Chapter 10 Bond Prices and Yields

10-2 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Bond Characteristics Face or par value Face or par value Coupon rate Coupon rate –Zero coupon bond Compounding and payments Compounding and payments –Accrued Interest –invoice price versus quoted price Indenture Indenture

10-3 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Provisions of Bonds Secured or unsecured (debenture) Secured or unsecured (debenture) Call provision Call provision –refunding –call price –deferred callable bond –coupon rates and promised ytm at issuance

10-4 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Provisions of Bonds Convertible provision 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

10-5 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Provisions of Bonds Put provision (putable bonds) Put provision (putable bonds) –coupon rate & ytm at issuance Floating rate bonds Floating rate bonds –changing credit condition of issuer Sinking funds Sinking funds

10-6 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Other innovations Pay in kind bonds (pik) Pay in kind bonds (pik) reverse floaters reverse floaters indexed bonds (TIPS -Treasury Inflation Protection bonds) indexed bonds (TIPS -Treasury Inflation Protection bonds)

10-7 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Default Risk and Ratings Rating companies Rating companies –Moody’s Investor Service –Standard & Poor’s –Duff and Phelps –Fitch Rating Categories Rating Categories –Investment grade –Speculative grade

10-8 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Factors Used by Rating Companies Coverage ratios Coverage ratios Leverage ratios Leverage ratios Liquidity ratios Liquidity ratios Profitability ratios Profitability ratios Cash flow to debt Cash flow to debt

10-9 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Protection Against Default Sinking funds Sinking funds Subordination of future debt Subordination of future debt Dividend restrictions Dividend restrictions Collateral Collateral –mortgage bond –equipment obligation –collateral trust

10-10 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Bond Pricing P B =Price of the bond C t = interest or coupon payments T = number of periods to maturity y = semi-annual discount rate or the semi- annual yield to maturity

10-11 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 C t = 40 (SA) P= 1000 T= 20 periods r= 3% (SA) P B = $1, Solving for Price: 10-yr, 8% Coupon Bond, Face = $1,000 t=1 + 20= P B 40 1 ) ( 1+.03) t ( ) 20

10-12 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 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 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 When yields approach zero, the value of the bond approaches the sum of the cash flows

10-13 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Prices and Coupon Rates Price Yield

10-14 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 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 $ , 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?

10-15 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 YTM versus current yield versus coupon rate Bond selling at par Bond selling at par –coupon = YTM = current yield Bond selling at a premium Bond selling at a premium –coupon > current > YTM Bond selling at a discount Bond selling at a discount –coupon < current < YTM

10-16 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Yield to call (YTC) Similar to YTM, but use time to first call date and call price as future value. 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. 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.

10-17 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 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. 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 $

10-18 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 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 $ Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, and a price of $ –What is its ytm? –Realized compound yield if you reinvest at ytm? –RCY if you reinvest at 3 percent?

10-19 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998

10-20 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 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 $ Note: ytm = 8% Consider a bond with 10 years to maturity, coupon rate of 9 percent paid annually, and a price of $ Note: ytm = 8% Suppose you hold the bond one year and interest rates decline to 7 percent. Calculate your HPR. 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? Suppose instead that rates had risen to 9 percent. What is your HPR?

10-21 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Original Issue Discount (OID) Consider a 10 year Treasury strip with a yield of 5 percent and face of $10,000. Consider a 10 year Treasury strip with a yield of 5 percent and face of $10,000. –Price = $6, –After one year (yield = 5%) »P = $6, »Difference = implicit interest = $ »If you sold the strip for $6,500, then you would have interest income of $ and capital gain of $53.91

10-22 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Term Structure of Interest Rates Relationship between yields to maturity and maturity Relationship between yields to maturity and maturity Yield curve - a graph of the yields on bonds relative to the number of years to 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

10-23 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Yield Curves Yields Maturity Upward Sloping Downward Sloping

10-24 Irwin/McGraw-hill © The McGraw-Hill Companies, Inc., 1998 Theories of Term Structure Expectations Expectations Liquidity Preference Liquidity Preference –Upward bias over expectations Market Segmentation Market Segmentation –Preferred Habitat