1. Qinglei Dai for FEUNL, 2006 Finance I Sept 28

2. Qinglei Dai for FEUNL, 2006 Topic covered  Bonds  Pricing of bonds  Interest rates and bond prices  Yield to maturity

3. Qinglei Dai for FEUNL, 2006 Bonds  A bond  Maturity date:

4. Qinglei Dai for FEUNL, 2006 Bonds  Face value (par value or principal value):  Coupon:  Coupon rate: E.g. a 10% coupon bond with face value of $1000 will pay each year in coupon.

5. Qinglei Dai for FEUNL, 2006 Bonds WARNING The coupon rate IS NOT the discount rate used in the Present Value calculations.

6. Qinglei Dai for FEUNL, 2006 Bond Pricing The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.

7. typedescriptionFormulaexample Pure discount bonds (zero coupon bonds) Make one single payment on a specific date. Level-coupon bonds pay coupons at regular intervals ConsolsPay coupons at regular intervals without an end

8. Qinglei Dai for FEUNL, 2006 Bond Pricing Q: How did the calculation change, given semi- annual coupons versus annual coupon payments?

9. Qinglei Dai for FEUNL, 2006 Bond Pricing Q: How did the calculation change, given semi- annual coupons versus annual coupon payments? Time Periods Paying coupons twice a year, instead of once doubles the total number of cash flows to be discounted in the PV formula. Discount Rate Since the time periods are now half years, the discount rate is also changed from the annual rate to the half year rate.

10. Qinglei Dai for FEUNL, 2006 Example: Suppose it is December 2005. The annual coupon rate for a corporate bond is 20%. Face value of the bond is €1000. The coupon is paid twice a year in June and December. The maturity date is December 2008. The stated annual market interest rate is 10%. What is PV of the bond? Bond Pricing

11. Qinglei Dai for FEUNL, 2006  C=  Stated annual interest rate=10%  semi-annual interest rate=  PV= Bond Pricing

12. Qinglei Dai for FEUNL, 2006 Bond Price and Interest Rate  F=€1000, T=2, coupon rate=10% C=€1000*10%=€100  Coupon rate>interest rate E.g. r=8%

13. Qinglei Dai for FEUNL, 2006 Bond Price and Interest Rate  F=€1000, T=2, coupon rate=10% C=€1000*10%=€100  Coupon rate<interest rate E.g. r=12%

14. Qinglei Dai for FEUNL, 2006 Bond Price and Interest Rate  F=€1000, T=2, coupon rate=10% C=€1000*10%=€100  Coupon rate=interest rate r=10%

15. Qinglei Dai for FEUNL, 2006  Yield to maturity Yield to maturity

16. Qinglei Dai for FEUNL, 2006 Bond Yields Calculating Yield to Maturity (YTM=r) If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.

17. Qinglei Dai for FEUNL, 2006 Bond Yields Example What is the YTM of a 5.5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,056.03.