7 0 Interest Rates and Bond Valuation. 1 Key Concepts and Skills Know the important bond features and bond types Know the important bond features and.

11

77

Interest Rates and Bond ValuationInterest Rates and Bond Valuation

22

Key Concepts and SkillsKey Concepts and Skills Know the important bond features and bond typesKnow the important bond features and bond types Understand bond values and why they fluctuateUnderstand bond values and why they fluctuate Understand bond ratings and what they meanUnderstand bond ratings and what they mean Understand the impact of inflation on interest ratesUnderstand the impact of inflation on interest rates Understand the term structure of interest rates and Understand the term structure of interest rates and

the determinants of bond yieldsthe determinants of bond yields

33

Chapter OutlineChapter Outline Bonds and Bond ValuationBonds and Bond Valuation More on Bond FeaturesMore on Bond Features Bond RatingsBond Ratings Some Different Types of BondsSome Different Types of Bonds Bond MarketsBond Markets Inflation and Interest RatesInflation and Interest Rates Determinants of Bond YieldsDeterminants of Bond Yields

44

Bond DefinitionsBond Definitions

BondBond Par value (face value)Par value (face value) Coupon rateCoupon rate Coupon paymentCoupon payment Maturity dateMaturity date Yield or Yield to maturityYield or Yield to maturity

55

Present Value of Cash Flows as Present Value of Cash Flows as Rates ChangeRates Change

Bond Value = PV of coupons + PV of parBond Value = PV of coupons + PV of par Bond Value = PV of annuity + PV of lump sumBond Value = PV of annuity + PV of lump sum Remember, as interest rates increase present Remember, as interest rates increase present

values decreasevalues decrease So, as interest rates increase, bond prices So, as interest rates increase, bond prices

decrease and vice versadecrease and vice versa

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Valuing a Discount Bond with Valuing a Discount Bond with Annual CouponsAnnual Coupons

Consider a bond with a coupon rate of 10% and annual Consider a bond with a coupon rate of 10% and annual coupons. The par value is $1,000 and the bond has 5 coupons. The par value is $1,000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is years to maturity. The yield to maturity is 11%. What is the value of the bond?the value of the bond? Using the formula:Using the formula:

• B = PV of annuity + PV of lump sumB = PV of annuity + PV of lump sum• B = 100[1 – 1/(1.11)B = 100[1 – 1/(1.11)55] / .11 + 1,000 / (1.11)] / .11 + 1,000 / (1.11)55

• B = 369.59 + 593.45 = 963.04B = 369.59 + 593.45 = 963.04 Using the calculator:Using the calculator:

• N = 5; I/Y = 11; PMT = 100; FV = 1,000N = 5; I/Y = 11; PMT = 100; FV = 1,000• CPT PV = -963.04CPT PV = -963.04

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Valuing a Premium Bond with Valuing a Premium Bond with Annual CouponsAnnual Coupons

Suppose you are looking at a bond that has a 10% Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are annual coupon and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. 20 years to maturity and the yield to maturity is 8%. What is the price of this bond?What is the price of this bond? Using the formula:Using the formula:

• B = PV of annuity + PV of lump sumB = PV of annuity + PV of lump sum• B = 100[1 – 1/(1.08)B = 100[1 – 1/(1.08)2020] / .08 + 1000 / (1.08)] / .08 + 1000 / (1.08)2020

• B = 981.81 + 214.55 = 1196.36B = 981.81 + 214.55 = 1196.36 Using the calculator:Using the calculator:

• N = 20; I/Y = 8; PMT = 100; FV = 1000N = 20; I/Y = 8; PMT = 100; FV = 1000• CPT PV = -1,196.36CPT PV = -1,196.36

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Graphical Relationship Between Graphical Relationship Between Price and Yield-to-maturity (YTM)Price and Yield-to-maturity (YTM)

600

700

800

900

1000

1100

1200

1300

1400

1500

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

Bon

d P

rice

Yield-to-maturity (YTM)

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Bond Prices: Relationship Bond Prices: Relationship Between Coupon and YieldBetween Coupon and Yield

