Question

Your company currently has

$1,000

​par,

5%

coupon bonds with 10 years to maturity and a price of

$1,082.

If you want to issue new​ 10-year coupon bonds at​ par, what coupon rate do you need to​ set? Assume that for both​ bonds, the next coupon payment is due in exactly six months.

You need to set a coupon rate of

nothing​%.

​(Round to two decimal​ places.)

Answer 1

Information provided:

Par value = future value = $1,000

Coupon rate = 5%/2 = 2.5%

Coupon payment = 0.025*$1,000 = $25 per semi-annual period

Time= 10 years*2 = 20 semi-annual periods

Present value = $1,082

The question is solved by first calculating the yield to maturity of the current bonds.

The yield to maturity is calculated by entering the below in a financial calculator:

FV= 1,000

PV= -1,082

PMT= 25

N= 20

Press the CPT key and I/Y to compute the yield to maturity.

The value obtained is 1.9986.

Therefore, the yield to maturity is 2%.

The coupon payment is calculated by entering the below in a financial calculator:

FV= 1,000

PV= -1,000

N= 20

I/Y= 2

Press the CPT key and PMT to compute the amount of coupon payment.

The value obtained is 20.

Therefore, the amount of coupon payment is $20.

Coupon rate = Coupon payment / Par value

= $20 / $1,000

= 0.02*100

= 2%.