Chapter 6

Valuing Bonds

Copyright © 2011 by The McGraw-Hill Companies, Inc. All rights reserved.McGraw-Hill/Irwin

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Chapter 6 Learning GoalsLG1: Describe bond characteristics

LG2: Identify various bond issuers and their motivation for issuing debt

LG3: Read and interpret bond quotes

LG4: Compute bond prices using present value concepts

LG5: Explain the relationship between bond prices and interest rates

LG6: Compute bond yields

LG7: Find bond ratings and assess the effect of credit risk on bond yields

LG8: Assess bond market performance

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• We hear a lot about the stock market in the popular press, but not much about the bond market

• It may surprise you to learn that the U.S. bond market is over twice the size of the U.S. stock market– Total outstanding debt in 2007: $29.2 trillion– Total market value of common stock: $14.2 trillion

• In general, bonds are less risky than stocks– But, like all assets, high-yield bonds have higher

risk

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Bond Market Overview

• Bond Characteristics– Bonds are debt obligations

• Corporations• Federal government and federal agencies• States and local governments

– Bonds are also known as fixed-income securities

• Amount and timing of cash flows are known

– For the issuer, the bond is a loan that requires regular interest payments and repayment of the borrowed principal

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• The precise terms of a bond issue are outlined in the indenture– Maturity date– Par value (also called face value), usually

$1,000– Interest rate– Any property pledged as collateral– Steps the bondholder can take in event of

default

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• Call feature– Allows the issuing firm to refinance when

interest rates fall– The issuer “calls” the bonds back prior to

maturity• Pays the principal plus a call premium, which

is usually one year’s worth of interest payments

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• Coupon Rate– The bond’s interest rate is called a coupon rate

• The name “coupon” is an artifact of history, when bonds were issued with a coupon book. Every six months the bearer tore out the relevant coupon and sent it to the company, who would send the interest payment

• Now, bond owners are registered with the company. Interest payments are wired to the owner’s account

– The coupon rate is listed on the bond as a percentage of par value and determines the dollar amount of interest paid to bondholders

• A 5 percent coupon rate pays 5 percent of $1000 (or $50) each year, or $25 every six months

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• When first issued, bonds sell at par value– Bond prices change as interest rates and

firm risk change• When the bonds trade among investors in the

secondary market, the price will likely differ from par value

• Corporate bond prices are quoted in terms of percent of par– Examples: a bond worth $1,150 would be

listed at 115, while a bond worth $870 is quoted as 87

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• Bond Issuers– The financial industry has created many

new types of bonds in recent years• For example: TIGRS, CATS, PINES

– Nevertheless, there remains three primary types of bonds:

• U.S. Treasury bonds• Corporate bonds• Municipal bonds

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• U.S. Treasury bonds– Backed by the full faith and credit of the U.S.

government– These have been considered the safest

investments in the world– The federal government sells Treasury

securities through public auction to finance the federal deficit

– Maturities differ:• Less than one year: Treasury bills• One to ten years: Treasury notes• Greater than ten years: Treasury bonds

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• Corporate bonds– Used by corporations to raise capital– Firms have a choice when they raise capital:

• Debt (bonds)• Equity (stock)

– Firms seek to minimize their overall capital costs

– In the 1990s firms tended to issue equity– Beginning in 1998 they switched to raising

capital by issuing bonds

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• Municipal bonds– Issued by state and local governments

• Streets, highways, hospitals, schools, sewer systems

– Projects that benefit the entire community are typically funded by general obligation bonds

• Repaid through tax revenues

– Projects that benefit certain groups, such as toll roads and airports, are typically funded by revenue bonds

• Repaid from user fees

– There are important tax features with municipal bonds• Interest is not taxed at the federal level or by the relevant

state

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Other Bonds and Bond-based Securities

• Treasury Inflation Protected Securities (TIPS)– These were first issued in 1997– They have fixed coupon rates– They are indexed to inflation

• The federal government adjusts the par value to adjust for inflation reflected by changes in the CPI

• As the par value changes over time, so do the interest payments

– The total return from TIPS comes from the interest payments and the inflation adjustment to par value

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• U.S. Government Agency Securities– Government agencies issue debt to provide low-

cost financing for home ownership, education, and farming

– These agencies include:• Federal National Mortgage Association (Fannie Mae)• Federal Home Loan Mortgage Corporation (Freddie

Mac)• Student Loan Marketing Association (Sallie Mae)• Federal Farm Credit System• Federal Home Loan Banks• Small Business Administration

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• The government agencies issue agency securities to support particular sectors of the economy

• These agency securities do not carry the full-faith-and-credit guarantee of the federal government– The government has never let one of its agencies fail– Investors consider agency securities to be extremely

safe, but they provide a slightly higher return than Treasury securities to reflect the slightly higher risk

