How many of the bonds described below are trading at a premium? Bond I: 10 year annual, $100 par value, YTM = 8%, Coupon Rate = 5% Bond II: 100 year annual, $75 par value, YTM = 2%, zero coupon Bond III: 1 year annual, $1000 par value, YTM = 7%, Coupon Rate = 6% Bond IV: 6 year annual, $150 par value, YTM = 4%, Coupon Rate = 4%
Premium bonds are those trading above the par value of the bond.
The question is solved by calculating the present value to compute the current value of the bond.
Bond I
Information provided:
Par value=future value= $100
Yield to maturity= 8%
Time= 10 years
Coupon rate= 5%
Coupon payemnt= 0.05*100= $5
Enter the below in a financial calculator to compute the present value:
FV= 100
N= 10
PMT= 5
I/Y= 8
Press the CPT key and PV to compute the present value.
The value obtained is 79.87.
Therefore, the current value of the bond I is $79.87.
Bond II
Information provided:
Par value=future value= $75
Yield to maturity= 2%
Time= 100 years
Enter the below in a financial calculator to compute the present value:
FV= 75
N= 100
I/Y= 2
Press the CPT key and PV to compute the present value.
The value obtained is 10.35.
Therefore, the current value of the bond II is $10.35.
Bond III
Information provided:
Par value=future value= $1000
Yield to maturity= 7%
Time= 1 year
Coupon rate= 6%
Coupon payemnt= 0.06*1000= $60
Enter the below in a financial calculator to compute the present value:
FV= 1000
N= 1
PMT= 60
I/Y= 7
Press the CPT key and PV to compute the present value.
The value obtained is 990.65.
Therefore, the current value of the bond III is $990.65.
Bond IV
Information provided:
Par value=future value= $150
Yield to maturity= 4%
Time= 6 years
Coupon rate= 4%
Coupon payemnt= 0.04*150= $6
Enter the below in a financial calculator to compute the present value:
FV= 150
N= 6
PMT= 6
I/Y= 4
Press the CPT key and PV to compute the present value.
The value obtained is 150.
Therefore, the current value of the bond IV is $150.
In case of any query, kindly comment on the solution.
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