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

2. CHAPTER 6 Bond Valuation and Interest Rates

3. CHAPTER 6 – Bond Valuation and Interest Rates6 - 3 Lecture 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 Questions

4. CHAPTER 6 – Bond Valuation and Interest Rates6 - 4 Learning 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 market value of a bondHow to determine the discount rate or yield given the market 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 interest ratesThe factors (both domestic and global) that affect interest rates

5. CHAPTER 6 – Bond Valuation and Interest Rates6 - 5 Important 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) theoryInterest rate parity (IRP) theory Interest rate riskInterest rate risk Issue-specific premiumsIssue-specific premiums Liquidity preference theoryLiquidity preference theory Maturity valueMaturity value

6. CHAPTER 6 – Bond Valuation and Interest Rates6 - 6 Important 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 interest ratesTerm structure of interest rates Term to maturityTerm to maturity Yield curveYield curve Yield to maturityYield to maturity Zero coupon bondZero coupon bond

7. CHAPTER 6 – Bond Valuation and Interest Rates6 - 7 The Basic Structure of Bonds What is a bond?What is a bond? In its broadest sense, a bond is any debt instrument that promises a fixed income stream to the holderIn its broadest sense, a bond is any debt instrument that promises a fixed income stream to the holder Fixed income securities are often classified according to maturity, as follows:Fixed income securities are often classified according to maturity, as follows: –Less than one year – Bills or “Paper” –1 year < Maturity < 7 years – Notes –< 7 years – Bonds

8. CHAPTER 6 – Bond Valuation and Interest Rates6 - 8 The Basic Structure of Bonds A typical bond has the following characteristics:A typical bond has the following characteristics: –A fixed face or par value, paid to the holder of the bond, at maturity –A fixed coupon, which specifies the interest payable over 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 date

9. CHAPTER 6 – Bond Valuation and Interest Rates6 - 9 Bonds may be either:Bonds may be either: –Bearer bonds –Registered bonds Bond indenture - the contract between the issuer of the bond and the investors who hold itBond indenture - the contract between the issuer of the bond and the investors who hold it The market price of a bond is equal to the present value of the payments promised by the bondThe market price of a bond is equal to the present value of the payments promised by the bond (See the basic pattern of cash flows from a traditional bond on the next slide) The Basic Structure of Bonds

10. CHAPTER 6 – Bond Valuation and Interest Rates6 - 10 The Basic Structure of Bonds Cash Flow Pattern for a Traditional Coupon-Paying Bond 0123…nIIIIIF0123…nIIIIIF 0123…nIIIIIF0123…nIIIIIF FIGURE 6-1 I = interest payments, and F = principal repayment

11. CHAPTER 6 – Bond Valuation and Interest Rates6 - 11 Cash 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 02 3 4n1 Coupon Coupon + Face Value Purchase Price Cash Inflows to the Investor Cash Outflows to the Investor

12. CHAPTER 6 – Bond Valuation and Interest Rates6 - 12 Bond indenture is the contract between the issuer and the holder. It specifies:Bond indenture is the contract between the issuer and the holder. It specifies: –Details regarding payment terms –Collateral –Positive and negative covenants –Par or face value (usually increments of $1,000) –Bond pricing – usually shown as the price per $100 of par value, which is equal to the percentage of the bond’s face value The Basic Structure of Bonds

13. CHAPTER 6 – Bond Valuation and Interest Rates6 - 13 Term-to-maturity – the time remaining to the bond’s maturity dateTerm-to-maturity – the time remaining to the bond’s maturity date Coupon rate – the annual percentage interest paid on the bond’s face value; to calculate the dollar value of the annual coupon, multiply the coupon rate by the face valueCoupon rate – the annual percentage interest paid on the bond’s face value; to calculate the dollar value of the annual coupon, multiply the coupon rate by the face value –If the coupon is paid twice a year, divide the annual coupon by two –Example: A $1,000 bond with an 8% coupon rate will have an $80 coupon if paid annually or a $40 coupon if paid semi-annually The Basic Structure of Bonds

