Ajax Corporation issued 10,000 units of $1,000 face value bonds that mature in 20 years and have a 4% coupon rate that is paid semi-annually. If the bonds were sold at 103.5% of their face value,
Calculate the yield to maturity at the end of year 10.

Question

Quizplus · Accepted Answer

Step 1: Calculate the annual coupon payment:
Coupon rate = 4%
Face value = $1,000
Annual coupon payment = Coupon rate x Face value = 4% x $1,000 = $40
Semi-annual coupon payment = $40/2 = $20

Step 2: Calculate the semi-annual yield to maturity after 10 years using the bond pricing formula:
N = 20 x 2 = 40 (number of semi-annual periods)
PV = -$1,035 (cost of the bond)
PMT = $20 (semi-annual coupon payment)
FV = $1,000 (face value of the bond)
Using a financial calculator or Excel, we can solve for the semi-annual yield to maturity (YTM) to be 1.789%

Step 3: Convert the semi-annual yield to maturity to an annual yield to maturity:
Yield to maturity = 2 x Semi-annual yield to maturity = 2 x 1.789% = 3.578%

Therefore, the yield to maturity at the end of year 10 is 3.58%, which is closest to option B) 3.58%.

Ajax Corporation Issued 10,000 Units of $1,000 Face Value Bonds