Case Study 14

1. a. Interest rates have risen over the last 25 years, and that explains the coupon rates vary so widely. b. Maturity years | 5 | 15 | 25 | FV | $ 1,000 | $ 1,000 | $ 1,000 | Payment/year | 1 | 1 | 1 | Payment | $ 45 | $ 82.50 | $ 126.25 | Int/year | 10% | 10% | 10% | n | 5 | 15 | 25 | PV | $ 791.5 | $ 866.9 | $ 1,238.7 | c. Maturity years | 5 | 15 | 25 | FV | $ 1,000 | $ 1,000 | $ 1,000 | Payment/year | 2 | 2 | 2 | Payment | $ 23 | $ 41.25 | $ 63.13 | Int/year | 10% | 10% | 10% | n | 10 | 30 | 50 | PV | $ 787.6 | $ 865.5 | $ 1,239.6 | | Discount | Discount | Premium | d. EAR: Effective Annual Rate EAR = (1+r)t – 1 = (1.05)2 – 1 = 10.25% e. It is expected that the semiannual payment bond would be sold at a higher price than an otherwise equivalent annual payment bond. Comparing the annual and semiannual coupon bond prices we observe that the values are different because the effective rate for the semiannual payment bond is 10.25% and that of the annual payment bond is 10%. Concerning the consistency of the prices, if both values were evaluated at the same effective rate, the earlier payment would give the semiannual bond the higher value. 2. a. 5-year bond: YTM/2= 4.817 ; YTM = 9.634% 15-yearbond: YTM/2 = 5% ; YTM=10% 25-year bond YTM/2 = 5.091 ; YTM = 10.181% b. Effective Annual YTM: 5-yearbond: EAR = (1.04817)2 - 1 = 9.866% 15-year bond: EAR = (1.5)2 – 1 = 10.25% 25-year bond: EAR = (1.05091)2 – 10.441% c. Since for several yields on other securities we have different payment periods, then the effective annual rates shall be used. On the other hand, bonds are given by brokers on a semiannual basis, so to compare one bond with another it is not necessary to convert to effective rates. d.