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Valuing BondsChapter 6

Fin 325, Section 04 - Spring 2010

Washington State University

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The U.S. bond market is over twice the size of the U.S. stock marketTotal outstanding debt in 2007: $29.2

trillionTotal market value of common stock:

$14.2 trillion

In general, bonds are less risky than stocksBut, like all assets, high-yield bonds

have higher risk

Overview

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Bond CharacteristicsBonds 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 indentureMaturity datePar value (also called face value), usually

$1,000Interest rateAny property pledged as collateralSteps the bondholder can take in event of

default

Bond Terms

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The bond’s interest rateThe name “coupon” is an artifact of historyNow, bond owners are registered with the

company. Interest payments are wired to the owner’s account

The coupon rate is listed as a percentage of par valueA 5 percent coupon rate pays 5 percent

of $1000 (or $50) each year, or $25 every six months

Coupon Rate

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When first issued, bonds sell at par valueBond prices change as interest rates and

firm risk changeWhen 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 parExamples: a bond worth $1,150 would be listed

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

Bond Price

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U.S. Treasury bonds

Corporate bonds

Municipal bonds

Bond Issuers

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Backed by the full faith and credit of the U.S. government

Safest fixed-income investmentsFed sells Treasury securities through

public auction Finance the federal deficit; implement

monetary policyMaturities differ:

Less than one year: Treasury bills One to ten years: Treasury notes Greater than ten years: Treasury bonds

U.S. Treasury Bonds

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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 (capital structure decision)

Corporate Bonds

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Issued by state and local governments Streets, highways, hospitals, schools,

sewer systems

General Obligation Bonds Projects that benefit the entire community Repaid through tax revenues

Revenue Bonds Projects that benefit certain groups, such as

toll roads and airports Repaid from user fees Interest is tax-free

Municipal Bonds

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Other Bonds and Bond-based Securities Treasury Inflation Protected Securities

(TIPS)These were first issued in 1997They have fixed coupon ratesThey 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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Reading Bond QuotesVolume of trading in Treasury

bonds and notes is hugeAverage 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 percentExample: 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.

Bid price, Ask price, Bid-Ask spreadPremium bonds - sell at premiumDiscount bonds - sell at discountSell at par

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Corporate bonds quotes are listed as a percentage of parExample: a quote of 97.876 -> price $978.76

Corporate bonds are riskier than TreasuriesCoupon rate (default risk, maturity,

market interest rate)In the U.S., corporate bonds typically

pay their coupons semiannually.Example: pays $55.70 per year, or $27.85

every six months

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Municipal bonds are quoted in terms of percent of par

Municipal bonds often have a par value of $5,000 rather than $1,000Example: a quote of 100.46 translates into

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

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Bond ValuationThe 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

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

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Zero coupon bonds 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

Zero Coupon Bond

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What if it is an ordinary 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 RiskA bond’s interest payments and par

value are fixed

Interest rates rise

Bond prices fall

Interest rates fall

Bond prices rise

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Example:5% bonds, semiannual compounding15 years to maturityPar value = $1,000Required 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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Same problem, interest rates increase from 6% to 7%, coupon rate 10%:

The price percentage change is smaller:Price change = 1,553.51 – 1,374.17 =

179.34, or a 11.5% decrease

Reinvestment rate riskBondholders 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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Term Structure of Interest RatesDifferent interest rates apply to

bonds with different terms to maturity

Yield Curve

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Bond YieldsCurrent 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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YTM measures the total return to the bond holder 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

Yield to Maturity (YTM)

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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 Premium Bonds have a YTM less than coupon

rate Discount Bonds have a YTM greater than

coupon rate

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The issuer “calls” the bonds back prior to maturityAdvantage for the issuer, but a

disadvantage for the investorPays the principal plus a call premium,

which is usually one year’s worth of interest payments

Allows the issuing firm to refinance when interest rates fall

Callable Bond

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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

The return from when the bond is purchased to when the bond is called is YTC.

Yield to Call (YTC)

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Example:20-year bond with 7 percent coupons,

semiannualThe bond can be called in 5 years at a

call price of $1,070The bond’s market price is $1,106.38.

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

OUTPUT 2.875

YTC = 2 x 2.875 = 5.75%

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Municipal Bonds and YieldMunicipal 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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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

Equivalent Taxable Yield

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Credit RiskBond Ratings

Measure of an issuer’s credit qualityBond rating agencies, such as Moody’s

and Standard & Poor’s, monitor debt and report their findings as a grade, or rating Investment grade Junk bond (speculative bond)

Bonds are sometimes downgraded or upgraded based on changing conditions

“Fallen Angels”

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Bond MarketsThe majority of bond trading occurs in a

decentralized, over-the-counter market, a small number of corporate bonds are listed on centralized exchanges such as the NYSE

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

Bond Indexes track bond price and yield changes

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