Prepared by Ken Hartviksen and Robert Ironside INTRODUCTION TO CORPORATE FINANCE Laurence Booth W....

Prepared byPrepared by

Ken Hartviksen and Robert IronsideKen Hartviksen and Robert Ironside

INTRODUCTION TOINTRODUCTION TO CORPORATE FINANCECORPORATE FINANCELaurence Booth Laurence Booth •• W. Sean Cleary W. Sean Cleary

CHAPTER 6CHAPTER 6 Bond Valuation and Interest Bond Valuation and Interest

RatesRates

CHAPTER 6 – Bond Valuation and Interest Rates 6 - 3

Lecture AgendaLecture Agenda

• Learning ObjectivesLearning Objectives• Important TermsImportant Terms• Basic Structure of BondsBasic Structure of Bonds• Bond ValuationBond Valuation• Bond YieldsBond Yields• Interest Rate DeterminantsInterest Rate Determinants• Other Types of Bonds/Debt InstrumentsOther Types of Bonds/Debt Instruments• Summary and ConclusionsSummary and Conclusions

– Concept Review QuestionsConcept Review Questions


Learning ObjectivesLearning Objectives

• The basic features of different types of bondsThe basic features of different types of bonds• How to value bonds given an appropriate discount rateHow to value bonds given an appropriate discount rate• How to determine the discount rate or yield given the How to determine the discount rate or yield given the

market value of a bondmarket value of a bond• How market interest rates or yields affect bond investorsHow market interest rates or yields affect bond investors• How bond prices change over timeHow bond prices change over time• The factors (both domestic and global) that affect The factors (both domestic and global) that affect

interest ratesinterest rates


Important Chapter TermsImportant Chapter Terms

• Balloon paymentBalloon payment• BillsBills• Bond indentureBond indenture• Bullet paymentBullet payment• Call pricesCall prices• Callable bondsCallable bonds• Canada Savings BondsCanada Savings Bonds• Collateral trust bondsCollateral trust bonds• CouponsCoupons• Current yieldCurrent yield• DebenturesDebentures• Debt ratingsDebt ratings• Default freeDefault free

• Default riskDefault risk• Discount (premium)Discount (premium)• DurationDuration• Equipment trust certificatesEquipment trust certificates• Expectations theoryExpectations theory• Extendible bondsExtendible bonds• Face valueFace value• Floating rate bondsFloating rate bonds• Interest paymentsInterest payments• Interest rate parity (IRP) Interest rate parity (IRP)

theorytheory• Interest rate riskInterest rate risk• Issue-specific premiumsIssue-specific premiums• Liquidity preference theoryLiquidity preference theory• Maturity valueMaturity value


Important Chapter TermsImportant Chapter Terms

• Mortgage bondsMortgage bonds• Nominal interest ratesNominal interest rates• NotesNotes• PaperPaper• Par valuePar value• Protective covenantsProtective covenants• Purchase fund provisionsPurchase fund provisions• Real return bondsReal return bonds

• Retractable bondsRetractable bonds• Risk-free rateRisk-free rate• Sinking fund provisionsSinking fund provisions• SpreadSpread• Term structure of Term structure of

interest ratesinterest rates• Term to maturityTerm to maturity• Yield curveYield curve• Yield to maturityYield to maturity• Zero coupon bondZero coupon bond


The Basic Structure of BondsThe Basic Structure of Bonds

• What is a What is a bondbond??• In its broadest sense, a bond is any debt In its broadest sense, a bond is any debt

instrument that promises a fixed income instrument that promises a fixed income stream to the holderstream to the holder

• Fixed income securities are often classified Fixed income securities are often classified according to maturity, as follows:according to maturity, as follows:– Less than one year – Bills or “Paper”Less than one year – Bills or “Paper”– 1 year 1 year < Maturity < 7 years – Notes< Maturity < 7 years – Notes– < 7 years – Bonds< 7 years – Bonds



• A typical bond has the following A typical bond has the following characteristics:characteristics:– A fixed face or par value, paid to the holder of the A fixed face or par value, paid to the holder of the

bond, at maturitybond, at maturity– A fixed coupon, which specifies the interest payable A fixed coupon, which specifies the interest payable

over the life of the bondover the life of the bond• Coupons are usually paid either annually or semi-annuallyCoupons are usually paid either annually or semi-annually

– A fixed maturity dateA fixed maturity date


• Bonds may be either:Bonds may be either:– Bearer bondsBearer bonds– Registered bondsRegistered bonds

• Bond indenture - the contract between the Bond indenture - the contract between the issuer of the bond and the investors who hold issuer of the bond and the investors who hold itit

• The market price of a bond is equal to the The market price of a bond is equal to the present value of the payments promised by present value of the payments promised by the bondthe bond

