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TOWSON FIN 331 - Bonds and Their Valuation

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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 (when do they to it? If the convertible price is less than the market price of the stock). Investors like this. Other issues: income bond=only interest payments, if possible. Indexed bonds=coupon payments are based on an inflation index, Collateral backing, - - - Bond Valuation: What is value?=worth, ultimately subjective, but we try to teach you so that you use 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)Aside) You are considering a security ABC with Co = -$100, C1 = $110. The best other alternative (opportunity cost) is 8% return, that is Co = -$100, C1 = $108. Explain why you choose ABC?#1 Approach (comparing PV and the price): Determine the PV of ABC and compare the price (cost) of ABC, $100. PV=110*(1/1.08)=$101.85. Since the value of ABC, $101.85 is greater thanthe price of ABC, you will buy the ABC security.#2 Approach (comparing ROI and the discount rate): Based on the ABC security cash flows, you can determine the return on investment (how? Solve for 100*(1+k) = 110 (FV approach) or 100=110/(1+k) (PV approach)). Since the ROI(discount rate which makes the PV=price) > the discount rate, you want to take the ABC security.How to determine the PV of a bond:PV=C*PVIFA(r%, n) + F*PVIF(r%, n)or C PMT, F FV, r i/y, n N, CPT => PVA typical bond makes interest (coupon) payments semi-annually. For a semi-annual coupon bond, C=1/2 of an annual coupon payment, N=2*#years, discount rate=r=APR rate/2Ex: 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 opportunities available. 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 the Price should 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 substantially different from the market price.* Bond Valuation: Negative relationship between interest (=discount) rates and bond values as wealready talked about earlier.WARNING: 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 1) Bond sells at a discount (premium, par) => the PV or price of the bond is less (higher, equal to) than the Face Value. Note that PVs are different for different coupon rates with the same discount rate=10% just like PVs are different for different discount rates for any given bond. Note that when the coupon rate is higher than the discount rate, then the bond sells at a premium 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 at maturity). 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 should be the same. (It does not matter how you make money as a combination of income and capital gains, once the total return is fixed) However, the composition of the total return between income return (current yield for a bond) and the capital gains return may be different depending on the coupon rates vis-à-vis the discount rate. See below in our discussion about YTM.* YTM (yield to maturity): (Given the price), a special discount rate which makes PV=price. YTM is the (total) return


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