14. CHAPTER 6 – Bond Valuation and Interest Rates6 - 14 Security and Protective Provisions Mortgage bonds – secured by real assetsMortgage bonds – secured by real assets Debentures – either unsecured or secured with a floating charge over the firm’s assetsDebentures – either unsecured or secured with a floating charge over the firm’s assets Collateral trust bonds – secured by a pledge of financial assets, such as common stock, other bonds or treasury billsCollateral trust bonds – secured by a pledge of financial assets, such as common stock, other bonds or treasury bills Equipment trust certificates – secured by a pledge of equipment, such as railway rolling stockEquipment trust certificates – secured by a pledge of equipment, such as railway rolling stock

15. CHAPTER 6 – Bond Valuation and Interest Rates6 - 15 Security and Protective Provisions CovenantsCovenants –Positive covenants – things the firm agrees to do Supply periodic financial statementsSupply periodic financial statements Maintain certain ratiosMaintain certain ratios –Negative covenants – things the firm agrees not to do 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 assetsPrevents the firm from acquiring or disposing of assets

16. CHAPTER 6 – Bond Valuation and Interest Rates6 - 16 More Bond Features Call feature – allows the issuer to redeem or pay off the bond prior to maturity, usually at a premiumCall feature – allows the issuer to redeem or pay off the bond prior to maturity, usually at a premium Retractable bonds – allows the holder to sell the bonds back to the issuer before maturityRetractable bonds – allows the holder to sell the bonds back to the issuer before maturity Extendible bonds – allows the holder to extend the maturity of the bondExtendible bonds – allows the holder to extend the maturity of the bond Sinking funds – funds set aside by the issuer to ensure the firm is able to redeem the bond at maturitySinking funds – funds set aside by the issuer to ensure the firm is able to redeem the bond at maturity Convertible bonds – can be converted into common stock at a pre-determined conversion priceConvertible bonds – can be converted into common stock at a pre-determined conversion price

17. CHAPTER 6 – Bond Valuation and Interest Rates6 - 17 Bond Valuation The value of a bond is a function of:The value of a bond is a function of: –Par value –Term to maturity –Coupon rate –Investor’s required rate of return (discount rate is also known as the bond’s yield to maturity)

18. CHAPTER 6 – Bond Valuation and Interest Rates6 - 18 Bond Value General Formula [ 6-1] Where: I = interest (or coupon ) payments k b = the bond discount rate (or market rate) n = the term to maturity F = Face (or par) value of the bond

19. CHAPTER 6 – Bond Valuation and Interest Rates6 - 19 Bond Valuation: Example 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%?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%? Calculator Approach: 1,000 FV 50PMT 10N I/Y 6 CPT PV926.40

20. CHAPTER 6 – Bond Valuation and Interest Rates6 - 20 Factors Affecting Bond Prices Bond Price-Yield Curve Market Yield (%) FIGURE 6-2 Price ($) When interest rates increase, bond prices fall

21. CHAPTER 6 – Bond Valuation and Interest Rates6 - 21 The relationship between the coupon rate and the bond’s yield-to-maturity (YTM) determines if the bond will sell at a premium, at a discount, or at parThe relationship between the coupon rate and the bond’s yield-to-maturity (YTM) determines if the bond will sell at a premium, at a discount, or at par IfThenBond Sells at a: Coupon < YTM Market < Face Discount Coupon = YTM Market = Face Par Coupon > YTM Market > Face Premium Factors Affecting Bond Prices

22. CHAPTER 6 – Bond Valuation and Interest Rates6 - 22 Bond Valuation: Semi-Annual Coupons So far, we have assumed that all bonds have annual pay coupons. While this is true for many Eurobonds, it is not true for most domestic bond issues, which have coupons that are paid semi-annuallySo far, we have assumed that all bonds have annual pay coupons. While this is true for many Eurobonds, it is not true for most domestic bond issues, which have coupons that are paid semi-annually To adjust for semi-annual coupons, we must make three changes:To adjust for semi-annual coupons, we must make three changes: –Size of the coupon payment (divide by 2) –Number of periods (multiply by 2) –Yield-to-maturity (divide by 2)

