Chapter 6 is primarily the application of principles from past chapters to various bonds and securities with some new terminology and formulas to efficiently handle calculations. Sections 6.1 and 6.2 of the textbook briefly discuss different types of bonds and stocks. Example 6.1 illustrates the calculation of a yield rate for a zero coupon bond. Sections 6.1, 6.2, 6.3 Example 6.2 illustrates the use of simple discount to calculate the price for a 13-week Treasury bill (T-bill). A bond is issued by a borrower to a lender. Terms and symbols are as follows: F = the par value or face value of a bond, whose primary purpose is to define the series of coupon payments to be made by the borrower C = the redemption value of a bond; often C = F, but not always (Unless otherwise stated, it is assumed that C = F.) r = the coupon rate of a bond, with semiannual frequency being most common

Fr = the amount of the coupon g = the modified coupon rate of a bond, defined by Fr = Cg ; g = Fr/C is the coupon rate per unit of redemption value rather than per unit of par value and is convertible at the same frequency as r; g = r if F = C n = the number of coupon payment periods from the date of calculation to the maturity (or redemption) date NOTE: F, C, r, g, and n are fixed by the terms of the bond. i = the yield rate (yield to maturity) of a bond, convertible at the same frequency as the coupon rate, defined to be the interest rate actually earned by the investor. P = the price of a bond (which can be defined to be the present value of future coupons plus the present value of the redemption value)

Bond X and Bond Y are each a two-year bond with a par value of $5000. Bond X has a coupon rate of 6% payable semiannually, and Bond Y has a coupon rate of 8% payable semiannually. If both bonds are to be brought to yield 7% convertible semiannually, find the price for each by (a) finding the present value of future coupons plus the present value of the redemption value. This is the basic formula. Bond XBond Y F =F = r =r = Fr =Fr = n =n = P =P = 5000 = C a – 4 |  = $ = C a – 4 |  = $ i = 0.035

Fr = the amount of the coupon g = the modified coupon rate of a bond, defined by Fr = Cg ; g = Fr/C is the coupon rate per unit of redemption value rather than per unit of par value and is convertible at the same frequency as r; g = r if F = C n = the number of coupon payment periods from the date of calculation to the maturity (or redemption) date NOTE: F, C, r, g, and n are fixed by the terms of the bond. i = the yield rate (yield to maturity) of a bond, convertible at the same frequency as the coupon rate, defined to be the interest rate actually earned by the investor. P = the price of a bond (which can be defined to be the present value of future coupons plus the present value of the redemption value) K = Cv n = the present value of the redemption value (with yield rate i) G = the base amount of a bond, defined by Gi = Fr ; G = Fr/i is the amount which, if invested at the yield rate i, would produce periodic interest payments equal to the coupons on the bond

There are four (equivalent) formulas to find the price of a bond: P = Fr + C a – n | i 1  = (1 + i) n Fr + Cv n = a – n | Fr + K a – n | The basic formula is The premium/discount formula is P = Fr + C a – n | i 1  = (1 + i) n Fr + C(1  i ) = a – n | a – n | C + (Fr  Ci) a – n | (where interest functions are understood to be calculated with yield rate i)

The base amount formula is P = Fr + C a – n | i 1  = (1 + i) n Gi + Cv n = G(1  v n ) + Cv n = a – n | G + (C  G)v n (where interest functions are understood to be calculated with yield rate i) The Makeham formula is P = Fr + C a – n | i 1  = (1 + i) n Cv n + Cg Cv n + (C  Cv n ) = K + (C  K) 1  v n  = i g  i g  i On page 202 of the textbook the terms nominal yield (note the ambiguity), current yield, and yield to maturity are defined.

Bond X and Bond Y are each a two-year bond with a par value of $5000. Bond X has a coupon rate of 6% payable semiannually, and Bond Y has a coupon rate of 8% payable semiannually. If both bonds are to be brought to yield 7% convertible semiannually, find the price for each by (a) finding the present value of future coupons plus the present value of the redemption value. This is the basic formula. Bond XBond Y F =F = r =r = Fr =Fr = n =n = P =P = 5000 = C a – 4 |  = $ = C a – 4 |  = $ i = 0.035

(b) using the premium/discount formula, the base amount formula, and the Makeham formula. Bond XBond Y F =F = r =r = Fr =Fr = n =n = K =K = G =G = 5000 = C = C i = C + (Fr  Ci) = a – n | (150  175)= a – 4 | $ C + (Fr  Ci) = a – n | (200  175)= a – 4 | $  =  = With the premium/discount formula, P =  =  = With the premium/discount formula, P =

(b) using the premium/discount formula, the base amount formula, and the Makeham formula. Bond XBond Y F =F = r =r = Fr =Fr = n =n = K =K = G =G = 5000 = C = C i =  =  = With the base amount formula, P = G + (C  G)v n = (5000  ) $  =  = With the base amount formula, P = G + (C  G)v n = (5000  ) $  =  =

(b) using the premium/discount formula, the base amount formula, and the Makeham formula. Bond XBond Y F =F = r =r = Fr =Fr = n =n = K =K = G =G = 5000 = C = C i =  =  = With the Makeham formula, P = K + (C  K) = (5000  ) = $  =  = With the Makeham formula, P = K + (C  K) = (5000  ) = $   g  i g  i g = r = 0.03 g = r = 0.04