1 valuing bonds chapter 6 fin 325, section 04 - spring 2010 washington state university
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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