(See the basic pattern of cash flows from a traditional bond on the next slide)



The The Basic Structure of BondsBasic Structure of BondsCash Flow Pattern for a Traditional Coupon-Paying BondCash Flow Pattern for a Traditional Coupon-Paying Bond

0 1 2 3 … n

I I I I I

F

0 1 2 3 … n

I I I I I

F

FIGURE 6-1

I = interest payments, and F = principal repayment


Cash Flow Pattern of a BondCash Flow Pattern of a Bond

The Purchase Price or Market Price of a bond is simply the present value of the cash inflows, discounted at the bond’s yield-to-maturity

0 2 3 4 n1

Coupon Coupon Coupon Coupon Coupon +Face Value

Purchase Price

Cash Inflows to the Investor

Cash Outflows to the Investor


• Bond indentureBond indenture is the contract between the is the contract between the issuer and the holder. It specifies:issuer and the holder. It specifies:– Details regarding payment termsDetails regarding payment terms– CollateralCollateral– Positive and negative covenantsPositive and negative covenants– Par or face value (usually increments of $1,000)Par or face value (usually increments of $1,000)– Bond pricing – usually shown as the price per $100 of Bond pricing – usually shown as the price per $100 of

par value, which is equal to the percentage of the par value, which is equal to the percentage of the bond’s face valuebond’s face value



• Term-to-maturityTerm-to-maturity – the time remaining to the – the time remaining to the bond’s maturity datebond’s maturity date

• Coupon rateCoupon rate – the annual percentage interest – the annual percentage interest paid on the bond’s face value; to calculate paid on the bond’s face value; to calculate the dollar value of the annual coupon, the dollar value of the annual coupon, multiply the coupon rate by the face valuemultiply the coupon rate by the face value– If the coupon is paid twice a year, divide the annual If the coupon is paid twice a year, divide the annual

coupon by twocoupon by two– Example: A $1,000 bond with an 8% coupon rate will Example: A $1,000 bond with an 8% coupon rate will

have an $80 coupon if paid annually or a $40 coupon have an $80 coupon if paid annually or a $40 coupon if paid semi-annuallyif paid semi-annually



Security and Protective ProvisionsSecurity and Protective Provisions

• Mortgage bondsMortgage bonds – secured by real assets – secured by real assets• DebenturesDebentures – either unsecured or secured – either unsecured or secured

with a floating charge over the firm’s assetswith a floating charge over the firm’s assets• Collateral trust bondsCollateral trust bonds – secured by a pledge – secured by a pledge

of financial assets, such as common stock, of financial assets, such as common stock, other bonds or treasury billsother bonds or treasury bills

• Equipment trust certificatesEquipment trust certificates – secured by a – secured by a pledge of equipment, such as railway rolling pledge of equipment, such as railway rolling stockstock


Security and Protective ProvisionsSecurity and Protective Provisions

• CovenantsCovenants– Positive covenantsPositive covenants – things the firm agrees – things the firm agrees toto dodo

• Supply periodic financial statementsSupply periodic financial statements

• Maintain certain ratiosMaintain certain ratios

– Negative covenantsNegative covenants – things the firm agrees – things the firm agrees not to not to dodo

• Restricts the amount of debt the firm can take onRestricts the amount of debt the firm can take on

• Prevents the firm from acquiring or disposing of Prevents the firm from acquiring or disposing of assetsassets


More Bond FeaturesMore Bond Features

• Call featureCall feature – allows the issuer to redeem or pay – allows the issuer to redeem or pay off the bond prior to maturity, usually at a off the bond prior to maturity, usually at a premiumpremium

• Retractable bondsRetractable bonds – allows the holder to sell the – allows the holder to sell the bonds back to the issuer before maturitybonds back to the issuer before maturity

• Extendible bondsExtendible bonds – allows the holder to extend – allows the holder to extend the maturity of the bondthe maturity of the bond

• Sinking fundsSinking funds – funds set aside by the issuer to – funds set aside by the issuer to ensure the firm is able to redeem the bond at ensure the firm is able to redeem the bond at maturity maturity

• Convertible bondsConvertible bonds – can be converted into – can be converted into common stock at a pre-determined conversion common stock at a pre-determined conversion priceprice


Bond ValuationBond Valuation

• The value of a bond is a function of:The value of a bond is a function of:– Par valuePar value– Term to maturityTerm to maturity– Coupon rateCoupon rate– Investor’s required rate of return (discount rate is also Investor’s required rate of return (discount rate is also

known as the bond’s yield to maturity)known as the bond’s yield to maturity)


Bond ValueBond ValueGeneral FormulaGeneral Formula

)k(

Fk

)k(IB

nbb

nb

1

111

1

[ 6-1]

Where:I = interest (or coupon ) paymentskb = the bond discount rate (or market rate)n = the term to maturityF = Face (or par) value of the bond


Bond Valuation: ExampleBond Valuation: Example

• What is the market price of a ten-year, $1,000 bond with a What is the market price of a ten-year, $1,000 bond with a 5% coupon, if the bond’s yield-to-maturity is 6%?5% coupon, if the bond’s yield-to-maturity is 6%?

