Question

the following nominal default-free bonds are traded in a well functioning capital market today: bond type face value coupon maturity price a zero coupon bond $100 - 1 year $95.00 b coupon bond $100 6% 2 years $97.92 c coupon bond $100 10% 3 years $104.00 (a) assuming that all the bonds make only annual payments, what discount factors (df1, df2, df3) are embedded in these prices? show all your calculations

Answer 1

The discount factors for the given bonds are df1 = 0.95, df2 = 1.9889, and df3 = 2.7961.

Step-by-step explanation:

To calculate the discount factors for the given bonds, we need to find the present value of each bond using the given prices and face values. The discount factor for each year is calculated by dividing the present value of the bond by its face value:

(a) For the zero-coupon bond: df1 = 95.00 / 100 = 0.95

(b) For the coupon bond with a 6% coupon rate and 2-year maturity: df1 = (100 - 6)/97.92 = 0.9504, df2 = (100 - 6 + 6 * 0.9504) / 97.92 = 194.7496 / 97.92 = 1.9889

(c) For the coupon bond with a 10% coupon rate and 3-year maturity: df1 = (100 - 10) / 104 = 0.902, df2 = (100 - 10 + 10 * 0.902) / 104 = 193.62 / 104 = 1.8615, df3 = (100 - 10 + 10 * 0.902 + 10 * 0.902 * 1.8615) / 104 = 290.949 / 104 = 2.7961