Rogue Racing Inc. has $1,000 par value bonds with a coupon rate of 8% per year making semiannual coupon payments. If there are twelve years remaining prior to maturity and these bonds are selling for $876.40, what is the yield to maturity for these bonds?

Question

Quizplus · Accepted Answer

To calculate the yield to maturity (YTM), we can use the following formula:

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

Where:
C = the annual coupon payment
F = the face value (or par value) of the bond
P = the market price of the bond
n = the number of years to maturity
(Note: Since the coupon payments are made semiannually, we need to divide n by 2 and multiply C by 2)

Plugging in the values given in the question, we get:

YTM = [4% + (1000 - 876.40) / 24] / [(1000 + 876.40) / 2]
YTM = 0.0497 = 4.97%

Since the YTM is for a semiannual period, we need to double it to get the annual YTM:

Annual YTM = 2 * 4.97% = 9.94%

Therefore, the closest answer choice to our calculated YTM is C) 9.77%.