Lecture 6: Valuing Bonds

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

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.

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) = 103.1875% of face value (1.031875) * ($1,000) = $1,031.875 • 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.

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.

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

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%.

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%?

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.

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.

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.

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?

13. 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

14. 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?

15. 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. The Yield Curve: Example

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

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?

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.

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

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.

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

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

23. Appendix C: Credit Ratings