23. CHAPTER 6 – Bond Valuation and Interest Rates6 - 23 Bond Valuation: Semi-Annual Coupons For example, suppose you want to value a five-year, $10,000 Government of Canada bond with a 4% coupon, paid twice a year, given a YTM of 6%. Calculator Approach: 10,000FV 400 ÷ 2 = PMT 5 x 2 =N 6 ÷ 2 = I/Y CPT PV926.40

24. CHAPTER 6 – Bond Valuation and Interest Rates6 - 24 Factors Affecting Bond Prices There are three factors that affect the price volatility of a bondThere are three factors that affect the price volatility of a bond –Yield to maturity –Time to maturity –Size of coupon

25. CHAPTER 6 – Bond Valuation and Interest Rates6 - 25 Factors Affecting Bond Prices Yield to maturityYield to maturity –Bond prices go down when the YTM goes up –Bond prices go up when the YTM goes down Look at the graph on the next slide. It shows how the price of a 25 year, 10% coupon bond changes as the bond’s YTM varies from 1% to 30%Look at the graph on the next slide. It shows how the price of a 25 year, 10% coupon bond changes as the bond’s YTM varies from 1% to 30% Note that the graph is not linear – instead it is said to be convex to the originNote that the graph is not linear – instead it is said to be convex to the origin

26. CHAPTER 6 – Bond Valuation and Interest Rates6 - 26 Factors Affecting Bond Prices Price and Yield: 25 Year Bond, 10% Coupon

27. CHAPTER 6 – Bond Valuation and Interest Rates6 - 27 The convexity of the price/YTM graph reveals two important insights:The convexity of the price/YTM graph reveals two important insights: –The price rise due to a fall in YTM is greater than the price decline due to a rise in YTM, given an identical change in the YTM –For a given change in YTM, bond prices will change more when interest rates are low than when they are high Factors Affecting Bond Prices Bond Convexity

28. CHAPTER 6 – Bond Valuation and Interest Rates6 - 28 Factors Affecting Bond Prices Time to maturityTime to maturity –Long bonds have greater price volatility than short bonds The longer the bond, the longer the period for which the cash flows are fixedThe longer the bond, the longer the period for which the cash flows are fixed Size of couponSize of coupon –Low coupon bonds have greater price volatility than high coupon bonds High coupons act like a stabilizing device, since a greater proportion of the bond’s total cash flows occur closer to today & are therefore less affected by a change in YTMHigh coupons act like a stabilizing device, since a greater proportion of the bond’s total cash flows occur closer to today & are therefore less affected by a change in YTM

29. CHAPTER 6 – Bond Valuation and Interest Rates6 - 29 Interest Rate Risk & Duration The sensitivity of bond prices to changes in interest rates is a measure of the bond’s interest rate riskThe sensitivity of bond prices to changes in interest rates is a measure of the bond’s interest rate risk A bond’s interest rate risk is affected by:A bond’s interest rate risk is affected by: –Yield to maturity –Term to maturity –Size of coupon These three factors are all captured in one number called durationThese three factors are all captured in one number called duration

30. CHAPTER 6 – Bond Valuation and Interest Rates6 - 30 Duration Duration is a measure of interest rate riskDuration is a measure of interest rate risk The higher the duration, the more sensitive the bond is to changes in interest ratesThe higher the duration, the more sensitive the 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 lower –Term to maturity is longer –Coupon is lower

31. CHAPTER 6 – Bond Valuation and Interest Rates6 - 31 Bond Quotations IssuerCouponMaturityPriceYield Canada5.5002009-Jun-01103.794.16

32. CHAPTER 6 – Bond Valuation and Interest Rates6 - 32 Cash Versus Quoted Prices The quoted price is the price reported by the mediaThe quoted price is the price reported by the media 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 plus any interest that has accrued since the last coupon payment dateThe cash price includes both the quoted price plus any interest that has accrued since the last coupon payment date

33. CHAPTER 6 – Bond Valuation and Interest Rates6 - 33 Cash Versus Quoted Price: Example Assume you want to purchase a $1,000 bond with a 5% coupon, paid semi-annually. Today is July 15 th. The last coupon was paid June 30 th. If the quoted price is $902, how much is the cash price?Assume you want to purchase a $1,000 bond with a 5% coupon, paid semi-annually. Today is July 15 th. The last coupon was paid June 30 th. If the quoted price is $902, how much is the cash price? Solution: The cash price is equal to:Solution: The cash price is equal to: –Quoted price of $902 –Plus 15 days of interest

