increase of $14.60. Total taxable income is: $40.00 + $14.60 = $54.60 20. a. The bond sells for $1,124.72 based on the 3.5% yield to maturity. [n = 60; i = 3.5; FV = 1000; PMT = 40] Therefore, yield to callis 3.368% semiannually, 6.736% semi-annually. [n = 10 semiannual periods; PV = –1124.72; FV = 1100; PMT = 40] b. If the call price were $1,050, we would set FV = 1,050 and redo part (a) to find that yield to call is 2.976% semiannually, 5.952% annually. With a lower call price, the yield to call is lower. c. Yield to call is 3.031% semiannually, 6.602% annually. [n = 4; PV = −1124.72; FV = 1100; PMT = 40] 14-7
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21. The stated yield to maturity, based on promised payments, equals 16.075%. [n = 10; PV = –900; FV = 1000; PMT = 140] Based on expectedcoupon payments of $70 annually, the expected yield to maturity is 8.526%. 22.The bond is selling at par value. Its yield to maturity equals the coupon rate, 10%. If the first-year coupon is reinvested at an interest rate of r percent, then total proceeds at the end of the second year will be: [$100 × (1 + r)] + $1,100 Therefore, realized compound yield to maturity is a function of r, as shown in the following table: r Total proceeds Realized YTM = Proceeds/1000 – 1 8% $1,208 1208/1000 – 1 = 0.0991 = 9.91% 10% $1,210 1210/1000 – 1 = 0.1000 = 10.00% 12% $1,212 1212/1000 – 1 = 0.1009 = 10.09% 23. Zero coupon bonds provide no coupons to be reinvested. Therefore, the investor's proceeds from the bond are independent of the rate at which coupons could be reinvested (if they were paid). There is no reinvestment rate uncertainty with zeros. 24. April 15 is midway through the semiannual coupon period. Therefore, the invoice price will be higher than the stated ask price by an amount equal to one-half of the semiannual coupon. The ask price is 101.125 percent of par, so the invoice price is: $1,011.25 + (½ × $50) = $1,036.25 25. Factors that might make the ABC debt more attractive to investors, therefore justifying a lower coupon rate and yield to maturity, are: i. The ABC debt is a larger issue and therefore may sell with greater liquidity. ii. An option to extend the term from 10 years to 20 years is favorable if interest rates ten years from now are lower than today’s interest rates. In contrast, if interest rates increase, the investor can present the bond for payment and reinvest the money for a higher return. iii. In the event of trouble, the ABC debt is a more senior claim. It has more underlying security in the form of a first claim against real property. iv. The call feature on the XYZ bonds makes the ABC bonds relatively more attractive since ABC bonds cannot be called from the investor. v. The XYZ bond has a sinking fund requiring XYZ to retire part of the issue each year. Since most sinking funds give the firm the option to retire this amount at the lower of par or market value, the sinking fund can be detrimental for bondholders. 14-8