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• U.S. government agencies invented mortgage-backed securities (MBS)– Fannie Mae began in 1938 and became a

publicly-held corporation in 1968– Freddie Mac was chartered as a publicly-held

corporation at its inception in 1970– Together, these agencies offer subsidies or

mortgage guarantees for people who wouldn’t otherwise qualify for mortgages

– They increase the amount of money available for the home mortgage market by purchasing home mortgages from banks and other lenders

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– They combine the mortgages into portfolios of loans and then issue mortgage-backed securities to investors

• As homeowners pay off the underlying portfolio of home loans, MBS investors receive interest and principal payments

– After selling mortgages to Fannie Mae and Freddie Mac, banks have new cash to provide more mortgage loans

• This principal has been applied to a variety of other pooled debt, such as credit card debt, auto loans, home equity loans, and equipment leases

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Reading Bond Quotes

• Volume of trading in Treasury bonds and notes is huge– Average over a half billion dollars daily

• Trading in corporate bonds and municipals is much less active

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• Treasury bonds are quoted in 32s of a percent– Example: a quoted price of 105:19 means 105

and 19/32 percent, or 105.594% of par. This translates into a dollar price of $1,055.94.

• There are two prices listed for Treasuries: a bid price and an asked price– The bid and asked price are presented from

the standpoint of the securities dealer– The investor can sell at the bid price and buy

at the asked price

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– The bid-ask spread is part of the security dealer’s compensation

• Bonds that sell for more than $1,000 are said to sell at a premium to par. These are called premium bonds

• Bonds that sell for less than par are called discount bonds

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• Corporate bonds quotes are listed as a percentage of par– Example: a quote of 97.876 translates into a

dollar price of $978.76

• Corporate bonds are riskier than Treasuries and therefore offer a higher return

• In the U.S., corporate bonds typically pay their coupons semiannually.– Example: a bond that pays a 5.570 percent

coupon pays $55.70 per year, or $27.85 every six months

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• Companies set a bond’s coupon rate when they first issue the bonds

• The coupon rate is determined by several factors:– The amount of uncertainty about whether

the company will be able to make all of the payments (default risk)

– The term of the loan– The level of interest rates in the overall

economy at the time

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• Municipal bonds are quoted in terms of percent of par

• Unlike other bonds however, municipal bonds often have a par value of $5,000 rather than $1,000– Example: a quote of 100.46 translates into

a dollar price of (1.0046 x $5,000) = $5,002.30

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Bond Valuation

• The value of a bond represents the present value of future cash flows.

• Bonds are easier to value than stocks because in the case of bonds, the cash flows are known– Coupon amount– Par value

• Investors also know the time remaining to maturity, and the prevailing market interest rate for bonds of similar risk

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• The easiest type of bond to value is a zero coupon bond– Zeros sell at a substantial discount to par– Example: Par value = $1,000; maturity =

20 years from now; discount rate = 6% (assume semi-annual compounding)

INPUT 40 3 0 1000N I/YR PV PMT FV

OUTPUT 306.56

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• As a comparison, let’s rework the above example for a bond that pays a 7 percent coupon

INPUT 40 3 35 1000N I/YR PV PMT FV

OUTPUT 1,115.37

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Bond Prices and Interest Rate Risk

• A bond’s interest payments and par value are fixed

• What if interest rates rise after a bond is issued? In order to make the bond marketable, the bond’s price would have to fall in order to enable a purchaser to obtain the new, higher market yield.

• Similarly, when interest rates fall, market prices for outstanding bonds rise to bring the offered return on older bonds with higher coupons in line with new issues

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• The change in bond prices as a result of changes in prevailing interest rates is called interest rate risk

• Interest rate risk does not affect all bonds equally– Short-term bonds are less affected that

long-term bonds

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• Example:– 5% bonds, semiannual compounding– 15 years to maturity– Par value = $1,000– Required yield to maturity = 9%

INPUT 30 4.5 25 1000N I/YR PV PMT FV

OUTPUT 674.22

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• Same problem, but now the time to maturity is only 5 years:

• The amount of the discount is much less for the 5-year bond versus the 15-year bond

INPUT 10 4.5 25 1000N I/YR PV PMT FV

OUTPUT 841.75

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• The size of a bond’s coupon also affects its interest rate risk

• The larger the coupon, the less the bond’s price changes when interest rates change

• Example: 30 year maturity, 7% semiannual coupons, 6% yield to maturity, $1,000 par

INPUT 60 3 35 1000N I/YR PV PMT FV

OUTPUT 1,138.38

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• Now let’s say interest rates increase by 1% so that the yield to maturity equals 7%

• So the price changed by 1,138.38 – 1,000 = 138.38, or a decrease of 12.16%

INPUT 60 3.5 35 1000N I/YR PV PMT FV

OUTPUT 1,000

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• What if we worked the same problem, where interest rates increase from 6% to 7%, with a higher coupon bond, say 10% coupons:

