Chapter 4 Topic Overview Chapter 4 Valuing Bond Characteristics Annual and Semi-Annual Bond Valuation Reading Bond Quotes Finding Returns on Bond Risk and Other Important Bond Valuation Relationships Bond Characteristics Characteristics of Par (or Face) Value (F) = stated face value that is the amount the issuer must repay, usually $1,000 Coupon Interest Rate Coupon (C) = Coupon Rate x Face Value Maturity Date = when the face value is repaid. A legal contract called the bond indenture specifies these values. This makes a bond s cash flows look like this: pay fixed coupon (interest) payments at fixed intervals (usually every 6 months) and pay the par value at maturity. C/2 C/2 C/2 C/2 C/2+F 0 1 2... n
Bond Pricing The price of a bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return. Bond Valuation Discount the bond s cash flows at the investor s required rate of return. the coupon payment (C) stream (an annuity). the par (F) value payment (a lump sum). PV = C (PVAF r, n) + F /(1+r) n PV cpn cpn ( cpn + par) = + +... + 1 2 ( 1+ r) ( 1+ r) ( 1+ r) t C C C + F 0 1 2... n Bond Valuation Example #1 Duff s Beer has $1,000 par value bonds outstanding that make annual coupon payments. These bonds have a 7.5% annual coupon rate and 15 years left to maturity. with similar risk have a required return of 9%, and Moe Szyslak thinks this required return is reasonable. What s the most that Moe is willing to pay for a Duff s Beer bond? 1000? 75 75 75... 75 0 1 2 3... 15 r = 9%
Let s Play with Example #1 Homer Simpson is interested in buying a Duff Beer bond but demands an 7.5 percent required return. What is the most Homer would pay for this bond? 1000? 75 75 75... 75 0 1 2 3... 15 r = 7.5% Let s Play with Example #1 some more. Barney (belch!) Gumble is interested in buying a Duff Beer bond and demands on a 6 percent required return. What is the most Barney (belch!) would pay for this bond? 1000? 75 75 75... 75 0 1 2 3... 15 r = 6%
Lesson from Example 1: Bond Prices and Interest Rates have an inverse relationship! ($)M arket Value 1400 1200 1000 800 600 400 200 0 Bond Values for 7.5% Annual Coupon Bond 0% 2% 4% 6% 8% 10% Required Return 15-yr Bond Another Example 1 Lesson: 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 r > Coupon Interest Rate r = Coupon Interest Rate r < Coupon Interest Rate P 0 < par value P 0 = par value P 0 > par value DISCOUNT = = = PAR PREMIUM with Semiannual Coupons Double the number of years, and divide required return and annual coupon by 2. P 0 = C/2(PVFA r/2,2n ) + F /(1+r/2) 2n Semiannual Example Kwickee-Mart has an $1000 par value bond with an annual coupon rate of 6% that pays coupons semiannually with 20 years left to maturity. What is the most you would be willing to pay for this bond if your required return is 7% APR? Semiannual coupon = 6%/2($1000) = $30 20x2 = 40 remaining coupons
1000 30 30 30... 30 0 1 2 3... 40 Bond Yields Coupon (Current) Yield - Annual coupon payments divided by bond price. Yield To Maturity - Interest rate for which the present value of the bond s payments equal the price. Also known as the market s required rate of return. Yield To Maturity = total expected return = coupon yield + expected capital gains yield (change in price) Bond Yields Calculating Yield to Maturity (YTM=r) If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r. cpn cpn ( cpn + par) PV = + +... + 1 2 ( 1+ r) ( 1+ r) ( 1+ r) t Yield to Maturity Example Burns Power $1000 face value bond with a 5% coupon rate paid annually with 10 years left to maturity sells for $890. What is this bond s yield to maturity?
