The following table summarizes prices of various

default-free zero-coupon 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 zero-coupon yield curve (for the first five years).

c.

c. Is

the yield curve upward sloping, downward sloping, or flat?

Problem 8-4

Suppose the current zero-coupon yield curve for risk-free 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 two-year, zero-coupon, risk-free bond?

b. What is the price per $100 face

value of a four-year, zero-coupon, risk-free bond?

d.

What is the risk-free interest rate for a

five-year maturity?

**Problem 8-12 **

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 8-13

Suppose you purchase a 30-year, zero-coupon 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 8-22

Suppose you are given the following information about the

default-free, coupon-paying 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 two-year, zero-coupon bond.

Term: 1 2 3 4

Yield

to maturity on zero coupon 2.00% 4.00% 6.00% 6.00%

b.What is the zero-coupon yield curve for years 1 through 4?

Problem 8-26

HMK Enterprises would like to raise $10 million to invest in

capital expenditures. The company plans to issue five-year 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 five-year (annual-pay) 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?