Bonds and Valuing Bonds

1. Bonds and Valuing Bonds Professor Dr. Rainer Stachuletz Corporate Finance Berlin School of Economics Fußzeile

2. The Basic Valuation Model • P0 = Price of asset at time 0 (today) • CFt = 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 Fußzeile

3. Valuation Fundamentals: Example • 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 10th year • Company issues a 5% coupon interest rate, 10‑year instrument with a $1,000 par value • Assume annual interest payments Fußzeile

4. Yield to Maturity (YTM) Estimate of return investors earn if they buy the bond at P0 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. Fußzeile

5. r > Coupon Interest Rate P0 < par value DISCOUNT = r < Coupon Interest Rate P0> par value PREMIUM = 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 Fußzeile

6. 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 Fußzeile

7. 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. Fußzeile

8. Interest Rate Risk What does this tell you about the relationship between bond prices and yields for bonds with different maturities? Fußzeile

9. 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. Fußzeile

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

11. 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 Fixed vs. Floating Rates • 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 Secured vs. Unsecured Bonds Bonds by Features Fußzeile

12. Discount bonds or pure discount bonds • Sell below par value • Treasury Bills (Tbills) • Treasury STRIPs Zero-Coupon Bonds 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 Bonds by Features (Continued) Fußzeile

13. 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. Callable and Putable Bonds • Sinking fund provisions: the issuer is required to gradually repurchase outstanding bonds. • Protective covenants: requirements the bond issuer must meet • Positive and negative covenants Protection from Default Risk Bonds by Features (Continued) Fußzeile

14. Rate Ask Yield Coupon rate of 5.5% Yield to maturity on the ask price Bid price:the price traders receive if they sell a bond to the dealer. Quoted in increments of 32nds of a dollar Bid prices Ask prices (percentage of par value) Ask price:the price traders pay to the dealer to buy a bond Bid-ask spread: difference between ask and bid prices. U.S. Treasury Bond Quotations Fußzeile

15. 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 Bond Ratings Bond ratings:grades assigned to bond issues based on degree of default risk Fußzeile

16. 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? Fußzeile

17. May 1981 January 1995 August 1996 October 1993 Yield Curves U.S. Treasury Securities 16 14 12 10 Interest Rate % 8 6 4 2 1 3 5 10 15 20 30 Years to Maturity Fußzeile

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