If YTM = coupon rate, then par value = bond priceIf YTM = coupon rate, then par value = bond price If YTM > coupon rate, then par value > bond priceIf YTM > coupon rate, then par value > bond price

Why? The discount provides yield above coupon rateWhy? The discount provides yield above coupon rate Price below par value, called a discount bondPrice below par value, called a discount bond

If YTM < coupon rate, then par value < bond priceIf YTM < coupon rate, then par value < bond price Why? Higher coupon rate causes value above parWhy? Higher coupon rate causes value above par Price above par value, called a premium bondPrice above par value, called a premium bond

1010

The Bond Pricing EquationThe Bond Pricing Equation

t

t

r)(1

F

rr)(1

1-1

C Value Bond

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Example 7.1Example 7.1

Find present values based on the payment Find present values based on the payment periodperiod How many coupon payments are there?How many coupon payments are there? What is the semiannual coupon payment?What is the semiannual coupon payment? What is the semiannual yield?What is the semiannual yield? B = 70[1 – 1/(1.08)B = 70[1 – 1/(1.08)1414] / .08 + 1,000 / (1.08)] / .08 + 1,000 / (1.08)1414 = 917.56 = 917.56 Or PMT = 70; N = 14; I/Y = 8; FV = 1,000; CPT PV = -Or PMT = 70; N = 14; I/Y = 8; FV = 1,000; CPT PV = -

917.56917.56

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Interest Rate RiskInterest Rate Risk Price RiskPrice Risk

Change in price due to changes in interest ratesChange in price due to changes in interest rates Long-term bonds have more price risk than short-term bondsLong-term bonds have more price risk than short-term bonds Low coupon rate bonds have more price risk than high coupon Low coupon rate bonds have more price risk than high coupon

rate bondsrate bonds

Reinvestment Rate RiskReinvestment Rate Risk Uncertainty concerning rates at which cash flows can be Uncertainty concerning rates at which cash flows can be

reinvestedreinvested Short-term bonds have more reinvestment rate risk than long-Short-term bonds have more reinvestment rate risk than long-

term bondsterm bonds High coupon rate bonds have more reinvestment rate risk than High coupon rate bonds have more reinvestment rate risk than

low coupon rate bondslow coupon rate bonds

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Figure 7.2Figure 7.2

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Computing Yield-to-maturityComputing Yield-to-maturity

Yield-to-maturity is the rate implied by the Yield-to-maturity is the rate implied by the current bond pricecurrent bond price

Finding the YTM requires trial and error if you do Finding the YTM requires trial and error if you do not have a financial calculator and is similar to not have a financial calculator and is similar to the process for finding r with an annuitythe process for finding r with an annuity

If you have a financial calculator, enter N, PV, If you have a financial calculator, enter N, PV, PMT, and FV, remembering the sign convention PMT, and FV, remembering the sign convention (PMT and FV need to have the same sign, PV (PMT and FV need to have the same sign, PV the opposite sign)the opposite sign)

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YTM with Annual CouponsYTM with Annual Coupons

Consider a bond with a 10% annual coupon rate, Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1,000. 15 years to maturity and a par value of $1,000. The current price is $928.09.The current price is $928.09. Will the yield be more or less than 10%?Will the yield be more or less than 10%? N = 15; PV = -928.09; FV = 1,000; PMT = 100N = 15; PV = -928.09; FV = 1,000; PMT = 100 CPT I/Y = 11%CPT I/Y = 11%

1616

YTM with Semiannual CouponsYTM with Semiannual Coupons

Suppose a bond with a 10% coupon rate and Suppose a bond with a 10% coupon rate and semiannual coupons, has a face value of semiannual coupons, has a face value of $1,000, 20 years to maturity and is selling for $1,000, 20 years to maturity and is selling for $1,197.93.$1,197.93. Is the YTM more or less than 10%?Is the YTM more or less than 10%? What is the semiannual coupon payment?What is the semiannual coupon payment? How many periods are there?How many periods are there? N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT

I/Y = 4% (Is this the YTM?)I/Y = 4% (Is this the YTM?) YTM = 4%*2 = 8%YTM = 4%*2 = 8%

