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 4.

Question

Quizplus · Accepted Answer

Step 1: Calculate the price of the bond
The bonds were sold at 103.5% of their face value, so the price per bond is:

Price per bond = $1,000 × 1.035 = $1,035

Since there are 10,000 bonds, the total price of the bonds issued is:

Total price of bonds = $1,035 × 10,000 = $10,350,000

Step 2: Calculate the annual coupon payment
The coupon rate is 4%, which is paid semi-annually. Therefore, the annual coupon payment is:

Annual coupon payment = $1,000 × 4% × 2 = $80

Step 3: Calculate the yield to maturity
We can use trial and error or a financial calculator to find the yield to maturity. Using trial and error, we find that a yield of approximately 3.71% gives a price close to the actual price of the bond:

N = 16 (since there are 20 years to maturity and coupons are paid semi-annually, there are 2 × 20 = 40 semi-annual periods over the life of the bond, and 4 years have passed, so there are 2 × 4 = 8 semi-annual periods remaining)
I/Y = 3.71% (guess)
PMT = $80 (semi-annual coupon payments)
FV = $1,000 (face value at maturity)
PV = -$1,035 (negative since this is a cash outflow)
Solve for I/Y = 3.71%

Therefore, the yield to maturity at the end of year 4 is approximately 3.71%. The closest answer choice is D, 3.71%.

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