Financial Planning Problems
821. Consider a fouryear, defaultfree security with annual coupon payments and a face value of $1000 that is issued at par. What is the coupon rate of this bond?
822. Consider a fiveyear, defaultfree bond with annual coupons of 5% and a face value of $1000.
a. Without doing any calculations, determine whether this bond is trading at a premium or at a discount. Explain.
b. What is the yield to maturity on this bond?
c. If the yield to maturity on this bond increased to 5.2%, what would the new price be?
.
823. Prices of zerocoupon, defaultfree securities with face values of $1000 are summarized in the following table:
Suppose you observe that a threeyear, defaultfree security with an annual coupon rate of 10% and a face value of $1000 has a price today of $1183.50. Is there an arbitrage opportunity? If so, show specifically how you would take advantage of this opportunity. If not, why not?
824. Assume there are four defaultfree bonds with the following prices and future cash flows:
Do these bonds present an arbitrage opportunity? If so, how would you take advantage of this opportunity? If not, why not?
825. Suppose you are given the following information about the defaultfree, couponpaying yield curve:
a. Use arbitrage to determine the yield to maturity of a twoyear, zerocoupon bond.
b. What is the zerocoupon yield curve for years 1 through 4?
Less: oneyear zero ($120 face value) 
(120) 

Less: twoyear zero ($120 face value) 
— 
(120) 

Less: threeyear zero ($120 face value) 
— 
— 
(120) 

Fouryear zero ($1120 face value) 
— 
— 
— 
1,120 
.
826. Explain why the expected return of a corporate bond does not equal its yield to maturity.
827. Grummon Corporation has issued zerocoupon corporate bonds with a fiveyear maturity. Investors believe there is a 20% chance that Grummon will default on these bonds. If Grummon does default, investors expect to receive only 50 cents per dollar they are owed. If investors require a 6% expected return on their investment in these bonds, what will be the price and yield to maturity on these bonds?
828. The following table summarizes the yields to maturity on several oneyear, zerocoupon securities:
a. What is the price (expressed as a percentage of the face value) of a oneyear, zerocoupon corporate bond with a AAA rating?
b. What is the credit spread on AAArated corporate bonds?
c. What is the credit spread on Brated corporate bonds?
d. How does the credit spread change with the bond rating? Why?
.
829. Andrew Industries is contemplating issuing a 30year bond with a coupon rate of 7% (annual coupon payments) and a face value of $1000. Andrew believes it can get a rating of A from Standard and Poor’s. However, due to recent financial difficulties at the company, Standard and Poor’s is warning that it may downgrade Andrew Industries bonds to BBB. Yields on Arated, longterm bonds are currently 6.5%, and yields on BBBrated bonds are 6.9%.
a. What is the price of the bond if Andrew maintains the A rating for the bond issue?
b. What will the price of the bond be if it is downgraded?
830. HMK Enterprises would like to raise $10 million to invest in capital expenditures. The company plans to issue fiveyear bonds with a face value of $1000 and a coupon rate of 6.5% (annual payments). The following table summarizes the yield to maturity for fiveyear (annualpay) coupon corporate bonds of various ratings:
a. Assuming the bonds will be rated AA, what will the price of the bonds be?
b. How much total principal amount of these bonds must HMK issue to raise $10 million today, assuming the bonds are AA rated? (Because HMK cannot issue a fraction of a bond, assume that all fractions are rounded to the nearest whole number.)
c. What must the rating of the bonds be for them to sell at par?
d. Suppose that when the bonds are issued, the price of each bond is $959.54. What is the likely rating of the bonds? Are they junk bonds?
.
831. A BBBrated corporate bond has a yield to maturity of 8.2%. A U.S. Treasury security has a yield to maturity of 6.5%. These yields are quoted as APRs with semiannual compounding. Both bonds pay semiannual coupons at a rate of 7% and have five years to maturity.
a. What is the price (expressed as a percentage of the face value) of the Treasury bond?
b. What is the price (expressed as a percentage of the face value) of the BBBrated corporate bond?
c. What is the credit spread on the BBB bonds?

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Solution: Financial Planning Problems