1)Ghost Rider Corporation has bonds on the market with 14 years to maturity, a Y
ID: 2769019 • Letter: 1
Question
1)Ghost Rider Corporation has bonds on the market with 14 years to maturity, a YTM of 6.4 percent, and a current price of $962. What must the coupon rate be on the company’s bonds? Coupon rate ---% ?
2)Atlantis Fisheries issues zero coupon bonds on the market at a price of $426 per bond. These are callable in 9 years at a call price of $660. Using semiannual compounding, what is the yield to call for these bonds?
3)Great Wall Pizzeria issued 11-year bonds one year ago at a coupon rate of 5.3 percent. If the YTM on these bonds is 8.2 percent, what is the current bond price?
4)Consider a 7.6 percent coupon bond with seven years to maturity and a current price of $1,032.20. Suppose the yield on the bond suddenly increases by 2 percent
Use duration to estimate the new price of the bond ?
Calculate the new bond price ?
Thank you
4)Consider a 7.6 percent coupon bond with seven years to maturity and a current price of $1,032.20. Suppose the yield on the bond suddenly increases by 2 percent
a.Use duration to estimate the new price of the bond ?
b.Calculate the new bond price ?
Thank you
Explanation / Answer
1)
C = coupon payment
n = number of payments
i = interest rate, or required yield
M = value at maturity, or par value
962 = C *(Cumulative discount factor @ 6.4%,year 14)+1000{Assume}*(Discount rate @ year 14)
962 = [C* 9.069026]+[1000* 0.42]
C = 59.76
C = 60
Coupon rate = (60/1000)*100
= 6%
2)
= 0 + [(660-426)/(9*2)]/ [600+426/2]
= 13/513
= 0.02534
= 2.534%
3)
Year
Particulars
Cash flow
PVF@8.2
Present value
1
Interest
5.3
0.924214418
4.90
2
Interest
5.3
0.85417229
4.53
3
Interest
5.3
0.789438346
4.18
4
Interest
5.3
0.729610301
3.87
5
Interest
5.3
0.674316359
3.57
6
Interest
5.3
0.623212902
3.30
7
Interest
5.3
0.575982349
3.05
8
Interest
5.3
0.532331191
2.82
9
Interest
5.3
0.491988162
2.61
10
Interest
5.3
0.454702553
2.41
Redemption value
(Assume) 100
0.454702553
45.47
Total
80.72
4)
C = coupon payment
n = number of payments
i = interest rate, or required yield
M = value at maturity, or par value
1,032.20 = 76*(Cumulative discount factor @ X%,year 7) + 1000 *Discount rate at year 7
X (Yield on bond) = 7%
Suppose the yield on the bond suddenly increases by 2 percent
Year (A)
Particulars
Cash flow
PVF@7
Present value
Weight (B)
Duration (c) = (A)*(B)
1
Interest
76
0.934579439
71.03
0.069
0.07
2
Interest
76
0.873438728
66.38
0.064
0.13
3
Interest
76
0.816297877
62.04
0.060
0.18
4
Interest
76
0.762895212
57.98
0.056
0.22
5
Interest
76
0.712986179
54.19
0.052
0.26
6
Interest
76
0.666342224
50.64
0.049
0.29
7
Interest
76
0.622749742
47.33
0.046
0.32
7
Redemption value
1000
0.622749742
622.75
0.603
4.22
1032.20
1.000
5.70
Modified Duration = Duration /(1+YTM)
= 5.70/1.07
= 5.33 times
% change in bond price = -Modified duration * % Change in bond yield
= -5.33*0.02
= -0.1066
= -10.66%
New bond price = 1032.20 – (10.32.20*0.1066)
= 110.032
Year
Particulars
Cash flow
PVF@8.2
Present value
1
Interest
5.3
0.924214418
4.90
2
Interest
5.3
0.85417229
4.53
3
Interest
5.3
0.789438346
4.18
4
Interest
5.3
0.729610301
3.87
5
Interest
5.3
0.674316359
3.57
6
Interest
5.3
0.623212902
3.30
7
Interest
5.3
0.575982349
3.05
8
Interest
5.3
0.532331191
2.82
9
Interest
5.3
0.491988162
2.61
10
Interest
5.3
0.454702553
2.41
Redemption value
(Assume) 100
0.454702553
45.47
Total
80.72
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