3636 chapter 3

28. An eight-year corporate bond has a 7 percent coupon rate. What should be the bond's price if the required return is 6 percent and the bond pays interest semiannually? A. $1,062.81 B. $1,062.10 C. $1,053.45 D. $1,052.99 E. $1,049.49 Price = 35.00 × PVIFA (3%, 16) + 1,000 × PVIF (3%, 16)

a

29. A 15-year corporate bond pays $40 interest every six months. What is the bond's price if the bond's promised YTM is 5.5 percent? A. $1,261.32 B. $1,253.12 C. $1,250.94 D. $1,263.45 E. $1,264.79 Using P/Y2 for semiannual; FV $1,000; PMT $40; N 15 years; and I/Y 5.5 percent. Solve bond price (PV) = $1,253.12.

a

37. An annual payment bond with a $1,000 par has a 5 percent quoted coupon rate, a 6 percent promised YTM, and six years to maturity. What is the bond's duration? A. 5.31 years B. 5.25 years C. 4.76 years D. 4.16 years E. 3.19 years Σ[(t*CFt/(1.06)t)]/$950.83

a

44. A six-year maturity bond has a five-year duration. Over the next year maturity will decline by one year and duration will decline by A. less than one year. B. more than one year. C. one year. D. N years. E. N/(N-1) years.

a

49. The duration of a 180-day T-Bill is (in years) A. 0.493. B. 0.246. C. 1. D. 0. E. indeterminate. 180/365

a

22. The interest rate used to find the present value of a financial security is the A. expected rate of return. B. required rate of return. C. realized rate of return. D. realized yield to maturity. E. current yield.

b

20. Duration is A. the elasticity of a security's value to small coupon changes. B. the weighted average time to maturity of the bond's cash flows. C. the time until the investor recovers the price of the bond in today's dollars. D. greater than maturity for deep discount bonds and less than maturity for premium bonds. E. the second derivative of the bond price formula with respect to the YTM.

b

30. A corporate bond has a coupon rate of 10 percent and a required return of 10 percent. This bond's price is A. $924.18. B. $1,000.00. C. $879.68. D. $1,124.83. E. not possible to determine from the information given.

b

32. An eight-year annual payment 7 percent coupon Treasury bond has a price of $1,075. The bond's annual E(r) must be A. 13.49 percent. B. 5.80 percent. C. 7.00 percent. D. 1.69 percent. E. 4.25 percent. $1,075 = 70 × PVIFA (E(r)%, 8) + 1,000 × PVIF (E(r)%, 8), trial and error or calculator

b

42. A decrease in interest rates will A. decrease the bond's PV. B. increase the bond's duration. C. lower the bond's coupon rate. D. change the bond's payment frequency. E. not affect the bond's duration.

b

50. For large interest rate increases, duration _____________ the fall in security prices, and for large interest rate decreases, duration ______________ the rise in security prices. A. overpredicts; overpredicts B. overpredicts; underpredicts C. underpredicts; overpredicts D. underpredicts; underpredicts E. None of the options presented

b

23. A security has an expected return less than its required return. This security is A. selling at a premium to par. B. selling at a discount to par. C. selling for more than its PV. D. selling for less than its PV. E. a zero coupon bond.

c

25. You would want to purchase a security if P ____________ PV or E(r) ____________ r. A. ≥; ≤ B. ≥; ≥ C. ≤; ≥ D. ≤; ≤

c

26. A 10-year annual payment corporate bond has a market price of $1,050. It pays annual interest of $100 and its required rate of return is 9 percent. By how much is the bond mispriced? A. $0.00 B. Overpriced by $14.18 C. Underpriced by $14.18 D. Overpriced by $9.32 E. Underpriced by $9.32 PV = 100 × PVIFA [9%, 10 yrs.] + 1,000 × PVIF (9%, 10 yrs.) = $1,064.18

c

38. If an N year security recovered the same percentage of its cost in PV terms each year, the duration would be A. N. B. 0. C. sum of the years/N. D. N!/N2. E. none of the options.