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Table 7.1Table 7.1

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Current Yield vs. Yield to MaturityCurrent Yield vs. Yield to Maturity

Current Yield = annual coupon / priceCurrent Yield = annual coupon / price Yield to maturity = current yield + capital gains yieldYield to maturity = current yield + capital gains yield Example: 10% coupon bond, with semiannual coupons, Example: 10% coupon bond, with semiannual coupons,

face value of 1,000, 20 years to maturity, $1,197.93 priceface value of 1,000, 20 years to maturity, $1,197.93 price Current yield = 100 / 1,197.93 = .0835 = 8.35%Current yield = 100 / 1,197.93 = .0835 = 8.35% Price in one year, assuming no change in YTM = 1,193.68Price in one year, assuming no change in YTM = 1,193.68 Capital gain yield = (1,193.68 – 1,197.93) / 1,197.93 = -.0035 = Capital gain yield = (1,193.68 – 1,197.93) / 1,197.93 = -.0035 =

-.35%-.35% YTM = 8.35 - .35 = 8%, which the same YTM computed earlierYTM = 8.35 - .35 = 8%, which the same YTM computed earlier

1919

Bond Pricing TheoremsBond Pricing Theorems

Bonds of similar risk (and maturity) will be priced Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the to yield about the same return, regardless of the coupon ratecoupon rate

If you know the price of one bond, you can If you know the price of one bond, you can estimate its YTM and use that to find the price of estimate its YTM and use that to find the price of the second bondthe second bond

This is a useful concept that can be transferred This is a useful concept that can be transferred to valuing assets other than bondsto valuing assets other than bonds

2020

Bond Prices with a SpreadsheetBond Prices with a Spreadsheet

There is a specific formula for finding bond There is a specific formula for finding bond prices on a spreadsheetprices on a spreadsheet

PRICE(Settlement,Maturity,Rate,Yld,Redemption, PRICE(Settlement,Maturity,Rate,Yld,Redemption, Frequency,Basis)Frequency,Basis)

YIELD(Settlement,Maturity,Rate,Pr,Redemption, YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis)Frequency,Basis)

Settlement and maturity need to be actual datesSettlement and maturity need to be actual dates The redemption and Pr need to be input as % of par valueThe redemption and Pr need to be input as % of par value

Click on the Excel icon for an exampleClick on the Excel icon for an example

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Differences Between Debt and Differences Between Debt and EquityEquity

DebtDebt Not an ownership interestNot an ownership interest Creditors do not have Creditors do not have

voting rightsvoting rights Interest is considered a Interest is considered a

cost of doing business cost of doing business and is tax deductibleand is tax deductible

Creditors have legal Creditors have legal recourse if interest or recourse if interest or principal payments are principal payments are missedmissed

Excess debt can lead to Excess debt can lead to financial distress and financial distress and bankruptcybankruptcy

EquityEquity Ownership interestOwnership interest Common stockholders Common stockholders

vote for the board of vote for the board of directors and other issuesdirectors and other issues

Dividends are not Dividends are not considered a cost of doing considered a cost of doing business and are not tax business and are not tax deductibledeductible

Dividends are not a Dividends are not a liability of the firm and liability of the firm and stockholders have no stockholders have no legal recourse if dividends legal recourse if dividends are not paidare not paid

An all equity firm can not An all equity firm can not go bankrupt merely due to go bankrupt merely due to debt since it has no debtdebt since it has no debt

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The Bond IndentureThe Bond Indenture Contract between the company and the Contract between the company and the

bondholders that includesbondholders that includes The basic terms of the bondsThe basic terms of the bonds The total amount of bonds issuedThe total amount of bonds issued A description of property used as security, if A description of property used as security, if

applicableapplicable Sinking fund provisionsSinking fund provisions Call provisionsCall provisions Details of protective covenantsDetails of protective covenants

