Question

Bond A is a one-year zero-coupon bond with $1,000 face value and a market price of $925. Bond B is a two-year zero-coupon bond with $1,000 face value and a market price of $895. Bond C is a two-year bond that trades in the same market as Bonds A and B, has the same risks as these bonds, and has a $1,000 face value, and an annual coupon payment of 5%. What do you think the market price of Bond C should be________.

Answer 1

Answer:

The Market Price of Bond C

Coupon (R) = 5% x 1,000 = $50

Bond yield Kd = 5% = 0.05

Po = R(1-(1+r)-n)/k +  FV/ (1+r)n

Po = 50(1-(1+0.05)-2)/0.05 + 1,000/(1 + 0.05)2

Po = 50(1-(1.05)-2)/0.05 + 1,000/ (1.05)2

Po = 50(1-(0.9070))/0.05 + 1,000/ (1.05)2

Po = 50/1.86 + 907.03

Po = 26.88 + 907.03

Po = $933.91

Explanation:

The market price of bond C equals present value of the coupon plus the present value of the face value. The present value of the coupon is obtained by discounting the coupon at the present value of annuity factor of 5% for 2 years. The 5% bond yield is used because the bonds belong to the same risk class and the yield of this class is 5%.

The present value of the face value of the bond is determined by discounting the face value at the present value factor of 5% for 2 years.

The aggregate of the two present values give the current market price of Bond C.