ANSWERS TO QUESTIONS FOR CHAPTER 3 (Questions are in bold print followed by answers.) 1. A debt obligation offers the following payments:
Years from Now 1 2 3 4
Cash Flow to Investor $2,000 $2,000 $2,500 $4,000
Suppose that the price of this debt obligation is $7,704.What is the yield or internal rate of return offered by this debt obligation?
2. What is the effective annual yield if the semiannual periodic interest rate is 4.3%?
3. What is the yield to maturity of a bond?
4. What is the yield to maturity calculated on a bond-equivalent basis? 5. Answer the below questions. (a) Show the cash flows for the following four bonds, each of which has a par value of $1,000 and pays interest semiannually.
Bond W X Y Z
Coupon Rate (%) Number of Years to Maturity 7 5 8 7 9 4 0 10
Price $884.20 $948.90 $967.70 $456.39
(b) Calculate the yield to maturity for the four bonds.
6. A portfolio manager is considering buying two bonds. Bond A matures in three years and has a coupon rate of 10% payable semiannually. Bond B, of the same credit quality, matures in 10 years and has a coupon rate of 12% payable semiannually. Both bonds are priced at par. (a) Suppose that the portfolio manager plans to hold the bond that is purchased for three years. Which would be the best bond for the portfolio manager to purchase?
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(b) Suppose that the portfolio manager plans to hold the bond that is purchased for six years instead of three years. In this case, which would be the best bond for the portfolio manager to purchase?
(c) Suppose that the portfolio manager is managing the assets of a life insurance company that has issued a five-year guaranteed investment contract (GIC). The interest rate that the life insurance company has agreed to pay is 9% on a semiannual basis. Which of the two bonds should the portfolio manager purchase to ensure that the GIC payments will be satisfied and that a profit will be generated by the life insurance company?
7. Consider the following bond:
Coupon rate = 11% Maturity = 18 years Par value = $1,000 First par call in 13 years Only put date in five years and putable at par value Suppose that the market price for this bond $1,169. (a) Show that the yield to maturity for this bond is 9.077%.
(b) Show that the yield to first par call is 8.793%.
(c) Show that the yield to put is 6.942%.
(d) Suppose that the call schedule for this bond is as follows: Can be called in eight years at $1,055 Can be called in 13 years at $1,000 And suppose this bond can only be put in five years and assume that the yield to first par call is 8.535%.What is the yield to worst for this bond? 8. Answer the below questions. (a) What is meant by an amortizing security? (b) What are the three components of the cash flow for an amortizing security?
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(c) What is meant by a cash flow yield?
9. How is the internal rate of return of a portfolio calculated?
10. What is the limitation of using the internal rate of return of a portfolio as a measure of the portfolio¶s yield?
11. Suppose that the coupon rate of a floating-rate security resets every six months at a spread of 70 basis points over the reference rate. If the bond is trading at below par value, explain whether the discount margin is greater than or less than 70 basis points.
12. An investor is considering the purchase of a 20-year 7% coupon bond selling for $816 and a par value of $1,000. The yield to maturity for this bond is 9%. Answer the below questions. (a) What would be the total future dollars if this investor invested $816 for 20 years earning 9% compounded semiannually? (b) What are the total coupon payments over the life of this bond? (c) What would be the total future dollars from the coupon payments and the repayment of principal at the end of 20 years? (d) For the bond to produce the same total future dollars as in part (a), how much must the interest on interest be? (e) Calculate the interest on interest from the bond assuming that the semiannual coupon payments can be reinvested at 4.5% every six months and demonstrate that the resulting amount is the same as in part (d). 13. What is the total return for a 20-year zero-coupon bond that is offering a yield to maturity of 8% if the bond is held to maturity? 14. Explain why the total return from holding a bond to maturity will be between the yield to maturity and the reinvestment rate.
15. For a long-term high-yield coupon bond, do you think that the total return from holding a bond to maturity will be closer to the yield to maturity or the reinvestment rate?
16. Suppose that an investor with a five-year investment horizon is considering purchasing
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a seven-year 9% coupon bond selling at par. The investor expects that he can reinvest the coupon payments at an annual interest rate of 9.4% and that at the end of the investment horizon two-year bonds will be selling to offer a yield to maturity of 11.2%. What is the total return for this bond?
17. Two portfolio managers are discussing the investment characteristics of amortizing securities. Manager A believes that the advantage of these securities relative to nonamortizing securities is that because the periodic cash flows include principal repayments as well as coupon payments, the manager can generate greater reinvestment income. In addition, the payments are typically monthly so even greater reinvestment income can be generated. Manager B believes that the need to re-invest monthly and the need to invest larger amounts than just coupon interest payments make amortizing securities less attractive. Whom do you agree with and why?
18. Assuming the following yields:
Week 1: 3.84% Week 2: 3.51% Week 3: 3.95% Answer the below questions. (a) Compute the absolute yield change and percentage yield change from week 1 to week 2. (b) Compute the absolute yield change and percentage yield change from week 2 to week 3.
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