Finance problems
The following table summarizes prices of various defaultfree zerocoupon bonds (expressed as a percentage of face value):
Maturity (years) 1 2 3 4 5
Price (per $100 face value) $95.51 $91.05 $86.38 $81.65 $76.51
a. Compute the yield to maturity for each bond.
b. b. Plot the zerocoupon yield curve (for the first five years).
c. c. Is the yield curve upward sloping, downward sloping, or flat?
Problem 84
Suppose the current zerocoupon yield curve for riskfree bonds is as follows:
Maturity (years) 1 2 3 4 5
YTM 5.00% 5.50% 5.75% 5.95% 6.05%
a. What is the price per $100 face value of a twoyear, zerocoupon, riskfree bond?
b. What is the price per $100 face value of a fouryear, zerocoupon, riskfree bond?
d. What is the riskfree interest rate for a fiveyear maturity?
Problem 812
Consider the following bonds:
Coupon Rate Maturity
Bond (annual payments) (years)
A 0% 15
B 0% 10
C 4% 15
D 8% 10
a. What is the percentage change in the price of each bond if its yields to maturity falls from 6% to 5%?
b. Which of the bonds A–D are most sensitive to a 1% drop in interest rates from 6% to 5% and why? Which bond is least sensitive? Explain how you could determine this without doing the calculations in part (a).
Problem 813
Suppose you purchase a 30year, zerocoupon bond with a yield to maturity of 6%. You hold the bond for five years before selling it.
a. If the bond’s yield to maturity is 6% when you sell it, what is the internal rate of return of your investment?
b. If the bond’s yield to maturity is 7% when you sell it, what is the internal rate of return of your investment?
c. If the bond’s yield to maturity is 5% when you sell it, what is the internal rate of return of your investment?
d. Even if a bond has no chance of default, is your investment risk free if you plan to sell it before it matures? Explain.
Problem 822
Suppose you are given the following information about the defaultfree, couponpaying yield curve:
Maturity (years) 1 2 3 4 5
YTM 5.00% 5.50% 5.75% 5.95% 6.05%
a. Use arbitrage to determine the yield to maturity of a twoyear, zerocoupon bond.
Term: 1 2 3 4
Yield to maturity on zero coupon 2.00% 4.00% 6.00% 6.00%
b.What is the zerocoupon yield curve for years 1 through 4?
Problem 826
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:
Maturity (years) 1 2 3 4 5
YTM 5.00% 5.50% 5.75% 5.95% 6.05%
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?

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Solution: Finance problems