A bond has a $1000 face value,ten years to maturity,and 7% semi-annual coupon payments.What would be the expected difference in this bond's price immediately before and immediately after the next coupon payment?

Question

Quizplus · Accepted Answer

Since the bond has semi-annual coupon payments, the next coupon payment will occur in 6 months. Immediately before the coupon payment, the bond price will be the sum of the present value of the remaining coupon payments and the present value of the face value. Immediately after the coupon payment, the bond price will decrease by the amount of the coupon payment, since the bondholder will have just received that payment.

To calculate the present value of the remaining coupon payments, we need to know the yield to maturity (YTM) of the bond. Let's assume a YTM of 6%. Then we can use the following formula to calculate the present value of the remaining coupon payments:

PV = C * (1 - 1/(1+r)^n) / r + F/(1+r)^n

where PV is the present value, C is the semi-annual coupon payment ($35), r is the semi-annual yield to maturity (3%), n is the number of semi-annual periods remaining (20), and F is the face value ($1000).

Using this formula, we can calculate that the present value of the remaining coupon payments is $602.30. Adding the present value of the face value ($553.68) gives us a total bond price of $1155.98 immediately before the next coupon payment.

Immediately after the coupon payment, the bond price will decrease by the amount of the coupon payment ($35), giving us a new bond price of $1120.98. The expected difference in price is therefore $1155.98 - $1120.98 = $35. Answer choice B is the closest to this amount, so it is the best answer.

A Bond Has a $1000 Face Value,ten Years to Maturity,and