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

7. 1 Key Concepts and Skills • Know the important bond features and bond 7. 1 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 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 2 Chapter Outline • • Bonds and Bond Valuation More on Bond Features 7. 2 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 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 3 Bond Definitions 7. 1 • Bond – interest-only loan • Par value 7. 3 Bond Definitions 7. 1 • Bond – interest-only loan • Par value (face value) – principal amount of a bond • Coupon rate – annual coupon pay/face value • Coupon payment – interest payment • Maturity date – date when face value is paid • Yield or Yield to maturity – interest rate: when bond price is equal to the bond’s PV Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 4 Present Value of Cash Flows as Rates Change • Bond Value = 7. 4 Present Value of Cash Flows as Rates Change • Bond Value = PV of coupons + PV of par • Bond Value = PV annuity + PV of lump sum • Remember, as interest rates increase the PV’s decrease • So, as interest rates increase, bond prices decrease and vice versa Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 5 Valuing a Discount Bond with Annual Coupons • Consider a bond with 7. 5 Valuing a Discount Bond with Annual Coupons • Consider a bond with a coupon rate of 10% and coupons paid annually. The par value is $1000 and the bond has 5 years to maturity. The yield to maturity is 11%. What is the value of the bond? – Using the formula: • B = PV of annuity + PV of lump sum • B = 100[1 – 1/(1. 11)5] /. 11 + 1000 / (1. 11)5 • B = 369. 59 + 593. 45 = 963. 04 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 6 Valuing a Premium Bond with Annual Coupons • Suppose you are looking 7. 6 Valuing a Premium Bond with Annual Coupons • Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are 20 years to maturity and the yield to maturity is 8%. What is the price of this bond? – Using the formula: • B = PV of annuity + PV of lump sum • B = 100[1 – 1/(1. 08)20] /. 08 + 1000 / (1. 08)20 • B = 981. 81 + 214. 55 = 1196. 36 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 7 Graphical Relationship Between Price and Yield-to-Maturity Copyright © 2005 Mc. Graw-Hill Ryerson 7. 7 Graphical Relationship Between Price and Yield-to-Maturity Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 8 Bond Prices: Relationship Between Coupon and Yield • If YTM = coupon 7. 8 Bond Prices: Relationship Between Coupon and Yield • If YTM = coupon rate, then par value = bond price (return = “dividend yield” + capital gains yield) • If YTM > coupon rate, then par value > bond price – Why? – Selling at a discount, called a discount bond • If YTM < coupon rate, then par value < bond price – Why? – Selling at a premium, called a premium bond Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 9 The Bond-Pricing Equation Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights 7. 9 The Bond-Pricing Equation Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 10 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved. 7. 10 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 11 Example – Semiannual Coupons • Most bonds in Canada make coupon payments 7. 11 Example – Semiannual Coupons • Most bonds in Canada make coupon payments semiannually. • Suppose you have a 8% semiannual-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? – The bondholder receives a payment of $40 every six months (a total of $80 per year) – The market automatically assumes that the yield is compounded semiannually – The number of semiannual periods is 14 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 12 Example – Semiannual Coupons continued Copyright © 2005 Mc. Graw-Hill Ryerson Limited. 7. 12 Example – Semiannual Coupons continued Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 13 Interest Rate Risk • Price Risk – Change in price due to 7. 13 Interest Rate Risk • Price Risk – Change in price due to changes in interest rates – Long-term bonds have more price risk than shortterm bonds • Reinvestment Rate Risk – Uncertainty concerning the interest rates at which cash flows can be reinvested – Short-term bonds have more reinvestment rate risk than long-term bonds Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 14 Figure 7. 2 – Interest Rate Risk and Time to Maturity Copyright 7. 14 Figure 7. 2 – Interest Rate Risk and Time to Maturity Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 15 Computing Yield-to-Maturity • Yield-to-maturity is the rate implied by the current bond 7. 15 Computing Yield-to-Maturity • Yield-to-maturity is the rate implied by the current bond price • Finding the YTM requires trial and error if you do not have a financial calculator and is similar to the process for finding r with an annuity Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 16 Example – Finding the YTM • Consider a bond with a 10% 7. 16 Example – Finding the YTM • Consider a bond with a 10% annual coupon rate, 15 years to maturity and a par value of $1000. The current price is $928. 09. – Will the yield be more or less than 10%? – N = 15; PV = -928. 09; FV = 1000; PMT = 100 – CPT I/Y = 11% Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 17 YTM with Semiannual Coupons • Suppose a bond with a 10% coupon 7. 17 YTM with Semiannual Coupons • Suppose a bond with a 10% coupon rate and semiannual coupons has a face value of $1000, 20 years to maturity and is selling for $1197. 93. – Is the YTM more or less than 10%? – What is the semiannual coupon payment? – How many periods are there? – N = 40; PV = -1197. 93; PMT = 50; FV = 1000; CPT I/Y = 4% (Is this the YTM? ) – YTM = 4%*2 = 8% Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 18 Table 7. 1 – Summary of Bond Valuation Copyright © 2005 Mc. 7. 18 Table 7. 1 – Summary of Bond Valuation Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 19 Bond Pricing Theorems • Bonds of similar risk (and maturity) will be 7. 19 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 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 20 Bond Prices with a Spreadsheet • There is a specific formula for 7. 20 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 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 21 Differences Between Debt and Equity 7. 2 • Equity • Debt – 7. 21 Differences Between Debt and Equity 7. 2 • Equity • 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 – 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 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 22 The Bond Indenture • Contract between the company and the bondholders and 7. 22 The Bond Indenture • Contract between the company 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 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 23 Bond Classifications • Registered vs. Bearer Forms • Security – Collateral – 7. 