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.
select correct answer

Answer 1

The nominal yield to maturity of the bond is 5.68% and the nominal yield to call is 8.94%. Investors should expect to earn the nominal yield to maturity if the bonds are not called and held until maturity.

Step-by-step explanation:

The nominal yield to maturity is the annualized return that an investor would receive if they hold the bond until its maturity date. To calculate it, we need to find the yield that equates the present value of all future cash flows to the current market price of the bond. The bond's cash flows include semiannual coupon payments and the face value at maturity.

In this case, the bond has a 14-year maturity, so there will be 28 semiannual periods. The coupon payment is 8% of the face value, which is $80, and the face value is $1,000. We can use the bond pricing formula to calculate the nominal yield to maturity:

Nominal Yield to Maturity = (Annual Coupon Payment + (Face Value - Current Price) / Years to Maturity) / ((Face Value + Current Price) / 2)

Plugging in the values, we get:

Nominal Yield to Maturity = (80 + (1000 - 1118.85) / 14) / ((1000 + 1118.85) / 2) = 5.68%

The nominal yield to call is the yield an investor would earn if the bond is called at the earliest call date. To calculate it, we use a similar formula but substitute the call price for the face value in the numerator:

Nominal Yield to Call = (Annual Coupon Payment + (Call Price - Current Price) / Years to Call) / ((Call Price + Current Price) / 2)

In this case, the bond is callable in 7 years at a call price of $1,062. Plugging in the values, we get:

Nominal Yield to Call = (80 + (1062 - 1118.85) / 7) / ((1062 + 1118.85) / 2) = 8.94%

Investors should expect to earn the nominal yield to maturity if the bonds are not called and are held until maturity. Therefore, the correct answer is I. Investors would not expect the bonds to be called and to earn the YTM because the YTM is less than the YTC.