# Berlin, 04.01.2006Fußzeile1 Bonds and Valuing Bonds Professor Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics.

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Berlin, 04.01.2006Fußzeile1 Bonds and Valuing Bonds Professor Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics

Berlin, 04.01.2006Fußzeile2 The Basic Valuation Model P 0 = Price of asset at time 0 (today) CF t = Cash flow expected at time t r = Discount rate (reflecting asset’s risk) n = Number of discounting periods (usually years) This model can express the price of any asset at t = 0 mathematically. Marginal benefit of owning the asset: right to receive the cash flows Marginal cost: opportunity cost of owning the asset

Berlin, 04.01.2006Fußzeile3 Valuation Fundamentals: Example Company issues a 5% coupon interest rate, 10 ‑ year instrument with a \$1,000 par value Assume annual interest payments  Investors in company’s financial instrument receive the contractual rights -\$50 coupon interest paid at the end of each year -\$1,000 principal at the end of the 10 th year

Berlin, 04.01.2006Fußzeile4 Yield to Maturity (YTM) Estimate of return investors earn if they buy the bond at P 0 and hold it until maturity The YTM on a bond selling at par will always equal the coupon rate. YTM is the discount rate that equates the PV of a bond’s cash flows with its price.

Berlin, 04.01.2006Fußzeile5 Bond Premiums and Discounts What happens to bond values if required return is not equal to the coupon rate? The bond's price will differ from its par value P 0 < par value r > Coupon Interest Rate DISCOUNT = P 0 > par value r < Coupon Interest Rate PREMIUM =

Berlin, 04.01.2006Fußzeile6 Semi-Annual Interest Payments Value a T-Bond Par value = \$1,000 Maturity = 2 years Coupon rate = 4% r = 4.4% per year = \$992.43

Berlin, 04.01.2006Fußzeile7 Factors that Affect Bond Prices Time to maturity: bond prices converge to par value (plus final coupon) with passage of time. Interest rates: bond prices and interest rates move in opposite directions. Changes in interest rates have larger impact on long- term bonds than on short-term bonds.

Berlin, 04.01.2006Fußzeile8 Interest Rate Risk What does this tell you about the relationship between bond prices and yields for bonds with different maturities ?

Berlin, 04.01.2006Fußzeile9 Primary vs. Secondary Markets Primary market: the initial sale of bonds by issuers to large investors or syndicates Secondary market: the market in which investors trade with each other Trades in the secondary market do not raise any capital for issuing firms.

Berlin, 04.01.2006Fußzeile10 Bonds by Issuer Corporate Bonds Usually with par \$1000 and semi- annual coupon Bonds if maturity > 10 years; notes if maturity < 10 years Municipal Bonds Issued by local and state government Interest on municipal bonds tax-free Treasury Bonds If maturity < 1 year: Treasury Bills If 1 year < maturity < 10 years: Treasury Notes Maturity > 10 years: Treasury Bonds Used to fund budget deficits Agency Bonds Issued by government agencies: FHLB, FNMA (Fannie Mae), GNMA (Ginnie Mae), FHLMC (Freddie Mac)

Berlin, 04.01.2006Fußzeile11 Bonds by Features Fixed vs. Floating Rates Floating-rate bonds: coupon tied to prime rate, LIBOR, Treasury rate or other interest rate Floating rate = benchmark rate + spread Floating rate can also be tied to the inflation rate: TIPS, for example Secured vs. Unsecured Bonds Unsecured bonds (debentures) are backed only by general faith and credit of issuer Secured bonds are backed by specific assets (collateral) Mortgage bonds, collateral trust bonds, equipment trust certificates

Berlin, 04.01.2006Fußzeile12 Bonds by Features (Continued) Zero-Coupon Bonds Discount bonds or pure discount bonds Sell below par value Treasury Bills (Tbills) Treasury STRIPs Convertible and Exchangeable Bonds Convertible bonds, in addition to paying coupon, offers the right to convert the bond into common stock of the issuer of the bond Exchangeable bonds are convertible in shares of a company other than the issuer’s

Berlin, 04.01.2006Fußzeile13 Bonds by Features (Continued) Callable and Putable Bonds Callable bonds: bond issuer has the right to repurchase the bonds at a specified price (call price). Firms could retire and reissue debt if interest rates fall. Putable bonds: the investors have the right to sell the bonds to the issuer at the put price. Protection from Default Risk Sinking fund provisions: the issuer is required to gradually repurchase outstanding bonds. Protective covenants: requirements the bond issuer must meet Positive and negative covenants

Berlin, 04.01.2006Fußzeile15 Bond Ratings Bond ratings: grades assigned to bond issues based on degree of default risk Investment- grade bonds Moody’s Aaa to Baa3 ratings S&P and Fitch AAA to BBB- ratings Junk bonds Moody’s Ba1 to Caa1 or lower S&P and Fitch BB to CCC+ or lower

Berlin, 04.01.2006Fußzeile16 Term Structure of Interest Rates  Relationship between yield and maturity is called the Term Structure of Interest Rates -Graphical depiction called a Yield Curve -Usually, yields on long-term securities are higher than on short-term securities. -Generally look at risk-free Treasury debt securities  Yield curves normally upwards-sloping -Long yields > short yields -Can be flat or even inverted during times of financial stress What do you think a Yield Curve would look like graphically?

Berlin, 04.01.2006Fußzeile17 Yield Curves U.S. Treasury Securities 2 4 6 8 10 12 14 16 510152030 Years to Maturity Interest Rate % August 1996 October 1993 May 1981 January 1995 13

Berlin, 04.01.2006Fußzeile18 Bond Valuation r Bond price equals present value of its coupons and principal. r Bond prices are inversely related to interest rates. r Bonds could have a number of features: such as convertibility, callability.

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