13
47. Calculate the duration of a 6%, $1,000 par bond maturing in three years if the yield to maturity is 10%
and interest is paid semiannually.
a.
1.35 years
b.
1.78 years
c.
2.50 years
d.
2.78 years
e.
2.95 years
48. Calculate the modified duration for a 10-year, 12% bond with a yield to maturity of 10% and a
Macaulay duration of 7.2 years.
a.
6.43 years
b.
6.55 years
c.
6.79 years
d.
6.86 years
e.
7.01 years
49. A 12-year, 8% bond with a YTM of 12% has a Macaulay duration of 9.5 years. If interest rates decline
by 50 basis points, what will be the percentage change in price for this bond?
a.
+4.48%
b.
+4.61%
c.
+8.48%
d.
+8.96%
e.
+17.92%
14
50. Consider a bond with a duration of 6 years having a yield to maturity of 8% and interest rates are
expected to rise by 50 basis points. What is the percentage change in the price of the bond?
a.
2.88%
b.
3.45%
c.
−3.89%
d.
−3.45%
e.
−2.88%
51. If the price before yields changed was $950, what is the resulting price?
a.
$922.64
b.
$918.66
c.
$1000.00
d.
$968.50
e.
$1012.45
52. Consider a bond with a duration of 7 years having a yield to maturity of 7% and interest rates are
expected to rise by 50 basis points. What is the percentage change in the price of the bond?
a.
3.62%
b.
3.45%
c.
−3.38%
d.
3.38%
e.
−3.62%
15
53. If the price before yields changed was $925, what is the resulting price?
a.
$865.22
b.
$918.66
c.
$889.11
d.
$1000.00
e.
$1012.45
54. Consider a bond with a duration of 8 years having a yield to maturity of 8% and interest rates are
expected to rise by 50 basis points. What is the percentage change in the price of the bond?
a.
3.85%
b.
3.45%
c.
−4.02%
d.
−3.45%
e.
−3.85%
55. If the price before yields changed was $975, what is the resulting price?
a.
$937.46
b.
$918.66
c.
$965.55
d.
$898.62
e.
$1012.45
56. Suppose the current 6 year spot rate is 8% and the current 5 year spot rate is 7%. What is the one year
forward rate in five years?
a.
12.62%
b.
11.58%
c.
13.14%
d.
14.65%
e.
15.14%
16
57. Suppose the current 6 year rate is 9% and the current 5 year rate is 7%. What is the one year forward
rate for five years?
a.
19.57%
b.
18.62%
c.
15.80%
d.
14.65%
e.
12.67%
58. Suppose the current 7 year rate is 8% and the current 6 year rate is 6%. What is the one year forward
rate for six years?
a.
16.33%
b.
18.22%
c.
20.82%
d.
14.65%
e.
15.14%
59. Assume that you purchase a 3-year $1,000 par value bond, with a 8% coupon, and a yield of 10%.
After you purchase the bond, one- year interest rates are as follow, year 1 = 10%, year 2 = 8%, year 3
= 6% (these are the reinvestment rates). Calculate the realized horizon yield if you hold the bond to
maturity. Interest is paid annually.
a.
8.37%
b.
7.28%
c.
9.76%
d.
10.67%
e.
14.0%
17
60. Assume that you purchase a 10-year $1,000 par value bond, with a 12% coupon, and a yield of 9%.
Immediately after you purchase the bond, yields fall to 8% and remain at that level to maturity.
Calculate the realized horizon yield, if you hold the bond for 5 years and then sell. Interest is paid
annually.
a.
16.25%
b.
12.15%
c.
7.75%
d.
10.05%
e.
9.34%
61. Assume that you purchase a 5-year $1,000 par value bond, with a 6% coupon, and a yield of 7%.
Immediately after you purchase the bond, yields rise to 8% and remain at that level to maturity.
Calculate the realized horizon yield if you hold the bond to maturity. Interest is paid annually.
a.
6.0%
b.
7.11%
c.
8.0%
d.
15.25%
e.
8.18%
62. Estimate the percentage price change for a 5-year $1,000 par value bond, with a 6% coupon, if the
yield rises from 8% to 8.5%. Interest is paid semiannually.
a.
