Chapter 10 Bond Prices and Yields. 10-2 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Bond Characteristics Face or par value Face or par value.

Chapter 10Chapter 10

Bond Prices and YieldsBond Prices and Yields

10-10-22Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Bond CharacteristicsBond Characteristics

• Face or par valueFace or par value

• Coupon rateCoupon rate

– Zero coupon bondZero coupon bond

• Compounding and paymentsCompounding and payments

–Accrued InterestAccrued Interest

– invoice price versus quoted priceinvoice price versus quoted price

• IndentureIndenture

10-10-33Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Provisions of BondsProvisions of Bonds

• Secured or unsecured (debenture)Secured or unsecured (debenture)

• Call provisionCall provision

– refundingrefunding

– call pricecall price

– deferred callable bonddeferred callable bond

– coupon rates and promised ytm coupon rates and promised ytm at issuanceat issuance

10-10-44Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Provisions of BondsProvisions of Bonds

• Convertible provisionConvertible provision– conversion ratioconversion ratio– market conversion valuemarket conversion value– conversion premiumconversion premium– coupon rate & ytm at issuancecoupon rate & ytm at issuance– Convertible exampleConvertible example»conversion ratio = 25conversion ratio = 25»market price of stock = $42market price of stock = $42»callable bond price = $1150callable bond price = $1150

10-10-55Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Provisions of BondsProvisions of Bonds

• Put provision (putable bonds)Put provision (putable bonds)

– coupon rate & ytm at issuancecoupon rate & ytm at issuance

• Floating rate bondsFloating rate bonds

– changing credit condition of changing credit condition of issuerissuer

• Sinking fundsSinking funds

10-10-66Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Other innovationsOther innovations

• Pay in kind bonds (pik)Pay in kind bonds (pik)

• reverse floatersreverse floaters

• indexed bonds (TIPS -Treasury indexed bonds (TIPS -Treasury Inflation Protection bonds)Inflation Protection bonds)

10-10-77Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Default Risk and RatingsDefault Risk and Ratings

• Rating companiesRating companies– Moody’s Investor ServiceMoody’s Investor Service– Standard & Poor’sStandard & Poor’s– Duff and PhelpsDuff and Phelps– FitchFitch

• Rating CategoriesRating Categories– Investment gradeInvestment grade– Speculative gradeSpeculative grade

10-10-88Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Factors Used by Rating Factors Used by Rating CompaniesCompanies

• Coverage ratiosCoverage ratios

• Leverage ratiosLeverage ratios

• Liquidity ratiosLiquidity ratios

• Profitability ratiosProfitability ratios

• Cash flow to debtCash flow to debt

10-10-99Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Protection Against DefaultProtection Against Default

• Sinking fundsSinking funds

• Subordination of future debtSubordination of future debt

• Dividend restrictionsDividend restrictions

• CollateralCollateral

–mortgage bondmortgage bond

– equipment obligationequipment obligation

– collateral trustcollateral trust

10-10-1010Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Bond PricingBond Pricing

)1()1(1 rParValue

rCP T

T

T

tt

tB

PPBB = = Price of the bondPrice of the bond

CCtt = = interest or coupon paymentsinterest or coupon payments

TT = = number of periods to maturitynumber of periods to maturity

yy = = semi-annual discount rate or the semi-semi-annual discount rate or the semi-annual yield to maturityannual yield to maturity

10-10-1111Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

CCtt = 40 (SA)= 40 (SA)

PP = 1000= 1000TT = 20 periods= 20 periodsrr = 3% (SA)= 3% (SA)

PB = $1,148.77

Solving for Price: 10-yr, 8% Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000Coupon Bond, Face = $1,000

tt=1=1++

2020

== PPBB 4040 11(1+.03)) t 1000 1

(1+.03) 20

10-10-1212Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Bond Prices and YieldsBond Prices and Yields

Prices and Yields (required rates of Prices and Yields (required rates of return) have an inverse return) have an inverse relationshiprelationship

• When yields get very high the When yields get very high the value of the bond will be very lowvalue of the bond will be very low

• When yields approach zero, the When yields approach zero, the value of the bond approaches the value of the bond approaches the sum of the cash flowssum of the cash flows

10-10-1313Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Prices and Coupon RatesPrices and Coupon Rates

Price

Yield

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Yield to MaturityYield to Maturity

YTM = the discount rate that makes the present YTM = the discount rate that makes the present value of the bond’s promised payments equal value of the bond’s promised payments equal to its price.to its price.

Bond is priced at $1067.95, it has a coupon rate of Bond is priced at $1067.95, it has a coupon rate of 9% paid semiannually, a par value of $1000, and 9% paid semiannually, a par value of $1000, and 10 years to maturity. Find the bond’s ytm.10 years to maturity. Find the bond’s ytm.

What is the current yield?What is the current yield?

