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?

- Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM.
- Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM.
- Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.
- 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.'

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