1. 1 Chapter Twelve Principles of Bond Valuations and Investments McGraw-Hill/Irwin © 2006 The McGraw-Hill Companies, Inc., All Rights Reserved.

2. 2 Bond: Players and Factors Indebted entity Indebted entity Investors Investors Certificate (or bond) Certificate (or bond) Interest rate (coupon rate)Interest rate (coupon rate) Coupon payment dates (semi-annually)Coupon payment dates (semi-annually) Maturity dateMaturity date

3. 3 Fundaments of the Bond Valuation Process Rates of Return Current Yield Current Yield Yield to Maturity Yield to Maturity Yield to Call Yield to Call Anticipated Realized Yield Anticipated Realized Yield Reinvestment Assumption Reinvestment Assumption

4. 4 Yield Principal (amount invested) Principal (amount invested) Dollar amount of return on investment Dollar amount of return on investment Percentage return (at an annual rate) Percentage return (at an annual rate)

5. 5 Current Yield Current bond price Current bond price Annual coupon rate Annual coupon rate Ignores capital gains or losses. Ignores capital gains or losses.

6. Current Yield Calculation Current Yield =

7. 7 Current Yield Calculation - Example An example might be a 10% coupon rate $1000 par value bond selling for $950. An example might be a 10% coupon rate $1000 par value bond selling for $950. The current yield would be: $100 / $950 = 10.53%

8. 8 Yield to maturity (YTM) Return (coupon payments received) Return (coupon payments received) Maturity value Maturity value Market price Market price YTM equates the sum of the present value of the cash flows of the bond with its market price (IRR) YTM equates the sum of the present value of the cash flows of the bond with its market price (IRR)

9. 9 Risk vs. Expected Return Rate of return (high/Low) Rate of return (high/Low) Degree of risk Degree of risk Default riskDefault risk Bond ratingsBond ratings

10. Calculating Bond Prices and YTM Method 1 - using Tables Present Value of Coupon Payments (C t ) Present value of Maturity Value (P n ) (from Table 12-1 or Appendix D) (from Table 12-2 or Appendix C) n = 20, i = 12 % n = 20, i = 12% $100 x 7.469 = $746.90 $1,000 x 0.104 = $104.00 Present value of coupon payments = $746.90 Present value of maturity value = $104.00 Value of bond = $850.90

11. 11 Calculating Bond Prices – Method 2 – Using Equation Based on the principle of: Based on the principle of: Time value of money Time value of money Present Value Present Value Future Value Future Value Interest rate Interest rate ---------  --------- 

12. Fundamentals of the Bond Valuation Process – The Value of a Bond

13. 13 Yield to Maturity (YTM) Current market price Current market price Par value Par value Coupon interest rate Coupon interest rate Time to maturity Time to maturity Assumption: all coupons are reinvested at the same (YTM) rate.

14. The Formula for Approximate Yield to Maturity

15. 15 Yield to Call Call date Call date Yield to call value is determined by: Yield to call value is determined by: the coupon rate,the coupon rate, the length of time to the call date, andthe length of time to the call date, and the market price.the market price.

16. 16 Yield to Call Example Assume a 20-year bond was initially issued at 11.5% interest rate, and after two years, rates have dropped. Let us assume the bond is currently selling for $1,180, and the yield to maturity on the bond is 9.48%. However, the investor who purchases the bond for $1,180 may not be able to hold the bond for the remaining 18 years because the issue can be called. Under theses circumstances, yield to maturity may not be the appropriate measure of return over the expected holding period.

17. 17 Yield to Call Calculation – Example cont. In the present case, we assume the bond can be called at $1,090 five years after issue. Thus, the investor who buys the bond two years after issue can have his bond called back after three more years at $1,090. To compute yield to call, we determine the approximate interest rate that will equate a $1,180 investment today with $115 (11.5%) per year for the next three years plus a payoff or call price value of $1,090 at the end of three years.

