ValueST vs LT

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What is reinvestment rate risk?

The risk that CFs will have to be reinvested in the future at lower rates, reducing income.

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0 1r=10%

1100

0 1 2 10r=10%

100=$1,000*10%

1,100100

...

Or, Buying a long-term, 10-year bond in a declining interest rate environment

r=7%

0 1

r=7%

70

...

1070

9

Buying a short-term bond and rolling over 9 years in a declining interest rate environment

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

Short-term bonds: Low interest rate risk, high reinvestment rate risk.

Nothing is riskless!

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True or False: “All 10-year bonds have the same price and reinvestment rate risk.”

False! Low coupon bonds have less reinvestment rate risk but more price risk than high coupon bonds.

If two bonds with different coupon rates have the same maturity, then the value of the one with the lower coupon is proportionately more dependent on the value amount to be received at maturity.

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Summary: Risks in Bond Trading

Long-Term Bond

Short-Term Bond

High-Coupon Bond

Low-Coupon Bond

Interest Rate Risk

Higher Lower Lower Higher

Reinvestment Risk

Lower Higher Higher Lower

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Other Types of Bonds

Treasury Bond: Issued by the federal government

Callable bond: The seller has an option to buy back their bonds from bond investors.

Convertible bond: The seller grant bondholders the right to exchange each bond for a designated number of common stock shares of the issuing firm.

Zero-coupon bonds: “zeros” or “deep discount” bonds

Floating-rate bonds

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Callable bond: A 10-year, 10% annual coupon,$1,000 par value bond is selling for $1,134.20 with an 8% yield to maturity.

It can be called after 5 years at $1,050.

What’s the bond’s nominal yield tocall (YTC)?

5 -1134.2 100 1050 N I/YR PV PMT FV

7.54%

INPUTS

OUTPUT

Callable Bond

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Yield to Call

A callable bond allows the issuer to buy back the bond at a specified call price anytime after an initial call protection period, until the bond matures.

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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 the investor.

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

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If you bought bonds, would you be more likely to earn YTM or YTC?

Coupon rate = 10% vs. YTC = rd = 7.54%. Could raise money by selling new bonds which pay 7.54%.

Could thus replace bonds which pay $100/year with bonds that pay only $75.40/year.

Investors should expect a call, hence YTC = 7.54%, not YTM = 8%.

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

So, expect to earn:YTC on premium bonds.YTM on par & discount bonds.

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Bond Indentures or Provisions

Secured versus unsecured debtDebenture: Unsecured bond

Senior versus subordinated debt Guarantee provisions Sinking fund provisions Restrictive covenants

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Bankruptcy

Two main chapters of Federal Bankruptcy Act:Chapter 11, ReorganizationChapter 7, Liquidation

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

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Summary A bond is a debt security. YTM = Rate of return to be earned if holding until

maturity YTM = Current yield + Capital gains (loss) yield Price and yield are negatively correlated. At maturity, price = par value A premium bond is not necessary “better”

investment opportunity than a discount bond. Default risk, reinvestment risk, and price risk are

three most important risk factors in trading bonds. Reinvestment risk and price risk can move in

opposite direction for a given bond. Callable bond carries a higher reinvestment risk than

a straight bond, from the buyer’s perspective.

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Bonds Quotation at www.bondpage.com

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Quiz

You could buy, for $1,000, either a 10%, 10-year, annual payment bond or an equally risky 10%, 10-year semiannual bond. Which would you prefer?

The semiannual bond’s EFF% is:

EFFi

mNom

m

%.

.

1 1 1

0 10

21 10 25%

2