Penang Manufacturing intends to issue callable, perpetual bonds with annual coup

Question

Penang Manufacturing intends to issue callable, perpetual bonds with annual coupon payments. The bonds are callable at $1,180. One-year interest rates are 8 percent. There is a 60 percent probability that long-term interest rates one year from today will be 9 percent, and a 40 percent probability that they will be 7 percent. Assume that if interest rates fall the bonds will be called. What coupon rate should the bonds have in order to sell at par value? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Penang Manufacturing intends to issue callable, perpetual bonds with annual coupon payments. The bonds are callable at $1,180. One-year interest rates are 8 percent. There is a 60 percent probability that long-term interest rates one year from today will be 9 percent, and a 40 percent probability that they will be 7 percent. Assume that if interest rates fall the bonds will be called. What coupon rate should the bonds have in order to sell at par value? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

Explanation / Answer

Solution:

If interest rates rise , bonds price will fall. If interest rate rises the price of the bonds in one year will be :

P1= C+C/0.09

If interest rate fall, bonds price will increase , there bond will be called . So. Price of the bonds will be

P1= 1180 +C

1000= [0.60(C+C/0.09)+0.40(1180+C)]/1.08

1000*1.08= 0.60C+6.67C +472+0.40C

1080= 7.67C+472

1080-472= 7.67C

608 = 7.67C

C= 79.27

Coupon rate at par value= (79.27/1000)*100= 7.93%

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