A bond has a face value of $1,000 and a call price of $1,035. The bond is callable in 3 years and pays a 4.5%, semiannual coupon. What is the current price if the yield to call is 5%?

Question

Quizplus · Accepted Answer

To calculate the price of the bond, we need to calculate the present value of each cash flow and then sum them up.
The semiannual coupon payment is: $1,000 × 4.5% × 6/12 = $22.50
The number of semiannual periods remaining until the call date is: 3 years × 2 = 6 semiannual periods
Using the formula for present value of a bond:
Price = PV(coupon payments) + PV(face value)
Price = [$22.50 × (1 – 1 / (1 + 5%/2)^6) / (5%/2)] + [$1,000 / (1 + 5%/2)^6]
Price = $916.11 + $100.03
Price = $1,016.14
So, the best choice is B.

A Bond Has a Face Value of $1,000 and a Call