1. © 2003 The McGraw-Hill Companies, Inc. All rights reserved. Interest Rates and Bond Valuation Chapter Seven

2. 7.1 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Key Concepts and Skills  Know the important bond features and bond types  Understand bond values and why they fluctuate  Understand bond ratings and what they mean  Understand the impact of inflation on interest rates  Understand the term structure of interest rates and the determinants of bond yields

3. 7.2 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Chapter Outline  Bonds and Bond Valuation  More on Bond Features  Bond Ratings  Some Different Types of Bonds  Bond Markets  Inflation and Interest Rates  Determinants of Bond Yields

4. 7.3 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Bond Definitions 7.1  Bond – a long term debt obligation issued by a corporation  Par value (face value) – the amount of money that will be repaid at the maturity date of the bond  Coupon rate – the percentage of the bond’s face value that will be paid in interest every year  Coupon payment – the dollar value of the interest that is paid  Maturity date – the point in time when the bond will be redeemed by the issuer. The investor will receive cash equal to the face value of the bond.  Yield or Yield to maturity – also known as the Internal Rate of Return on the bond. It is the return to the investor that is derived from both the coupons received plus any capital gain or loss.

5. 7.4 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Treasury Bills  Treasury Bills (T Bills) are issued by both provincial & federal governments  Federal government T Bills are considered the risk-free security  T Bills are bought at a discount and mature at their face value. The difference between the purchase price and face value is the interest earned on the T Bill  To price a T Bill, use the following formula  Where: BEY = the bond equivalent yield n = the number of days until maturity B = the annual basis (365 days in Canada)

6. 7.5 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Treasury Bills – Example  Assume that you want to purchase a 91 day Treasury Bill with a face value of $1,000,000. If the BEY is 6%, what is the purchase price?

7. 7.6 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Present Value of Cash Flows as Rates Change  The market price of a bond is simply the present value of the bond’s future cash flows  Bonds have two types of future cash flows  Interest annuity (the stream of coupons)  Face value at maturity  When interest rates go up, the market value of the bond will go down  When interest rates go down, the market value of the bond will go up

8. 7.7 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. The Bond-Pricing Equation Where: $ Coupon = the periodic interest paid by the bond r = the yield-to-maturity for the bond t = the number of time periods to maturity

9. 7.8 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Valuing a Bond with Annual Coupons  Consider a bond with a $1,000 face value, a coupon rate of 10%, paid annually and 5 years to maturity. The yield to maturity is 11%. What is the market value of the bond? Formula Approach Calculator Approach 1,000FV 100PMT 5N 11I PV$963.04

10. 7.9 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Valuing a Bond with Annual Coupons  Now consider a second bond, also with a $1,000 face value and a 10% coupon, paid annually, but with 20 years to maturity and a yield to maturity of 8%. What is the price of this bond? Formula Approach Calculator Approach 1,000FV 100PMT 20N 8I PV$1,196.36

11. 7.10 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Graphical Relationship Between Price and Yield-to-Maturity The important concept to note is the inverse relationship between price & YTM Based on a 10 year, $1,000 bond with an 8% coupon

12. 7.11 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Bond Prices: Relationship Between Coupon and Yield  If YTM = coupon rate, then face value = market price  If YTM > coupon rate, then face value > market price  The bond is selling at a discount  Why?  If YTM < coupon rate, then face value < market price  The bond is selling at a premium  Why?

13. 7.12 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example – Semiannual Coupons  Most bonds in Canada make coupon payments semi-annually.  Suppose you have an 8% semi-annual pay bond with a face value of $1,000 that matures in 7 years. If the yield is 10%, what is the price of this bond?  Formula Approach Calculator Approach 1,000FV 80 ÷ 2 =PMT 7 x 2 =N 10 ÷ 2 =I PV$901.01

14. 7.13 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Interest Rate Risk  Price Risk  Change in price due to a change in interest rates  Long-term bonds have more price risk than short-term bonds  Bonds with low coupons have more price risk than bonds with high coupons  Reinvestment Rate Risk  Uncertainty concerning the interest rate at which future cash flows can be reinvested  Long-term bonds have more reinvestment rate risk than short-term bonds  Bonds with high coupons have more reinvestment rate risk than bonds with low coupons

15. 7.14 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Figure 7.2 – Interest Rate Risk and Time to Maturity This graph shows the impact on price as the YTM changes for both a one- year bond and a thirty-year bond. Both bonds have a $1,000 face value and a 10% coupon. Note how much more sensitive the long bond is to a change in the YTM.