10

10

1 1

1

1 1.06 1,00050

0.06 1.06

$926.40

n

bn

b b

k FB I

k k

Calculator Approach:1,000 FV50PMT10NI/Y 6CPT PV 926.40


Factors Affecting Bond PricesFactors Affecting Bond PricesBond Price-Yield CurveBond Price-Yield Curve

Market Yield (%)

FIGURE 6-2

Price ($)

When interest rates increase, bond prices fallWhen interest rates increase, bond prices fall


• The relationship between the coupon rate and the The relationship between the coupon rate and the bond’s yield-to-maturity (YTM) determines if the bond’s yield-to-maturity (YTM) determines if the bond will sell at a premium, at a discount, or at parbond will sell at a premium, at a discount, or at par

If Then Bond Sells at a:

Coupon < YTMCoupon < YTM Market < FaceMarket < Face DiscountDiscount

Coupon = YTMCoupon = YTM Market = FaceMarket = Face ParPar

Coupon > YTMCoupon > YTM Market > FaceMarket > Face PremiumPremium

Factors Affecting Bond PricesFactors Affecting Bond Prices


Bond Valuation: Semi-Annual CouponsBond Valuation: Semi-Annual Coupons

• So far, we have assumed that all bonds have So far, we have assumed that all bonds have annual pay coupons. While this is true for annual pay coupons. While this is true for many Eurobonds, it is not true for most many Eurobonds, it is not true for most domestic bond issues, which have coupons domestic bond issues, which have coupons that are paid semi-annuallythat are paid semi-annually

• To adjust for semi-annual coupons, we must To adjust for semi-annual coupons, we must make three changes:make three changes:– Size of the coupon payment (divide by 2)Size of the coupon payment (divide by 2)– Number of periods (multiply by 2)Number of periods (multiply by 2)– Yield-to-maturity (divide by 2)Yield-to-maturity (divide by 2)


Bond Valuation: Semi-Annual CouponsBond Valuation: Semi-Annual Coupons

For example, suppose you want to value a five-For example, suppose you want to value a five-year, $10,000 Government of Canada bond with a year, $10,000 Government of Canada bond with a 4% coupon, paid twice a year, given a YTM of 6%.4% coupon, paid twice a year, given a YTM of 6%.

2

2

2 5

2 5

1 12

212 2

.061 1

400 10,00020.062 .06

12 2

$9,146.98

n

b

nb b

x

x

kI F

Bk k

Calculator Approach:10,000 FV400 ÷ 2 = PMT5 x 2 = N6 ÷ 2 = I/YCPT PV 926.40



• There are three factors that affect the price There are three factors that affect the price volatility of a bondvolatility of a bond– Yield to maturityYield to maturity– Time to maturityTime to maturity– Size of couponSize of coupon



• Yield to maturityYield to maturity– Bond prices go down when the YTM goes upBond prices go down when the YTM goes up– Bond prices go up when the YTM goes downBond prices go up when the YTM goes down

• Look at the graph on the next slide. It shows Look at the graph on the next slide. It shows how the price of a 25 year, 10% coupon bond how the price of a 25 year, 10% coupon bond changes as the bond’s YTM varies from 1% to changes as the bond’s YTM varies from 1% to 30%30%

• Note that the graph is not linear – instead it is Note that the graph is not linear – instead it is said to be convex to the originsaid to be convex to the origin


Factors Affecting Bond Prices Factors Affecting Bond Prices Price and Yield: 25 Year Bond, 10% CouponPrice and Yield: 25 Year Bond, 10% Coupon

Price/Yield Relationship

0

50

100

150

200

250

300

350

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Percent YTM

Pri

ce p

er

$100 o

f F

ace

Valu

e


• The convexity of the price/YTM graph reveals The convexity of the price/YTM graph reveals two important insights:two important insights:– The price rise due to a fall in YTM is greater than the The price rise due to a fall in YTM is greater than the

price decline due to a rise in YTM, given an identical price decline due to a rise in YTM, given an identical change in the YTMchange in the YTM

– For a given change in YTM, bond prices will change For a given change in YTM, bond prices will change more when interest rates are low than when they are more when interest rates are low than when they are high high

Factors Affecting Bond Prices Factors Affecting Bond Prices Bond ConvexityBond Convexity



