Question

The International Publishing Group is raising $10 million by issuing 15-year bonds with a coupon rate of 10.31 percent. Coupon payments will be made annually. Investors buying the bonds today will earn a yield to maturity of 10.31 percent. At what price will the bonds sell in the marketplace? Explain. (Round intermediate calculations to 4 decimal places, e.g. 1.2514 and final answer to 2 decimal places, e.g. 15.25.)

Sale value $

Answer 1

When the bond YTM and coupon rate are same the bond sells at its Par value or Face value.Thus in this case since the coup0on rate and the YTM are the same the bond will sell at its Par value.It can also be cross checked by below formula

Price of bond=Present value of coupon payments+Present value of face value

Price of bond=Coupon payment*((1-(1/(1+r)^n))/r)+Face value/(1+r)^n

Here

Assume Face value =1000

n=number of periods to maturity=15

r-intrest rate per period=YTM=10.31%

annual Coupon payment=coupon rate *face value=10.31%*1000=103.1

Putting values in formuLA

Price of bond=103.1*((1-(1/(1+10.31%)^15))/10.31%)+1000/(1+10.31%)^15

Solving we get

Price of bond=$1000

Thus as we can see ,when copupon rate and YTM are same ,the bond sells at its par value