6-1 Lecture 6: 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

6-2 Bond Basics 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. 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.

6-3 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? 103% + (06/32) = % of face value ( ) * ($1,000) = $1, 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.

6-4 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.

6-5 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%.

6-6 Bond Pricing A bond is a package of two investments: an annuity and a final repayment.

6-7 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%.

6-8 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%?

6-9 Bond Yields To calculate how much we earn on a bond investment, we can calculate two types of bond yields:  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.

6-10 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.

6-11 Yield to Maturity Yield to Maturity: Yield to Maturity – Interest rate for which the present value of the bond’s payments equals the price.

6-12 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?

6-13 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.

6-14 Rate of Return: Example Suppose you purchase a 5% coupon bond, par value $1,000, with 5 years until maturity, for $ today. After one year you sell the bond for $ What was the rate of return during the period?

6-15 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.

6-16 Interest Rates & Inflation In the presence of inflation, an investor’s real interest rate is always less than the nominal interest rate.

6-17 Interest Rates & Inflation If you invest in a security that pays 10% interest annually and inflation is 6%, what is your real interest rate?

6-18 The Risk of Default When investing in bonds, there is always the risk that the issuer may default. 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.

6-19 The Risk of Default Bonds come in many categories, with returns commensurate with risk. Credit agency: An agency that rates the safety of most corporate bonds. Examples: Moody’s, Standard & Poor‘  Investment-grade bonds: Bonds rated Baa or above by Moody’s or BBB or above by Standard & Poor’s.  Junk bonds: Bond with a rating below Baa or BBB

6-20 Types of Corporate 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.

6-21 Appendix A: Treasury Bond Rates 10-year U.S. Treasury bond interest rates,

6-22 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

6-23 Appendix C: Credit Ratings