• Time to maturityTime to maturity– Long bonds have greater price volatility than short Long bonds have greater price volatility than short

bondsbonds• The longer the bond, the longer the period for which the The longer the bond, the longer the period for which the

cash flows are fixedcash flows are fixed

• Size of couponSize of coupon– Low coupon bonds have greater price volatility Low coupon bonds have greater price volatility

than high coupon bondsthan high coupon bonds• High coupons act like a stabilizing device, since a greater High coupons act like a stabilizing device, since a greater

proportion of the bond’s total cash flows occur closer to proportion of the bond’s total cash flows occur closer to today & are therefore less affected by a change in YTMtoday & are therefore less affected by a change in YTM


Interest Rate Risk & DurationInterest Rate Risk & Duration

• The sensitivity of bond prices to changes in The sensitivity of bond prices to changes in interest rates is a measure of the bond’s interest rates is a measure of the bond’s interest rate riskinterest rate risk

• A bond’s interest rate risk is affected by:A bond’s interest rate risk is affected by:– Yield to maturityYield to maturity– Term to maturityTerm to maturity– Size of couponSize of coupon

• These three factors are all captured in one These three factors are all captured in one number called number called durationduration


DurationDuration

• Duration is a measure of interest rate riskDuration is a measure of interest rate risk• The higher the duration, the more sensitive The higher the duration, the more sensitive

the bond is to changes in interest ratesthe bond is to changes in interest rates• A bond’s duration will be higher if its:A bond’s duration will be higher if its:

– YTM is lowerYTM is lower– Term to maturity is longerTerm to maturity is longer– Coupon is lowerCoupon is lower


Bond QuotationsBond Quotations

Issuer Coupon Maturity Price Yield

Canada 5.500 2009-Jun-01 103.79 4.16


Cash Versus Quoted PricesCash Versus Quoted Prices

• The quoted price is the price reported by the The quoted price is the price reported by the mediamedia

• The cash price is the price paid by an investorThe cash price is the price paid by an investor• The cash price includes both the quoted price The cash price includes both the quoted price

plus any interest that has accrued since the plus any interest that has accrued since the last coupon payment datelast coupon payment date


Cash Versus Quoted Price: ExampleCash Versus Quoted Price: Example

• Assume you want to purchase a $1,000 bond with a 5% Assume you want to purchase a $1,000 bond with a 5% coupon, paid semi-annually. Today is July 15coupon, paid semi-annually. Today is July 15thth. The last . The last coupon was paid June 30coupon was paid June 30thth. If the quoted price is $902, . If the quoted price is $902, how much is the cash price? how much is the cash price?

• Solution: The cash price is equal to:Solution: The cash price is equal to:– Quoted price of $902Quoted price of $902– Plus 15 days of interestPlus 15 days of interest

15902 1,000 0.05

365

902 2.05

$904.05

Cash price = Quoted Price+ Accrued Interest


Bond YieldsBond Yields

• Yield-to-maturity (YTM) – the discount rate Yield-to-maturity (YTM) – the discount rate used to evaluate bondsused to evaluate bonds– The yield earned by a bond investor who:The yield earned by a bond investor who:

• Purchases the bond at the current market pricePurchases the bond at the current market price• Held the bond to maturityHeld the bond to maturity• Reinvested all of the coupons at the YTMReinvested all of the coupons at the YTM

– Is the bond’s Internal Rate of Return (IRR) Is the bond’s Internal Rate of Return (IRR)


Bond Yield to MaturityBond Yield to Maturity

• The yield to maturity is that discount rate that causes The yield to maturity is that discount rate that causes the sum of the present value of promised cash flows the sum of the present value of promised cash flows to equal the current bond price.to equal the current bond price.

YTM)(

FYTM

YTM)(IB

n

n

1

111

1

[ 6-2]


Solving for YTMSolving for YTM

• To solve for YTM, solve for YTM in the following To solve for YTM, solve for YTM in the following formula:formula:

• ProblemProblem: can’t solve for YTM algebraically; : can’t solve for YTM algebraically; therefore, must either use a financial calculator, therefore, must either use a financial calculator, spreadsheet, trial and error, or approximation spreadsheet, trial and error, or approximation formula.formula.

1 1

1

n

n

YTM FB I

YTM YTM


Solving for YTMSolving for YTM

• Example: What is the YTM on a 10 year, 5% coupon Example: What is the YTM on a 10 year, 5% coupon bond (annual pay coupons) that is selling for $980?bond (annual pay coupons) that is selling for $980?

