Final answer:
To find the coupon rate of a bond with semiannual payments, a present value, face value, yield to maturity, and time to maturity are used in a formula to solve for the semiannual coupon payment. This rate is then multiplied by 2 to obtain the annual coupon rate.
Step-by-step explanation:
The student is asking how to determine the coupon rate for a company's bond that has a current value of $836.02, a par value of $1,000, 12 years to maturity, and a yield-to-maturity of 8.8 percent with semiannual payments.
To find the coupon rate, we can use the formula for the present value of a bond which takes into account the coupon payments (C), face value (F), yield to maturity (YTM), number of years to maturity (N), and number of payments per year (M):
Present Value = C * [(1 - (1 + YTM/M) ^ (-N*M)) / (YTM/M)] + F / ((1 + YTM/M)^(N*M))
Here, the Present Value is $836.02, the face value F is $1,000, the YTM is 8.8% or 0.088, the number of years to maturity is 12, and since the bond has semiannual payments, M is 2. We would solve for C, which represents the semiannual coupon payment. The annual coupon rate is then C multiplied by 2.
Unfortunately, calculating C involves complex algebra or using a financial calculator, but we can set up the equation as above. Once C is found, multiplying by 2 gives us the coupon rate.