corporate finance_bond&stock
1. You have a cash obligation of $132,240 to be made at the end of year 5. Show how you can use coupon bonds with a coupon rate of 8%, a face value of $1,000, a maturity date at the end of year 6, and a yield to maturity of 8% to ensure that you can meet your cash obligation at the end of year 5. Suppose that you purchase the bonds at the beginning of year 1 and that the market interest rate changes only once right after you have purchased the bonds. There are three possible interest rates, 7.9%, 8%, and 8.1%, each of which occurs with probability 1/3.
$132,240/(1.08)5=$90,000
Duration of the bond=5years
Thus, I need to buy 90units of the bond to immunize against the invest rate risk.
1/3*{$80(1.079)4+$80(1.079)3+$80(1.079)2+$80(1.079)+$80+$1080/1.079}*90
+1/3*{$80(1.08)4+$80(1.08)3+$80(1.08)2+$80(1.08)+$80+$1080/1.08}*90
+1/3*{$80(1.081)4+$80(1.081)3+$80(1.081)2+$80(1.081)+$80+$1080/1.081}*90
=1/3*($132,240+$132,240+$132,240)
=$132,240
2. Consider a 6-year 5.5% coupon bond that is rated BBB when issued at par (i.e. $1,000) at the beginning of this year. Assume that the recovery rate is 46% of the face value in the case of default.
Rating one year later Probability Yield
AAA 0.03 4.43
AA 0.21 4.56
A 4.56 4.8
BBB 89.38 5.5
BB 4.82 9.45
B 0.68 11.7
CCC 0.24 15.15
Default 0.08 -
(a) Plot the probability distribution of the bond value one year later, where the first-year coupon is included. What do you find?
Rating Probability Value
AAA 0.03 $1,102.06
AA 0.21 $1,096.2
A 4.56 $1,085.47
BBB 89.38 $1,055
BB 4.82 $903.14
B 0.68 $829.83
CCC 0.24 $723.66
Default 0.08 $460
(b) What is the expected value of the bond one year later? What is the standard deviation of the bond value one year later?
Expected value of the bond one year later
=0.03%*$1,102.06+0.21%*$1,096.2+4.56%*$1,085.47+89.38%*$1,055+4.82%*$903.14+0.68%*$829.83+0.24%*$723.66+0.08%*$460=$1,046.37
(c) If you plan to hold this bond for one year, what is the VAR in
$132,240/(1.08)5=$90,000
Duration of the bond=5years
Thus, I need to buy 90units of the bond to immunize against the invest rate risk.
1/3*{$80(1.079)4+$80(1.079)3+$80(1.079)2+$80(1.079)+$80+$1080/1.079}*90
+1/3*{$80(1.08)4+$80(1.08)3+$80(1.08)2+$80(1.08)+$80+$1080/1.08}*90
+1/3*{$80(1.081)4+$80(1.081)3+$80(1.081)2+$80(1.081)+$80+$1080/1.081}*90
=1/3*($132,240+$132,240+$132,240)
=$132,240
2. Consider a 6-year 5.5% coupon bond that is rated BBB when issued at par (i.e. $1,000) at the beginning of this year. Assume that the recovery rate is 46% of the face value in the case of default.
Rating one year later Probability Yield
AAA 0.03 4.43
AA 0.21 4.56
A 4.56 4.8
BBB 89.38 5.5
BB 4.82 9.45
B 0.68 11.7
CCC 0.24 15.15
Default 0.08 -
(a) Plot the probability distribution of the bond value one year later, where the first-year coupon is included. What do you find?
Rating Probability Value
AAA 0.03 $1,102.06
AA 0.21 $1,096.2
A 4.56 $1,085.47
BBB 89.38 $1,055
BB 4.82 $903.14
B 0.68 $829.83
CCC 0.24 $723.66
Default 0.08 $460
(b) What is the expected value of the bond one year later? What is the standard deviation of the bond value one year later?
Expected value of the bond one year later
=0.03%*$1,102.06+0.21%*$1,096.2+4.56%*$1,085.47+89.38%*$1,055+4.82%*$903.14+0.68%*$829.83+0.24%*$723.66+0.08%*$460=$1,046.37
(c) If you plan to hold this bond for one year, what is the VAR in