CHAPTER 14: BOND PRICES AND YIELDSPROBLEM SETS1.The bond callable at 105 should sell at a lower price because the call provision is more valuable to the firm. Therefore, its yield to maturity should be higher.2.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.3.A bond’s coupon interest payments and principal repayment are not affected by changes in market rates. Consequently, if market rates increase, bond investors in the secondary markets are not willing to pay as much for a claim on a given bond’s fixed interest and principal payments as they would if market rates were lower. This relationship is apparent from the inverse relationship between interest rates and present value. An increase in the discount rate (i.e., the market rate) decreases the present valueof the future cash flows.4.a.Effective annual rate for 3-month T-bill:100,000 41 1.024124 1 0.100 10.0%97,645 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 annual interest rate.5.The effective annual yield on the semiannual coupon bonds is 8.16%. If the annual coupon bonds are to sell at par they must offer the same yield, which requires an annual coupon rate of 8.16%.6.The bond price will be lower. As time passes, the bond price, which is now above parvalue, will approach par.

Chapter 14 - Bond Prices and Yields14-1

7.Yield to maturity: Using a financial calculator, enter the following:n = 3; PV = 953.10; FV = 1000; PMT = 80; COMP iThis 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 = $1,268.16Then find the rate (yrealized) that makes the FV of the purchase price equal to $1,268.16:$953.10 (1 + yrealized)3= $1,268.16 yrealized= 9.99% or approximately 10%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$60.88$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.9.a.On a financial calculator, enter the following:n = 40; FV = 1000; PV = –950; PMT = 40You will find that the yield to maturity on a semi-annual basis is 4.26%. This implies a bond equivalent yield to maturity equal to: 4.26% 2 = 8.52%Effective annual yield to maturity = (1.0426)2– 1 = 0.0870 = 8.70%14-2

b.