16. 7.15 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Computing Yield-to-Maturity  Yield-to-maturity is the discount rate implied by the current bond price  For example, assume that a ten year, $1,000 bond with a 6% coupon, paid annually, is currently trading at $950 in the market. What is the bond’s yield-to-maturity (YTM)? Formula Approach  The YTM is the discount rate that makes the equality true in the bond pricing formula.  Solve for it using the function keys on the calculator or trial & error if using algebra Calculator Approach 1,000FV 60PMT 950 +/-PV 10N I6.7021%

17. 7.16 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example – Finding the YTM  Consider another bond with a 10% annual coupon rate, 15 years to maturity and a face value of $1000. The current price is $928.09.  Will the yield-to-maturity be more or less than 10%? Calculator Approach 1,000FV 100PMT 928.09 +/-PV 15N I11%

18. 7.17 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Understanding YTM  The YTM can always be decomposed into its two component parts. These are:  Coupon Yield  Capital gain or loss  Assume that you buy a 10 year, $1,000 bond with an 8% coupon, priced to yield 6%.  Step #1: First calculate the price of the bond. Calculator Approach 1,000FV 80PMT 10N 6I PV$1,147.20

19. 7.18 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Understanding YTM  In Step #2, we calculate the new price after one year has passed, assuming all else remains equal.  Step #3: Calculate the coupon yield by dividing the annual coupon payment by the beginning price Calculator Approach 1,000FV 80PMT 9N 6I PV$1,136.03

20. 7.19 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Understanding YTM  Step #4: Calculate the capital gain or loss  Step #5: Calculate the Yield to Maturity

21. 7.20 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. YTM with Semiannual Coupons  Suppose a 20 year, $1,000 bond with a 10% coupon, paid semi-annually, is selling for $1197.93.  Is the YTM more or less than 10%?  What is the semiannual coupon payment?  How many periods are there? Calculator Approach 1,000FV 100 ÷ 2 =PMT 1,197.93 +/-PV 20 x 2 =N I4 x 2 = 8% Since the coupon is paid twice a year, the rate you calculate is a semi-annual yield. Double it to obtain the quoted YTM.

22. 7.21 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Bond Pricing Theorems  Bonds of similar risk (and maturity) will be priced to yield about the same return, regardless of the coupon rate  If you know the price of one bond, you can estimate its YTM and use that to find the price of the second bond  This is a useful concept that can be transferred to valuing assets other than bonds

23. 7.22 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Bond Prices with a Spreadsheet  There is a specific formula for finding bond prices on a spreadsheet  PRICE(Settlement,Maturity,Rate,Yld,Redemption,Frequency,Basis)  YIELD(Settlement,Maturity,Rate,Pr,Redemption, Frequency,Basis)  Settlement and maturity need to be actual dates  The redemption and Pr need to given as % of par value  Click on the Excel icon for an example

24. 7.23 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Differences Between Debt and Equity 7.2  Debt  Not an ownership interest  Bondholders do not have voting rights  Interest is considered a cost of doing business and is tax deductible  Bondholders have legal recourse if interest or principal payments are missed  Excess debt can lead to financial distress and bankruptcy  Equity  Ownership interest  Common shareholders vote for the board of directors and other issues  Dividends are not considered a cost of doing business and are not tax deductible  Dividends are not a liability of the firm and shareholders have no legal recourse if dividends are not paid  An all equity firm can not go bankrupt

25. 7.24 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. The Bond Indenture  Contract between the company (the issuer of the bond) and the bondholders and includes  The basic terms of the bonds  The total amount of bonds issued  A description of property used as security, if applicable  Sinking fund provisions  Call provisions  Details of protective covenants

