chaper 14 note - Chapter14...

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1 Chapter 14 THE VALUATION OF FIXED INCOME SECURITIES By Dr. M. Metghalchi In chapter 13 we discussed various types of bonds; in this chapter we will discuss how a bond is valued. Perpetual Securities: These are securities with indefinite life, the buyer of these securities collect each year till infinity interest (In case of bonds) or dividend (In case of preferred stock). Bonds that pay interest for ever are usually called consoles. Consoles and preferred stocks are valued the same way If you buy a console or a preferred stock t you will get each year for ever a fixed payment (PMT) per year. PMT1=PMT2=PMT3= …… PMT4 = PMT n Using time value of money formula, the present value of a constant amount forever, is perpetuity, and we get: P = PMT/i P = Current price or Value of a console or Preferred stock and i is the required rate of return on the console or preferred stock. Example1: Assume Victoria Inc. ‘s last year dividend was $2.0 and this dividend is expected to remain constant for the foreseeable future. If the required rate of return for VI is 10%, what is the value of VI’s preferred stock? P = PMT/ i = 2/.10 = $20 Example 2: You buy a console that pay each year $100 interest payment, if the required rate of return for this bond (Console) is 8%, what would be the price of this console? P = PMT/ i = 80/.08 = $1000
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2 BONDS WITH MATURITY DATES In finance, the intrinsic or theoretical value of any asset is the present value of cash flows generated from the asset. Applying this concept to a bond, we get: Value of bond if interest payments are paid annually: I I I I I+M 0 1 2 3 4 N= maturity date So if Metghalchi buys this bond that has N yeas to maturity, then Metghalchi will receive each year $I (interest income, or PMT) for the next N years (N=Maturity) and at maturity Metghalchi will receive $M (the face value of the bond), using time value concept, the present value of the N years interest income (I) is: I*PVIFA and the present value of the single sum of $M at maturity is: M*PFIV, so that we can say: P= V(bond) = I* PVIFA(K d , N) + M*PVIF(K d , N) The above formula is for annual coupon payment or annual compounding. V = market value of bond or Price of the bond I = annual interest payment = Coupon rate * par value (Face Value) Coupon rate is constant for the life of the bond. N = number of years to maturity M = Par value or face value, also called maturity value, usually $1,000 or $10,000 K d = The going interest rate or the yield to maturity or the required rate of return on the bond or the expected rate of return of the bond, it is not constant, it changes every day . So K d is a function of economic conditions and it is also related to the rating (riskiness) of the bond. For example the lower the bond rating the higher will be K d and the higher the inflation rate (economic condition), the higher will be K d . Since K d changes every day, the above formula
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3 implies that market value of a bond changes also every day. (In your textbook’s notation, i is for K d and PMT is for I).
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chaper 14 note - Chapter14...

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