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ASSIGNMENT on Introduction to Finance Topic: Bond Valuation

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ASSIGNMENT on Introduction to Finance Topic: Bond Valuation ASSIGNMENT ON Introduction to Finance Topic: Bond Valuation Course code: FIN 501 Prepared To M M Mustafiz Munir Prepared By Name: Md .Shohel Shikdar ID: 11-2-14-0075 Section: C MBA Program, summer 2011 ASA UNIVERSITY BANGLADESH Abstract: Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected cash flows to the present using an appropriate discount rate. In practice, this discount rate is often determined by reference to similar instruments, provided that such instruments exist. Types of Bond by issuer: Non zero coupon bond: A zero-coupon bond (also called a discount bond or deep discount bond) is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity.[1] It does not make periodic interest payments, or have so-called "coupons," hence the term zero-coupon bond. When the bond reaches maturity, its investor receives its par (or face) value. Zero Coupon bond :A zero-coupon bond (also called a discount bond or deep discount bond) is a bond bought at a price lower than its face value, with the face value repaid at the time of maturity.[1] It does not make periodic interest payments, or have so-called "coupons," hence the term zero-coupon bond. When the bond reaches maturity, its investor receives its par (or face) value Perpetual bond: Perpetual bond, which is also known as a Perpetual or just a Prep, is a bond with no maturity date.[1] Therefore, it may be treated as equity, not as debt. Perpetual bonds pay coupons forever, and the issuer does not have to redeem them. Their cash flows are, therefore, those of a perpetuity. Fixed rate bond: In finance, a fixed rate bond is a bond with a fixed coupon (interest) rate, as opposed to a floating rate note. A fixed rate bond is a long term debt paper that carries a predetermined interest rate. The interest rate is known as coupon rate and interest is payable at specified dates before bond maturity.. Floating rate bond: Floating rate notes (FRNs) are bonds that have a variable coupon, equal to a money market reference rate, like LIBOR or federal funds rate, plus a spread. The spread is a rate that remains constant. Almost all FRNs have quarterly coupons, i.e. they pay out interest every three months, though counter examples do exist. At the beginning of each coupon period, the coupon is calculated by taking the fixing of the reference rate for that day and adding the spread. A typical coupon would look like 3 months USD LIBOR +0.20%. Inflation linked bond: Inflation-indexed bonds (also known as inflation-linked bonds or colloquially as linkers) are bonds where the principal is indexed to inflation. They are thus designed to cut out the inflation risk of an investment. The first known inflation-indexed bond was issued by the Massachusetts Bay Company in 1780. The market has grown dramatically since the British government began issuing inflation- linked Gilts in 1981. As of 2008, government-issued inflation-linked bonds comprise over Tk1.5 trillion of the international debt market. Lottery bond: Lottery Bonds are a type of government bond in which some randomly selected bonds within the issue are redeemed at a higher value than the face value of the bond. They are government bonds and only issued by a government. They have been issued by France, Belgium and the other major nations of Europe. Outwardly, lottery bonds resemble ordinary fixed rate bonds, they have a fixed, though usually long, tenor and pay regular coupons. The Maturity Value The maturity value (MV) [or face value ] of a bond is the stated value - In the case of US bond, the MV is usually Tk1000. - In the case of Bangladeshi bond prize bond, the MV is usually Tk.100. Coupon rate: The coupon or coupon rate of a bond is the amount of interest paid per year expressed as a percentage of the face value of the bond. It is the interest rate that a bond issuer pays to a bondholder. The coupon rate (coupon yield) of a bond is the stated rate of interest For Example: Annual coupon payments = Tk80 Face Value=Tk1000 Coupon rate=Tk80/Tk1000 =.08=8% The Discount Rate: The discount rate (or capitalization rate) of a bond is dependent on the risk of the bond. The discount rate (kd ) is composed of the risk free rate plus a premium for risk. Bond Valuation Bond value- PV of coupons + PV of MV Bond value – PV of annuity+ PV of lump sum Note that as interest increase, PVs decrease, so as interest increase bond prize decrease. V=CP(PVIFAkd,n )+ MV ( PVIFkd,n ) As sample: bonds has a TK 1000 face value and provide an 8% annual coupon for 30 years. The appropriate discount rate is 10% . What is the value of bond? V= CP(MVIFAkd,n)+ MV(PVIFkd,n) =Tk80(9.427)+Tk1000(0.057) =Tk754.16+Tk57=Tk811.16 Semi annual compounding Most bond coupon payments twice a year. The pay ½ of the annual coupon payments . Adjustment needed for semi annual compounding 1. Divide kd by 2. 2. Multiply n by 2. 3. Divide CP by 2. A non zero compound bond adjusted for semiannual compounding is, V= CP/2 (PVIFAkd/2,n*2)+ MV( PVIFkd/2,n*2) Zero Coupon Bond Valuation A zero coupon bond is a bond that pays no interest but sells at a deep discount from its face value’ V= MV (PVIFkd,n) Example: A bond has a Tk1000 face value and a 30 years life. The appropriate discount rate is 10 %. What is the value of the zero compound bonds? V= MV( PVIFkd,n) =Tk1000 (PVIF10%,30) =Tk1000*0.057 =Tk57 Perpetual Bond Valuation A perpetual bond is a bond that never matures. It has an infinite life. V= CP/kd Example: A bond has a $1000 face value and provides an 8% coupon. The appropriate discount rate is 10% .What is the value of perpetual bond? CP=Tk1000(8%) =Tk80 Kd=10% V= Tk 80/ 0.10 =Tk800 Yield to Maturity The Yield to maturity of a bond is the discount rate which returns the market price of the bond. YTM is often used to price a bond. Bond price are often quoted in terms of YTM. Premium Vs Discount bond A bond is selling for more than its face value is called a Premium bond A bond is selling for less than its face value is called a discount bond. Current Vs Coupon Yield The current yield is the coupon payment as a percentage of the current bond price (CP) Current Yield=CP/V The coupon yield of a bond is the stated rate of interest. Coupon Rate=Annual coupon payments/maturity value YMT Current & Coupon Yield When a bond sells at a discount YMT > Current Yield > Coupon Yield When a bond sells at a premium Coupon yield > Current yield > YTM When a bond sells at par YTM=current yield=coupon yield Consultation: As above, the fair price of a straight bond (a bond with no embedded option; see Embedded Option) is usually determined by discounting its expected cash flows at the appropriate discount rate. The formula commonly applied is discussed initially. Although this present value relationship reflects the theoretical approach to determining the value of a bond, in practice its price is (usually) determined with reference to other, more liquid instruments. The two main approaches, Relative pricing and Arbitrage-free pricing, are discussed next. Finally, where it is important to recognise that future interest rates are uncertain and that the discount rate is not adequately represented by a single fixed number - for example when an option is written on the bond in question - stochastic calculus may be employed. References Frank Fabozzi (1998). Valuation of fixed income securities and derivatives (3rd ed.). John Wiley. ISBN 978-1-883249-25-0. http://www.investopedia.com/university/advancedbond/advancedbond 2.asp http://www.investopedia.com/terms/a/amortizable-bond-premium.asp Cox et al. (1985b) - A Theory of the Term Structure of Interest Rates1985) http://en.wikipedia.org/wiki/Zero-coupon_bond http://en.wikipedia.org/wiki/Perpetual_bond http://en.wikipedia.org/wiki/Fixed_rate_bond http://en.wikipedia.org/wiki/Floating-rate_bond.
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