10

10

1 1

1

1 1 1,000980 50

1

5.26%

n

n

YTM FB I

YTM YTM

YTM

YTM YTM

YTM

Financial Calculator1,000 FV980 +/- PV50 PMT51 NI/Y 5.26%


Solving for YTM: Semi-annual CouponsSolving for YTM: Semi-annual Coupons

• When solving for YTM with a semi-annual pay When solving for YTM with a semi-annual pay coupon, the yield obtained must be multiplied coupon, the yield obtained must be multiplied by two to obtain the annual YTMby two to obtain the annual YTM

• Example: What is the YTM for a 20 year, Example: What is the YTM for a 20 year, $1,000 bond with a 6% coupon, paid semi-$1,000 bond with a 6% coupon, paid semi-annually, given a current market price of annually, given a current market price of $1,030?$1,030?


Solving for YTM: Semi-annual CouponsSolving for YTM: Semi-annual Coupons

40

40

1 1

1

1 1 1,0001,030 30

1

2.87 2 5.74%

n

n

YTM FB I

YTM YTM

YTM

YTM YTM

YTM x

Financial Calculator1,000 FV1,030 +/- PV30 PMT40 NI/Y 2.87 x

2 =

5.746%


The Approximation FormulaThe Approximation Formula

WhereWhere

F = Face Value = Par Value = $1,000F = Face Value = Par Value = $1,000

B = Bond PriceB = Bond Price

I = the semi annual coupon interestI = the semi annual coupon interest

N = number of semi-annual periods left to maturityN = number of semi-annual periods left to maturity

1YTM) annual-semi (1YTM

YTM annual-semi 2YTM2

nB-F

Maturity toYield annual-Semi

2

BF

I


ExampleExample

• Find the yield-to-maturity of a 5 year 6% Find the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. coupon bond that is currently priced at $850. (Always assume the coupon interest is paid (Always assume the coupon interest is paid semi-annually.)semi-annually.)

• Therefore there is coupon interest of $30 paid Therefore there is coupon interest of $30 paid semi-annuallysemi-annually

• There are 10 semi-annual periods left until maturity There are 10 semi-annual periods left until maturity


SolutionSolution

The actual answer is 9.87%...so of course, the approximation approach only gives us an approximate answer…but that is just fine for tests and exams.

The actual answer is 9.87%...so of course, the approximation approach only gives us an approximate answer…but that is just fine for tests and exams.

%97.91)0486.1(1YTM) annual-semi (1YTM

9.3%0.0927320.0486YTM annual-semi 2YTM

0486.0925$

30$15$

2850,1$

30$10

850$000,1$

2

nB-F

Maturity toYield annual-Semi

22

BF

I


The Logic of the EquationThe Logic of the EquationApproximation Formula for YTMApproximation Formula for YTM

• The numerator simply represents the average semi-The numerator simply represents the average semi-annual returns on the investment; it is made up of two annual returns on the investment; it is made up of two components:components:– The first component is the average capital gain (if it is a discount The first component is the average capital gain (if it is a discount

bond) or capital loss (if it is a premium priced bond) per semi-annual bond) or capital loss (if it is a premium priced bond) per semi-annual period.period.

– The second component is the semi-annual coupon interest received.The second component is the semi-annual coupon interest received.• The denominator represents the average price of the The denominator represents the average price of the

bond.bond.• Therefore the formula is basically, average semi-annual Therefore the formula is basically, average semi-annual

return on average investment.return on average investment.• Of course, we annualize the semi-annual return so that Of course, we annualize the semi-annual return so that

we can compare this return to other returns on other we can compare this return to other returns on other investments for comparison purposes.investments for comparison purposes.


Yield to CallYield to Call

• If a bond has a call feature, the issuer can call If a bond has a call feature, the issuer can call the bond prior to its stated maturitythe bond prior to its stated maturity

• To calculate the yield to call, replace the To calculate the yield to call, replace the maturity date with the first call datematurity date with the first call date


Yield to CallYield to Call

• The yield to call is that discount rate that causes the The yield to call is that discount rate that causes the present value of all promised cash flows including the present value of all promised cash flows including the call price (CP) to equal the current bond price.call price (CP) to equal the current bond price.

YTC)(

CPYTC

YTC)(IB

n

n

1

111

1

[ 6-3]


Solving for YTC: Semi-Annual CouponsSolving for YTC: Semi-Annual Coupons

Financial Calculator1,050 FV1,030 +/- PV30 PMT10 NI/Y 3.081 x

2 =

6.16%

YTC on a 20-year 6 percent bond that is callable in five years at a call price of $1,050. The bond pays semi-annual coupons and is selling for $1,030.

