Question

A corporate bond has a face value of $1 000, a coupon rate of interest of 10.5% per annum, payable semi-annually, and 20 years remaining to maturity. The market interest rate for bonds of similar risk and maturity is currently 8.5% per annum. Required:

i. What is the coupon payment of the bond? (1 mark)

ii. What is the present value of the bond?

iii. If the coupon payment is payable annual (based on the same information), what is the value of the bond?

Answer 1

i.Coupon rate= 10.5%/2= 5.25% per semi-annual period

Coupon payment= 0.0525*1000

= $52.50

ii.Information provided:

Face value= future value= $1,000

Time= 20 years*2= 40 semi-annual periods

Coupon rate= 10.5%/2= 5.25% per semi-annual period

Coupon payment= 0.0525*1000= $52.50 per semi-annual period

Yield to maturity= 8.5%/2= 4.25% per semi-annual period

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

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 52.50

I/Y= 4.25

N= 40

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

The value obtained is 1,190.77.

Therefore, the present value of the bond is $1,190.77.

iii.Information provided:

Face value= future value= $1,000

Time= 20 years

Coupon rate= 10.5%

Coupon payment= 0.105*1000= $105

Yield to maturity= 8.5%

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

Enter the below in a financial calculator to compute the present value:

FV= 1,000

PMT= 105

I/Y= 8.5

N= 20

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

The value obtained is 1,189.27.

Therefore, the value of the bond is $1,189.27.