Consider a 11.00 percent coupon bond with eight years to maturity and a current
ID: 2709041 • Letter: C
Question
Consider a 11.00 percent coupon bond with eight years to maturity and a current price of $981.50. Suppose the yield on the bond suddenly increases by 2 percent.
Use duration to estimate the new price of the bond. (Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Calculate the new bond price. (Round your answer to 2 decimal places. Omit the "$" sign in your response.)
Consider a 11.00 percent coupon bond with eight years to maturity and a current price of $981.50. Suppose the yield on the bond suddenly increases by 2 percent.
Explanation / Answer
Approximate Yield-to-Maturity Percentage
=
Annual Interest Payment + (Par Value - Bond Price)/Number of Years until Maturity
(Par Value + Bond Price)/2
Current price= 981.50
Years to maturity =8
Par value =1000
Coupon = 110
YTM = [110+ (1000-981.50)/8]/(1000+981.50)/2
= 112.31/990.75=11.33%
So current YTM is 11.33%
Revised YTM =13.33%
a.
Year 1
Year 2
Year 3
Year 4
Year 5
Year 6
Year 7
Year 8
Interest
110.00
110.00
110.00
110.00
110.00
110.00
110.00
110.00
Maturity value
1,000.00
Total Cash flow
110.00
110.00
110.00
110.00
110.00
110.00
110.00
1,110.00
Discount Factor @13.33%
0.882
0.779
0.687
0.606
0.535
0.472
0.416
0.367
PV of cash Flow
97.06
85.65
75.57
66.68
58.84
51.92
45.81
407.91
PV of Total cash Flow
889.44
So revised Bond Price
$ 889.44
b.
Revised Bond price as per YTM formula ;
YTM=13.33%
Let the bond price be b
So, 0.1333= [110+(1000-b)/8]/(1000+b)/2
Or,0.1333(1000+b)= 2[110+(1000-b)/8]= 2[880+1000-b]/8=[880+1000-b]/4
Or 0.5332(1000+b)=880+1000-b
Or, 533.2 +0.5332b=1880-b
Or, 1.5332b=1346.8
Or b= 878.42
So revised bond price as per YTM formula = $878.42
Approximate Yield-to-Maturity Percentage
=
Annual Interest Payment + (Par Value - Bond Price)/Number of Years until Maturity
(Par Value + Bond Price)/2
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