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6-2 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

6-3 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.  Coupon The interest payments paid to the bondholder.  Coupon Rate Annual interest payment as a percentage of face value.

6-4 Bond Pricing: Example Treasury bond prices are quoted in 32nds rather than in decimals. 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?

6-5 Bond Pricing

6-6 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%.

6-7 Bond Pricing A bond is a package of two investments: an annuity and a final repayment.

6-8 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%.

6-9 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%?

6-10 Bond Yields To calculate how much we earn on a bond investment, we can calculate two types of bond yields:  Current Yield  Yield to Maturity

6-11 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?

6-12 Yield to Maturity Yield to Maturity:

6-13 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?

6-14 Rate of Return 

6-15 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?

6-16 The Yield Curve

6-17 Interest Rates & Inflation In the presence of inflation, an investor’s real interest rate is always less than the nominal interest rate.

6-18 Interest Rates & Inflation If you invest in a security that pays 10% interest annually and inflation is 6%, what is your real interest rate?

6-19 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? Year123 Real cash flows \$50 \$1,050

6-20 The Risk of Default When investing in bonds, there is always the risk that the issuer may default.  Default risk  Default premium

6-21 The Risk of Default Bonds come in many categories, with returns commensurate with risk.  Credit agency  Investment-grade bonds  Junk bonds

6-22 Types of Corporate Bonds Zero-Coupon Bonds Floating-Rate Bonds Convertible Bonds

6-23 Appendix A: Treasury Bond Rates 10-year U.S. Treasury bond interest rates, 1900-2010

6-24 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

6-25 Appendix C: Credit Ratings