23 Bond Classifications • Registered vs. Bearer Forms • Security – Collateral – secured by financial securities – 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 – Sinking Fund – Account managed by the bond trustee for early bond redemption Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 24 Bond Classifications Continued • Call Provision – Call premium – Deferred call 7. 24 Bond Classifications Continued • Call Provision – Call premium – Deferred call – Call protected – Canada plus call • Protective Covenants – Negative covenants – Positive covenants Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 25 Bond Characteristics and Required Returns • The coupon rate depends on the 7. 25 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 debt versus a debenture – Subordinated debenture versus senior debt – A bond with a sinking fund versus one without – A callable bond versus a non-callable bond Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 26 Bond Ratings – Investment Quality 7. 3 • High Grade – DBRS’s 7. 26 Bond Ratings – Investment Quality 7. 3 • High Grade – DBRS’s AAA – capacity to pay is exceptionally strong – DBRS’s AA – capacity to pay is very strong • Medium Grade – DBRS’s A – capacity to pay is strong, but more susceptible to changes in circumstances – DBRS’s BBB – capacity to pay is adequate, adverse conditions will have more impact on the firm’s ability to pay Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 27 Bond Ratings - Speculative • Low Grade – DBRS’s BB, B, CCC, 7. 27 Bond Ratings - Speculative • Low Grade – DBRS’s BB, B, CCC, CC – Considered speculative with respect to capacity to pay. • Very Low Grade – DBRS’s C – bonds are in immediate danger of default – DBRS’s D – in default, with principal and/or interest in arrears Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 28 Stripped or Zero-Coupon Bonds 7. 4 • Make no periodic interest payments 7. 28 Stripped or Zero-Coupon Bonds 7. 4 • Make no periodic interest payments (coupon rate = 0%) • The entire yield-to-maturity comes from the difference between the purchase price and the par value • Cannot sell for more than par value • Sometimes called zeroes, or deep discount bonds • Bondholder must pay taxes on accrued interest every year, even though no interest is received Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 29 Floating Rate Bonds • Coupon rate floats depending on some index value 7. 29 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” Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 30 Other Bond Types • • • Disaster bonds Income bonds Convertible bonds 7. 30 Other Bond Types • • • Disaster bonds Income bonds Convertible bonds Put bond (retractable bond) LYON bond There are many other types of provisions that can be added to a bond and many bonds have several provisions – it is important to recognize how these provisions affect required returns Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 31 Bond Markets 7. 5 • Primarily over-the-counter transactions with dealers connected electronically 7. 31 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 • Treasury securities are an exception Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 32 Bond Quotations • From Figure 7. 3 Canada 5. 000 Dec 01/03 7. 32 Bond Quotations • From Figure 7. 3 Canada 5. 000 Dec 01/03 101. 9 3. 05 – Issue is a Government of Canada bond – Coupon rate is 5% (assumed to be semiannual) – Maturity date is December 1, 2003 – Price that a bondholder can sell for is $1, 019 – Yield to maturity is 3. 05% compounded semiannually Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 33 Inflation and Interest Rates 7. 6 • Real rate of interest – 7. 33 Inflation and Interest Rates 7. 6 • Real rate of interest – compensation for change in purchasing power • Nominal rate of interest – quoted rate of interest, includes compensation for change in purchasing power and inflation Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 34 The Fisher Effect • The Fisher Effect defines the relationship between real 7. 34 The Fisher Effect • The Fisher Effect defines the relationship between real rates, nominal rates and inflation • Exact relationship is (1 + R) = (1 + r)(1 + h), where: – R = nominal rate – r = real rate – h = expected inflation rate • Approximation of the above relationship is: –R=r+h Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 35 Example – Fisher Effect • If we require a 10% real return 7. 35 Example – Fisher Effect • If we require a 10% real return and we expect inflation to be 8%, what is the nominal rate? • R = (1. 1)(1. 08) – 1 =. 188 = 18. 8% • Approximation: R = 10% + 8% = 18% • Since the real return and expected inflation are relatively high, there is significant difference between the actual Fisher Effect and the approximation. Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 36 Term Structure of Interest Rates 7. 7 • Term structure is the 7. 36 Term Structure of Interest Rates 7. 7 • Term structure is the relationship between time to maturity and yields, all else equal • It is important to recognize that we pull out the effect of default risk, different coupons, etc. • Yield curve – graphical representation of the term structure – Normal – upward-sloping, long-term yields are higher than short-term yields – Inverted – downward-sloping, long-term yields are lower than short-term yields Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 37 Figure 7. 4 – Upward-Sloping Yield Curve Copyright © 2005 Mc. Graw-Hill 7. 37 Figure 7. 4 – Upward-Sloping Yield Curve Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 38 Figure 7. 4 – Downward-Sloping Yield Curve Copyright © 2005 Mc. Graw-Hill 7. 38 Figure 7. 4 – Downward-Sloping Yield Curve Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 39 Figure 7. 5 – Government of Canada Yield Curve November 29, 2002 7. 39 Figure 7. 5 – Government of Canada Yield Curve November 29, 2002 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 40 Factors Affecting Required Return • Default risk premium – remember bond ratings 7. 40 Factors Affecting Required Return • Default risk premium – remember bond ratings • Liquidity premium – bonds that have more frequent trading will generally have lower required returns • Anything else that affects the risk of the cash flows to the bondholders, will affect the required returns Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 41 Quick Quiz • How do you find the value of a bond 7. 41 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? Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.

7. 42 Summary 7. 8 • You should know: – How to price a 7. 42 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 Copyright © 2005 Mc. Graw-Hill Ryerson Limited. All rights reserved.