2.1%
b.
−2.1%
c.
4.4%
d.
−4.4%
e.
None of the above
63. Calculate the Macaulay duration for a 5-year $1,000 par value bond, with a 6% coupon and a yield to
maturity of 8%. Interest is paid annually.
a.
6.44 years
b.
5.25 years
c.
4.44 years
d.
2.50 years
e.
None of the above
19
64. A 15-year bond has a $1,000 par value bond, a 4% coupon and a yield to maturity of 3.3%. Interest is
paid annually. The bond’s current yield is
a.
3.7%
b.
4.0%
c.
3.3%
d.
7.3%
e.
None of the above
65. A 5-year bond has a $1,000 par value bond, a 12% coupon and a yield to maturity of 8%. Interest is
paid semiannually. The bond’s price is
a.
$864.65
b.
$1081.78
c.
$852.80
d.
$1162.22
e.
None of the above
20
66. A 15-year bond, purchased 5 years ago, has a $1,000 par value bond, a 10% coupon and a yield to
maturity of 12%. Interest is paid annually. The bond’s price is
a.
$864
b.
$887
c.
$1152
d.
$1123
e.
None of the above
Exhibit 12-1
THE FOLLOWING INFORMATION IS FOR THE NEXT PROBLEM(S)
A $1000 par value bond with 5 years to maturity and a 6% coupon has a yield to maturity of 8%.
Interest is paid semiannually.
67. Refer to Exhibit 12-1. Calculate the current price of the bond.
a.
$1579.46
b.
$918.89
c.
$789.29
d.
$1000
e.
$743.29
21
68. Refer to Exhibit 12-1. Calculate the Macaulay duration for the bond.
a.
4.19 years
b.
4.36 years
c.
8.72 years
d.
8.38 years
e.
9.52 years
69. Refer to Exhibit 12-1. Calculate the modified duration for the bond.
a.
4.19 years
b.
4.36 years
c.
8.72 years
d.
8.38 years
e.
9.52 years
70. Refer to Exhibit 12-1. Estimate the percentage price change for this 5-year $1,000 par value bond, with
a 6% coupon, if the yield rises from 8% to 8.5%. Interest is paid semiannually.
a.
2.1%
b.
−2.1%
c.
4.4%
d.
−4.4%
e.
None of the above
22
Exhibit 12-2
USE THE FOLLOWING INFORMATION FOR THE NEXT PROBLEM(S)
Talmart Corporation bonds have a $1,000 face value and will mature in 4 years. The bonds have a 7%
coupon rate. Interest is paid annually and the required rate of return is 6% for these bonds.
71. Refer to Exhibit 12-2. What is the price of the Talmart corporate bonds?
a.
$965.63
b.
$966.13
c.
$1,034.65
d.
$1,135.10
e.
$1,051.97
72. Refer to Exhibit 12-2. What is the Macaulay duration of the Talmart corporate bonds?
a.
3.43
b.
3.64
c.
3.76
d.
3.85
e.
4.11
73. Refer to Exhibit 12-2. What is the Modified duration of the Talmart corporate bonds?
a.
3.43
b.
3.64
c.
3.76
d.
3.85
e.
4.11
23
74. Refer to Exhibit 12-2. If interest rates increase 50 basis points, what will be the approximate price
change for the Talmart bond?
a.
−17.0%
b.
−1.7%
c.
1.7%
d.
1.8%
e.
17.0%
75. Zappo Corporation just issued $1,000 face value bonds that will mature in 20 years and have a 7%
coupon rate. Interest is paid semi-annually and the required rate of return is 9% for these bonds. The
bonds have a 5 year call provision that will pay a call premium of $1,050 if they are called in. What is
the price of the Zappo Corporation bond?
a.
$815.98
b.
$817.43
c.
$826.35
d.
$920.87
e.
$953.07
76. Calculate the modified duration of a bond that has a Macaulay duration of 7.6 and the bond pays
interest semi-annually with a coupon rate of 6% and a required rate of return of 8%.
a.
7.04
b.
7.17
c.
7.31
d.
7.38
e.
8.12