• The price change is smaller:– Price change = 1,553.51 – 1,374.17 = 179.34, or

a 11.5% decrease• The reason for the differing interest rate risk

for differing coupons is due to reinvestment rate risk– Bondholders with higher coupon bonds can take

those coupons and reinvest them at the new interest rate, thus offsetting a portion of the effect on price

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Bond Prices and the Term Structure of Interest Rates

• Different interest rates apply to bonds with differing terms to maturity

• This is known as the term structure of interest rates

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• While the relationship between interest rates and bond term to maturity (the yield curve) is usually upward sloping (normal), it can also be flat or downward sloping (inverted)

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Bond Yields

• Current Yield– Current yield measure the portion of total

return that is due to the coupon interest payments

– It ignores the portion of return due to price changes, or capital gains

price Bond

coupon AnnualyieldCurrent

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• Yield to Maturity– The YTM measures the total return to the

bondholder if the bond is held to maturity– It takes into account both the price paid

for the bond and the amount of coupon interest

– Example: Coupon rate = 7%, semiannual, 8 years left to maturity, current price = $1,150. What is the yield to maturity?

INPUT 16 -1150 35 1000N I/YR PV PMT FV

OUTPUT 2.363

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• However, this 2.363 yield is for a 6-month period. We must convert this into an annual return

• YTM = 2.363 x 2 = 4.73%

• Bond prices and yields are inversely related– As a bond price falls, its YTM increases

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• Bonds at discount have a yield to maturity greater than their coupon

• Bonds at premium have a yield to maturity less than the coupon

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• Yield to Call– The YTM calculation assumes that the

bond is held to maturity– What if the bond is called by the issuer

prior to maturity? The investor would receive only the coupon payments up to the point of call, plus the call price

– This is called the Yield to Call

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• Callable bonds are an advantage for the issuer, but a disadvantage for the investor– If interest rates fall, the issuer can recall the more

expensive debt and issue new debt at the new lower interest rate

– The investor is left with cash, just when interest rates are lower

• The call provision effectively puts a ceiling on the price of a bond– If interest rates fall enough, the bond will be called

• Investors are not stupid – they require higher yields from callable bonds versus otherwise equivalent non-callable bonds

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• Example:– 20-year bond with 7 percent coupons, semiannual– The bond can be called in 5 years at a call price of

1,070– The bond’s market price is $1,106.38. – Calculate the Yield to Call:

– YTC = 2 x 2.875 = 5.75%

INPUT 10 -1106.38 35 1070N I/YR PV PMT FV

OUTPUT 2.875

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Municipal Bonds and Yield

• Municipal bonds appear to offer low yields compared with corporate bonds and Treasury securities.– This is because the interest from municipal

bonds is tax exempt at the federal level, and generally at the state level as well

• In order to compare yields, we must compute the after-tax yield on municipal bonds

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• Taxable equivalent yield

• Example: Pre-tax yield on municipal bond is 5%, and investor’s marginal tax rate is 35%– Equivalent taxable yield = 5 / (1-.35) = 7.69%

• Municipal bonds are more attractive to high-income investors (with high marginal tax rates)

rate tax - 1

yield Muni Yield Taxable Equivalent

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Credit Risk

• Bond Ratings– Measure of an issuer’s credit quality– Bond rating agencies, such as Moody’s

and Standard & Poor’s, monitor debt and report their findings as a grade, or rating

• Issuers’ financial condition• General economic conditions• Economic value of underlying collateral

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• Bonds with ratings below BB are considered high-yield debt, or “junk” bonds

• Investors will only purchase riskier bonds if the bonds offer higher returns

• Some kinds of institutional investors are prohibited from holding non-investment grade bonds

• Bonds are sometimes downgraded or upgraded based on changing conditions– Bonds that were once investment grade that are

downgraded to junk status are known as “fallen angels”

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• Different bonds issued by the same company may have different ratings if they have different characteristics– Debenture: unsecured corporate bonds

backed by the ability of the corporation to pay

– Mortgage bonds or equipment trust certificates: bonds backed by collateral in the form of real estate or factory equipment

– Senior bonds vs. junior bonds

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Bond Markets

• The majority of bond trading occurs in a decentralized, over-the-counter market

• Most trades occur between bond dealers and large institutional investors such as mutual funds, pension funds, and insurance companies

• A small number of corporate bonds are listed on centralized exchanges such as the NYSE

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• Following the Bond Market– The biggest factor associated with changes

in bonds prices is changes in interest rates– The financial media often reports changes

in interest rates by referring to a specific bond: the 10-year Treasury

– Bond Indexes track segments of the bond market

• Lehman Brothers Aggregate Bond Index• Merrill Lynch Taxable Bond Index• Bond Buyer Municipal Bond Index