Question

Your company currently has $1,000 par, 6% 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.

Answer 1

First we will calculate the Yield to maturity of current bond

Face value = $1000, Coupon rate = 6%, Years to maturity = 10 years , Current price = $1082

As the bond pays coupon semi annually, therefore

Semi annual coupon payment = (Coupon rate x face value) / 2 = (6% x 1000) / 2 = 60 / 2 = $30

No of half years to maturity = 2 x no of years to maturity = 2 x 10 = 20

Yield to maturity = 2 x semi annual yield to maturity

To find yield to maturity of current bond, we now will calculate semi annual yield to maturity of current bond

We can find semi annual yield to maturity using RATE function in excel

Formula to be used in excel: =RATE(nper,-pmt,pv,-fv)

Using RATE function in excel we get semi annual yield to maturity = 2.4752%

Yield to maturity of current bond = 2 x 2.4752% = 4.9504% = 4.9504%

New bonds will also have same yield to maturity of 4.9504% because i) They are issued by same company and hence carry same risk ii) They have same maturity as current bonds of the company.

Hence Yield to maturity of new bonds = 4.9504%

Now company wants to issue new bonds at par. We know that if bonds are issued or trading at par, then yield to maturity of bond will be equal to coupon rate on bond.

Hence Coupon rate of new bonds = 4.9504% = 4.95% (rounded to two decimal places)