1. 1 Chapter 8: Valuation of Known Cash Flows: Bonds Copyright © Prentice Hall Inc. 2000. Author: Nick Bagley, bdellaSoft, Inc. Objectives Value contracts with a stream of cash flows Change of bond prices & Yields across time

2. 2 Contents 1. Using Present Value Formulas to Value Known Cash Flows 2. The Basic Building Blocks: Pure Discount Bonds 3. Coupon Bonds, Current Yield, and Yield- to-Maturity 4. Reading Bond Listings 5. Why Yields for the same Maturity may differ 6. The Behavior of Bond Prices Over Time

3. 3 Valuation of fixed income security: single risk-free interest rate  Write the PV of the fixed income security as the sum of terms

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5. 5 Pure Discount Bonds,Zero Coupon Bonds Bonds that promise a single payment of cash at some date in the future, called the maturity date

6. 6 Pure Discount Bonds  The pure discount bond is an example of the present value of a lump sum equation we analyzed in Chapter 4  The yield-to-maturity on a pure discount bond is given by the relationship:

7. 7 Pure Discount Bonds

8. 8 Prices of Pure Discount Bonds and Yields MaturityPrice per $1 of Face Value Yield (per year) 1 year0.955.26% 2 year0.886.60% 3 year0.807.72

9. 9 Valuation of a fixed income security  A security with an annual payment of $100 for 3 years.

10. 10 Coupon Bond Obligates the issuer to make periodic payments of interest (coupon payments) to the bondholder for the life of the bond and then to pay the face value at maturity

11. 11 A 10 years coupon bond with an annual coupon of $56, FV=$1000, interest rate=5.6% |__|__|__|__|__|__|__|__|__|__| $56 56 ……………………………….. $56 $1000

12. 12 Valuation of the coupon bond

13. 13 Valuation of the coupon bond A year has gone by, the bond has 9 years to maturity, the interest rate had risen to 7.6%

14. 14 Discount Bond Our Bond is selling for less than its $1000 face value. Why? Compared to the 7.6% market interest rate, it pays only 5.6%, so investors are only willing to buy it less than the $1000 promised repayment.

15. 15 Discount Bond A bond that sells for less than face value

16. 16 Previous Example  The price of $873 is $127 less than the face value, so the investor would have a $127 additional gain at maturity.  In fact the $56 coupon is $20 below the coupon on a newly issued par value bond, so the investor gives up $20 per year for nine years. At 7.6%, this annuity is worth:

17. 17 What if interest rates had dropped by 2% instead of rising by 2%?

18. 18 Yield to Maturity The Discount rate that makes the present value of the bond’s stream of promised cash payments equal to its price.

19. 19 Coupon Rate, Current Yield, Yield to Maturity

20. 20 Bonds Trading at Par  Bond Pricing Principle #1: (Par Bonds) If a bond’s price equals its face value, then its yield-to-maturity = current yield = coupon rate.

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22. 22 Bond Pricing Principle 2: Premium Bonds Yield to Maturity < Current Yield <Coupon Rate

23. 23 Bond Pricing Principle 3: Discount Bonds Yield to Maturity > Current Yield >Coupon Rate

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26. 26 Why Yields for the Same Maturity May Differ, The Effect of the Coupon Rate  Two different two-year coupon bonds: 1. Coupon rate: 5% 2. Coupon rate: 10% MaturityPrice per $1Yield 1 year$0.9615384% 2 year$0.8899966%

27. 27 The Effect of the Coupon Rate  For the 5% coupon bond:  For the 10% coupon bond:

28. 28 The Effect of the Coupon Rate  For the 5% coupon bond:  For the 10% coupon bond:

29. 29 The Effect of the Coupon Rate  When the yield curve is not flat, bonds of the same maturity with different coupon rates have different yields to maturity.

30. 30 The Effect of Default Risk and Taxes  A bond promising to pay $1,000 a year from now.  The one-year U.S. Treasury rate is 6% per year.  If the bond is default free, its price =$1,000/1.06=$943.40  If subject to some default risk, its price will be less than $943.40

31. 31 Other Effects on Bond Yields  Callability.Gives the issuer of the bond the right to redeem it before the final maturity date.  Convertibility. Gives the holder of a bond issued by a corporation the right to convert the bond into a prespecified number of shares of common stock.

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