Chapter 6 Learning Objectives Distinguish among a bond’s coupon rate, current yield, and yield to maturity. Find the market price of a bond given its yield to maturity, find a bond’s yield given its price, and demonstrate why prices and yields move in opposite directions. Show why bonds exhibit interest rate risk. Understand why investors pay attention to bond ratings and demand a higher interest rate for bonds with low ratings.

Valuing Bonds A bond is a debt instrument issued by governments or corporations to raise money The successful investor must be able to: Understand bond structure Calculate bond rates of return Understand interest rate risk Differentiate between real and nominal returns Chapter 06 Outline Bonds Bond Pricing Bond Prices and Interest Rates Bond Yields Current Yield Yield to Maturity Bond Rates of Return The Yield Curve Interest Rates & Inflation Nominal & Real Interest Rates How to Hedge Against Inflation Default Risk Credit Agencies Bond Classifications Variations in Corporate Bonds Appendices: Historical Treasury Bond Rates Historical Real vs. Nominal Bond Yields Credit Ratings

Bond Basics Bond Face Value Coupon Coupon Rate When governments or companies issue bonds, they promise to make a series of interest payments and then repay the debt. Bond Security that obligates the issuer to make specified payments to the bondholder. Face Value Payment at the maturity of the bond. Coupon The interest payments paid to the bondholder. Coupon Rate Annual interest payment as a percentage of face value. Bond – Security that obligates the issuer to make specified payments to the bondholder. Face Value – Payment at the maturity of the bond. Also called “principal ” or “par value ” Coupon – The interest payments paid to the bondholder. Coupon Rate – Annual interest payment as a percentage of face value.

Treasury bond prices are quoted in 32nds rather than in decimals. Bond Pricing: Example Treasury bond prices are quoted in 32nds rather than in decimals. Example: For a $1000 face value bond with a bid price of 103:05 and an asked price of 103:06, how much would an investor pay for the bond? Asked Price – The price that investors need to pay to buy the bond. Bid Price – The price asked by an investor who owns the bond and wishes to sell it. Spread – The difference between the bid price and the asked price. The spread is how a seller of a bond makes a profit. Note: While Treasury bonds are quoted in 32nds, corporate bonds are quoted in decimals. 103% + (06/32) = 103.1875% of face value (1.031875) * ($1,000) = $1,031.875

Bond Pricing The value of a bond is the present value of all cash flows generated by the bond (coupons and repayment of face value), discounted at the required rate of return.

Bond Pricing: Example What is the price of a 9% annual coupon bond with a par value of $1,000 that matures in 3 years? Assume a required rate of return of 4%.    

Bond Pricing A bond is a package of two investments: an annuity and a final repayment.

Bond Pricing: Example What is the value of a 3-year annuity that pays $90 each year and an additional $1,000 at the date of the final repayment? Assume a discount rate of 4%.   Notice how we obtain the same value despite calculating the bond’s price two different ways.

Bond Prices & Interest Rates As interest rates change, so do bond prices. What is the present value of a 4% coupon bond with face value $1,000 that matures in 3 years? Assume a discount rate of 5%.   What is the present value of this same bond at a discount rate of 2%? When the interest rate rises, the present value of the payments to be received by the bondholder falls and bond prices fall. When the interest rate decreases, the present value of the payments to be received by the bondholder increases and bond prices rise. Interest rate risk – The risk in bond prices due to fluctuations in interest rates.  

Bond Yields Current Yield Yield to Maturity To calculate how much we earn on a bond investment, we can calculate two types of bond yields: Current Yield Yield to Maturity Current Yield – Annual coupon payments divided by bond price. Yield to Maturity – Interest rate for which the present value of the bond’s payments equals the price.

Current Yield: Example Suppose you spend $1,150 for a $1,000 face value bond that pays a $60 annual coupon payment for 3 years. What is the bond’s current yield?   Current Yield – Annual coupon payments divided by bond price.

Yield to Maturity Yield to Maturity: Yield to Maturity – Interest rate for which the present value of the bond’s payments equals the price.

Yield to Maturity: Example Suppose you spend $1,150 for a $1,000 face value bond that pays a $60 annual coupon payment for 3 years. What is the bond’s yield to maturity? Note: Solve yield to maturity using a spreadsheet or a financial calculator. See the Appendix of Chapter 8 for help on this type of problem (which is essentially an internal rate of return)  

Rate of Return   A bond’s yield to maturity is only helpful if the investor plans on holding the bond until it matures. A bond’s rate of return can be calculated regardless of how long the bond is held. Rate of return – Total income per period per dollar invested.  

Rate of Return: Example Suppose you purchase a 5% coupon bond, par value $1,000, with 5 years until maturity, for $975.00 today. After one year you sell the bond for $965.00. What was the rate of return during the period? Note: If the investor held the bond all 5 years until maturity, the rate of return would equal the yield to maturity.  

The Yield Curve: Example Yield Curve – Plot of the relationship between bond yields to maturity and time to maturity. The yield curve usually slopes upwards, implying that long term bonds generally earn higher yields than short-term bonds. When interest rates are expected to rise, the yield curve is often upward sloping.

Interest Rates & Inflation In the presence of inflation, an investor’s real interest rate is always less than the nominal interest rate.  

Interest Rates & Inflation If you invest in a security that pays 10% interest annually and inflation is 6%, what is your real interest rate?    

Interest Rates & Inflation: Example Treasury Inflation Protected Securities (TIPS) Example: If you invest in 5% coupon, 3 year TIPS and inflation is 3% each year, what are your real annual cash flows? TIPS: U.S. Treasury issued debt with fixed real flows, but with nominal cash flows (interest and principal) that are increased as the consumer price index increases. Note: What are the nominal cash flows for the example above? Year 1 2 3 Real cash flows $50 $1,050

The Risk of Default When investing in bonds, there is always the risk that the issuer may default. Default risk Default premium Default Risk – The risk that a bond issuer may default on his bonds. Companies compensate investors for bearing this added risk in the form of higher interest rates on their bonds. Default Premium – The additional yield on a bond that investors require for bearing credit risk. Usually the difference between the promised yield on a corporate bond and the yield on a U.S. Treasury bond with the same coupon and maturity.

Bonds come in many categories, with returns commensurate with risk. The Risk of Default Bonds come in many categories, with returns commensurate with risk. Credit agency Investment-grade bonds Junk bonds Credit agency – An agency that rates the safety of most corporate bonds. Examples: Moody’s, Standard & Poor’s Investment grade bonds – Bonds rated Baa or above by Moody’s or BBB or above by Standard & Poor’s. Junk bond – Bond with a rating below Baa or BBB

Types of Corporate Bonds Zero-Coupon Bonds Floating-Rate Bonds Convertible Bonds Zero-Coupon Bonds – Bonds that are issued well below face value with no coupon payment. At maturity investors receive $1,000 face value for the bond. Are corporate bonds the only bonds which can be offered as zero-coupon bonds? Floating-Rate Bonds – Bonds with coupon payments that are tied to some measure of current market rates. A common example would be a bond with coupon rate tied to the short-term Treasury rate plus 2%. Convertible Bonds – Bonds that allow the holder to exchange the bond at a later date for a specified number of shares of common stock.

Appendix A: Treasury Bond Rates 10-year U.S. Treasury bond interest rates, 1900-2010

Appendix B: Real vs. Nominal Yields Red line – Real yield on long-term UK indexed bonds Blue line – Nominal yield on long-term UK bonds

Appendix C: Credit Ratings