26. 7.25 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Bond Classifications  Registered vs. Bearer Bonds  Registered – can only be sold by the registered owner  Bearer – similar to cash; possession implies ownership  Security  Collateral – assets pledged as a secondary source of repayment  Mortgage – secured by real property, normally land or buildings  Debentures – unsecured debt with original maturity of 10 years or more  Notes – unsecured debt with original maturity less than 10 years  Seniority  Senior versus Junior debt – refers to preference in position with respect to other lenders (Senior debt is paid first; junior debt paid last)  Subordinated debt – indicates that it has a lower priority than other, more senior debt

27. 7.26 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Bond Classifications Continued  Repayment  Sinking Fund – Account managed by the bond trustee for early bond redemption. Reduces default risk & improves marketability.  Call Provision – allows the company to repurchase all or a portion of the issue prior to the original maturity  Call premium – amount above the face value the borrower agrees to pay, should they call the bond before its original maturity  Deferred call -  Call protected -  Canada plus call – Protects the investor against a call by providing compensation equal to the foregone interest, should a call occur The issuer usually cannot call the bond during the years immediately after the issue date.

28. 7.27 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Covenants  Protective Covenants  Negative covenants – things the borrower agrees to not do  Agrees to limit the amount of dividends paid  Agree to not pledge assets to other lenders  Agree to not merge with, sell to or acquire another firm  Agree to not buy new capital assets above $x in value  Agree to not issue new debt  Positive covenants – things the borrower agrees to do  Maintain a minimum current ratio  Provide audited financial statements  Maintain collateral in good condition

29. 7.28 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Bond Characteristics and Required Returns  The coupon rate depends on the risk characteristics of the bond when issued  Which bonds will have the higher coupon, all else equal?  Secured versus unsecured debt?  Subordinated debenture versus senior debt?  A bond with a sinking fund versus one without?  A callable bond versus a non-callable bond?

30. 7.29 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Credit Ratings: Investment Grade Credit RiskMoody’sStandard & Poors FitchDuff & Phelps Highest quality AaaAAA High quality (very strong) AaAA Upper Medium (strong) AAAA Medium grade BaaBBB

31. 7.30 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Credit Ratings: Speculative or Junk Debt Credit RiskMoody’sStandard & Poors FitchDuff & Phelps Lower Medium BaBB Low grade (Speculative) BBBB Poor QualityCaaCCC Most speculative CaCC

32. 7.31 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Standard & Poor's Bond Rating Scale  AAA - An obligor rated 'AAA' has EXTREMELY STRONG capacity to meet its financial commitments.  AA - An obligor rated 'AA' has VERY STRONG capacity to meet its financial commitments. It differs from the highest rated obligors only in small degree.  A - An obligor rated 'A' has STRONG capacity to meet its financial commitments but is somewhat more susceptible to the adverse effects of changes in circumstances and economic conditions than obligors in higher-rated categories.  BBB - An obligor rated 'BBB' has ADEQUATE capacity to meet its financial commitments. However, adverse economic conditions or changing circumstances are more likely to lead to a weakened capacity of the obligor to meet its financial commitments.  BB - An obligor rated 'BB' is LESS VULNERABLE in the near term than other lower-rated obligors. However, it faces major ongoing uncertainties and exposure to adverse business, financial, or economic conditions which could lead to the obligor's inadequate capacity to meet its financial commitments.  B - An obligor rated 'B' is MORE VULNERABLE than the obligors rated 'BB', but the obligor currently has the capacity to meet its financial commitments. Adverse business, financial, or economic conditions will likely impair the obligor's capacity or willingness to meet its financial commitments.  CCC - An obligor rated 'CCC' is CURRENTLY VULNERABLE, and is dependent upon favorable business, financial, and economic conditions to meet its financial commitments.  CC - An obligor rated 'CC' is CURRENTLY HIGHLY VULNERABLE.  R - An obligor rated 'R' is under regulatory supervision owing to its financial condition. During the pendency of the regulatory supervision the regulators may have the power to favor one class of obligations over others or pay some obligations and not others. Please see Standard & Poor's issue credit ratings for a more detailed description of the effects of regulatory supervision on specific issues or classes of obligations.  SD and D - An obligor rated 'SD' (Selective Default) or 'D' has failed to pay one or more of its financial obligations (rated or unrated) when it came due. A 'D' rating is assigned when Standard & Poor's believes that the default will be a general default and that the obligor will fail to pay all or substantially all of its obligations as they come due. An 'SD' rating is assigned when Standard & Poor's believes that the obligor has selectively defaulted on a specific issue or class of obligations but it will continue to meet its payment obligations on other issues or classes of obligations in a timely manner. Please see Standard & Poor's issue credit ratings for a more detailed description of the effects of a default on specific issues or classes of obligations.  Note: Obligors rated 'BB', 'B', 'CCC', and 'CC' are regarded as having significant speculative characteristics. 'BB' indicates the least degree of speculation and 'CC' the highest. While such obligors will likely have some quality and protective characteristics, these may be outweighed by large uncertainties or major exposures to adverse conditions. Plus (+) or minus (?): Ratings from 'AA' to 'CCC' may be modified by the addition of a plus or minus sign to show relative standing within the major rating categories.  Source: Standard & Poors

