Question

A firm's bonds have a maturity of 14 years with a $1,000 face value, have an 8% semiannual coupon, are callable in 7 years at $1,062, and currently sell at a price of $1,118.85.

a.What is their nominal yield to maturity? Do not round intermediate calculations. Round your answer to two decimal places. %
b.What is their nominal yield to call? Do not round intermediate calculations. Round your answer to two decimal places. %
c.What return should investors expect to earn on these bonds?
I.Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC.
II.Investors would expect the bonds to be called and to earn the YTC because the YTC is less than the YTM.
III.Investors would expect the bonds to be called and to earn the YTC because the YTM is less than the YTC.
IV.Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM.
V.Investors would not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.

Answer 1

The nominal yield to maturity of the bond is 6.42% while the nominal yield to call is 6.71%. Investors should expect the bonds to be called and to earn the yield to call (YTC) because the yield to maturity (YTM) is less than the YTC.

Step-by-step explanation:

a. The nominal yield to maturity of the firm's bonds can be calculated using the following formula:

YTM = (Annual Coupon Payment + (Face Value - Current Price) / Number of Years) / ((Face Value + Current Price) / 2)

Substituting in the given values:

YTM = (80 + (1000 - 1118.85) / 14) / ((1000 + 1118.85) / 2)

YTM = 6.42%

b. The nominal yield to call can be calculated using the same formula, but with the number of years equal to the number of years until the call date:

YTC = (Annual Coupon Payment + (Face Value - Call Price) / Number of Years) / ((Face Value + Call Price) / 2)

Substituting in the given values:

YTC = (80 + (1000 - 1062) / 7) / ((1000 + 1062) / 2)

YTC = 6.71%

c. Investors should expect to earn the yield to maturity (YTM) because it is lower than the yield to call (YTC). Therefore, the correct statement is: III. Investors would expect the bonds to be called and to earn the YTC because the YTM is less than the YTC. Final answer:

The nominal yield to maturity of the bond is 6.42% while the nominal yield to call is 6.71%. Investors should expect the bonds to be called and to earn the yield to call (YTC) because the yield to maturity (YTM) is less than the YTC.

Step-by-step explanation:

a. The nominal yield to maturity of the firm's bonds can be calculated using the following formula:

YTM = (Annual Coupon Payment + (Face Value - Current Price) / Number of Years) / ((Face Value + Current Price) / 2)

Substituting in the given values:

YTM = (80 + (1000 - 1118.85) / 14) / ((1000 + 1118.85) / 2)

YTM = 6.42%

b. The nominal yield to call can be calculated using the same formula, but with the number of years equal to the number of years until the call date:

YTC = (Annual Coupon Payment + (Face Value - Call Price) / Number of Years) / ((Face Value + Call Price) / 2)

Substituting in the given values:

YTC = (80 + (1000 - 1062) / 7) / ((1000 + 1062) / 2)

YTC = 6.71%

c. Investors should expect to earn the yield to maturity (YTM) because it is lower than the yield to call (YTC). Therefore, the correct statement is: III. Investors would expect the bonds to be called and to earn the YTC because the YTM is less than the YTC.