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##### Financial Planning Problems

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Question;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?

Paper#50992 | Written in 18-Jul-2015

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