33. 7.32 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Stripped or Zero-Coupon Bonds 7.4  Make no periodic interest payments (coupon rate = 0%)  All cash flows occur on the maturity date  Sometimes called zeroes, or deep discount bonds  Bondholder must pay taxes on accrued interest every year, even though no interest is received (thus are best held in a tax- deferred account, such as an RRSP)  Market price is the PV of the face value at maturity

34. 7.33 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Zero Coupon or Stripped Bonds  Assume that you want to purchase a 30 year stripped bond with a $100,000 face value. If the appropriate YTM is 8%, how much will you have to pay today to buy this bond? Calculator Approach 100,000FV 0PMT 30N 8I PV$9,937.73

35. 7.34 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Floating Rate Bonds  Coupon rate floats depending on some index value  There is less price risk with floating rate bonds  The coupon floats, so it is less likely to differ substantially from the yield-to-maturity  Coupons may have a “collar” – the rate cannot go above a specified “ceiling” or below a specified “floor”

36. 7.35 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Other Bond Types  Disaster (CAT) bonds – payout to the investor is dependent on the occurrence of some major catastrophic event  Income bonds – coupons are tied to firm profitability  Convertible bonds – bonds may be converted into common stock  Real Return bonds – the bond is adjusted for inflation  Put bond (retractable bond) – the investor may sell the bond back to the issuer at a fixed price  LYON (Liquid Yield Option Note) - created by Merrill Lynch. Bond is a callable, puttable, convertible, zero coupon, subordinated note

37. 7.36 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Bond Markets 7.5  Primarily over-the-counter transactions with dealers connected electronically  Extremely large number of bond issues, but generally low daily volume in single issues  Makes getting up-to-date prices difficult, particularly on small corporate issues. One alternative for the retail investor is http://www.cbidmarkets.com  Treasury securities are an exception

38. 7.37 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Bond Quotations  From the Financial Post, October 20, 2005 Canada 10.000 Jun 01/08 115.94 3.55  The issuer is the Government of Canada  The coupon rate is 10% (assumed to be semiannual)  The maturity date is June 1, 2008  The quoted price can be interpreted as either the price per $100 of face value or as a percentage of face value  The yield to maturity is 3.55% Issuer Coupon MaturityPriceYTM

39. 7.38 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Inflation and Interest Rates 7.6  Nominal rate of interest – quoted rate of interest, includes compensation for deferring consumption and expected inflation  Real rate of interest – compensation for deferring consumption  Expected Inflation – the expected fall in purchasing power of the dollar, due to rising prices

40. 7.39 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. The Fisher Effect  The Fisher Effect defines the relationship between real rates, nominal rates and inflation  Exact relationship  Where:  R Real = the real interest rate  R Nominal = the nominal interest rate  Expected Inflation = the expected future inflation rate  Approximation of the above relationship is:

