A 30-year maturity, 8% coupon bond paying coupons semiannually is callable in five years at a call price of $1,100. the bond currently sells at a yield to maturity of 7% (3.5% per half-year). (lo 10-4)

a. what is the yield to call?

b. what is the yield to call if the call price is only $1,050?

c. what is the yield to call if the call price is $1,100 but the bond can be called in two years instead of five years?

a.

5.72%

b.

6.83%

c.

2.86%

Explanation:

The rate of return bondholders receives on a callable bond until the call date is called Yield to call.

Yield to Call = [ C + ( F - P ) / n ] / [ (F + P ) / 2 ]

Assuming $1,000 is the face value of bond.

a.

Yield to Call = [ ($1,000 x 8% x 6/12 ) + ( $1,000 - $1,100 ) / (5 x 2) ] / [ ( $1,000 + $1,100 ) / 2 ]

Yield to Call = [ $40 - 10 ] / $1,050 = 2.86% semiannually = 5.72% yearly

b.

Yield to Call = [ ($1,000 x 8% x 6/12 ) + ( $1,000 - $1,050 ) / (5 x 2) ] / [ ( $1,000 + $1,050 ) / 2 ]

Yield to Call = [ $40 - 5 ] / $1,025 = 3.415% semiannually = 6.83% yearly

c.

Yield to Call = [ ($1,000 x 8% x 6/12 ) + ( $1,000 - $1,100 ) / (2 x 2) ] / [ ( $1,000 + $1,100 ) / 2 ]

Yield to Call = [ $40 - 10 ] / $1,050 = 1.43% semiannually = 2.86% yearly