The discussion of zero-coupon bonds in the text gave an instance of two zero-coupon bonds issued through Commerzbank. The DM300, 000,000 issues due in the year of 1995 sold at 50 percent of face value and the DM300, 000,000 due in the year of 2000 sold at 33 1/3 percent of face value; both were issued in the year of 1985. Compute the implied yield-to-maturity of each of these two zero-coupon bond issues.
The bonds due in the year of 1995 sold at 50% percent of face value. As they were issued in the year of 1985, they had a ten year maturity. Supposing a DM1,000 par value, their yield-to-maturity is: (DM1,000/DM500)1/10 - 1 = .07177 or 7.177% per annum. The bonds due in the year of 2000 sold at 33 1/3%. They contain a 15 year maturity. Their yield-to-maturity is: (DM1,000/DM333.33)1/15 - 1 =.07599 or 7.599% per annum.