41. 7.40 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Example – Fisher Effect  If we require a 4% real return and we expect inflation to be 6%, what is the nominal rate?  Therefore, the nominal rate is 10.24%  If both inflation and the real return are low, we can safely use the approximation, which would give us a nominal rate of 10%

42. 7.41 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Term Structure of Interest Rates 7.7  Term structure is the relationship between time to maturity and yield-to-maturity, all else equal  The term structure is always derived using government bonds, as they are the only issuer with sufficient bonds in all maturities with the identical default risk (zero).  The terms yield curve and term structure may be used interchangeably. Both depict a graphical representation of the relationship between term and yield  The term structure typically has one of four shapes  Upward-sloping - long-term yields are higher than short-term yields  Downward-sloping - long-term yields are lower than short-term yields  Flat – yields of all maturities are the same  Humped – yields rise and then fall

43. 7.42 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Theories of the Term Structure  Unbiased Expectations Theory – the long rate is the geometric average of expected future short rates  Allows us to calculate an implied forward rate, which is the markets consensus estimate of a future short rate 0 12 5% 6% ?% Implied Forward Rate The example shows a one year spot rate of 5% and a two year spot rate of 6%. What is the market predicting for the one year rate, one year from today?

44. 7.43 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. To solve for the implied forward rate, we solve the following equation for R 1,2 Where: R 0,2 = the rate starting at time period zero and ending at time period two R 0, 1 = the rate starting at time period zero and ending at time period one R 1,2 = the implied forward rate, which is the rate starting at time period one and ending at time period two Unbiased Expectations Theory of the Term Structure

45. 7.44 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Unbiased Expectations Theory of the Term Structure  The implied forward rate is the market consensus estimate of the short interest rate that will prevail at some future time period  As the market receives new information, the consensus estimate will be updated in a continuous fashion, as market participants buy and sell based on their expectations  The unbiased expectations theory of the term structure tells us that:  An upward sloping term structure suggests future short rates will be higher than current short rates  A downward sloping term structure suggests that future short rates will be lower than current short rates

46. 7.45 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Theories of the Term Structure  Liquidity Preference Theory  The observed term structure includes a liquidity premium for less liquid bonds  Long bonds are less liquid than short bonds  Investors prefer liquidity; therefore they are willing to accept a lower yield for more liquid bonds  Issuers are willing to pay a liquidity premium for longer bonds, since they incur lower issue costs  Segmented Markets/Preferred Habitat Theory  Market participants operate in only one segment of the term structure, due to institutional restrictions, asset/liability matching considerations, etc.  Probably has little validity in today’s world, given the existence of derivatives

47. 7.46 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Figure 7.4 – Upward-Sloping Yield Curve

48. 7.47 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Figure 7.4 – Downward-Sloping Yield Curve

49. 7.48 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Figure 7.5 – Government of Canada Yield Curve November 29, 2002

50. 7.49 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Factors Affecting Required Return  Default risk – the probability that the issuer will not be able to repay the bond as contractually obligated to do  Liquidity premium – liquidity refers to the ability to:  Convert to cash  At or near face value  Short bonds with high coupons that are more frequently traded have greater liquidity & hence a lower required return  Call features – since a call feature allows the bond to be redeemed early, it increases risk to the bond investor  Anything else that affects the risk of the cash flows to the bondholders, will affect the required returns

51. 7.50 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Quick Quiz  How do you find the value of a bond and why do bond prices change?  What is a bond indenture and what are some of the important features?  What are bond ratings and why are they important?  How does inflation affect interest rates?  What is the term structure of interest rates?  What factors determine the required return on bonds?

52. 7.51 Copyright © 2005 McGraw-Hill Ryerson Limited. All rights reserved. Summary 7.8  You should know:  How to price a bond or find the yield  Bond prices move inversely with interest rates  Bonds have a variety of features that are spelled out in the indenture  Bonds are rated based on their default risk  Most bonds trade OTC  Fisher effect links interest rates and inflation  Term structure of interest rates shows the relationship between interest rates and maturity