Hood Corporation recently issued 20-year bonds. The bonds have a coupon rate of 8 percent and pay interest semiannually. Also, the bonds are callable in 6 years at a call price equal to 115 percent of par value. The par value of the bonds is $1,000. If the yield to maturity is 7 percent, what is the yield to call?

Question

Quizplus · Accepted Answer

To calculate the yield to call, we need to find the present value of cash flows till the call date, assume that after the call date the bond will be redeemed at par value.

The annual coupon payment is $80 (=$1,000 × 8%). Since the bond pays semiannual interest, the semiannual coupon payment is $40. The bond has 40 semiannual periods (20 years × 2 semiannual periods per year).

Using the formula for the present value of a bond, we can find the price today of $1 of face value received in 6 years: 
PV = $1,000 × 1.15⁶ = $1,781.56

The present value of the interest payments is: 
PV = $40 × [1− 1 / (1 + (7% / 2))⁴⁰] / (7% / 2) = $702.24

The present value of the face value received in 20 years is: 
PV = $1,000 / (1 + 7%)²⁰ = $214.55

Therefore, the price of the bond today is: 
Price = $702.24 + $214.55 = $916.79

The yield to call is the interest rate that makes the present value of cash flows equal to the current market price ($916.79), assuming the bond is called in 6 years:

$916.79 = $40 × [1− 1 / (1 + (YTC / 2))¹²] / (YTC / 2) + $1,781.56 / (1 + YTC / 2)¹²

Using trial and error or a financial calculator, we find that the yield to call is approximately 7.75%. Therefore, the answer is B) 7.75%.

Hood Corporation Recently Issued 20-Year Bonds