Question

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%

Answer 1

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.