Question

It is now January 1, 2019, and you are considering the purchase of an outstanding bond that was issued on January 1, 2017. It has an 8.5% annual coupon and had a 15-year original maturity. (It matures on December 31, 2031.) There is 5 years of call protection (until December 31, 2021), after which time it can be called at 108—that is, at 108% of par, or $1,080. Interest rates have declined since it was issued, and it is now selling at 111.55% of par, or $1,115.50.

a. What is the yield to maturity? Do not round intermediate calculations. Round your answer to two decimal places.

What is the yield to call? Do not round intermediate calculations. Round your answer to two decimal places.

b. If you bought this bond, which return would you actually earn?

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 YTC is greater than the YTM.

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

c. Suppose the bond had been selling at a discount rather than a premium. Would the yield to maturity have been the most likely return, or would the yield to call have been most likely?

I. Investors would expect the bonds to be called and to earn the YTC because the YTC is greater than the YTM.

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 not expect the bonds to be called and to earn the YTM because the YTM is greater than the YTC.

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

Answer 1

a]

YTM is calculated using RATE function in Excel with these inputs :

nper = 13 (13 years to maturity with 1 annual coupon payment each year)

pmt = 1000 * 8.5% (annual coupon payment = face value * annual coupon rate. This is a positive figure as it is an inflow to the bondholder)

pv = -1115.50 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 7.11%. This is the YTM.

YTC is calculated using RATE function in Excel with these inputs :

nper = 3 (3 years to call date with 1 annual coupon payment each year)

pmt = 1000 * 8.5% (annual coupon payment = face value * annual coupon rate. This is a positive figure as it is an inflow to the bondholder)

pv = -1115.50 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1080 (call price of the bond receivable on call date. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 6.63%. This is the YTC.

b]

The bond is likely to be called because interest rates have declined since the bond was issued. The bond issuer can call the bonds and refinance their debt at the lower market interest rate.

The investors will earn the YTC because the bonds are likely to be called, and the YTC is less than YTM.

The correct option is II.

c]

For a discount bond, the YTM is higher than coupon rate.

If the bond was selling at a discount, then the interest rates have risen since the bond was issued. The bond issuer is not likely to call the bonds as it is not advantageous to do so.

The bond investors will earn the YTM because the bond will not be called, and YTM is higher than YTC.

The correct option is III.