34. CHAPTER 6 – Bond Valuation and Interest Rates6 - 34 Bond Yields Yield-to-maturity (YTM) – the discount rate used to evaluate bondsYield-to-maturity (YTM) – the discount rate used to evaluate bonds –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)

35. CHAPTER 6 – Bond Valuation and Interest Rates6 - 35 Bond Yield to Maturity The yield to maturity is that discount rate that causes the sum of the present value of promised cash flows to equal the current bond price.The yield to maturity is that discount rate that causes the sum of the present value of promised cash flows to equal the current bond price. [ 6-2]

36. CHAPTER 6 – Bond Valuation and Interest Rates6 - 36 Solving for YTM To solve for YTM, solve for YTM in the following formula:To solve for YTM, solve for YTM in the following formula: Problem: can’t solve for YTM algebraically; therefore, must either use a financial calculator, spreadsheet, trial and error, or approximation formula.Problem: can’t solve for YTM algebraically; therefore, must either use a financial calculator, spreadsheet, trial and error, or approximation formula.

37. CHAPTER 6 – Bond Valuation and Interest Rates6 - 37 Solving for YTM Example: What is the YTM on a 10 year, 5% coupon bond (annual pay coupons) that is selling for $980?Example: What is the YTM on a 10 year, 5% coupon bond (annual pay coupons) that is selling for $980? Financial Calculator 1,000FV 980 +/-PV 50 PMT 10 N I/Y5.26%

38. CHAPTER 6 – Bond Valuation and Interest Rates6 - 38 Solving for YTM: Semi-annual Coupons When solving for YTM with a semi-annual pay coupon, the yield obtained must be multiplied by two to obtain the annual YTMWhen solving for YTM with a semi-annual pay coupon, the yield obtained must be multiplied by two to obtain the annual YTM Example: What is the YTM for a 20 year, $1,000 bond with a 6% coupon, paid semi-annually, given a current market price of $1,030?Example: What is the YTM for a 20 year, $1,000 bond with a 6% coupon, paid semi-annually, given a current market price of $1,030?

39. CHAPTER 6 – Bond Valuation and Interest Rates6 - 39 Solving for YTM: Semi-annual Coupons Financial Calculator 1,000 FV 1,030 +/- PV 30 PMT 40 N I/Y 2.87 x 2 = 5.746%

40. CHAPTER 6 – Bond Valuation and Interest Rates6 - 40 The Approximation Formula Where F = Face Value = Par Value = $1,000 B = Bond Price I = the semi annual coupon interest N = number of semi-annual periods left to maturity

41. CHAPTER 6 – Bond Valuation and Interest Rates6 - 41 Example Find the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. (Always assume the coupon interest is paid semi- annually.)Find the yield-to-maturity of a 5 year 6% coupon bond that is currently priced at $850. (Always assume the coupon interest is paid semi- annually.) Therefore there is coupon interest of $30 paid semi-annuallyTherefore there is coupon interest of $30 paid semi-annually There are 10 semi-annual periods left until maturityThere are 10 semi-annual periods left until maturity

42. CHAPTER 6 – Bond Valuation and Interest Rates6 - 42 Solution 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.

43. CHAPTER 6 – Bond Valuation and Interest Rates6 - 43 The Logic of the Equation Approximation Formula for YTM The numerator simply represents the average semi- annual returns on the investment; it is made up of two components:The numerator simply represents the average semi- annual returns on the investment; it is made up of two components: –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 period. –The second component is the semi-annual coupon interest received. The denominator represents the average price of the bond.The denominator represents the average price of the bond. Therefore the formula is basically, average semi-annual return on average investment.Therefore the formula is basically, average semi-annual return on average investment. Of course, we annualize the semi-annual return so that we can compare this return to other returns on other investments for comparison purposes.Of course, we annualize the semi-annual return so that we can compare this return to other returns on other investments for comparison purposes.