1000-890 50 50 50... 50 0 1 2 3... 10 What is bond s YTM? RATE 8.875 U.S. Treasury Bond Quotations MATURITY MO/YR Feb 19 BID Government & Notes 139:27 ASKED 139:28 CHG 3 ASK YLD 4.73 Rate Coupon rate of 8.875% What is the bond s current yield? Bid prices Ask prices (percentage of par value) Ask Yield Bid price: the price traders receive if they sell a bond to the dealer. Quoted in increments of 32 nds of a dollar Ask price: the price traders pay to the dealer to buy a bond Bid-ask spread: difference between ask and bid prices. Yield to maturity on the ask price Verifying the T-bond s YTM (Ask Yld) Par Value = $1000, semi-annual coupons Ask Price = 139.875%($1000) = $1398.75 C/2 = 8.875%($1000)/2 = $44.375 N = 2019-2006 = 13, 2N = 26 Company (Ticker) Ford Corporate Bond Quotations Coupon 6.625 Maturity Feb15,20 28 Last Price 68.25 Last Yield 10.298 Estimated Spread 565 UST 30 Est $ Vol (000s) 110,064 Corporate prices are quoted as percentage of par, without the 32 nds of a dollar quoting convention Yield spread: the difference in yield-to-maturities between a corporate bond and a Treasury bond with same maturity The greater the default risk, the higher the yield spread
Causes of Bond Price Changes Since a bond s cash flows are fixed: 1. Changes in interest rates, and 2. Passage of time. cause changes in a bond s price. Bond Value Changes Over Time Returning to the Duff s Beer original example #1, where k = 9%, N = 15, C (PMT) = $75, par (FV) = $1000, & PV = $879.09. What is bond value one year later when N = 14 and r is still = 9%? Interest Rate Risk Interest Rate Risk Example Measures Bond Price Sensitivity to changes in interest rates. In general, long-term bonds have more interest rate risk than short-term bonds. Also, for bonds with same time to maturity, lower coupon bonds have more interest rate risk than higher coupon bonds. Recall from our earlier example (#1), the 15-year, 7.5% annual coupon bond has the following values at k d = 6%, 7.5%, & 9%. Let s compare with a 2-yr, 7.5% annual coupon bond. 15-year bond 2-year bond r=6%: PV = $1,145.68 PV = $1,027.50 r=7.5%: PV = $1,000 PV = $1,000 r=9%: PV = $879.09 PV = $973.61
Interest Rate Risk: Bond Price Sensitivity Graph Default Risk 2400 2150 1900 1650 1400 1150 900 650 400 Bond Values for 7.5% Annual Coupon 2.0% 4.0% 6.0% 8.0% 10.0% 12.0% 14.0% 2-yr Bond 15-yr Bond 30-yr Bond Credit risk Default premium Investment grade Speculative grade (Junk bonds) Default Risk Standard Moody' s & Poor's Safety Aaa AAA The strongest rating; ability to repay interest and principal is very strong. Aa AA Very strong likelihood that interest and principal will be repaid A A Strong ability to repay, but some vulnerability to changes in circumstances Baa BBB Adequate capacity to repay; more vulnerability to changes in economic circumstances Ba BB Considerable uncertainty about ability to repay. B B Likelihood of interest and principal payments over sustained periods is questionable. Caa CCC in the Caa/CCC and Ca/CC classes may already be Ca CC in default or in danger of imminent default C C C-rated bonds offer little prospect for interest or principal on the debt ever to be repaid. by Issuer Corporate Municipal Treasury Agency Usually with par $1000 and semiannual coupon if maturity > 10 years; notes if maturity < 10 years 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 Used to fund budget deficits Issued by government agencies: FHLB, FNMA (Fannie Mae), GNMA (Ginnie Mae), FHLMC (Freddie Mac)
by Features Fixed vs. Floating Rates Secured vs. Unsecured 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 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 by Features (Continued) Zero-Coupon Convertible and Exchangeable Discount bonds or pure discount bonds Sell below par value Treasury Bills (Tbills) Treasury STRIPs 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 by Features (Continued) Callable and Putable 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