Question

Huntsville Enterprise's bonds have a 20-year maturity, a yield to maturity of 8.20%, and an annual coupon rate of 8.60%. The bond makes semi-annual payments. Complete the following questions: The bond's current price = Enter your answer as a number with two decimal places of precision (i.e. 1.23) and no dollar signs or commas. Do not enter your answer as a negative number.

The bond's current yield? = Enter your answer as a decimal with a leading zero and 4 decimal places of precision (i.e. 0.1234)

What type of bond is this? Base your answer on the bond's relationship between the yield to maturity and coupon rate.

Answer 1

Annual coupon rate = 8.6%

Yield to maturity r = 8.2% = 0.082

Let the face value of bond be $ 100.

Semi-annual coupon payment = 8.6/ 2 = 4.3 % of $ 100 = $ 4.3

Current price of bond = [coupon/(1+r)] + [coupon/(1+r)²] + ...+ [[coupon/(1+r)ⁿ] + Maturity value/(1+r)ⁿ  

= [ 4.3 /(1+0.082)] + [ 4.3 /(1+0.082)²] + ...+ [[4.3 / (1+0.082)⁴⁰] + 100 /(1+0.082)⁴⁰  

= $ 54.47

If the face value of bond is $ 1000, then the current price of bond will be $ 544.72

Current bond yield = Annual dividend payment / Current price = 8.6 / 54.47 = .0.1579

The YTM (8.2%) is less than the coupon rate (8.6%), hence it is a premium bond.