Question

A 2-year 10% annual coupon bond of a company is trading at $1072.27 per $1000 face value. A 2-year zero coupon bond of the same issuer is trading at $907.03 per $1000 face value. Use no-arbitrage arguments to find what should be the price of a 1-year zero coupon bond of the same issuer for $100 face value? Select one: a. $62.89 b. $65.62 c. $55.85 d. $74.54 e. $72.27

Answer 1

Let's calculate the current 2-year spot rate using the bond price for 2-year zero coupon bond

r2 = (FV / PV)^(1/2) - 1 = (1000 / 907.03)^(1/2) - 1 = 5.00%

Price of 2-year coupon bond, PV = CF1 / (1 + r1) + CF2 / (1 + r2)^2

=> 1072.27 = 100 / (1 + r1) + (100 + 1000) / (1 + 5%)^2

=> Price of 1-year zero coupon bond with $100 face value = 100 / (1 + r1) = 1072.27 - 997.73 = $74.54

Hence, d is correct.