2323

Bond ClassificationsBond Classifications

Registered vs. Bearer FormsRegistered vs. Bearer Forms SecuritySecurity

Collateral – secured by financial securitiesCollateral – secured by financial securities Mortgage – secured by real property, normally land or Mortgage – secured by real property, normally land or

buildingsbuildings Debentures – unsecuredDebentures – unsecured Notes – unsecured debt with original maturity less Notes – unsecured debt with original maturity less

than 10 yearsthan 10 years

SenioritySeniority

2424

Bond Characteristics and Bond Characteristics and Required ReturnsRequired Returns

The coupon rate depends on the risk The coupon rate depends on the risk characteristics of the bond when issuedcharacteristics of the bond when issued

Which bonds will have the higher coupon, all Which bonds will have the higher coupon, all else equal?else equal? Secured debt versus a debentureSecured debt versus a debenture Subordinated debenture versus senior debtSubordinated debenture versus senior debt A bond with a sinking fund versus one withoutA bond with a sinking fund versus one without A callable bond versus a non-callable bondA callable bond versus a non-callable bond

2525

Bond Ratings – Investment QualityBond Ratings – Investment Quality High GradeHigh Grade

Moody’s Aaa and S&P AAA – capacity to pay is Moody’s Aaa and S&P AAA – capacity to pay is extremely strongextremely strong

Moody’s Aa and S&P AA – capacity to pay is very strongMoody’s Aa and S&P AA – capacity to pay is very strong Medium GradeMedium Grade

Moody’s A and S&P A – capacity to pay is strong, but Moody’s A and S&P A – capacity to pay is strong, but more susceptible to changes in circumstancesmore susceptible to changes in circumstances

Moody’s Baa and S&P BBB – capacity to pay is Moody’s Baa and S&P BBB – capacity to pay is adequate, adverse conditions will have more impact on adequate, adverse conditions will have more impact on the firm’s ability to paythe firm’s ability to pay

2626

Bond Ratings - SpeculativeBond Ratings - Speculative Low GradeLow Grade

Moody’s Ba, B, Caa and CaMoody’s Ba, B, Caa and Ca S&P BB, B, CCC, CCS&P BB, B, CCC, CC Considered speculative with respect to capacity to pay. Considered speculative with respect to capacity to pay.

The “B” ratings are the lowest degree of speculation.The “B” ratings are the lowest degree of speculation. Very Low GradeVery Low Grade

Moody’s C and S&P C – income bonds with no interest Moody’s C and S&P C – income bonds with no interest being paidbeing paid

Moody’s D and S&P D – in default with principal and Moody’s D and S&P D – in default with principal and interest in arrearsinterest in arrears

2727

Government BondsGovernment Bonds Treasury SecuritiesTreasury Securities

Federal government debtFederal government debt T-bills – pure discount bonds with original maturity of one year or T-bills – pure discount bonds with original maturity of one year or

lessless T-notes – coupon debt with original maturity between one and T-notes – coupon debt with original maturity between one and

ten yearsten years T-bonds coupon debt with original maturity greaterT-bonds coupon debt with original maturity greater than ten than ten

yearsyears Municipal SecuritiesMunicipal Securities

Debt of state and local governmentsDebt of state and local governments Varying degrees of default risk, rated similar to corporate debtVarying degrees of default risk, rated similar to corporate debt Interest received is tax-exempt at the federal levelInterest received is tax-exempt at the federal level

2828

Example 7.4Example 7.4

A taxable bond has a yield of 8% and a A taxable bond has a yield of 8% and a municipal bond has a yield of 6%municipal bond has a yield of 6% If you are in a 40% tax bracket, which bond do you If you are in a 40% tax bracket, which bond do you

prefer?prefer?• 8%(1 - .4) = 4.8%8%(1 - .4) = 4.8%• The after-tax return on the corporate bond is 4.8%, The after-tax return on the corporate bond is 4.8%,

compared to a 6% return on the municipalcompared to a 6% return on the municipal At what tax rate would you be indifferent between the At what tax rate would you be indifferent between the

two bonds?two bonds?• 8%(1 – T) = 6%8%(1 – T) = 6%• T = 25%T = 25%

2929

Zero Coupon BondsZero Coupon Bonds

Make no periodic interest payments (coupon rate = 0%)Make no periodic interest payments (coupon rate = 0%) The entire yield-to-maturity comes from the difference The entire yield-to-maturity comes from the difference