44. CHAPTER 6 – Bond Valuation and Interest Rates6 - 44 Yield to Call If a bond has a call feature, the issuer can call the bond prior to its stated maturityIf a bond has a call feature, the issuer can call the bond prior to its stated maturity To calculate the yield to call, replace the maturity date with the first call dateTo calculate the yield to call, replace the maturity date with the first call date

45. CHAPTER 6 – Bond Valuation and Interest Rates6 - 45 Yield to Call The yield to call is that discount rate that causes the present value of all promised cash flows including the call price (CP) to equal the current bond price.The yield to call is that discount rate that causes the present value of all promised cash flows including the call price (CP) to equal the current bond price. [ 6-3]

46. CHAPTER 6 – Bond Valuation and Interest Rates6 - 46 Solving for YTC: Semi-Annual Coupons Financial Calculator 1,050 FV 1,030 +/- PV 30 PMT 10 N I/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.

47. CHAPTER 6 – Bond Valuation and Interest Rates6 - 47 Current Yield The current yield is the yield on the bond’s current market price provided by the annual couponThe current yield is the yield on the bond’s current market price provided by the annual coupon –It is not a true measure of the return to the bondholder because it does not consider potential capital gain or capital losses based on the relationship between the purchase price of the bond and it’s par value. [ 6-4]

48. CHAPTER 6 – Bond Valuation and Interest Rates6 - 48 Current Yield Example The current yield is the yield on the bond’s current market price provided by the annual couponThe current yield is the yield on the bond’s current market price provided by the annual coupon Example: If a bond has a 5.5% annual pay coupon and the current market price of the bond is $1,050, the current yield is:Example: If a bond has a 5.5% annual pay coupon and the current market price of the bond is $1,050, the current yield is:

49. CHAPTER 6 – Bond Valuation and Interest Rates6 - 49 Interest 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 – when the demand for loanable funds rises –Down – when the demand for loanable funds falls

50. CHAPTER 6 – Bond Valuation and Interest Rates6 - 50 Risk-free Interest Rate Usually use the yield on short federal government treasury bills as a proxy for the risk- free rate (RF)Usually use the yield on short federal government treasury bills as a proxy for the risk- free rate (RF) The risk-free rate is comprised of two components:The risk-free rate is comprised of two components: –Real rate – compensation for deferring consumption –Expected inflation – compensation for the expected loss in purchasing power (See Figure 6-3 to see rates of inflation and yields on long Canada bonds since 1961)

51. CHAPTER 6 – Bond Valuation and Interest Rates6 - 51 Inflation and Yields over Time FIGURE 6-3

52. CHAPTER 6 – Bond Valuation and Interest Rates6 - 52 Fisher Equation If we call the risk-free rate the nominal rate, then the relationship between the real rate, the nominal rate and expected inflation is usually referred to as the Fisher Equation (after Irving Fisher)If we call the risk-free rate the nominal rate, then the relationship between the real rate, the nominal rate and expected inflation is usually referred to as the Fisher Equation (after Irving Fisher) [ 6-5]

53. CHAPTER 6 – Bond Valuation and Interest Rates6 - 53 Fisher Equation When inflation is low, can safely use the approximation formula:When inflation is low, can safely use the approximation formula: When inflation is high, use the exact form of the Fisher Equation:When inflation is high, use the exact form of the Fisher Equation:

54. CHAPTER 6 – Bond Valuation and Interest Rates6 - 54 Fisher Equation Example If the real rate is 3% and the nominal rate is 5.5%, what is the approximate expected future inflation rate?If the real rate is 3% and the nominal rate is 5.5%, what is the approximate expected future inflation rate?