Bond is priced at $945.40 , it has a coupon rate of Bond is priced at $945.40 , it has a coupon rate of 6% paid semiannually, a par value of $1000, and 6% paid semiannually, a par value of $1000, and 14 years to maturity. Find the bond’s ytm.14 years to maturity. Find the bond’s ytm.

What is the current yield?What is the current yield?

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YTM versus current yield YTM versus current yield versus coupon rateversus coupon rate

• Bond selling at parBond selling at par

– coupon = YTM = current yieldcoupon = YTM = current yield

• Bond selling at a premiumBond selling at a premium

– coupon > current > YTMcoupon > current > YTM

• Bond selling at a discountBond selling at a discount

– coupon < current < YTMcoupon < current < YTM

10-10-1616Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Yield to call (YTC)Yield to call (YTC)

• Similar to YTM, but use time to first Similar to YTM, but use time to first call date and call price as future call date and call price as future value.value.

• Bond with 15 years to maturity, par Bond with 15 years to maturity, par of $1000, a coupon rate of 8% (paid of $1000, a coupon rate of 8% (paid semiannually), price of $1025, semiannually), price of $1025, callable in 5 years at $1080. Find callable in 5 years at $1080. Find YTC.YTC.

10-10-1717Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Realized compound yield Realized compound yield versus yield to maturityversus yield to maturity

• YTM will equal the realized return YTM will equal the realized return over the life of the bond if all over the life of the bond if all payments are reinvested at an payments are reinvested at an interest rate equal to the bond’s interest rate equal to the bond’s yield.yield.– Consider a bond with 10 years to Consider a bond with 10 years to

maturity, coupon rate of 9 percent maturity, coupon rate of 9 percent paid annually, and a price of $1067.10.paid annually, and a price of $1067.10.

10-10-1818Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Realized compound yield (RCY) Realized compound yield (RCY) versus yield to maturity (YTM)versus yield to maturity (YTM)

• Consider a bond with 10 years to maturity, Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, coupon rate of 9 percent paid annually, and a price of $1067.10.and a price of $1067.10.

–What is its ytm?What is its ytm?

–Realized compound yield if you Realized compound yield if you reinvest at ytm?reinvest at ytm?

–RCY if you reinvest at 3 percent?RCY if you reinvest at 3 percent?

10-10-1919Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Time CF FV(CF)@8% FV(CF)@3%1 $90.00 $179.91 $117.432 $90.00 $166.58 $114.013 $90.00 $154.24 $110.694 $90.00 $142.82 $107.465 $90.00 $132.24 $104.336 $90.00 $122.44 $101.307 $90.00 $113.37 $98.358 $90.00 $104.98 $95.489 $90.00 $97.20 $92.7010 $1,090.00 $1,090.00 $1,090.00

Total $2,303.79 $2,031.75

RCY 8.00% 6.65%

10-10-2020Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Holding period return (HPR) Holding period return (HPR) versus YTM.versus YTM.

• Consider a bond with 10 years to maturity, Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, coupon rate of 9 percent paid annually, and a price of $1067.10. Note: ytm = 8%and a price of $1067.10. Note: ytm = 8%

• Suppose you hold the bond one year and Suppose you hold the bond one year and interest rates decline to 7 percent. interest rates decline to 7 percent. Calculate your HPR.Calculate your HPR.

• Suppose instead that rates had risen to 9 Suppose instead that rates had risen to 9 percent. What is your HPR?percent. What is your HPR?

10-10-2121Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Original Issue Discount (OID)Original Issue Discount (OID)

• Consider a 10 year Treasury strip with a Consider a 10 year Treasury strip with a yield of 5 percent and face of $10,000.yield of 5 percent and face of $10,000.– Price = $6,139.13Price = $6,139.13– After one year (yield = 5%)After one year (yield = 5%)»P = $6,446.09P = $6,446.09»Difference = implicit interest = $306.96Difference = implicit interest = $306.96» If you sold the strip for $6,500, then you If you sold the strip for $6,500, then you

would have interest income of $306.96 would have interest income of $306.96 and capital gain of $53.91and capital gain of $53.91

10-10-2222Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Term Structure of Interest RatesTerm Structure of Interest Rates

• Relationship between yields to maturity Relationship between yields to maturity and maturityand maturity

• Yield curve - a graph of the yields on Yield curve - a graph of the yields on bonds relative to the number of years bonds relative to the number of years to maturityto maturity– Usually Treasury BondsUsually Treasury Bonds– Have to be similar risk or other Have to be similar risk or other

factors would be influencing yieldsfactors would be influencing yields

10-10-2323Irwin/McGraw-hill ©The McGraw-Hill Companies, Inc., 1998

Yield CurvesYield Curves

Yields

Maturity

Upward Upward SlopingSloping

Downward Downward SlopingSloping

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Theories of Term StructureTheories of Term Structure

• ExpectationsExpectations

• Liquidity PreferenceLiquidity Preference

–Upward bias over expectationsUpward bias over expectations

• Market Segmentation Market Segmentation

–Preferred HabitatPreferred Habitat