Question

A corporation had a face value of $1,000 of a 30 year fixed coupon bond 10 years ago with a coupon rate of 4%. Currently this bond is trading at $960 with a current yield of 3.65% and yield to maturity of 4.00%. Since this Corp needs funding for a new project it intends to issue a new 10-year bond and would like to price it at par when the new bond is issued. What should be the coupon rate of this new bond in order for it to be priced at par?

Answer 1

Coupon Rate is 4%

The Formula for Current Price or Market price of Bond =PV of Coupon Interest @ YTM rate + PV Redemption Value of Bond or Par value of Bond

Here Corp wants to price Its bond at par is $1000 , hence from above formulae we get ,

1000 = PV of Coupon interest for 10 year + PV of Par value or redemption at par

1000=C (PVAF , 4%,10year )+ 1000( PVF 4%, 10th year)

1000=C×8.111+ 1000×0.676

1000=8.111C +676

8.111C=324

C =40

Coupon interest Rate = Interest ÷Par value of Bond

=4%

Or

Formula for YTM = {C+(F-P)/n}/(F+P)/2

Where C is Coupon interest

F is face value or par Value of bond

P = Issued price of bond

n = Life of Bond , number of year

From above formula

0.04=[C+(1000-1000)/10]/(1000+1000)/2

0.04=[C+0]/2000/2

0.04=[C]/1000

C=40

Interest Rate =40/1000

=4%