55. CHAPTER 6 – Bond Valuation and Interest Rates6 - 55 Global Influences on Interest Rates Canadian domestic interest rates are heavily influenced by global interest ratesCanadian domestic interest rates are heavily influenced by global interest rates Interest rate parity (IRP) theory states that FX forward rates will be established that equalize the yield an investor can earn, whether investing domestically or in a foreign jurisdictionInterest rate parity (IRP) theory states that FX forward rates will be established that equalize the yield an investor can earn, whether investing domestically or in a foreign jurisdiction –A country with high inflation and high interest rates will have a depreciating currency

56. CHAPTER 6 – Bond Valuation and Interest Rates6 - 56 Term Structure of Interest Rates Is that set of rates (YTM) for a given risk-class of debt securities (for example, Government of Canada Bonds) at a given point in time.Is that set of rates (YTM) for a given risk-class of debt securities (for example, Government of Canada Bonds) at a given point in time. When plotted on a graph, the line is called a Yield CurveWhen plotted on a graph, the line is called a Yield Curve

57. CHAPTER 6 – Bond Valuation and Interest Rates6 - 57 Term Structure of Interest Rates The Yield Curve is the graph created by putting term to maturity on the X axis, YTM on the Y axis and then plotting the yield at each maturity.The Yield Curve is the graph created by putting term to maturity on the X axis, YTM on the Y axis and then plotting the yield at 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)

58. CHAPTER 6 – Bond Valuation and Interest Rates6 - 58 Historical Yield Curves 1990, 1994, 1998, 2004 Percent Term Left to Maturity 16 14 12 10 8 6 4 2 0 1 mth 3 mths 6 mths1 yr2yrs 5 yrs 7 yrs 10 yrs30 yrs FIGURE 6-4 1990199419982004

59. CHAPTER 6 – Bond Valuation and Interest Rates6 - 59 Theories of the Term Structure Three theories are used to explain the shape of the term structureThree theories are used to explain the shape of the term structure –Liquidity preference theory Investors must be paid a “liquidity premium” to hold less liquid, long-term debtInvestors must be paid a “liquidity premium” to hold less liquid, long-term debt –Expectations theory The long rate is the average of expected future short interest ratesThe long rate is the average of expected future short interest rates –Market segmentation theory Distinct markets exist for securities of different maturitiesDistinct markets exist for securities of different maturities

60. CHAPTER 6 – Bond Valuation and Interest Rates6 - 60 Term Structure of Interest Rates Risk Premiums More risky bonds (i.e.. BBB rated Corporate Bonds) will have their own yield curve and it will plot at higher YTM at every term to maturity because of the default risk that BBBs carryMore risky bonds (i.e.. BBB rated Corporate Bonds) will have their own yield curve and it will plot at higher YTM at every term to maturity because of the default risk that BBBs carry The difference between the YTM on a 10-year BBB corporate bond and a 10-year Government of Canada bond is called a yield spread and represents a default- risk premium investors demand for investing in more risky securities.The difference between the YTM on a 10-year BBB corporate bond and a 10-year Government of Canada bond is called a yield spread and represents a default- risk premium investors demand for investing in more risky securities. Spreads will increase when pessimism increases in the economySpreads will increase when pessimism increases in the economy Spreads will narrow during times of economic expansion (confidence)Spreads will narrow during times of economic expansion (confidence)

61. CHAPTER 6 – Bond Valuation and Interest Rates6 - 61 Yield Curves for Different Risk Classes Risk Premiums (Yield Spreads) Percent Term Left to Maturity 16 14 12 10 8 6 4 2 0 1 mth 3 mths 6 mths1 yr2yrs 5 yrs 7 yrs 10 yrs30 yrs BBB CorporatesGovernment of Canada Bonds Yield Spread

62. CHAPTER 6 – Bond Valuation and Interest Rates6 - 62 Risk 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 term structureThe maturity yield differential is explained by the term structure Spread is the additional yield due to default riskSpread is the additional yield due to default risk [ 6-6]

63. CHAPTER 6 – Bond Valuation and Interest Rates6 - 63 Debt Ratings All publicly traded bonds are assigned a “risk rating” by a rating agency, such as Dominion Bond Rating Service (DBRS), Standard & Poors (S&P), Moodys, Fitch, etc.All publicly traded bonds are assigned a “risk rating” by a rating agency, such as Dominion Bond Rating Service (DBRS), Standard & Poors (S&P), Moodys, Fitch, etc. Bonds are categorized asBonds are categorized as –Investment grade – top four rating categories (AAA, AA, A & BBB) –Junk or high yield – everything below investment grade (BB, B, CCC, CC, D, Suspended)

