Question

The D’Arcy World Headquarters has bonds on the market with 8 years left to maturity and face value of $1000. They make semi-annual coupon payments and are currently trading for $650. If they have a yield to maturity of 15.88%, what must be the annual coupon rate?

Select one:

a. About 6%

b. About 7%

c. About 8%

d. About 9%

e. None of the above.

Answer 1

The current price is the sum of the
*PV of the face value, and
*The semiannual coupons
when discounted at 15.88%/2 per
half year.
Now, PV of face value = 1000/1.0794^16 =	$               294.50
Therefore, PV of interest payments = 650-294.50 =	$               355.50
Semiannual coupons are unknown. Let it be denoted
as "c".
Now, 355.50 = c*(1.0794^16-1)/(0.0794*1.0794^16)
c = 355.50*0.0794*1.0794^16/(1.0794^16-1) =	$                 40.01
As "c" = 40.01, annual interest = 40.01*2 = 80.02
Therefore, coupon rate = 80.02/1000 =	8.00%
Answer: [c] About 8%