Aurand,Inc.has outstanding bonds with an 8% annual coupon rate paid semiannually.The bonds have a face value of $1,000,a current price of $904,and will mature in 14 years.What is the annual yield to maturity on the bond?

Question

Quizplus · Accepted Answer

Step 1: Calculate the semi-annual coupon payment:
Coupon payment = Face Value * Coupon Rate/2
Coupon payment = $1,000 * 8%/2= $40

Step 2: Calculate the number of semi-annual periods:
Number of periods = 14 years * 2 = 28

Step 3: Calculate the semi-annual yield to maturity using the bond pricing formula:
Price = Coupon payment * (1-1/(1+y)^n)/y + Face value/(1+y)^n
Where y is the semi-annual yield to maturity and n is the number of semi-annual periods.

Plugging in the numbers,
$904 = $40 * (1-1/(1+y)^28)/y + $1,000/(1+y)^28

We need to solve for y using trial and error or a financial calculator. The answer is approximately 4.62%.

Step 4: Convert the semi-annual yield to an annual yield by doubling it:
Annual yield = 2 * Semi-annual yield = 2 * 4.62% = 9.24%

Therefore, the annual yield to maturity on the bond is 9.24%, which is closest to option (C) 9.24%.