Question

Big Canyon Enterprises has bonds on the market making annual payments, with 17 years to maturity, a par value of $1,000, and a price of $969. At this price, the bonds yield 8.1 percent. What must the coupon rate be on the bonds? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

Answer:

Coupon rate = 3.8%

Explanation:

we know that :

   r = YTM =  [C + ( F-P)/n]  / (F+P)/2

where r= bond yield rate = 8.1% = .081

          F= Face valye of bond = $1000

         P= Price of bond = $ 969

        n = number of periods to maturity= 17 years

       C= coupon payment = ?

   Solution:

             0.081 = C + [ (1000-969)/17 ]  /  (1000+969)/2

             0.081 = (C + 1.8235) / 492.25

          0.081  * 492.25 =  C + 1.8235

              39.872  = C + 1.8235

             39.872-1.8235 = C

            C  =  38.04 ( coupon payment).

    we know that:

        Coupon rate = annualized interest (coupon) / par value of bond

                        =  38.04 / 1000

                       =  3.8%