between the purchase price and the par valuebetween the purchase price and the par value Cannot sell for more than par valueCannot sell for more than par value Sometimes called zeroes, deep discount bonds, or Sometimes called zeroes, deep discount bonds, or

original issue discount bonds (OIDs)original issue discount bonds (OIDs) Treasury Bills and principal-only Treasury strips are good Treasury Bills and principal-only Treasury strips are good

examples of zeroesexamples of zeroes

3030

Floating-Rate BondsFloating-Rate Bonds

Coupon rate floats depending on some index valueCoupon rate floats depending on some index value Examples – adjustable rate mortgages and inflation-Examples – adjustable rate mortgages and inflation-

linked Treasurieslinked Treasuries There is less price risk with floating rate bondsThere is less price risk with floating rate bonds

The coupon floats, so it is less likely to differ substantially The coupon floats, so it is less likely to differ substantially from the yield-to-maturityfrom the yield-to-maturity

Coupons may have a “collar” – the rate cannot go above Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”a specified “ceiling” or below a specified “floor”

3131

Other Bond TypesOther Bond Types Disaster bondsDisaster bonds Income bondsIncome bonds Convertible bondsConvertible bonds Put bondsPut bonds There are many other types of provisions that There are many other types of provisions that

can be added to a bond and many bonds have can be added to a bond and many bonds have several provisions – it is important to recognize several provisions – it is important to recognize how these provisions affect required returnshow these provisions affect required returns

3232

Bond MarketsBond Markets Primarily over-the-counter transactions with Primarily over-the-counter transactions with

dealers connected electronicallydealers connected electronically Extremely large number of bond issues, but Extremely large number of bond issues, but

generally low daily volume in single issuesgenerally low daily volume in single issues Makes getting up-to-date prices difficult, Makes getting up-to-date prices difficult,

particularly on small company or municipal particularly on small company or municipal issuesissues

Treasury securities are an exceptionTreasury securities are an exception

3333

Work the Web ExampleWork the Web Example

Bond quotes are available onlineBond quotes are available online One good site is Bonds OnlineOne good site is Bonds Online Click on the web surfer to go to the siteClick on the web surfer to go to the site

Follow the bond search, corporate linksFollow the bond search, corporate links Choose a company, enter it under Express Search Choose a company, enter it under Express Search

Issue and see what you can find!Issue and see what you can find!

3434

Treasury QuotationsTreasury Quotations Highlighted quote in Figure 7.4Highlighted quote in Figure 7.4

8 Nov 21 128:07 128:08 5 5.318 Nov 21 128:07 128:08 5 5.31 What is the coupon rate on the bond?What is the coupon rate on the bond? When does the bond mature?When does the bond mature? What is the bid price? What does this mean?What is the bid price? What does this mean? What is the ask price? What does this mean?What is the ask price? What does this mean? How much did the price change from the previous How much did the price change from the previous

day?day? What is the yield based on the ask price?What is the yield based on the ask price?

3535

Clean vs. Dirty PricesClean vs. Dirty Prices Clean price: quoted priceClean price: quoted price Dirty price: price actually paid = quoted price plus Dirty price: price actually paid = quoted price plus

accrued interestaccrued interest Example: Consider T-bond in previous slide, assume Example: Consider T-bond in previous slide, assume

today is July 15, 2007today is July 15, 2007 Number of days since last coupon = 61Number of days since last coupon = 61 Number of days in the coupon period = 184Number of days in the coupon period = 184 Accrued interest = (61/184)(.04*100,000) = 1,326.09Accrued interest = (61/184)(.04*100,000) = 1,326.09

Prices (based on ask):Prices (based on ask): Clean price = 128,250Clean price = 128,250 Dirty price = 128,250 + 1,326.09 = 129,576.09Dirty price = 128,250 + 1,326.09 = 129,576.09

So, you would actually pay $ 129,576.09 for the bondSo, you would actually pay $ 129,576.09 for the bond

