Chapter7. Bonds and Their Valuation What is a bond? A well structured IOU with a Face Value (FV), maturity date, and (typically, equal) coupon payments.Coupon (Interest) rate is rather specified instead of coupon payments. However, we can determine coupon payments: Each coupon payment=FV*coupon rate per periodEx: $1,000, coupon rate=8%, semi-annual coupon paying bond, 10 year bond => Time line?Each coupon payment=$40, the last payment $40+$1,000=$1,040, N=2*10=20Who issues? Federal government (treasury bonds=securities), municipal bonds (munis) issued by state and local governments, corporate bonds, foreign governments and corporations.Aside) Coupon income on munis is tax exempt from both federal and the issuing state/local taxes.Default risk is a major concern for corporate bonds.Bond characteristics: Par value=Face value=Principal, Coupon (fixed, variable, or zero-coupon=deep discount), Maturity date, (Indenture) Provisions=fine prints: examples of provisions are Call (callable bonds)-issuer has theoption to retire the bond prior to its maturity at a specified value. It is not good for investors and the price (return on this bond) should be lower (higher). Sinking fund=fund set aside to pay off the bonds, giving bond investors a piece of mind=> higher bond price/lower returns, Puttable-investor has an option to terminate the bond prior to its maturity (or extend the maturity) =>good for investors, higher bond price/lower returns, Convertibility (CB): investors can covert a bond into equity. Investors like this. Other issues: income bond=only interest payments, if possible, indexed bonds=coupon payments are based on an inflation index, - - - Bond Valuation: What is value?=worth, ultimately subjective, but we try to teach you to learn an “educated” way to come up with a “reasonable” value.Why important? Our basic economic (investment) decision whether to buy (investing=buying the asset) is based on the comparison between the value & the (market) price, which is given to an individual.How? Many different approaches. In basic finance, the best approach is the PV model. Given a prospective stream of future cash flows, we determine the (present) value at a (given) investor’s required rate of return (discount rate, opportunity cost (returns or interest rates from the best alternative)Example:PV=C*PVIFA(r%, n) + F*PVIF(r%, n)or C PMT, F FV, r i/y, n N, CPT => PVEx: 15 year annual coupon paying bond with 10% coupon rate, FV=$1000. What is the PV at r=10%? Note that C=1000*0.1=$100, 15 N, 1000 FV, 10% i/Y CPT PV=$1,000 What if r=7%? PV=$1,273.24What if r=15%? PV=$707.63 Note that there is an inverse (negative) relationship between the discount rate (r) and the PV. Does it make sense? Given a bond (or all the payments from the bond), how much youmay think about the bond varies inversely as what other investment opportunitiesavailable. If there is a great opportunity out there with r=opportunity cost high, the value you may have for the given bond could be less. Alternatively, - - -. . * Value vs. PriceOnce you determine a PV, you compare the PV with the price of the bond (which is given) to make an investment decision. If PV>Po, then the bond is undervalued (or underpriced) and you want to buy (invest in) the bond. Otherwise, the bond is overvalued (or overpriced). While everyone is trying to identify “good’ bonds to invest, if the market is “efficient”, then Price should be close to the “average” Value of most investors, and Price should be close to the Value and move close to Value pretty quickly, even if there is a disparity between the value and the price. In real life, it is hard and almost impossible to find a bond which has the value a way more than the market price.* Bond Valuation (p.200 – p.203, p.209 – p.210): Negative relationship between interest (=discount) rates and bond values as we already talked about earlier.A typical bond makes interest (coupon) payments semi-annually. For a semi-annual coupon bond, C=INT = Face Value*APR coupon rate/2, N=2*#years, required rate of return (=discount rate), rd =APR rate/2WARNING: some books inadvertently use “price” instead of “value”! An individual cannot determine the (market) price as it is already given. All you can do is to determine your own assessment of the value, not the price. However, the price is very close to the value in reality, even thought they are conceptually totally different.Aside) Bond sells at a discount (premium, par) => the PV or price is less (higher, equal to) than the Face Value. Examples on p.203 and p208 are about different discount rates (rd=10%, 15%, 5%) for the same bond (coupon rate=10%). Note that PVs are different for different coupon rates (coupon rate=13%, 10%, 7%) with the same discount rate=10%. Note that when the coupon rate is high (higher than the discount rate or yield), then the bond sells at a par and the bond PV curve will be placed above the face value. For this bond, you will have a negative capital gains (or capital loss) as the PV > Face Value (Face value can be thought of the payment you will get when you return (resell) the bond back tothe issuer). Whether the bond is at a par (PV=FV), or at a premium (PV>FV), or at a discount (PV<FV), the expected total return (YTM) should be the same as you get a competitive return as the market return. However, the composition of the total return between income return (current yield for a bond) and the capital gains return may change. See below in our discussion about YTM.* YTM (yield to maturity): (Given the price), a special discount rate which makes PV=price. Example (p.203 – P.205) – Return on bond investment if the bond is held until maturity. For this, all you need to do is enter all the information including the price of the bond (entered into PV), then try to compute the discount rate, i/Y Ex. 9.5% semi-annual coupon 20 year maturity bond with 15 years remaining. FV=1000 and the current price is $1,137.76. What is the YTM? => 47.5 PMT, 30 N, 1000 FV & -1137.76 PV, then CPT i/Y = 3.96*2=7.92% Aside: What is the current yield (coupon income rate) of the bond = annual coupon payment/current bond price=$95/$1137.76=8.35%. What is then the expected capital gains rate from the current price of $1137.76 to $1000 Face Value? Total return measured by YTM=7.92% minus the current yield of 8.35% = -0.43%.YTC (yield to call)? If the bond is callable, you can determine the yield based only on the