c

40. You bought a stock three years ago and paid $45 per share. You collected a $2 dividend per share each year you held the stock and then you sold the stock for $47 per share. What was your annual compound rate of return? A. 8.89 percent B. 8.51 percent C. 5.84 percent D. 4.44 percent E. 2.96 percent Use a financial calculator to solve for IRR as follows: CFO = -$45, CO1 = $2, FO1 = 1, CO2 = $2, FO2 = 1, FO3 = $47, FO3 = 1 Compute for IRR = 5.82%.

c

43. A 10-year maturity coupon bond has a six-year duration. An equivalent 20-year bond with the same coupon has a duration A. equal to 12 years. B. less than six years. C. less than 12 years. D. equal to six years. E. greater than 20 years.

c

46. A bond that pays interest annually has a 6 percent promised yield and a price of $1,025. Annual interest rates are now projected to fall 50 basis points. The bond's duration is six years. What is the predicted new bond price after the interest rate change? (Watch your rounding.) A. $1,042.33 B. $995.99 C. $1,054.01 D. $987.44 E. None of the options presented 1,025 + [-6 × (-0.0050/1.06) × $1,025]

c

21. Which of the following bond terms are generally positively related to bond price volatility? I. Coupon rate II. Maturity III. YTM IV. Payment frequency A. II and IV only B. I and III only C. II and III only D. II only E. II, III, and IV only

d

24. A bond that you held to maturity had a realized return of 8 percent, but when you bought it, it had an expected return of 6 percent. If no default occurred, which one of the following must be true? A. The bond was purchased at a premium to par. B. The coupon rate was 8 percent. C. The required return was greater than 6 percent. D. The coupons were reinvested at a higher rate than expected. E. The bond must have been a zero coupon bond.

d

27. A 12-year annual payment corporate bond has a market price of $925. It pays annual interest of $60 and its required rate of return is 7 percent. By how much is the bond mispriced? A. $0.00 B. Overpriced by $7.29 C. Underpriced by $7.29 D. Overpriced by $4.43 E. Underpriced by $4.43 FPV = 60 × PVIFA [7%, 12 yrs.] + 1,000 × PVIF (7%, 12 yrs.) = $920.57

d

31. A 10-year annual payment corporate coupon bond has an expected return of 11 percent and a required return of 10 percent. The bond's market price is A. greater than its PV. B. less than par. C. less than its E(r). D. less than its PV. E. $1,000.00.

d

33. A six-year annual payment corporate bond has a required return of 9.5 percent and an 8 percent coupon. Its market value is $20 over its PV. What is the bond's E(r)? A. 8.00 percent B. 10.21 percent C. 9.98 percent D. 9.03 percent E. 3.53 percent PV = 933.70 = 80 × PVIFA (9.5%, 6 yrs.) + 1,000 × PVIF (9.5%, 6 yrs.); (933.70 + 20) = 80 × PVIFA (E(r), 6 yrs.) + 1,000 × PVIF (E(r), 6 yrs.), trial and error or calculator

d

34. Corporate Bond A returns 5 percent of its cost in PV terms in each of the first five years and 75 percent of its value in the sixth year. Corporate Bond B returns 8 percent of its cost in PV terms in each of the first five years and 60 percent of its cost in the sixth year. If A and B have the same required return, which of the following is/are true? I. Bond A has a bigger coupon than Bond B. II. Bond A has a longer duration than Bond B. III. Bond A is less price-volatile than Bond B. IV. Bond B has a higher FPV than Bond A. A. III only B. I, III, and IV only C. I, II, and IV only D. II and IV only E. I, II, III, and IV

d

47. A bond that pays interest semiannually has a 6 percent promised yield and a price of $1,045. Annual interest rates are now projected to increase 50 basis points. The bond's duration is five years. What is the predicted new bond price after the interest rate change? (Watch your rounding.) A. $1,020.35 B. $1,069.65 C. $1,070.36 D. $1,019.64 E. None of the options presented ((-5/1.03) × 0.0050 × $1,045) + $1,045

d

48. Convexity arises because A. bonds pay interest semiannually. B. coupon changes are the opposite sign of interest rate changes. C. duration is an increasing function of maturity. D. present values are a nonlinear function of interest rates. E. duration increases at higher interest rates.