%16.62%081.3

%081.3

1

050,1$11

130$030,1$

1

111

1

10

10

YTC

annuallysemiYTC

YTC)(YTCYTC)(

YTC)(

CPYTC

YTC)(IB

n

n


Current YieldCurrent Yield

• The current yield is the yield on the bond’s current The current yield is the yield on the bond’s current market price provided by the annual couponmarket price provided by the annual coupon– It is not a true measure of the return to the bondholder because It is not a true measure of the return to the bondholder because

it does not consider potential capital gain or capital losses based it does not consider potential capital gain or capital losses based on the relationship between the purchase price of the bond and on the relationship between the purchase price of the bond and it’s par value.it’s par value.

B

interestAnnualCY [ 6-4]


Current YieldCurrent YieldExampleExample

• The current yield is the yield on the bond’s current The current yield is the yield on the bond’s current market price provided by the annual couponmarket price provided by the annual coupon

• Example:Example: If a bond has a 5.5% annual pay coupon If a bond has a 5.5% annual pay coupon and the current market price of the bond is $1,050, and the current market price of the bond is $1,050, the current yield is:the current yield is:

55

1,050

5.24%

Annual CouponCurrent Yield =

Current Market Price


Interest Rate DeterminantsInterest Rate Determinants

• Interest is the “price” of moneyInterest is the “price” of money• Basis points – 1/100 of 1%Basis points – 1/100 of 1%• Interest rates go:Interest rates go:

– Up Up – when the demand for loanable funds rises– when the demand for loanable funds rises– DownDown – when the demand for loanable funds falls – when the demand for loanable funds falls


Risk-free Interest RateRisk-free Interest Rate

• Usually use the yield on short federal Usually use the yield on short federal government treasury bills as a proxy for the government treasury bills as a proxy for the risk-free rate (RF)risk-free rate (RF)

• The risk-free rate is comprised of two The risk-free rate is comprised of two components:components:– Real rateReal rate – compensation for deferring consumption – compensation for deferring consumption– Expected inflationExpected inflation – compensation for the expected – compensation for the expected

loss in purchasing power loss in purchasing power

(See Figure 6-3 to see rates of inflation and yields on long Canada bonds since 1961)


Inflation and Yields over TimeInflation and Yields over Time

FIGURE 6-3


Fisher EquationFisher Equation

• If we call the risk-free rate the nominal rate, then If we call the risk-free rate the nominal rate, then the relationship between the real rate, the the relationship between the real rate, the nominal rate and expected inflation is usually nominal rate and expected inflation is usually referred to as the Fisher Equation (after Irving referred to as the Fisher Equation (after Irving Fisher)Fisher)

inflation Expectedrate RealRF [ 6-5]


Fisher EquationFisher Equation

• When inflation is low, can safely use the When inflation is low, can safely use the approximation formula:approximation formula:

• When inflation is high, use the exact form of the When inflation is high, use the exact form of the Fisher Equation:Fisher Equation:

Nominal RealR = R + Expected Inflation

1 1 1Nominal RealR = R Expected Inflation


Fisher Equation Fisher Equation ExampleExample

• If the real rate is 3% and the nominal rate is 5.5%, If the real rate is 3% and the nominal rate is 5.5%, what is the approximate expected future inflation what is the approximate expected future inflation rate?rate?

5.5 3

2.5%

Nominal RealR = R + Expected Inflation

Expected Inflation

Expected Inflation


Global Influences on Interest RatesGlobal Influences on Interest Rates

• Canadian domestic interest rates are heavily Canadian domestic interest rates are heavily influenced by global interest ratesinfluenced by global interest rates

• Interest rate parity (IRP) theory states that FX Interest rate parity (IRP) theory states that FX forward rates will be established that equalize forward rates will be established that equalize the yield an investor can earn, whether the yield an investor can earn, whether investing domestically or in a foreign investing domestically or in a foreign jurisdictionjurisdiction– A country with high inflation and high interest rates A country with high inflation and high interest rates

will have a depreciating currencywill have a depreciating currency


Term Structure of Interest RatesTerm Structure of Interest Rates

• Is that set of rates (YTM) for a given risk-class Is that set of rates (YTM) for a given risk-class of debt securities (for example, Government of debt securities (for example, Government of Canada Bonds) at a given point in time.of Canada Bonds) at a given point in time.

• When plotted on a graph, the line is called a When plotted on a graph, the line is called a Yield CurveYield Curve


Term Structure of Interest RatesTerm Structure of Interest Rates

• The Yield Curve is the graph created by The Yield Curve is the graph created by putting term to maturity on the X axis, YTM putting term to maturity on the X axis, YTM on the Y axis and then plotting the yield at on the Y axis and then plotting the yield at each maturity.each maturity.

