Financial Planning Problems

Question # 00005326 Posted By: spqr Updated on: 12/14/2013 05:51 AM Due on: 12/30/2013
Subject Finance Topic Finance Tutorials:
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8-1. A 30-year bond with a face value of $1000 has a coupon rate of 5.5%, with semiannual payments.

a. What is the coupon payment for this bond?

b. Draw the cash flows for the bond on a timeline.

8-2. Assume that a bond will make payments every six months as shown on the following timeline (using six-month periods):

a. What is the maturity of the bond (in years)?

b. What is the coupon rate (in percent)?

c. What is the face value?

8-3. The following table summarizes prices of various default-free, zero-coupon bonds (expressed as a percentage of face value):

a. Compute the yield to maturity for each bond.

b. Plot the zero-coupon yield curve (for the first five years).

c. Is the yield curve upward sloping, downward sloping, or flat?

8-4. Suppose the current zero-coupon yield curve for risk-free bonds is as follows:

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?

c. What is the risk-free interest rate for a five-year maturity?

8-5. In the box in Section 8.1, Bloomberg.com reported that the three-month Treasury bill sold for a price of $100.002556 per $100 face value. What is the yield to maturity of this bond, expressed as an EAR?

8-6. Suppose a 10-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading for a price of $1034.74.

a. What is the bond’s yield to maturity (expressed as an APR with semiannual compounding)?

b. If the bond’s yield to maturity changes to 9% APR, what will the bond’s price be?

8-7. Suppose a five-year, $1000 bond with annual coupons has a price of $900 and a yield to maturity of 6%. What is the bond’s coupon rate?

.

8-8. The prices of several bonds with face values of $1000 are summarized in the following table:

For each bond, state whether it trades at a discount, at par, or at a premium.

.

8-9. Explain why the yield of a bond that trades at a discount exceeds the bond’s coupon rate.

8-10. Suppose a seven-year, $1000 bond with an 8% coupon rate and semiannual coupons is trading with a yield to maturity of 6.75%.

a. Is this bond currently trading at a discount, at par, or at a premium? Explain.

b. If the yield to maturity of the bond rises to 7% (APR with semiannual compounding), what price will the bond trade for?

8-11. Suppose that General Motors Acceptance Corporation issued a bond with 10 years until maturity, a face value of $1000, and a coupon rate of 7% (annual payments). The yield to maturity on this bond when it was issued was 6%.

a. What was the price of this bond when it was issued?

b. Assuming the yield to maturity remains constant, what is the price of the bond immediately before it makes its first coupon payment?

c. Assuming the yield to maturity remains constant, what is the price of the bond immediately after it makes its first coupon payment?

8-12. Suppose you purchase a 10-year bond with 6% annual coupons. You hold the bond for four years, and sell it immediately after receiving the fourth coupon. If the bond’s yield to maturity was 5% when you purchased and sold the bond,

a. What cash flows will you pay and receive from your investment in the bond per $100 face value?

b. What is the internal rate of return of your investment?

Year

0

1

2

3

4

Purchase Bond

–$107.72

Receive Coupons

$6

$6

$6

$6

Sell Bond

$105.08

Cash Flows

–$107.72

$6.00

$6.00

$6.00

$111.08

8-13. Consider the following bonds:

a. What is the percentage change in the price of each bond if its yield to maturity falls from 6% to 5%?

b. Which of the bonds A–D is most sensitive to a 1% drop in interest rates from 6% to 5% and why? Which bond is least sensitive? Provide an intuitive explanation for your answer.

s

8-14. 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.

8-15. Suppose you purchase a 30-year Treasury bond with a 5% annual coupon, initially trading at par. In 10 years’ time, the bond’s yield to maturity has risen to 7% (EAR).

a. If you sell the bond now, what internal rate of return will you have earned on your investment in the bond?

b. If instead you hold the bond to maturity, what internal rate of return will you earn on your investment in the bond?

c. Is comparing the IRRs in (a) versus (b) a useful way to evaluate the decision to sell the bond? Explain.

8-16. Suppose the current yield on a one-year, zero coupon bond is 3%, while the yield on a five-year, zero coupon bond is 5%. Neither bond has any risk of default. Suppose you plan to invest for one year. You will earn more over the year by investing in the five-year bond as long as its yield does not rise above what level?

For Problems 17–22, assume zero-coupon yields on default-free securities are as summarized in the following table:

8-17. What is the price today of a two-year, default-free security with a face value of $1000 and an annual coupon rate of 6%? Does this bond trade at a discount, at par, or at a premium?

8-18. What is the price of a five-year, zero-coupon, default-free security with a face value of $1000?

8-19. What is the price of a three-year, default-free security with a face value of $1000 and an annual coupon rate of 4%? What is the yield to maturity for this bond?

8-20. What is the maturity of a default-free security with annual coupon payments and a yield to maturity of 4%? Why?

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