d

19. The required rate of return on a bond is A. the interest rate that equates the current market price of the bond with the present value of all future cash flows received. B. equivalent to the current yield for non-par bonds. C. less than the E(r) for discount bonds and greater than the E(r) for premium bonds. D. inversely related to a bond's risk and coupon. E. none of the options.

e

35. A corporate bond returns 12 percent of its cost (in PV terms) in the first year, 11 percent in the second year, 10 percent in the third year and the remainder in the fourth year. What is the bond's duration in years? A. 3.68 years B. 2.50 years C. 4.00 years D. 3.75 years E. 3.32 years 3.32 = (12% * 1) + (11% * 2) + (10% * 3) + (67% * 4)

e

36. A semiannual payment bond with a $1,000 par has a 7 percent quoted coupon rate, a 7 percent promised YTM, and 10 years to maturity. What is the bond's duration? A. 10.00 years B. 8.39 years C. 6.45 years D. 5.20 years E. 7.35 years Σ[(t * CFt/(1.035)t)]/(2 * $1,000)

e

39. The ___________ the coupon and the ______________ the maturity; the __________ the duration of a bond, ceteris paribus. A. larger; longer; longer B. larger; longer; shorter C. smaller; shorter; longer D. smaller; shorter; shorter E. None of the options presented

e

41. A four-year maturity 0 percent coupon corporate bond with a required rate of return of 12 percent has an annual duration of _______________ years. A. 3.05 B. 2.97 C. 3.22 D. 3.71 E. 4.00

e

45. An annual payment bond has a 9 percent required return. Interest rates are projected to fall 25 basis points. The bond's duration is 12 years. What is the predicted price change? A. -2.75 percent B. 33.33 percent C. 1.95 percent D. -1.95 percent E. 2.75 percent -12 × (-0.0025/1.09)

e

11. For a given interest rate change, a 20-year bond's price change will be twice that of a 10-year bond's price change.

f

18. Ignoring default risk, if a bond's expected return is greater than its required return, then the bond's market price must be greater than the present value of the bond's cash flows.

f

2. At equilibrium, a security's required rate of return will be less than its expected rate of return.

f

3. If a security's realized return is negative, it must have been true that the expected return was greater than the required return.

f

4. Suppose two bonds of equivalent risk and maturity have different prices such that one is a premium bond and one is a discount bond. The premium bond must have a greater expected return than the discount bond.

f

9. The longer the time to maturity, the lower the security's price sensitivity to an interest rate change, ceteris paribus.

f

1. If interest rates increase, the value of a fixed income contract decreases and vice versa.

t

10. The greater a security's coupon, the lower the security's price sensitivity to an interest rate change, ceteris paribus.

t

12. Any security that returns a greater percentage of the price sooner is less price-volatile.

t

13. A zero coupon bond has a duration equal to its maturity and a convexity equal to zero.

t

14. The lower the level of interest rates, the greater a bond's price sensitivity to interest rate changes.

t

15. The higher a bond's coupon, the lower the bond's price volatility.

t

16. Higher interest rates lead to lower bond convexity, ceteris paribus.

t

17. A 10-year maturity zero coupon bond will have lower price volatility than a 10-year bond with a 10 percent coupon.

t

5. A bond with an 11 percent coupon and a 9 percent required return will sell at a premium to par.

t

6. A fairly priced bond with a coupon less than the expected return must sell at a discount from par.

t

7. All else equal, the holder of a fairly priced premium bond must expect a capital loss over the holding period.

t

8. The duration of a four-year maturity 10 percent coupon bond is less than four years.

t