64. CHAPTER 6 – Bond Valuation and Interest Rates6 - 64 Why Do Bonds Have Different Yields? Default risk – the higher the default risk, the higher the required YTMDefault risk – the higher the default risk, the higher the required YTM Liquidity – the less liquid the bond, the higher the required YTMLiquidity – the less liquid the bond, the higher the required YTM Call features – increase required YTMCall features – increase required YTM Extendible feature – reduce required YTMExtendible feature – reduce required YTM Retractable feature – reduce required YTMRetractable feature – reduce required YTM

65. CHAPTER 6 – Bond Valuation and Interest Rates6 - 65 Treasury Bills Treasury bills are short-term obligations of government with an initial term to maturity of one year or lessTreasury bills are short-term obligations of government with 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 value is treated as interest incomeThe difference between the issue price and the face value is treated as interest income To calculate the price of a T-bill, use the following formulaTo calculate the price of a T-bill, use the following formula Where: P = market price of the T Bill F = face value of the T Bill BEY = the bond equivalent yield n = the number of days until maturity B = the annual basis (365 days in Canada)

66. CHAPTER 6 – Bond Valuation and Interest Rates6 - 66 Treasury Bills: Example What is the price of a $1,000,000 Canadian T bill with 80 days to maturity and a BEY of 4.5%?What is the price of a $1,000,000 Canadian T bill with 80 days to maturity and a BEY of 4.5%?

67. CHAPTER 6 – Bond Valuation and Interest Rates6 - 67 Solving for Yield on a T Bill To solve for the yield on a T bill, rearrange the previous formula and solve for BEY.To solve for the yield on a T bill, rearrange the previous formula and solve for BEY. Example: What is the yield on a $100,000 T bill with 180 days to maturity and a market price of $98,200?Example: What is the yield on a $100,000 T bill with 180 days to maturity and a market price of $98,200?

68. CHAPTER 6 – Bond Valuation and Interest Rates6 - 68 Zero Coupon Bonds A zero coupon bond is a bond issued at a discount that matures at par or face valueA zero coupon bond is a bond issued at a discount that matures at par or face value A zero coupon bond has no reinvestment rate risk, since there are no coupons to be reinvestedA zero coupon bond has no reinvestment rate risk, since there are no coupons to be reinvested To calculate the price of a zero coupon bond, solve for the PV of the face amountTo calculate the price of a zero coupon bond, solve for the PV of the face amount

69. CHAPTER 6 – Bond Valuation and Interest Rates6 - 69 Zero Coupon Bonds Example: What is the market price of a $50,000 zero coupon bond with 25 years to maturity that is currently yielding 6%?Example: What is the market price of a $50,000 zero coupon bond with 25 years to maturity that is currently yielding 6%?

70. CHAPTER 6 – Bond Valuation and Interest Rates6 - 70 Floating Rate & Real Return Bonds Floating rate bonds have a coupon that floats with some reference rate, such as the yield on T billsFloating rate bonds have a coupon that floats with some reference rate, such as the yield on T bills –Because the coupon floats, the market price will typically be close to the bond’s face value Real return bonds are issued by the Government of Canada to protect investors against unexpected inflationReal return bonds are issued by the Government of Canada to protect investors against unexpected inflation –Each period, the face value of the bond is grossed up by the inflation rate. The coupon is then paid on the grossed up face value.

71. CHAPTER 6 – Bond Valuation and Interest Rates6 - 71 Canada Savings Bonds A Canada Savings Bond (CSB) is a special type of bond issued by the Government of CanadaA Canada Savings Bond (CSB) is a special type of bond issued by the Government of Canada It is issued in two forms:It is issued in two forms: –Regular interest – interest is paid annually –Compound interest – interest compounds over the life of the bond CSBs are redeemable at any chartered bank in Canada at their face valueCSBs are redeemable at any chartered bank in Canada at their face value There is no secondary market for CSBsThere is no secondary market for CSBs

72. CHAPTER 6 – Bond Valuation and Interest Rates6 - 72 Summary and Conclusions In this chapter you have learned: –About the nature of bonds as an investment –How to value a bond using discounted cash flow concepts –About the determinants of interest rates and theories used to explain the term structure of interest rates

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