18. Click on the Bonds icon Yield to Call Calculation - An Alternative Method Click on the Bonds icon Y = yield to maturity expressed in % R = coupon rate (or i) P = price of the bond. M = the number of years to Call date. The relation is:

19. The Formula for Approximate Anticipated Realized Yield = == = = Coupon payment = Realized price V = Market price Y r = Anticipated realized yield C t = Coupon payment C t = Coupon payment P r = Realized price P r = Realized price V = Market price V = Market price n r = Number of periods to realization n r = Number of periods to realization

20. 20 Maturity Yield c Maturity Yield a Maturity b Yield d Normal Figure 12-1 Term Structure of Interest Rates Inverted

21. 21 Investment Strategy: Interest- Rate Considerations Bond-Pricing Rules Bond-Pricing Rules Example of Interest-Rate Change Example of Interest-Rate Change Deep Discount verses Par Bonds Deep Discount verses Par Bonds Yield Spread Considerations Yield Spread Considerations

22. 22 (7 rules) Investment Strategy: Interest-Rate Considerations (7 rules) Bond Pricing Rules 1.Bond prices and interest rates are inversely related. 2.Prices of long-term bonds are more sensitive to a change in yields to maturity than short-term bonds. 3.Bond price sensitivity increases at a decreasing rate as maturity increases.

23. 23 Investment Strategy: Interest-Rate Considerations (cont.) 4. Bond prices are more sensitive to a decline in market YTM than to a rise in YTM.4. Bond prices are more sensitive to a decline in market YTM than to a rise in YTM. 5. Prices of low-coupon bonds are more sensitive to a change in YTM than high coupon bonds.5. Prices of low-coupon bonds are more sensitive to a change in YTM than high coupon bonds.

24. 24 Investment Strategy: Interest-Rate Considerations (cont.) 6. Bond prices are more sensitive when YTM is low than when YTM is high.6. Bond prices are more sensitive when YTM is low than when YTM is high. 7. Margin trading magnifies profits and losses of bond investments by a factor of 1/(margin requirement).7. Margin trading magnifies profits and losses of bond investments by a factor of 1/(margin requirement).

25. 25 Deep Discount versus Par Bonds Significant discount from par value Significant discount from par value Coupon rate significantly less than the prevailing rates of fixed-income securities with similar risk profiles Coupon rate significantly less than the prevailing rates of fixed-income securities with similar risk profiles

26. 26 Bond Swaps Investor sells one bond and uses the proceeds to purchase another bond, often at the same price. Investor sells one bond and uses the proceeds to purchase another bond, often at the same price. Investors engage in bond swaps Investors engage in bond swaps to take a tax loss by selling one bond at a loss but then preserve their investment by simultaneously buying a similar bond.to take a tax loss by selling one bond at a loss but then preserve their investment by simultaneously buying a similar bond. to obtain a higher yield and return on their bond investments.to obtain a higher yield and return on their bond investments.

27. 27 Computing Bond Yields Yield Measure Purpose Nominal YieldMeasures the coupon rate Current yieldMeasures current income rate Promised yield to maturity Measures expected rate of return for bond held to maturity Promised yield to call Measures expected rate of return for bond held to first call date Realized (horizon) yield Measures expected rate of return for a bond likely to be sold prior to maturity.

28. 28 – A sample of the numerous useful bond websites – click on the links New York Stock Exchange New York Stock Exchange New York Stock Exchange New York Stock Exchange U.S. Securities and Exchange Commission U.S. Securities and Exchange Commission U.S. Securities and Exchange Commission U.S. Securities and Exchange Commission Terms Used in Bond Calculators Terms Used in Bond Calculators Terms Used in Bond Calculators Terms Used in Bond Calculators

29. 29 Click on the following hyperlinks 1. Treasury Direct 1. Treasury DirectTreasury DirectTreasury Direct 2. Public debt 2. Public debtPublic debtPublic debt 3. Online Financial Tutorial 3. Online Financial TutorialOnline Financial TutorialOnline Financial Tutorial