Question

A bond that matures in 19 years has a ​$1,000 par value. The annual coupon interest rate is 12 percent and the​ market's required yield to maturity on a​ comparable-risk bond is 17 percent. What would be the value of this bond if it paid interest​ annually? What would be the value of this bond if it paid interest​ semiannually?

Answer 1

1.Annual interest

Information provided:

Par value= future value= $1,000

Time=19 years

Coupon rate= 12%

Coupon payment= 0.12*1,000= $120

Yield to maturity= 17%

The value of the bond is calculated by computing the present value.

The following has to be entered in a financial calculator to compute the present value:

FV= 1,000

N= 19

PMT= 120

I/Y= 17

Press the CPT key and PV to compute the present value.

The value obtained is 720.78.

Therefore, value of the bond if the interest is paid annually is $720.78.

2.Semi-annual interest

Information provided:

Par value= future value= $1,000

Time=19 years82= 38 semi-annual periods

Coupon rate= 12%/2= 6%

Coupon payment= 0.06*1,000= $60

Yield to maturity= 17%/2= 8.50%

The value of the bond is calculated by computing the present value.

The following has to be entered in a financial calculator to compute the present value:

FV= 1,000

N= 38

PMT= 60

I/Y= 8.50

Press the CPT key and PV to compute the present value.

The value obtained is 719.13.

Therefore, value of the bond if the interest is paid semi-annually is $719.13.

In case of any query, kindly comment on the solution.