Question

A bond pays 11% coupon semiannually, has a par value of $1,000 and will mature in 10 years. If it currently sells for $942.65, what is its yield to maturity?

a) 7.5%
b) 11.6%
c) 12%
d) 8%

Answer 1

To find the yield to maturity of a bond, calculate the present value of future cash flows and solve for the discount rate.

Step-by-step explanation:

To find the yield to maturity of a bond, we need to calculate the present value of all future cash flows and solve for the discount rate. In this case, the bond pays a coupon of 11% semiannually, so each coupon payment is $55 (11% of $1,000 divided by 2). The bond will pay a total of 20 coupon payments (10 years * 2), and at maturity, the investor will receive the face value of $1,000. We can calculate the present value of these cash flows using the current price of $942.65 as the present value:

1. Calculate the present value of each coupon payment: $55 / (1 + r/2) + $55 / (1 + r/2)^2 + ... + $55 / (1 + r/2)^10, where r is the yield to maturity.
2. Calculate the present value of the face value payment: $1,000 / (1 + r/2)^10.
3. Add up all the present values calculated in steps 1 and 2.
4. Solve for r (the yield to maturity) by trial and error or by using financial calculator/excel.

Once we solve for r, we find that the yield to maturity is approximately 12%. Therefore, the correct answer is c) 12%.