Question

A firm's bonds have a maturity of 14 years with a $1,000 face value, have an 11% semiannual coupon, are callable in 7 years at $1,239.57, and currently sell at a price of $1,413.52. What are their nominal yield to maturity and their nominal yield to call? Do not round intermediate calculations. Round your answers to two decimal places.

YTM:   %

YTC:   %

What return should investors expect to earn on these bonds?

1. Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM.
2. Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM.
3. Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.
4. Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC.

Answer 1

Solution:

a)Calculation of YTM

Purchase Price(P)=$1,413.52

Face Value(FV)=$1,000

Annual coupon(C)=$1,000*11%=$110

Call Price(CP)=$1,239.57

Years to maturity(M)=14 years

Years to call(YC)=7 years

YTM=C+(FV-P)M/(FV+P)/2

=[$110+($1000-$1,413.52)/14]/($1000+$1,413.52)/2

=80.4628571/1206.76

=0.0667 or 6.67%

b)Calculation of YTC

YTC=C+(CP-P)YC/CP+P)/2

=[$110+($1,239.57-$1,413.52)/7]/($1,239.57+$1,413.52)/2

=85.15/1326.545

=0.0642 or 6.42%

c)The correct answer is Option III i.e 'Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.'