• The four typical shapes of yield curves:The four typical shapes of yield curves:• Upward sloping (the most common shape)Upward sloping (the most common shape)• Downward slopingDownward sloping• FlatFlat• HumpedHumped

(See Figure 6-4 for Yield curves that existed at various times in Canada)


Historical Yield CurvesHistorical Yield Curves1990, 1994, 1998, 20041990, 1994, 1998, 2004

Pe

rce

nt

Term Left to Maturity

16

14

12

10

8

6

4

2

0

1 mth 3 mths 6 mths 1 yr 2yrs 5 yrs 7 yrs 10 yrs 30 yrs

FIGURE 6-4

1990 1994 1998 2004


Theories of the Term StructureTheories of the Term Structure

• Three theories are used to explain the shape Three theories are used to explain the shape of the term structureof the term structure– Liquidity preference theoryLiquidity preference theory

• Investors must be paid a “liquidity premium” to hold less Investors must be paid a “liquidity premium” to hold less liquid, long-term debtliquid, long-term debt

– Expectations theoryExpectations theory• The long rate is the average of expected future short interest The long rate is the average of expected future short interest

ratesrates

– Market segmentation theoryMarket segmentation theory• Distinct markets exist for securities of different maturitiesDistinct markets exist for securities of different maturities


Term Structure of Interest RatesTerm Structure of Interest RatesRisk PremiumsRisk Premiums

• More risky bonds (i.e.. BBB rated Corporate Bonds) will More risky bonds (i.e.. BBB rated Corporate Bonds) will have their own yield curve and it will plot at higher YTM at have their own yield curve and it will plot at higher YTM at every term to maturity because of the default risk that BBBs every term to maturity because of the default risk that BBBs carrycarry

• The difference between the YTM on a 10-year BBB corporate The difference between the YTM on a 10-year BBB corporate bond and a 10-year Government of Canada bond is called a bond and a 10-year Government of Canada bond is called a yield spreadyield spread and represents a and represents a default-risk premiumdefault-risk premium investors demand for investing in more risky securities.investors demand for investing in more risky securities.

• Spreads will increase when pessimism increases in the Spreads will increase when pessimism increases in the economyeconomy

• Spreads will narrow during times of economic expansion Spreads will narrow during times of economic expansion (confidence)(confidence)


Yield Curves for Different Risk ClassesYield Curves for Different Risk ClassesRisk Premiums (Yield Spreads)Risk Premiums (Yield Spreads)

Pe

rce

nt

Term Left to Maturity

16

14

12

10

8

6

4

2

0

1 mth 3 mths 6 mths 1 yr 2yrs 5 yrs 7 yrs 10 yrs 30 yrs

BBB Corporates Government of Canada Bonds

Yield Spread


Risk PremiumsRisk Premiums

• The YTM on a corporate bond is comprised of:The YTM on a corporate bond is comprised of:

• The maturity yield differential is explained by the The maturity yield differential is explained by the term structureterm structure

• Spread is the additional yield due to default riskSpread is the additional yield due to default risk

Spread aldifferenti yieldMaturity -/ RFkb YTM[ 6-6]


Debt RatingsDebt Ratings

• All publicly traded bonds are assigned a “risk All publicly traded bonds are assigned a “risk rating” by a rating agency, such as Dominion rating” by a rating agency, such as Dominion Bond Rating Service (DBRS), Standard & Bond Rating Service (DBRS), Standard & Poors (S&P), Moodys, Fitch, etc.Poors (S&P), Moodys, Fitch, etc.

• Bonds are categorized asBonds are categorized as– Investment grade – top four rating categories (AAA, Investment grade – top four rating categories (AAA,

AA, A & BBB)AA, A & BBB)– Junk or high yield – everything below investment Junk or high yield – everything below investment

grade (BB, B, CCC, CC, D, Suspended)grade (BB, B, CCC, CC, D, Suspended)


Why Do Bonds Have Different Yields?Why Do Bonds Have Different Yields?

• Default riskDefault risk – the higher the default risk, the – the higher the default risk, the higher the required YTMhigher the required YTM

• LiquidityLiquidity – the less liquid the bond, the higher – the less liquid the bond, the higher the required YTMthe required YTM

• Call featuresCall features – increase required YTM – increase required YTM• Extendible featureExtendible feature – reduce required YTM – reduce required YTM• Retractable featureRetractable feature – reduce required YTM – reduce required YTM


Treasury BillsTreasury Bills

• Treasury billsTreasury bills are short-term obligations of government are short-term obligations of government with an initial term to maturity of one year or lesswith an initial term to maturity of one year or less

• Issued at a discount and mature at face valueIssued at a discount and mature at face value• The difference between the issue price and the face The difference between the issue price and the face

value is treated as interest incomevalue is treated as interest income• To calculate the price of a T-bill, use the following To calculate the price of a T-bill, use the following

formulaformula

1T Bill

FP

nBEY

B

Where:P = market price of the T BillF = face value of the T BillBEY = the bond equivalent yieldn = the number of days until maturityB = the annual basis (365 days in Canada)


Treasury Bills: ExampleTreasury Bills: Example

• What is the price of a $1,000,000 Canadian T bill with What is the price of a $1,000,000 Canadian T bill with 80 days to maturity and a BEY of 4.5%?80 days to maturity and a BEY of 4.5%?

