Question

Lopez Information Systems management is planning on issuing 10-year bonds at a yield to matu-rity of 8.125 percent. Assume coupon payments will be made semiannually. Management is currentlydeciding between issuing a 8 percent coupon bond or a 8.5 percent coupon bond. Lopez needs to raise$1 million.(a.)What will the price of the 8 percent coupon bond be?

Answer 1

Coupon (R) = 8% x $1,000 = $80

No of years to maturity = 10 years

Yield to maturity (Kd) = 8.125% = 0.08125

Po = R/2(1-(1+Kd/2)-n)/kd/2 + FV/ (1+Kd/2)n

Po = $80/2(1-(1+0.08125/2)-10 + $1,000/(1 + 0.08125)10

0.08125/2

Po = $40(1-(1+0.040625)-10 + $1,000/(1+0.040625)10

0.040625

Po = $40(8.0857) + $671.52

Po = $994.95 = $995

Explanation:

The current market price of a bond equals the present value of the semi-annual coupon and the present value of the face value. There is need to discount the coupon at the annuity factor of 8,125% for 10 years in order to obtain the present value of the coupon. We also need to discount the face value at 8,125% for 10 years to obtain the present value of the face value. The summation of the present value of coupon and the present value of face value gives the current market price of the bond.