ࡱ> /1.` Ebjbj .J 6666666J J$hQ666_^6666v ]"4u0v6 JJJdJJJJJJ666666 CHAPTER 14: BOND PRICES AND YIELDS 1. a. Effective annual rate for 3-month T-bill:  EMBED Equation.3  b. Effective annual interest rate for coupon bond paying 5% semiannually: (1.05)2 1 = 0.1025 or 10.25% Therefore the coupon bond has the higher effective 5. Yield to maturity: Using a financial calculator, enter the following: n = 3; PV = (953.10; FV = 1000; PMT = 80; COMP i This results in: YTM = 9.88% Realized compound yield: First, find the future value (FV) of reinvested coupons and principal: FV = ($80 1.10 1.12) + ($80 1.12) + $1,080 = $1,268.16 Then find the rate (yrealized ) that makes the FV of the purchase price equal to $1,268.16: 7. a. (i) Current yield = Coupon/Price = $70/$960 = 0.0729 = 7.29% (ii) YTM = 3.993% semiannually or 7.986% annual bond equivalent yield. On a financial calculator, enter: n = 10; PV = 960; FV = 1000; PMT = 35 Compute the interest rate. (iii) Realized compound yield is 4.166% (semiannually), or 8.332% annual bond equivalent yield. To obtain this value, first find the future value (FV) of reinvested coupons and principal. There will be six payments of $35 each, reinvested semiannually at 3% per period. On a financial calculator, enter: PV = 0; PMT = 35; n = 6; i = 3%. Compute: FV = 226.39 Three years from now, the bond will be selling at the par value of $1,000 because the yield to maturity is forecast to equal the coupon rate. Therefore, total proceeds in three years will be: $226.39 + $1,000 =$1,226.39 Then find the rate (yrealized) that makes the FV of the purchase price equal to $1,226.39: $960 (1 + yrealized)6 = $1,226.39 ( yrealized = 4.166% (semiannual) 8. a.Zero coupon8% coupon10% couponCurrent prices$463.19$1,000.00$1,134.20b. Price 1 year from now$500.25$1,000.00$1,124.94Price increase$ 37.06$ 0.00" $ 9.26Coupon income$ 0.00$ 80.00$100.00Pre-tax income$ 37.06$ 80.00$ 90.74Pre-tax rate of return8.00%8.00%8.00%Taxes*$ 11.12$ 24.00$ 28.15After-tax income$ 25.94$ 56.00$ 62.59After-tax rate of return5.60%5.60%5.52%c. Price 1 year from now$543.93$1,065.15$1,195.46Price increase$ 80.74$ 65.15$ 61.26Coupon income$ 0.00$ 80.00$100.00Pre-tax income$ 80.74$145.15$161.26Pre-tax rate of return17.43%14.52%14.22%Taxes**$ 19.86$ 37.03$ 42.25After-tax income$ UVijkl  ` a   & * D H  "$>@DTDEU jhS;hS;OJQJ hS;H*hS;CJOJQJ j-hS; hS;>* hS;H*jhS;EHU,j69C hS;CJOJQJUVmHnHujhS;UhS;'#$%Umn T  !8dx^8gdS;dx]^`gdS;gdS; Tdx^TgdS;8dx^8`gdS; 8d^8gdS; 8dx^8`gdS;dgdS;@&gdS; E  ~ 6 % n tj  8xgdS; 8dx^8gdS; x`gdS; 8d^8gdS;  `gdS; 8dx^8`gdS;0#dx]0^#gdS;8dx@&^8gdS; dx^gdS; !dx^gdS; +|$0d$If^`0a$gdS;$0d$If^`0a$gdS;$d$Ifa$gdS; d$If^`gdS;dgdS;dgdS; Td^TgdS;8dx]^8gdS;,w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd$$IfP4\ T4 Paf4,.0246qV??$0d$If^`0a$gdS;$>d$If]^`>a$gdS; 0d$If^`0gdS;ukd$$IfP4\ B4 Paf468jzw\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;8d$If^8`gdS;skd!$$IfP4\ B4 Paf4w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd$$IfP4\ B4 Paf4 #w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd9$$IfP4\ B4 Paf4#$3;CKw\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd$$IfP4\ B4 Paf4KLciouw\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skdQ$$IfP4\ B4 Paf4uv}w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd$$IfP4\ B4 Paf4w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skdi$$IfP4\ B4 Paf4w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd$$IfP4\ B4 Paf4w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;d$If^`gdS;skd$$IfP4\ B4 Paf4 &w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;8d$If^8`gdS;skd $$IfP4\ B4 Paf4&'6>FNw\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd $$IfP4\ B4 Paf4NO]fnvw\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd% $$IfP4\ B4 Paf4vww\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd $$IfP4\ B4 Paf4w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd= $$IfP4\ B4 Paf4w\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skd $$IfP4\ B4 Paf4DDDw\EE$0d$If^`0a$gdS;$>d$If]^`>a$gdS;0d$If^`0gdS;skdU $$IfP4\ B4 Paf460.88$108.12$119.01After-tax rate of return13.14%10.81%10.49%* In computing taxes, we assume that the 10% coupon bond was issued at par and that the decrease in price when the bond is sold at year end is treated as a capital loss and therefore is not treated as an offset to ordinary income. ** In computing taxes for the zero coupon bond, $37.06 is taxed as ordinary income (see part (b)) and the remainder of the price increase is taxed as a capital gain. 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