3636

Inflation and Interest RatesInflation and Interest Rates Real rate of interest – change in purchasing Real rate of interest – change in purchasing

powerpower Nominal rate of interest – quoted rate of Nominal rate of interest – quoted rate of

interest, change in purchasing power, and interest, change in purchasing power, and inflationinflation

The ex ante nominal rate of interest includes The ex ante nominal rate of interest includes our desired real rate of return plus an our desired real rate of return plus an adjustment for expected inflationadjustment for expected inflation

3737

The Fisher EffectThe Fisher Effect

The Fisher Effect defines the relationship The Fisher Effect defines the relationship between real rates, nominal rates, and inflationbetween real rates, nominal rates, and inflation

(1 + R) = (1 + r)(1 + h), where(1 + R) = (1 + r)(1 + h), where R = nominal rateR = nominal rate r = real rater = real rate h = expected inflation rateh = expected inflation rate

ApproximationApproximation R = r + hR = r + h

3838

Example 7.5Example 7.5

If we require a 10% real return and we expect If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate?inflation to be 8%, what is the nominal rate?

R = (1.1)(1.08) – 1 = .188 = 18.8%R = (1.1)(1.08) – 1 = .188 = 18.8% Approximation: R = 10% + 8% = 18%Approximation: R = 10% + 8% = 18% Because the real return and expected inflation Because the real return and expected inflation

are relatively high, there is significant are relatively high, there is significant difference between the actual Fisher Effect and difference between the actual Fisher Effect and the approximation.the approximation.

3939

Term Structure of Interest RatesTerm Structure of Interest Rates

Term structure is the relationship between time to Term structure is the relationship between time to maturity and yields, all else equalmaturity and yields, all else equal

It is important to recognize that we pull out the effect of It is important to recognize that we pull out the effect of default risk, different coupons, etc.default risk, different coupons, etc.

Yield curve – graphical representation of the term Yield curve – graphical representation of the term structurestructure

Normal – upward-sloping, long-term yields are higher than short-Normal – upward-sloping, long-term yields are higher than short-term yieldsterm yields

Inverted – downward-sloping, long-term yields are lower than Inverted – downward-sloping, long-term yields are lower than short-term yieldsshort-term yields

4040

Figure 7.6 – Upward-Sloping Figure 7.6 – Upward-Sloping Yield CurveYield Curve

4141

Figure 7.6 – Downward-Sloping Figure 7.6 – Downward-Sloping Yield CurveYield Curve

4242

Figure 7.7Figure 7.7

4343

Factors Affecting Bond YieldsFactors Affecting Bond Yields Default risk premium – remember bond ratingsDefault risk premium – remember bond ratings Taxability premium – remember municipal Taxability premium – remember municipal

versus taxableversus taxable Liquidity premium – bonds that have more Liquidity premium – bonds that have more

frequent trading will generally have lower frequent trading will generally have lower required returnsrequired returns

Anything else that affects the risk of the cash Anything else that affects the risk of the cash flows to the bondholders will affect the required flows to the bondholders will affect the required returnsreturns

4444

Quick QuizQuick Quiz

How do you find the value of a bond and why do bond How do you find the value of a bond and why do bond prices change?prices change?

What is a bond indenture and what are some of the What is a bond indenture and what are some of the important features?important features?

What are bond ratings and why are they important?What are bond ratings and why are they important? How does inflation affect interest rates?How does inflation affect interest rates? What is the term structure of interest rates?What is the term structure of interest rates? What factors determine the required return on bonds? What factors determine the required return on bonds?

4545

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End of ChapterEnd of Chapter

4646

Comprehensive ProblemComprehensive Problem

What is the price of a $1,000 par value bond What is the price of a $1,000 par value bond with a 6% coupon rate paid semiannually, if the with a 6% coupon rate paid semiannually, if the bond is priced to yield 5% YTM, and it has 9 bond is priced to yield 5% YTM, and it has 9 years to maturity?years to maturity?

What would be the price of the bond if the yield What would be the price of the bond if the yield rose to 7%.rose to 7%.

What is the current yield on the bond if the YTM What is the current yield on the bond if the YTM is 7%?is 7%?