1. T7.1 Chapter Outline Chapter 7 Interest Rates and Bond Valuation Chapter Organization 7.1Bonds and Bond Valuation 7.2More on Bond Features 7.3Bond Ratings 7.4Some Different Types of Bonds 7.5Bond Markets 7.6Inflation and Interest Rates 7.7Determinants of Bond Yields 7.8Summary and Conclusions CLICK MOUSE OR HIT SPACEBAR TO ADVANCE Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd.

2. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 2 T7.2 Bond Features Bond - evidence of debt issued by a corporation or a governmental body. A bond represents a loan made by investors to the issuer. In return for his/her money, the investor receives a legaI claim on future cash flows of the borrower. The issuer promises to: Make regular coupon payments every period until the bond matures, and Pay the face/par/maturity value of the bond when it matures. Default - since the above mentioned promises are contractual obligations, an issuer who fails to keep them is subject to legal action on behalf of the lenders (bondholders).

3. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 3 If a bond has five years to maturity, an $80 annual coupon, and a $1000 face value, its cash flows would look like this: Time012345 Coupons$80$80$80$80$80 Face Value$ 1000 Market Price $____ How much is this bond worth? It depends on the level of current market interest rates. If the going rate on bonds like this one is 10%, then this bond has a market value of $924.18. T7.2 Bond Features (concluded)

4. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 4 A bond has five years to maturity, an $80 annual coupon, and a $1000 face value, its cash flows would look like this: Time012345 Coupons$80$80$80$80$80 Face Value$ 1000 Coupons - the stated interest payments made on the bond Face Value - (Par Value) - the principal amount of a bond that is repaid at the end of the term Coupon rate - annual coupon divided by the face value Maturity - specified date at which the principal amount is paid T7.2 Bond Features (concluded)

5. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 5 A bond has five years to maturity, an $80 annual coupon, and a $1000 face value, its cash flows would look like this: Time012345 Coupons$80$80$80$80$80 Face Value$ 1000 Market Value = ‘s PV of the coupon payments (annuity) + PV of the principal (PV of a single cash flow) T7.2 Bond Value

6. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 6 If a bond has five years to maturity, an $80 annual coupon, and a $1000 face value, its cash flows would look like this: Time012345 Coupons$80$80$80$80$80 Face Value$ 1000 Market Value with r @ 10% = ? PV of the coupon payments (annuity) - $303.26 PV of the principal (PV of a single cash flow) - $620.92 =‘s $924.18 T7.2 Bond Value

7. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 7 T7.3 Bond Rates and Yields Consider again our example bond. It sells for $924.18, pays an annual coupon of $80, and it matures in 5 years. It has a face value of $1000. What are its coupon rate, current yield, and yield to maturity (YTM)?  1.The coupon rate (or just “coupon”) is the annual dollar coupon as a percentage of the face value: Coupon rate = $80 /$1000 = 8%  2.The current yield is the annual coupon divided by the current market price of the bond: Current yield = $80 / 924.18 = 8.66%

8. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 8 A bond has five years to maturity, an $80 annual coupon, and a $1000 face value, its cash flows would look like this: Time012345 Coupons$80$80$80$80$80 Face Value$ 1000 YTM - the market interest rate that equates a bond’s present value of interest payments and principal repayment with its price If you paid $924.18 for this bond and received the above cash flows - what is the YTM? T7.2 Bond Yield to Maturity - YTM

9. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 9 T7.3 Bond Rates and Yields (concluded) 3.The yield to maturity (or “YTM”) is the rate that makes the market price of the bond equal to the present value of its future cash flows. It is the unknown r in the equation below: $924.18 = $80  [1 - 1/(1 + r) 5 ]/r + $1000/(1 + r) 5 The only way to find the YTM is by trial and error: a.Try 8%: $80  [1 - 1/(1.08) 5 ]/.08 + $1000/(1.08) 5 = $1000 b.Try 9%: $80  [1 - 1/(1.09) 5 ]/.09 + $1000/(1.09) 5 = $961.10 c.Try 10%: $80  [(1 - 1/(1.10) 5 ]/.10 + $1000/(1.10) 5 = $924.18 So, the yield to maturity is 10%.

10. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 10 Bond Values and YTM Let’s understand what has happened before going much further........ We have a 5 year bond that with a coupon of $80 Face Value is $1000 - principal repayment in 5 years time will be $1000 Interest rates for 5 year bonds were about 8% when the bond was issued - let’s assume this - so the bond would have been issued at $1000 interest rates change - 5 year interest rates move up to the 10% level The value of this bond has declined - because there are competing products in the market place paying 10% interest when this bond only pays 8% - to buy this bond and still earn a 10% YTM I should only pay $924.18 What should we conclude? - bond values move up and down in response to financial events - in this case a change in interest rates

11. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 11 Bond Values and Yields - what is the relationship? there is a relationship between the value of the bond and rates of return (YTM) in market equilibrium  when interest rates change - we suddenly do not have market equilibrium - to achieve equilibrium the values of existing bonds in the marketplace need to shift to reflect the new financial reality!  If interest rates move up - bond values decline  If interest rates move down - bond values increase.....as the bond market strives for equilibrium in the face of changes in the financial/business marketplace

12. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 12 T7.4 Valuing a Bond Let’s do another one. Assume you have the following information. Seagrams bonds have a $1000 face value. The promised annual coupon is $100. The bonds mature in 20 years. The market’s required return on similar bonds is 10% What is the bond’s value?  1. Calculate the present value of the face value = $1000  [1/1.10 20 ] = $1000 .14864 = $148.64  2. Calculate the present value of the coupon payments = $100  [1 - (1/1.10 20 )]/.10 = $100  8.5136 = $851.36  3. The value of each bond = $148.64 + 851.36 = $1000

13. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 13 T7.5 Example: A Discount Bond Assume you have the following information. Seagrams bonds have a $1000 face value The promised annual coupon is $100 The bonds mature in 20 years The market’s required return on similar bonds is 12%  1. Calculate the present value of the face value = $1000  [1/1.12 20 ] = $1000 .10366 = $103.66  2. Calculate the present value of the coupon payments = $100  [1 - (1/1.12 20 )]/.12 = $100  7.4694 = $746.94  3. The value of each bond = $103.66 + 746.94 = $850.60 Why is this bond selling at a discount to its face value?

14. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 14 T7.6 Example: A Premium Bond Now you have the following information. Seagrams bonds have a $1000 face value The promised annual coupon is $100 The bonds mature in 20 years The market’s required return on similar bonds is 8%  1. Calculate the present value of the face value = $1000  [1/1.08 20 ] = $1000 .21455 = $214.55  2. Calculate the present value of the coupon payments = $100  [1 - (1/1.08 20 )]/.08 = $100  9.8181 = $981.81  3. The value of each bond = $214.55 + 981.81 = $1,196.36 Why is this bond selling at a premium to par?

15. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 15 T7.7 Bond Price Sensitivity to YTM 4%6%8%10% 12% 14%16% $1,800 $1,600 $1,400 $1,200 $1,000 $ 800 $ 600 Bond price Yield to maturity, YTM Coupon = $100 20 years to maturity $1,000 face value Key Insight: Bond prices and YTMs are inversely related.

16. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 16 T7.8 The Bond Pricing Equation Bond Value = Present Value of the Coupons + Present Value of the Face Value = C  [1 - 1/(1 + r ) t ]/r + F  1/(1 + r ) t where:C = Coupon paid each period r = Rate per period t = Number of periods F = Bond’s face value

17. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 17 T7.9 Interest Rate Risk and Time to Maturity (Figure 7.2)

18. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 18 Interest Rate Risk the ‘risk that arises for bond owners from fluctuating interest rates (market yields)’  the risk or sensitivity to interest rate changes is a function of time to maturity - the longer the time to maturity the greater the interest rate risk coupon rate - the lower the coupon rate the greater the interest rate risk  time to maturity - longer term bonds have greater interest rate risk due to the timing of the the principal repayment - if it occurs in 30 years a small interest rate change can have a major impact on the PV of that cash flow vs if the principal is due in one year  coupon rate - for a given YTM a higher coupon bond has larger cash flows earlier than another bond with the same YTM but lower coupon payments (more of the YTM is made up of the face amount to be received at maturity)

19. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 19 T7.10 Summary of Bond Valuation (Table 7.1) I.Finding the value of a bond Bond value = C [1 - 1/(1 + r ) t ]/r + F/(1 + r) t where:C = Coupon paid each period r = Rate per period t = Number of periods F = Bond’s face value II.Finding the yield on a bond Given a bond value, coupon, time to maturity, and face value, it is possible to find the implicit discount rate, or yield to maturity, by trial and error only. To do this, try different discount rates until the calculated bond value equals the given bond value. Remember that increasing the rate decreases the bond value. 

20. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 20 T7.11 Bond Pricing Theorems The following statements about bond pricing are always true.  1.Bond prices and market interest rates move in opposite directions.  2.When a bond’s coupon rate is (greater than / equal to / less than) the market’s required return, the bond’s market value will be (greater than / equal to / less than) its par value.  3.Given two bonds identical but for maturity, the price of the longer-term bond will change more (in percentage terms) than that of the shorter-term bond, for a given change in market interest rates.  4.Given two bonds identical but for coupon, the price of the lower-coupon bond will change more (in percentage terms) than that of the higher-coupon bond, for a given change in market interest rates.

21. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 21 Bond characteristics & Features Debt vs. Equity  debt is not an ownership interest in the firm - lenders or debt holders stand in line ahead of common stock holders in terms of a call on the firms cash flow interest on debt must be paid before dividend or in the event of bankruptcy debt holders are paid before any distribution is made to equity holders  interest on debt is tax deductible - it is considered a cost of doing business - dividends paid to stockholders are not tax deductible  unpaid debt is a liability of the firm - if it is not paid, creditors can legally claim the assets possibly leading to bankruptcy the ideal combination is a debt security that is really equity in that the firm receives the tax benefits of debt and the bankruptcy benefits of equity.

22. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 22 Bond Characteristics cont’d Bonds vs Debentures  a bond is a form of secured debt - certain assets are pledged as security  a debenture is a form of unsecured debt - specific assets are not pledged as security However, typically the term ‘bond’ is used for all forms of debt Public vs Private Debt  Public debt is offered to the public while private debt is where the debt is placed with a single lender - often a pension fund, insurance firm, etc.

23. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 23 T7.12 Features of a May Department Stores Bond Term Explanation Amount of issue$200 millionThe company issued $200 million worth of bonds. Date of issue 8/4/94The bonds were sold on 8/4/94. Maturity 8/1/24The principal will be paid 30 years after the issue date. Face Value$1,000The denomination of the bonds is $1,000. Annual coupon 8.375Each bondholder will receive $83.75 per bond per year (8.375% of the face value). Offer price 100The offer price will be 100% of the $1,000 face value per bond.

24. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 24 T7.12 Features of a May Department Stores Bond (concluded) Term Explanation Coupon payment dates2/1, 8/1Coupons of $83.75/2 = $41.875 will be paid on these dates. SecurityNoneThe bonds are debentures. Sinking fundAnnual The firm will make annual payments beginning 8/1/05toward the sinking fund. Call provisionNot callable The bonds have a deferred call feature. before 8/1/04(See Appendix 7C on Canada plus calls.) Call price104.188 initially,After 8/1/04, the company can buy back declining to 100the bonds for $1,041.88 per bond, declining to $1,000 on 8/1/14. RatingMoody’s A2This is one of Moody’s higher ratings. The bonds have a low probability of default.

25. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 25 7.13 The Bond Indenture The Bond Indenture The bond indenture is a three-party contract between the bond issuer, the bondholders, and the trustee. The trustee is hired by the issuer to protect the bondholders’ interests. The indenture includes  The basic terms of the bond issue  The total amount of bonds issued  A description of the security  The repayment arrangements  The call provisions  Details of the protective covenants

26. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 26 Additional Bond Features registered vs bearer security  bond  debenture  collateral  mortgage securities seniority  senior  junior  subordinated debt

27. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 27 Additional Bond Features Repayment  repaid at maturity  early repayment sinking fund - an account managed by a bond trustee for the purpose of repaying the bonds - the trustee uses the funds and purchases the required amounts in the open market or calling in a fraction of the outstanding bonds. value of a sinking fund to investors - reduces the risk that the company will be unable to repay the principal at maturity thus improving the marketability of the bonds  call provisions  protective covenants part of the loan agreement that limits actions of the borrowing firm - e.g. restrictions on dividends and sales of major assets

28. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 28 T7.14 Bond Ratings Low Quality, speculative, Investment-Quality Bond Ratings and/or “Junk” High GradeMedium GradeLow GradeVery Low Grade Moody’sAaaAaABaaBaBCaaCaCD DBRS (S&P)AAAAAABBBBBBCCCCCCD Moody’sDBRS AaaAAADebt rated Aaa and AAA has the highest rating. Capacity to pay interest and principal is extremely strong. AaAADebt rated Aa and AA has a very strong capacity to pay interest and repay principal. Together with the highest rating, this group comprises the high-grade bond class. AADebt rated A has a strong capacity to pay interest and repay principal, although it is somewhat more susceptible to the adverse effectsof changes in circumstances and economic conditions than debt in high rated categories.

29. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 29 T7.14 Bond Ratings (concluded) BaaBBBDebt rated Baa and BBB is regarded as having an adequate capacity to pay interest and repay principal. Whereas it normally exhibits adequate protection parameters, adverse economic conditions or changing circumstances are more likely to lead to a weakened capacity to pay interest and repay principal for debt in this category than in higher rated categories. These bonds are medium-grade obligations. Ba, BBB, BDebt rated in these categories is regarded, on balance, as Ca, C CC, Cpredominantly speculative with respect to capacity to pay interest and repay principal in accordance with the terms of the obligation. BB and Ba indicate the lowest degree of speculation, and CC and Ca the highest degree of speculation. Although such debt will likely have some quality and protective characteristics, these are out-weighed by large uncertainties or major risk exposures to adverse conditions. Some issues may be in default. DDDebt rated D is in default, and payment of interest and/or repayment of principal is in arrears

30. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 30 Different Types of Bonds Stripped bonds - a bond that makes not coupon payments and is initially priced at a deep discount  because all of the YTM is in the form of the principal repayment  interest is both deductible by the issuer and must be claimed by the investor - even though there is no interest coupon payments per se....it is imputed from discount Floating Rate Bonds (floaters) - the coupon payments are adjustable (not fixed like a traditional bond)  were introduced by issuers to control the risk of price fluctuations due to interest rate shifts. Income bond - coupon payments are dependent on company income - only if that income is sufficient

31. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 31 Different Types of Bonds Cont’d Real Return Bonds - coupons and principal are indexed to inflation to provide a stated real return Convertible Bonds - can be ‘converted’ for a fixed number of shares of the issuer’s stock - anytime before maturity and at the holder’s option - are considered a ‘hybrid’ of debt and equity. The convertible aspect provides the investor with additional incentive to purchase the bond Retractable Bonds or ‘put’ bonds - allows the holder to ‘put’ the bonds back to the issuer or force the issuer to buy the bonds back at a stated price - this effectively establishes a floor price for the bonds......issuers will combine various features at any given point in time to encourage investors to buy a new bond issue!

32. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 32 Bond Markets OTC (over the counter) market with dealers connected electronically the bond market in trading volume is many times larger than the trading volume in stocks  the U.S. Treasury market is the largest securities market in the world in terms of trading volume Bond Price Reporting  unlike stocks that are traded on an exchange - bonds do not have that price ‘transparency’ - bonds prices are indications only and are typically provided by bond dealers (not by the TSE for example)  the Monday edition of the Globe & Mail is one of the best sources for bond information

33. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 33 Inflation and Interest Rates Real vs Nominal Rates of Return  nominal rates - interest rates or rates of return that have not been adjusted for inflation  real rates - interest rates or rates of return that have been adjusted for inflation  nominal rate on an investment is the % change in the number of dollars you have  real rate on an investment is the % change in how much you can purchase with your dollars or the % change in buying power Fisher Effect ( or theory)  R = (r+h) +( r*h) where R is the Nominal rate, r is the real rate and h is the rate of inflation

34. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 34 T7.16 Inflation and Returns Key issues:  What is the difference between a real return and a nominal return?  How can we convert from one to the other? Example: Suppose we have $1000, and Coke costs $2.00 per six pack. We can buy 500 six packs. Now suppose the rate of inflation is 5%, so that the price rises to $2.10 in one year. We invest the $1000 and it grows to $1100 in one year. What’s our return in dollars? In six packs?

35. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 35 T7.16 Inflation and Returns (continued) A.Dollars. Our return is ($1,100 - $1,000)/$1,000 = $100/$1,000 =.10. The percentage increase in our investment is 10%; our return is 10%. B.Six packs. We can buy $1,100/$2.10 = 523.81 six packs, so our return is (523.81 - 500)/500 = 23.81/500 = 4.76% The percentage increase in the amount of coke is 4.76%; our return is 4.76%.

36. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 36 T7.16 Inflation and Returns (continued) Real versus nominal returns: Your nominal return is the percentage change in the amount of money you have. Your real return is the percentage change in the amount of stuff you can actually buy.

37. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 37 T7.16 Inflation and Returns (concluded) The relationship between real and nominal returns is described by the Fisher Effect. Let: R=the nominal return r=the real return h=the inflation rate According to the Fisher Effect: 1 + R = (1 + r)  (1 + h) From the example, the real return is 4.76%; the nominal return is 10%, and the inflation rate is 5%: (1 + R) = 1.10 (1 + r)  (1 + h) = 1.0476 x 1.05 = 1.10

38. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 38 Factors Affecting Bond Yields Key Issue: What factors affect observed bond yields? The real rate of interest Expected future inflation Interest rate risk....term structure of interest rates Default risk premium.... Unique aspects of the issue Taxability premium....taxation issues Liquidity premium

39. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 39 T7.17 U.S. Interest Rates: 1800-1997

40. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 40 Term Structure of Interest Rates Term structure of interest rates is the relationship between short and long term interest rates or ‘the relationship between nominal interest rates on default- free, pure discount securities and the time to maturity What determines the shape of the term structure?  Real rate of interest - pure time value of money  rate of inflation  interest rate risk

41. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 41 Term Structure of Interest Rates Real rate of interest - basic component underlying every interest rate - it is the ‘economic rent’ or compensation that investors demand for forgoing the use of their money.  Tends to influence the overall level of rates moreso than the shape of the structure Rate of Inflation - investor demand extra compensation or an ‘inflation premium’ for the expected erosion of the value of their investment from inflation -  the key here is the expected inflation - if inflation is expected to be higher in the future then long term rates will reflect this and be higher than short term rates Interest Rate Risk - risk of interest rates changing and the resulting impact on the value of the security  risk is greater over the longer term so this risk increases with the length of maturity

42. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 42 T7.18 The Term Structure of Interest Rates (Fig. 7.6)

43. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 43 T7.18 The Term Structure of Interest Rates (Fig. 7.6)

44. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 44 Factors Affecting Bond Yields Other factors in addition to the Term Structure of Interest Rates Credit risk & the default risk premium if the risk of default is perceived to be higher - investors will demand higher compensation - importance of bond ratings Taxation - is the return taxable and how is it taxed  U.S. Vs Canada  interest and capital gains Liquidity & liquidity premium - investors like ‘liquid’ issues where there is high levels of trading of that issue - provides confidence - low liquidity leads to higher yields - liquidity premium demanded by investors increases

45. Irwin/McGraw-Hillcopyright © 2002 McGraw-Hill Ryerson, Ltd Slide 45 Yield Curve the ‘yield curve’ is a reflection of the term structure of interest rates the ‘Canada Yield Curve’ reflecting Govt. of Canada bond yields is essentially the same Corporate yield curves - however bring in these other factors affecting yields - e.g. default risk premium, etc.....what does the yield curve look like today?