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Chapter 10

Chapter 10. Bond Prices and Yields. Bond Characteristics. Face or par value Coupon rate Zero coupon bond Compounding and payments Accrued Interest invoice price versus quoted price Indenture. Provisions of Bonds. Secured or unsecured (debenture) Call provision refunding call price

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Chapter 10

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  1. Chapter 10 Bond Prices and Yields

  2. Bond Characteristics • Face or par value • Coupon rate • Zero coupon bond • Compounding and payments • Accrued Interest • invoice price versus quoted price • Indenture

  3. Provisions of Bonds • Secured or unsecured (debenture) • Call provision • refunding • call price • deferred callable bond • coupon rates and promised ytm at issuance

  4. Provisions of Bonds • Convertible provision • conversion ratio • market conversion value • conversion premium • coupon rate & ytm at issuance • Convertible example • conversion ratio = 25 • market price of stock = $42 • callable bond price = $1150

  5. Provisions of Bonds • Put provision (putable bonds) • coupon rate & ytm at issuance • Floating rate bonds • changing credit condition of issuer • Sinking funds

  6. Other innovations • Pay in kind bonds (pik) • reverse floaters • indexed bonds (TIPS -Treasury Inflation Protection bonds)

  7. Default Risk and Ratings • Rating companies • Moody’s Investor Service • Standard & Poor’s • Duff and Phelps • Fitch • Rating Categories • Investment grade • Speculative grade

  8. Factors Used by Rating Companies • Coverage ratios • Leverage ratios • Liquidity ratios • Profitability ratios • Cash flow to debt

  9. Protection Against Default • Sinking funds • Subordination of future debt • Dividend restrictions • Collateral • mortgage bond • equipment obligation • collateral trust

  10. Bond Pricing PB = Price of the bond Ct = interest or coupon payments T = number of periods to maturity y = semi-annual discount rate or the semi-annual yield to maturity

  11. 20  1 1 = + P 40 1000 B t 20 (1+.03) (1+.03) t =1 Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000 PB = $1,148.77 Ct = 40 (SA) P = 1000 T = 20 periods r = 3% (SA)

  12. Bond Prices and Yields Prices and Yields (required rates of return) have an inverse relationship • When yields get very high the value of the bond will be very low • When yields approach zero, the value of the bond approaches the sum of the cash flows

  13. Prices and Coupon Rates Price Yield

  14. Yield to Maturity YTM = the discount rate that makes the present value of the bond’s promised payments equal to its price. Bond is priced at $1067.95, it has a coupon rate of 9% paid semiannually, a par value of $1000, and 10 years to maturity. Find the bond’s ytm. What is the current yield? Bond is priced at $945.40 , it has a coupon rate of 6% paid semiannually, a par value of $1000, and 14 years to maturity. Find the bond’s ytm. What is the current yield?

  15. YTM versus current yield versus coupon rate • Bond selling at par • coupon = YTM = current yield • Bond selling at a premium • coupon > current > YTM • Bond selling at a discount • coupon < current < YTM

  16. Yield to call (YTC) • Similar to YTM, but use time to first call date and call price as future value. • Bond with 15 years to maturity, par of $1000, a coupon rate of 8% (paid semiannually), price of $1025, callable in 5 years at $1080. Find YTC.

  17. Realized compound yield versus yield to maturity • YTM will equal the realized return over the life of the bond if all payments are reinvested at an interest rate equal to the bond’s yield. • Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, and a price of $1067.10.

  18. Realized compound yield (RCY) versus yield to maturity (YTM) • Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, and a price of $1067.10. • What is its ytm? • Realized compound yield if you reinvest at ytm? • RCY if you reinvest at 3 percent?

  19. Holding period return (HPR) versus YTM. • Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, and a price of $1067.10. Note: ytm = 8% • Suppose you hold the bond one year and interest rates decline to 7 percent. Calculate your HPR. • Suppose instead that rates had risen to 9 percent. What is your HPR?

  20. Original Issue Discount (OID) • Consider a 10 year Treasury strip with a yield of 5 percent and face of $10,000. • Price = $6,139.13 • After one year (yield = 5%) • P = $6,446.09 • Difference = implicit interest = $306.96 • If you sold the strip for $6,500, then you would have interest income of $306.96 and capital gain of $53.91

  21. Term Structure of Interest Rates • Relationship between yields to maturity and maturity • Yield curve - a graph of the yields on bonds relative to the number of years to maturity • Usually Treasury Bonds • Have to be similar risk or other factors would be influencing yields

  22. Yield Curves Yields Upward Sloping Downward Sloping Maturity

  23. Theories of Term Structure • Expectations • Liquidity Preference • Upward bias over expectations • Market Segmentation • Preferred Habitat

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