Yummy Tummy Bakeries has issued a 30-year par value bond that is callable in 5 years. If the coupon rate is 5.5% payable semiannually, what is the bond's yield to call if the yield to maturity is 8% and the call premium is one year's interest?

Question

Quizplus · Accepted Answer

To calculate the yield to call, we need to find out the call price first. Since the call premium is one year's interest, the call price would be $1,027.5 (0.055 x $1,000 x 0.5 + $1,000).

Next, we can use the bond pricing formula to calculate the yield to call. This formula takes into account the present value of the bond's future cash flows discounted at the yield to call rate.

PV = Coupon payment x (1 - 1/(1 + YTC/2)^(2n))/(YTC/2) + Par value/(1+YTC/2)^(2n)

Where:
PV = Present value of the bond
Coupon payment = Coupon rate x Par value/2
YTM = Yield to maturity
n = number of periods

Using the values given in the question, we can solve for YTC:

PV = 27.5 x (1 - 1/(1 + YTC/2)^(60))/(YTC/2) + 1,000/(1+YTC/2)^(60)
PV = 927.5482 when YTC = 14.42%

Since the yield to call (14.42%) is less than the yield to maturity (8%), it's likely that the bond will be called in 5 years when it becomes callable at a 5 year call price of $1,027.5. This means that the bond's cash flows will only be received for 5 years, after which the bond will be redeemed at the call price.

Therefore, the best choice is C.

Yummy Tummy Bakeries Has Issued a 30-Year Par Value Bond