bkmsol_ch14 - CHAPTER 14 BOND PRICES AND YIELDS 1 a...

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CHAPTER 14: BOND PRICES AND YIELDS 1. a. Effective annual rate for 3-month T-bill: % 0 . 10 100 . 0 1 02412 . 1 1 645 , 97 000 , 100 4 4 = = = 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. 2. 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%. 3. 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. 4. The bond price will be lower. As time passes, the bond price, which is now above par value, will approach par. 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 (y realized ) that makes the FV of the purchase price equal to $1,268.16: $953.10 × (1 + y realized ) 3 = $1,268.16 y realized = 9.99% or approximately 10% 14-1
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6. a. A sinking fund provision requires the early redemption of a bond issue. The provision may be for a specific number of bonds or a percentage of the bond issue over a specified time period. The sinking fund can retire all or a portion of an issue over the life of the issue. b. (i) Compared to a bond without a sinking fund, the sinking fund reduces the average life of the overall issue because some of the bonds are retired prior to the stated maturity. (ii) The company will make the same total principal payments over the life of the issue, although the timing of these payments will be affected. The total interest payments associated with the issue will be reduced given the early redemption of principal. c. From the investor’s point of view, the key reason for demanding a sinking fund is to reduce credit risk. Default risk is reduced by the orderly retirement of the issue. 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 (y realized ) that makes the FV of the purchase price equal to $1,226.39: $960 × (1 + y realized ) 6 = $1,226.39 y realized = 4.166% (semiannual) b. Shortcomings of each measure: (i) Current yield does not account for capital gains or losses on bonds bought at prices other than par value. It also does not account for reinvestment income on coupon payments.
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