1

1,000,00080

1 .045365

$990,233.32

T Bill

FP

nBEY

B


Solving for Yield on a T BillSolving for Yield on a T Bill

• To solve for the yield on a T bill, rearrange the To solve for the yield on a T bill, rearrange the previous formula and solve for BEY. previous formula and solve for BEY.

• ExampleExample: What is the yield on a $100,000 T bill with : What is the yield on a $100,000 T bill with 180 days to maturity and a market price of $98,200?180 days to maturity and a market price of $98,200?

100,000 98,200 365

98,200 180

3.72%

F P BBEY

P n


Zero Coupon BondsZero Coupon Bonds

• A A zero coupon bondzero coupon bond is a bond issued at a is a bond issued at a discount that matures at par or face valuediscount that matures at par or face value

• A zero coupon bond has no reinvestment rate A zero coupon bond has no reinvestment rate risk, since there are no coupons to be risk, since there are no coupons to be reinvestedreinvested

• To calculate the price of a zero coupon bond, To calculate the price of a zero coupon bond, solve for the PV of the face amount solve for the PV of the face amount


Zero Coupon BondsZero Coupon Bonds

• Example: What is the market price of a $50,000 Example: What is the market price of a $50,000 zero coupon bond with 25 years to maturity that is zero coupon bond with 25 years to maturity that is currently yielding 6%?currently yielding 6%?

25

F

1

50,000

1.06

$11,649.93

n

b

Bk


Floating Rate & Real Return BondsFloating Rate & Real Return Bonds

• Floating rate bondsFloating rate bonds have a coupon that floats have a coupon that floats with some reference rate, such as the yield with some reference rate, such as the yield on T billson T bills– Because the coupon floats, the market price will Because the coupon floats, the market price will

typically be close to the bond’s face valuetypically be close to the bond’s face value

• Real return bondsReal return bonds are issued by the are issued by the Government of Canada to protect investors Government of Canada to protect investors against unexpected inflationagainst unexpected inflation– Each period, the face value of the bond is grossed up Each period, the face value of the bond is grossed up

by the inflation rate. The coupon is then paid on the by the inflation rate. The coupon is then paid on the grossed up face value.grossed up face value.


Canada Savings BondsCanada Savings Bonds

• A Canada Savings Bond (CSB) is a special A Canada Savings Bond (CSB) is a special type of bond issued by the Government of type of bond issued by the Government of CanadaCanada

• It is issued in two forms:It is issued in two forms:– Regular interest – interest is paid annuallyRegular interest – interest is paid annually– Compound interest – interest compounds over the life Compound interest – interest compounds over the life

of the bondof the bond

• CSBs are redeemable at any chartered bank CSBs are redeemable at any chartered bank in Canada at their face valuein Canada at their face value

• There is no secondary market for CSBsThere is no secondary market for CSBs


Summary and ConclusionsSummary and Conclusions

In this chapter you have learned:In this chapter you have learned:– About the nature of bonds as an investmentAbout the nature of bonds as an investment– How to value a bond using discounted cash flow How to value a bond using discounted cash flow

conceptsconcepts– About the determinants of interest rates and theories About the determinants of interest rates and theories

used to explain the term structure of interest ratesused to explain the term structure of interest rates


CopyrightCopyright

Copyright © 2007 John Wiley & Sons Canada, Ltd. All rights Copyright © 2007 John Wiley & Sons Canada, Ltd. All rights reserved. Reproduction or translation of this work beyond that reserved. Reproduction or translation of this work beyond that permitted by Access Copyright (the Canadian copyright licensing permitted by Access Copyright (the Canadian copyright licensing agency) is unlawful. Requests for further information should be agency) is unlawful. Requests for further information should be addressed to the Permissions Department, John Wiley & Sons addressed to the Permissions Department, John Wiley & Sons Canada, Ltd.Canada, Ltd. The purchaser may make back-up copies for his or The purchaser may make back-up copies for his or her own use only and not for distribution or resale.her own use only and not for distribution or resale. The author The author and the publisher assume no responsibility for errors, omissions, and the publisher assume no responsibility for errors, omissions, or damages caused by the use of these files or programs or from or damages caused by the use of these files or programs or from the use of the information contained herein.the use of the information contained herein.

Prepared by Ken Hartviksen and Robert Ironside INTRODUCTION TO CORPORATE FINANCE Laurence Booth W....

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